University of Southern California Dissertations and Theses

Multiplexing techniques and reconfigurable networking functions for optical communications using orbital angular momentum beams

(USC Thesis Other)

Multiplexing techniques and reconfigurable networking functions for optical communications using orbital angular momentum beams

PDF

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content

MULTIPLEXING TECHNIQUES AND RECONFIGURABLE NETWORKING
FUNCTIONS FOR OPTICAL COMMUNICATIONS USING ORBITAL
ANGULAR MOMENTUM BEAMS

by
Hao Huang

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)

May 2015

Copyright 2015 Hao Huang

ii

Dedication

To my parents and my wife for their everlasting love
To my thesis advisor, OCLab members and friends
for their encouragement and support.

iii

Acknowledgements
The past five years spent at OCLab was so incredible and memorable for me. Many
people have to be acknowledged.
First of all, I would like to thank my thesis advisor, Prof. Alan Willner, for his
supervising, encouragement and strong support. Looking back to my research experience, it
is his unique guidance that incites me to raise new questions, to overcome difficult problems.
It would be impossible for me to achieve a single step of progress without his
encouragement and support. His advice is full of wisdom and will be a great fortune in my
cereer.
I would like to sincerely thank Prof. Constance Chang-Hasnain, Dr. Samuel Dolinar, Dr.
Baris Erkmen, Prof. Andy Molisch, Prof. Mark Neifeld, Prof. Miles Padgett, Prof. Siddharth
Ramachandran, Prof. Moshe Tur, Prof. Ming C. Wu, Prof. Wei Wu for their generous
support during my Ph. D study.
I am truly grateful to Dr. Antonella Bogoni, Dr. Xiaoying Liu, Dr. Guiling Wu, Dr.
Junli Wang, Dr. Changjian Ke, Dr. Sheng Cui, Dr. Jianji Dong and Dr. Chongfu Zhang.
They had been very kind to me in both research and personal lives and took the efforts to
mentor me in many of my research activities.
I would also like to express my sincere thanks to my colleagues and comrades in
OCLab. Dr. Lin Zhang, Dr. Scott Nuccio, Dr. Jian Wang, Dr. Irfan Fazal, Dr. Jeng-Yuan
Yang, Dr. Xiaoxia Wu, Dr. Omer Faruk Yilmaz, Dr. Salman Khaleghi, Dr. Mohammad Reza
Chitgarha, Yan Yan, Yongxiong Ren, Morteza Ziyadi, Guodong Xie, and Changjing Bao,

iv

Yinwen Cao, Long Li, Zhe Zhao, Bishara Shamee, Asher Voskoboinik, Nisar Ahmed helped
me tremendously in my projects. Moreover, I would like to thank my collaborators, Martin
Lavery, Giovanni Milione and Nenad Bozinovic for all the helpful discussions and
remarkable collaborations.
Last but not least, I would like to thank my parents and my wife for their deepest love.
Their support and love are so critical in every achievement I have.

v

Table of Contents
Dedication ................................................................................................................ ii
Acknowledgements .................................................................................................... iii
List of Figures .......................................................................................................... viii
Abstract .............................................................................................................. xv
Chapter 1 Introduction .......................................................................................... 1
1.1 Optical Communications and Multiplexing Techniques ........................ 1
1.2 Background of OAM .............................................................................. 2
1.3 Applications of OAM for Optical Communications .............................. 5
1.4 Thesis Outline ......................................................................................... 7
1.5 References .............................................................................................. 9
Chapter 2 100 Tb/s Free-Space Optical Link Using OAM combined with
WDM and PDM ................................................................................. 12
2.1 Introduction .......................................................................................... 12
2.2 Concept and experiment ....................................................................... 13
2.3 Data transmission results ...................................................................... 19
2.4 Discussion ............................................................................................. 23
2.5 Summary ............................................................................................... 25
2.6 References ............................................................................................ 26
Chapter 3 Crosstalk mitigation in an OAM-Multiplexed free-space
communication link using MIMO DSP ............................................ 28
3.1 Introduction .......................................................................................... 28
3.2 Turbulence Effects and Turbulence Emulator ...................................... 29
3.3 Crosstalk Mitigation Using MIMO DSP .............................................. 30
3.4 Results and Discussions ....................................................................... 34
3.5 Summary ............................................................................................... 37
3.6 Reference .............................................................................................. 38
Chapter 4 Spatial FFT and the application for OAM demultiplexing ............ 41
4.1 Introduction .......................................................................................... 41
4.2 Mode sorter using geometric transformation ....................................... 42
4.3 Analogy of OFDM in Frequency and Spatial Domain ......................... 44
4.4 Spatial FFT ........................................................................................... 46
4.5 OAM demultiplexing using FFT .......................................................... 47
4.6 Summary ............................................................................................... 50
4.7 Reference .............................................................................................. 51

vi

Chapter 5 Wavefront Characterization for Orbital Angular Momentum
Modes Using Homodyne Detection ................................................... 53
5.1 Introduction .......................................................................................... 53
5.2 Principle and experiment ...................................................................... 54
5.3 Summary ............................................................................................... 60
5.4 References ............................................................................................ 61
Chapter 6 Reconfigurable optical add/drop multiplexer for an OAM-
Multiplexed Optical Communication system ................................... 63
6.1 Introduction .......................................................................................... 63
6.2 Concept and principle ........................................................................... 65
6.3 Experiment and results ......................................................................... 68
6.4 Summary ............................................................................................... 73
6.5 References ............................................................................................ 74
Chapter 7 Tunable Filter for Orbital-Angular-Momentum Multiplexed
Optical Channels ................................................................................ 76
7.1 Introduction .......................................................................................... 76
7.2 Concept and Principle ........................................................................... 77
7.3 Experiment and results ......................................................................... 79
7.4 Summary ............................................................................................... 84
7.5 References ............................................................................................ 86
Chapter 8 Analog Signal Transmission in a High-Contrast-Gratings based
Hollow-Core- Waveguide ................................................................... 88
8.1 Introduction .......................................................................................... 88
8.2 Waveguide parameters ......................................................................... 89
8.3 Link modeling ...................................................................................... 91
8.4 Results and discussion .......................................................................... 97
8.5 Summary ............................................................................................. 103
8.6 References .......................................................................................... 105
Chapter 9 100-Gbit/s Amplitude and Phase Modulation Characterization of a
Single-Drive EO Polymer Mach-Zehnder Modulator .................. 107
9.1 Introduction ........................................................................................ 107
9.2 Modulator Structure ............................................................................ 108
9.3 Measuremens ...................................................................................... 109
9.4 Summary ............................................................................................. 116
9.5 Reference ............................................................................................ 117

vii

Chapter 10 Sub-Channel Data Updating for Multiple Channels of a 16-QAM
Signal using a Single PPLN Waveguide ......................................... 120
10.1 Introduction ........................................................................................ 120
10.2 Concept and principle of subchannel data erasing and updating........ 121
10.3 Experiment and Results ...................................................................... 124
10.4 Summary ............................................................................................. 128
10.5 Reference ............................................................................................ 129
Bibliography ........................................................................................................... 131

viii

List of Figures
Figure 1.1 The phase and intensity profile of a Gaussian beam (top) and an OAM
beam (bottom) with charge ℓ =3. Gaussian beam can be regarded as a
special case of OAM mode with ℓ =0. .................................................................. 3
Figure 1.2 Three approaches to convert a Gaussian beam into an OAM beam with
ℓ =+3. (a) A spiral phase plate. (b). Phase hologram with a spiral phase
pattern. (c) Phase hologram with a “fork” pattern. ................................................ 4
Figure 1.3. The second type application of OAM for optical communications. Each
OAM beam is used as a data carrier. They are multiplexed at the transmitter,
coaxially transmitted, and demultipexed at the receiver. ...................................... 7
Figure 2.1 Concept of using 3-dimensional multiplexing to increase the
multiplexed data channels. (a), (b) and (c) are performed successively to
achieve OAM, polarization and wavelength multiplexing, respectively. (The
arrows indicate the helical phase-change direction. Each arrow starting from
white colour and ending with black colour represents a phase change from 0
to 2π.) .................................................................................................................. 14
Figure 2.2 Experimental setup of 42 channel WDM transmitter, each channel
carrying 100 Gbit/s QPSK data. (a): optical spectrum of multiplexed 42 CW
lasers. (b) optical spectrum of 42 wavelengths, each one carrying 100 Gbit/s
QPSK signal. (c) and (d): optical spectrum of even channels and odd
channels, respectively, separated by a optical interleaver. LD: laser diode.
AWG: array waveguide grating. EDFA: erbium doped fiber amplifer. PC:
polarization controller. OC: optical coupler. ....................................................... 15
Figure 2.3 (a1-a4) Block diagram of OAM multiplexing and polarization
multiplexing. (MR: mirror, SLM: spatial light modulation, BS: non-
polarization beam splitter, PBS: polarization beam splitter, HWP: half wave
plate.) (b1-b4) Procedures of creating multiplexed 12 OAM beams, each
with 2 polarizations. (a1) and (b1): The generation of OAM with ℓ=+4, +10
and +16 using one SLM and the generation of OAM with ℓ=+7, +13 and
+19 using another SLM. (a2) and (b2): Multiplex OAM beams with ℓ=+4,
+10 and +16 with ℓ=+7, +13 and +19. (a3) and (b3): Create OAM beams
with ℓ=-4, -7, -10, -13, -16 and +19 using wavefront phase conjugation
(reflected by mirrors) and multiplex them. (a4) and (b4): Create the same set
of OAM beams in another polarization state, and multiplex them. ..................... 17
Figure 2.4 Designed holograms and images of multiplexed OAM beams. (a1):
Gaussian beam. (a2): Phase hologram for generating 3 OAM beams (ℓ=+4,
+10 and +16) (a3): The generated OAM beam including ℓ=+4, +10 and +16.
(b1): Gaussian beam. (b2): Phase hologram for generating 3 OAM beams

ix

(ℓ=+7, +13 and +19) (b3): Generated OAM beams (ℓ=+7, +13 and +19). (c):
Multiplexed OAM beams with ℓ=+4, +7, +10, +13, +16, and +19 (d):
Multiplexed OAM beams with ℓ=±4, ±7, ±10, ±13, ±16 and ±19 (e):
Polarization-multiplexed OAM beams including ℓ=±4, ±7, ±10, ±13, ±16
and ±19 on both x- and y- polarization................................................................ 18
Figure 2.5 Measured power distribution after OAM demultiplexing. ........................... 20
Figure 2.6 Measured optical spectra of a single beam (OAM+10 in x-polarization).
Blue solid: demultiplexing OAM+10 when sending OAM+4, OAM+10 and
OAM+16. Red dot: demultiplexing OAM+10 when sending all other modes
except OAM+4, OAM+10 and OAM+16. .......................................................... 21
Figure 2.7 BER as a function of OSNR for the demultiplexed channel with the
worst crosstalk. .................................................................................................... 22
Figure 2.8 Measured BER and OSNR for all 1008 channels (504 channels in x-pol
and the other 504 channels in y-pol). .................................................................. 22
Figure 3.1. (a) Turbulence emulator. (b). Measured power distribution of an OAM
beam after passing through turbulence with different strength [5]. ..................... 30
Figure 3.2: Block diagram for the experimental setup [13]. OAM: orbital angular
momentum. PC: polarization controller. BPF: bandpass filter. SMF: single
mode fiber. EDFA: erbium doped fiber amplifier. OC: optical coupler. LO:
local oscillator. ADC: analog to digital converter. PD: photo detector. BS:
free space beam splitter. ...................................................................................... 32
Figure 3.3: (a) Procedures of offline signal processing for heterodyne and MIMO
equalization. (b1)-(b3): signal spectrum of channel using heterodyne
detection. (b1) spectrum of the sampled signal. (b2) spectrum after bandpass
filtering. (b3): spectrum after frequency shifting. ............................................... 33
Figure 3.4 The convergent tap weights (FIR filter coefficients) of the equalizer
using CMA algorithm. (a)-(d) shows the absolute value of complex taps
weights of four FIR filters to equalize ch. 1, ch. 2, ch. 3 and ch. 4,
respectively. ......................................................................................................... 34
Figure 3.5 Recovered constellations of 20 Gbit/s QPSK signal in each of the four
channel (with and without MIMO equalization) ................................................. 35
Figure 4.1 Concept of an OAM demultiplexer (mode sorter) using optical
geometrical transformation. ................................................................................. 43
Figure 4.2 (a) Simulation results shows that OAM beams with l=1 and l=2 have an
overlapped power distribution after the demultiplexing using a mode sorter.
(b) Measured power overlap using the mode sorter [2]. ...................................... 44

x

Figure 4.4 (a) Analogy between all optical FFT in the frequency domain and
spatial domain [9, 12]. (b) The amplitude and phase response of the
designed spatial filter that functions as FFT calculator. ...................................... 46
Figure 4.5 Concept of using spatial FFT to separate overlapped beams at the
output of the mode sorter. The spatial FFT can be achieved using a spatial
light modulator. ................................................................................................... 47
Figure 4.7 Simulated results when use the designed filter as FFT calculator to
demultiplex overlapped beams after the mod sorter. ........................................... 49
Figure 5.1 Principle of OAM beam phase reconstruction based on the quadrature
phase-shift interference. ...................................................................................... 54
Figure 5.2 (a) Experiment setup. SLM: spatial light modulator. BS: beam splitter.
HWP: half wave plane. Col.: collimator. LCR: liquid crystal retarder. CL:
convex lens. MR: mirror. A forked phase hologram for generating OAM-4
is inserted. (b) The liquid crystal phase retarder and its phase-voltage
response. .............................................................................................................. 56
Figure 5.3. Measured intensity profiles (a) OAM-4 beam. (b) Reference beam. (c)
and (d): Fringe patterns without and with a π/2 phase-shift ................................ 57
Figure 5.4. Measured and simulated wavefronts of generated OAM beams.
(a1)~(a4): Measured intensity profiles of OAM
-2
, OAM
-4
, OAM
-6
and OAM
-
8
. (b1)~(b4): Measured phase profiles of OAM
-2
, OAM
-4
, OAM
-6
and OAM
-
8
.(c1)~(c4):. Simulated phase profiles. ................................................................ 58
Figure.5.5 Wavefront correlation between the generated OAM modes and the
theoretical LG modes as functions of azimuthal index. ...................................... 59
Figure 6.1 Concept of an add/drop multiplexer in a WDM system and a OAM-
multiplexed system. ............................................................................................. 64
Figure 6.2. (a) Concept of OAM channel add/drop multiplexing. The add/drop
operation includes three steps: down-conversion, add/drop and up-
conversion. (b) Concept of OAM down-conversion. (c) Concept of OAM
up-conversion. ..................................................................................................... 65
Figure 6.3 (a) Principle of add/drop operation and the design of the phase
hologram grating (b) Incident angle of the added beam as a function of the
incident angle of the pass-through beams (or the dropped beam). ...................... 66
Figure 6.4. (Left): Experimental setup of OAM mode add/drop multiplexing.
(Right): the phase holograms on SLM4, SLM5 and SLM6 for add/drop
operation. For example, to add/drop OAM+2, SLM4 is loaded with a phase
pattern of -2 for down-conversion, and SLM6 is loaded with a spiral phase
pattern of +2 for up-conversion. The phase pattern on SLM5 is the same for

xi

adding/dropping different OAM modes. (ECL: external cavity laser. PC:
polarization controller. EDFA: Erbium doped fiber amplifier. OC: optical
coupler. SLM: spatial light modulator. Pol. Polarizer. Col.: collimator. BS:
beam splitter. HWP: half wave plate. BPF: bandpass filter. ) ............................. 69
Figure 6.5. Experimental results: (a1-a4) Images of the generated three OAM
beams and their multiplexed intensity profile. (b1-b5) Images in each step of
adding/dropping the channel on OAM+2. (c1, c2): BER curves for the
added/dropped channels (c1) and the pass-through channels (c2). (d1-d3):
Recovered constellations of the added and the dropped channels. ...................... 71
Figure 6.6 (a) Experimental results for adding/dropping OAM-5. (a1-a4) Images
recorded by a camera. (a5) BER curves for each channel. (b) Experimental
results for adding/dropping OAM+8. (b1-b4) Images (b5) BER curves. ............ 72
Figure 7.1 Concept of a tunable OAM mode filter, which is similar to a tunable
wavelength filter. ................................................................................................. 77
Figure 7.2 Principle of the OAM mode filter. (a) A log-polar geometrical
transformation transforms an OAM beam to a rectangular shaped plane
wave, and vice versa. (b) Multiplexed OAM beams are mapped to different
positions at the focal plane of the convex lens (CL) after passing through the
mode sorter. (c) The reflected beams (after filtering) are converted back to
ring-shapes while back-propagating through the mode sorter. ............................ 78
Figure 7.3 Schematic overview of the OAM filter setup. SLM: spatial light
modulator. BS: non-polarization beam splitter.................................................... 80
Figure 7.4. The simulated beam profiles at each position of the setup. (a), (b), (c)
and (d) correspond to ○ a , ○
b
, ○
c
and ○
d
in Fig.7.3, respectively. (a): the
intensity (left) and phase front (right) of the input beam. (b): “ring” is
unfolded to a rectangular shape after the mode transformation. (c):
rectangular shaped beam is focused. (d) intensity (left) and phase (right) of
the beam at the filter output. ................................................................................ 81
Figure 7.5 Observed intensities and interferograms of both the input and the output
beams of the OAM filter in the experiment. Only one OAM beam is sent to
the filter each time. The filter is set to pass all the modes. ................................. 81
Figure 7.6. Simulated wavefront correlation between the input (ℓ=+4 and +9,
respectively) and output beam as a function of the reflector (mirror array or
SLM) position on the beam propagating axis (0 is the focal plane position). ..... 82
Figure 7.7 (a) Input of the OAM filter, including OAM beams with ℓ=±4, ±9. (b)
Intensity distribution after the first mode sorter. (c) The output of the OAM
filter without blocking any mode. (d) The intensity distribution after the
second mode sorter .............................................................................................. 83

xii

Figure 7.8. (a1): Four OAM modes are mapped to four spots after the first pass of
OAM mode sorter. (a2) all four channel pass. (b1-b3): block OAM
-9
. (c1-c3):
block OAM
-4
. (d1-d3):blcok two modes: OAM
-9
and OAM
+9
. (e1-e3): pass
OAM
-4
. (f1-f3): pass OAM
+4
. The grids indicate the grating patterns that are
used on the SLM to block selected OAM channels............................................ 84
Figure 8.1. Two-dimensional structure of an HCG-HW. k indicates the
propagation direction of the confined lightwave. ................................................ 90
Figure 8.2. (a) Calculated waveguide loss (dB/m) at 1550 nm for an HCG-HW
with a 15 μm core size as a function of grating period and air gap. (b)
Chromatic dispersion of HCG-HW as a function of wavelength. D: core size
of the HCG-HW. ................................................................................................. 90
Figure 8.3. Schematic of an analog link using HCG-HW. (a) and (b) describe the
spectra of the input RF signal and the output RF signal after transmission in
HCG-HW, respectively. ...................................................................................... 92
Figure 8.4. Power of RF carrier and distortions as functions of dispersion.
Modulation frequency: f1=40GHz, f2=41GHz. The propagation distance is
100 m. .................................................................................................................. 94
Figure 8.5 SFDR reduction as a function of link loss. The 3rd-order includes IM3
SFDR and THD SFDR. The 2nd-order indicates the SHD SFDR. ..................... 95
Figure 8.6. Power of RF carrier and distortions as functions of RF input power.
According to the definition, SFDRs can be obtained by measuring the
interval between two intersections, as shown in the figure. The link using
100 m HCG-HW with optimized parameters can achieve a SHD SFDR of
105.7 dB•Hz
1/2
, THD SFDR of 113.3 dB•Hz
2/3
and an IM3 SFDR of 109.9
dB•Hz
2/3
at 40 GHz. ............................................................................................. 97
Figure 8.7. (a) SFDRs as function of modulation frequency. IM3 SFDR and THD
SFDR have little change when the modulation rate is increased. However,
SHD SFDR decreases significantly due to the chromatic dispersion of the
HCG-HW. (b) SFDRs as functions of wavelength. HCG-HW shows an
optical bandwidth of 50 nm with IM3 SFDR > 100 dB•Hz
2/3
and SHD
SFDR > 85 dB•Hz
1/2
............................................................................................ 98
Figure 8.8 (a) SFDRs as functions of grating period. (b) Calculated propagating
loss as a function of grating period and air gap. The dotted arrow indicates
the trace of changing period while keep the air gap at 470 nm. Two peaks of
SFDR occur at period of around 690 nm and 750 nm, which correspond to
two low-loss areas. .............................................................................................. 99
Figure 8.9. (a) SFDR as function of grating air gap. (b) Calculated propagating
loss as a function of grating period and air gap. The dotted arrow indicates
the trace of changing air gap while keep the period at 750 nm. IM3 and

xiii

THD SFDR are almost flat within the low loss region between 370 nm to
470 nm of air gap. SHD SFDR drops ~10 dB with air gap due to the
dispersion........................................................................................................... 100
Figure 8.10. Parameter cube of the HCG-HW. The optimal point indicates the
HCG-HW with the optimized parameters, i.e., core size (D) of 15 μm, air
gap (a
g
) of 430 nm, grating thickness (t
g
) of 340 nm and period (Λ) of 750
nm ...................................................................................................................... 101
Figure 8.11 IM3 SFDR as a function of propagating length in an HCG-HW. ............ 103
Figure 8.12 SHD SFDR as a function of propagating length in an HCG-HW. ........... 103
Figure 9.1 (a) Package of the 100 GHz EO polymodulator with W1 RF connector.
(b) Electrode structure of the single drive MZM. .............................................. 109
Figure 9.2 (Left) S21 test setup. (Right) Frequency response of the single-drive EO
MZM, with a -3dB bandwidth of ~60GHz and -7dB bandwidth of > 110
GHz. VNA: vector network analyzer. LD: laser diode. PD: photo detector. .... 110
Figure 9.3 (a) Insertion loss of this MZM as a function of the input signal’s optical
wavelength. (b)Transmission power as a function of the square of the
applied bias current on this MZM ..................................................................... 111
Figure 9.4 Experimental setup for 100-Gbit/s serial data modulations. PPG: pulse
pattern generator. MUX: multiplexer. EA: electrical amplifier. PC:
polarization controller. VOA: variable optical attenuator. OC: optical
coupler. EDFA: Erbium-doped fiber amplifier. PD: photo-detector. BERT:
bit-error-ratio tester. .......................................................................................... 111
Figure 9.5 (a): Measured eye-diagram of 100-Gbit/s ETDM signal. (b): Measured
eye-diagram of the generated 100-Gbit/s optical OOK signal. ......................... 112
Figure 9.6. Waveforms of 100Gbit/s OOK signal measured by electrical sampling
scope (65GHz bandwidth) and a complex spectrum analyzer........................... 113
Figure 9.7 100-Gbit/s NRZ-OOK after down-sampling. (Left: eyediagrams. Right:
BER performances) ........................................................................................... 114
Figure 9.8 DPSK demodulator at 12.5 Gbit/s using a polarization-based
interferometer. ................................................................................................... 114
Figure 9.9 100-Gbit/s NRZ-DPSK after down-sampling. (Left: eyediagrams. Right:
BER performances) ........................................................................................... 115
Figure 10.1 A 16-QAM signal includes two independent QPSK sub-channels .......... 122

xiv

Figure 10.2 Concept and principle (a) Concept of data erasing. (b) Concept of data
updating. The symbol ‘+’ and ‘–’ indicate phase addition and subtraction,
respectively. (c) Principle of data updating using cascaded ① SFG and ②
DFG in a PPLN waveguide. QPM: quasi-phase matching. SFG/DFG: sum-
/difference-frequency generation ....................................................................... 123
Figure 10.3 Experimental setup. LD: laser diode. PC: polarization controller.
EDFA: erbium doped fiber amplifier. OC: optical coupler. BPF: band-pass
filter. ODL: optical delay line. OSA: optical spectral analyzer. LO: local
oscillator. ADC: analog to digital converter. DSP: digital signal processing.... 124
Figure 10. 4 Optical spectrum and constellations. (a)-(c): Back-to-back QPSK
signals and NRZ 16-QAM signal. (d): offset QPSK with the other sub-
channel erased. (e): updated NRZ 16-QAM. (f): updated RZ 16-QAM. .......... 125
Figure 10.6 (a) BER versus relative time offset among three input signals (OSNR
= 20 dB). (b). Conversion efficiencies as functions of frequency spacing
between pump a and pump b. (λc-λb=1.6 nm). ................................................. 127
Fig.10.7 Optical spectral of WDM NRZ 16-QAM information updating and the
constellations for each updated channel. ........................................................... 128
Fig. 10. 8 BER performance as a function of the received OSNR for each WDM
channel............................................................................................................... 128

xv

Abstract
As a fundamental property of light, orbital angular momentum (OAM) can be carried
by helically phased laser beams. A light beam carrying OAM could have different azimuthal
states. Each state is usually identified by an integer l indicating that phase twisting rate.
Similar to any orthogonal mode groups, coaxially propagating OAM beams with different
states are orthogonal due to the helical phase structure. The orthogonality of OAM beams
allows the multiplexing/demultiplexing of multiple data channels in a single data link, in
which each channel is identified by a different OAM state. OAM multiplexing shows
potential to enhance the capacity and spectral efficiency of data transmission systems.
In this dissertation, we briefly discussed the background of OAM, and the applications
of OAM for optical communications. In the first three chapters, we focus on the system level
demonstrations using OAM multiplexing, including a free-space data link with a capacity of
100.8 Tbit/s and an efficient OAM demultiplexing technique that can further reduce the
crosstalk of adjacent OAM channels. One of the challenges of free space OAM
communication is the atmospheric turbulence. In chapter 4 and 5, we demonstrated a method
to measure the wavefront of OAM beams, and a potential approach to mitigate the channel
crosstalk caused by atmospheric turbulence. An advanced communication system is not just
point –to-point static data transmission, but also requires reconfigurability. Basic function
elements in an OAM multiplexed system, including a reconfigurable add/drop multiplexer
and tunable mode filter is demonstrated in chapter 6 and 7, respectively. Waveguides and
modulators are critical for optical communications. We simulated the performance of a low-
loss hollow-core waveguide for analog signal transmission, and characterized a 100-GHz EO

xvi

polymer modulator using broadband data modulation. In the last section, we described a
subsystem in which subchannels of a 16-QAM signal can be erased or updated optically.

1

Chapter 1 Introduction
In this Chapter, I will introduce the background of optical communications and
multiplexing techniques. Then the basic concept of orbital angular momentum is discussed,
followed by the motivations of using OAM for optical communications.
1.1 Optical Communications and Multiplexing Techniques
There has been a long time since light was found to be a unique carrier for
communications due to the fact that the frequency of light is orders of magnitude higher than
the RF frequency. In the early stages of optical communication, a single light carrier with
simple intensity modulation (i.e., On-off keying) could provide a bit rate that is much higher
than RF communication technology [1, 2]. However, this was quickly found to be not
enough and achieving an ever higher communication capacity has always being the major
interest to the communication community. This has lead to the investigation of using many
different physical properties of the light for communications, including amplitude, phase,
wavelength, polarization, orthogonal modes and space. Generally, those efforts could be
summarized as two categories: 1) encode multiple bits on a single optical pulse. A typical
example is the advanced modulation format technology, which encodes information on both
amplitude and phase [3-5]. Sometimes polarization is also encoded as PS-QPSK [6]. 2)
multiplexing/demultiplexing technology allows parallel propagation of multiple independent
data channels, each of which is addressed by a different light property such as wavelength
[7].

2

Indeed, wavelength-division multiplexing (WDM) has played an important role in
maintaining the growth of optical data transmission capacity. Some advanced wavelength
multiplexing techniques including orthogonal frequency division multiplexing (OFDM) and
Nyquist-WDM have been proposed to squeeze as many data channels as possible into
limited bandwidth resource [8, 9]. The use of two orthogonal polarization states, namely
polarization-divison multiplexing (PDM) can provided an increase factor of 2 on the
transmission spectral efficiency and capacity [10]. Other than wavelength and polarization,
space domain seems to be an additional dimension for increasing the number of transmitted
data channels in an optical communication link [11, 12]. To make use of the space domain
for space-division multiplexing (SDM), one could use either a multi-core fiber/free space
laser beam arrays so that the data channels in each core/laser beam are spatially separated
[13], or use a group of orthogonal mode sets to carry different data channels in a multi-mode
fiber (MMF) or in free space [14]. >1 petabit/s data transmission in a multi-core fiber and up
to 6 LP modes each with 2 polarizations in a single core multi-mode fiber have been
reported [15,16].
1.2 Background of OAM
In classical mechanics, momentum is a well-estabilished physical quantity that is
normally carried on a moving object. An object can carry linear momentum if it moves along
a straight line, or angular momentum if with rotational motion. The angular momentum can
be further categorized into orbital angular momentum (OAM) and spin orbital angular
momentum (SAM), corresponding to the orbiting and spinning rotation of the object,
respectively. Interestingly, a light beam may also rotate along the beam axis as it propagates,
and can carry SAM (photon spins) or OAM (photon orbits), or both of them. A laser beam

3

carrying SAM is usually manifested as circularly polarized beam. The SAM carried on each
photon cold be ±h, corresponding to left/right circular polarization, respectively [17, 18]. In
contrast, OAM is linked to the spatial distribution of beam’s phase front. It was shown by
Allen in 1992 that a helically phased beam, comprising an azimuthal phase term exp(iℓθ)
carries an OAM of ℓh/2π per photon, where θ is the transverse azimuthal angle, ℓ is an
integer indicating the number of intertwined helices (i.e., the number of 2π phase shifts along
the circle around the beam axis), and h is Planck’s constant [19]. As one may expect, each
photon could have therotically infinite number of different OAM states, each of which is
indicated by a different ℓ value.

Figure 1.1 The phase and intensity profile of a Gaussian beam (top) and an OAM beam (bottom) with
charge ℓ =3. Gaussian beam can be regarded as a special case of OAM mode with ℓ =0.
It is worth to mention the well-know Laguerre-Gaussian (LG) beam here. In general, an
OAM-carrying beam could refer to any helically phased light beam, irrespective of its radial
distribution (although sometimes OAM could also be carried by a non-helically phased beam
[20]). LG beam is a special subset among all OAM-carrying beams, due to their being
paraxial eigen-solutions of the wave equation in a cylindrical coordinates. The analytical
expression of an LG beam is given by [21]:

-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1

0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
x 10
-5
Gaussian Beam
OAM Beam

1
2
3
4
5
6
x 10
-5
Intensity Profile
Intensity Profile
Phase Front
Phase Front

1
2
3
4
5
6
x 10
-5
0
1

1
2
3
4
5
6
x 10
-5
0
1

-3
-2
-1
0
1
2
3
-π
π

-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
-π
π

-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1

4

LG
ℓ , p
= √
2p !
π ( p + | ℓ | )
1
w ( z )
[
r √ 2
w ( z )
]
| ℓ |
ex p [
− r
2
w
2
( z )
] L
p
| ℓ |
(
2 r
2
w
2
( z )
)
ex p [ iℓ θ ] ex p [
i k
0
r
2
2 ( z
2
+ z
R
2
)
] ex p [ − i ( 2p + | ℓ | + 1 ) tan
− 1
(
z
z
R
) ] (1-1)
where z
R
is the Rayleigh range, L
p
|ℓ |
is the generalized Laguerre polynomial, and w ( z ) , the
beam size at a distance of z, is given by w ( z ) = w
0
√ 1 + ( z / z
R
)
2
. It can be seen that for an
LG beam, both azimuthal and radial wavefront distributions are well defined and indicated
by two index numbers (ℓ and p), of which ℓ has the same meaning as that of a general OAM
beam, and p refers to the radial nodes in the intensity distribution. Mathematical expressions
of LG beams form an orthogonal and complete basis in the spatial domain. In contrast, a
general OAM beam actually comprises a group of LG beams (each with the same ℓ but a
different p index) due to the absence of radial definition. In the rest of this article, the term of
“OAM beam” refers to all helically phased beams, and is to be distinguished from LG beams.

Figure 1.2 Three approaches to convert a Gaussian beam into an OAM beam with ℓ =+3. (a) A spiral
phase plate. (b). Phase hologram with a spiral phase pattern. (c) Phase hologram with a “fork” pattern.

5

Many different approaches can be used to generate an OAM beam [22-25]. For
example, a spiral phase palte is an optical element with a helical surface, as shown in Fig.
3(a). To produce an OAM beam with a state of ℓ, the thickness profile of the plate should be
machined as ℓλθ/2π(n-1), where n is the refractive index of the medium. A limitation of
using an SPP is that each OAM state requires a different specific plate. As an alternative,
reconfigurable diffractive optical elements, e.g., a pixelated spatial light modulator (SLM),
or a digital micro-mirror device [26] can be programmed to function as any refractive
element of choice at a given wavelength. As mentioned above, a helical phase profile
exp(iℓθ) converts a linearly polarized Gaussian laser beam into an OAM mode, whose wave
front resembles an ℓ-fold corkscrew, as shown in Fig. 3(b). Importantly, the generated OAM
beam can be easily changed by simply updating the hologram loaded on the SLM. To
spatially separate the phase-modulated beam from the zeroth-order non-phase-modulated
reflection from the SLM, a linear phase ramp is added to helical phase code (i.e., a “fork”-
like phase pattern, as shown in Fig.3(c)) to produce a spatially distinct first-order diffracted
OAM beam, carrying the desired charge [21] .
Note that almost all the mode conversion approaches can also be used to detect an
OAM beam. For example, an OAM beam can be converted back to a Gaussian-like non-
OAM beam if the helical phase front is removed, e.g., by passing the OAM beam through a
conjugate SPP or phase hologram [21, 27].
1.3 Applications of OAM for Optical Communications
Due to the fact that coaxially propagating light beams with different OAM states are
orthogonal and can be efficiently separated, OAM beams was found to have applications for

6

SDM data transmission. This is easy to understand for LG beams because they form a
complete and orthogonal mode basis. It is noted that this property also applies to general
OAM beams with cylindrical symmetry by relying only on the azimuthal phase. Considering
any two OAM beams with an azimuthal index of ℓ
1
and ℓ
2
, respectively.
𝑈 1
( 𝑟 , 𝜃 , 𝑧 ) = 𝐴 1
( 𝑟 , 𝑧 ) ex p ⁡ ( 𝑖 𝑙 1
𝜃 ) (1-2)
𝑈 2
( 𝑟 , 𝜃 , 𝑧 ) = 𝐴 2
( 𝑟 , 𝑧 ) ex p ⁡ ( 𝑖 𝑙 2
𝜃 ) (1-3)
Where r, θ and z are the cylindrical coordinates, A
1
and A
2
represents complex
amplitude of two OAM beams except the spiral phase term. They are irrelevant to θ due to
the cylindrical symmetry. One can quickly conclude that these two beams are spatially
orthogonal in the sense that:
∫ 𝑈 1
𝑈 2
∗
2 𝜋 0
𝑑𝜃 = {
0 𝑙 1
≠ 𝑙 2
𝐴 1
𝐴 2
∗
𝑙 1
= 𝑙 2
(1-4)
This property simply indicates that coaxially propagating OAM beams with different
azimuthal states do not interfere with each other, and can be distinguished after propagation.
As of applications for optical communications, this property may represent potential
opportunities in two aspects. In the first approach, N different OAM states can be encoded as
different data symbols of “0”, “1”, …, “N-1”, respectively. A sequence of OAM states sent
by the transmitter therefore represents data information. At the receiver side, the data can be
decoded by checking the received OAM state number. This approach is more favorable to
the quantum communication community, since OAM could provide multiple Qbits (log2(N))
per photon due to the theoretically infinite possibilities of the OAM states, and could
potentially achieve a higher photon efficiency [28]. The second approach is to use each

7

OAM beam as a different data carrier [29, 30]. Similar to the SDM using orthogonal mode
sets to create more data carries, monochromatical OAM beams with the same polarization
state each can carry an independent data channel and coaxially propagate through the link
path. Ideally, the orthogonality of OAM beams can be maintained after transmission, which
allows all the data channels to be separable and recovered. A typical conceptual scheme of
multiplexing using OAM beams is shown in Fig. 2. In the rest of this disertation, we mainly
focus on the discussion of the second type application [31].

Figure 1.3. The second type application of OAM for optical communications. Each OAM beam is
used as a data carrier. They are multiplexed at the transmitter, coaxially transmitted, and demultipexed
at the receiver.
1.4 Thesis Outline
This dissertation is organized with the following structure: Chapter 2 presents a three-
dimensional multiplexed free space optical communicationi link with a total capacity of 100
Tbit/s. Chapter 3 and 4 describe a method for measuring the wavefront of OAM beams and
the crosstalk mitigation approach in OAM multiplexed system. Chapter 5 discusses that the
OAM demultiplexer can be improved by using spatial FFT. An OAM based ROADM and a
tunable filter is demonstrated in chapter 6 and chapter 7, respectively. In chapter 8, the
performance of a high-contrast grating hollow core waveguide is analyzed, incluing the loss,

8

dispersion and linearity. The experimental characterization of a 100 GHz EO polymer
modulator is illustrated in chapter 9. In the last chapter, we discussed a approach for optical
erasing or updating a subchannel of 16 QAM signals.

9

1.5 References
[1] I. P. Kaminow, T. Li, and A. E. Willner, Optical Fiber Telecommunications 5th Edition.
Elsevier, (2008).
[2] I. P. Kaminow, C. R. Doerr, C. Dragone, T. Koch, U. Koren, A. A. M. Saleh, A. J.
Kirby, C. M. Ozveren, B. Schofield, R. E. Thomas, R. A. Barry, D. M. Castagnozzi, V. W.
S. Chan, B. R. Hemenway, D. Marquis, S. A. Parikh, M. L. Stevens, E. A. Swanson, S. G.
Finn, and R. G. Gallager, “A wideband all-optical WDM network,” Journal on Selected
Areas in Communications 14, 780-799 (1996).
[3] P. J. Winzer and R.-J. Essiambre, “Advanced modulation formats for high-capacity
optical transport networks,” J. Lightwave Technol. 24, 4711-4720 (2007).
[4] X. Zhou and J. Yu, “Multi-level, multi-dimensional coding for high-speed and high-
spectral-efficiency optical transmission,” J. Lightwave Technol. 27, 3641-3653 (2009).
[5] S. Okamoto, K. Toyoda, T. Omiya, K. Kasai, M. Yoshida, and M. Nakazawa, “512
QAM (54 Gbit/s) coherent optical transmission over 150 km with an optical bandwidth of
4.1 GHz,” in Proc. of ECOC’2010, Paper PD2-3 (2010).
[6] M. Sjödin, P. Johannisson, H. Wymeersch, P. A. Andrekson, and M. Karlsson,
"Comparison of polarization-switched QPSK and polarization-multiplexed QPSK at 30
Gbit/s," Opt. Express 19, 7839-7846 (2011)
[7] Dayou Qian, Ming-Fang Huang, Ezra Ip, Yue-Kai Huang, Yin Shao, Junqiang Hu, and
Ting Wang, "High Capacity/Spectral Efficiency 101.7-Tb/s WDM Transmission Using
PDM-128QAM-OFDM Over 165-km SSMF Within C- and L-Bands," J. Lightwave
Technol. 30, 1540-1548 (2012).
[8] W. Shieh, H. Bao, and Y. Tang, "Coherent optical OFDM: theory and design," Opt.
Express 16, 841-859 (2008).
[9] David Hillerkuss, Rene Schmogrow, Matthias Meyer, Stefan Wolf, Meinert Jordan,
Philipp Kleinow, Nicole Lindenmann, Philipp C. Schindler, Argishti Melikyan, Xin Yang,
Shalva Ben-Ezra, Bend Nebendahl, Michael Dreschmann, Joachim Meyer, Francesca
Parmigiani, Periklis Petropoulos, Bojan Resan, Andreas Oehler, Kurt Weingarten, Lars
Altenhain, Tobias Ellermeyer, Michael Moeller, Michael Huebner, Juergen Becker,
Christian Koos, Wolfgang Freude, and Juerg Leuthold, "Single-Laser 32.5 Tbit/s Nyquist
WDM Transmission," J. Opt. Commun. Netw. 4, 715-723 (2012)
[10] A. H. Gnauck, P. J. Winzer, A. Konczykowska, F. Jorge, J.-Y. Dupuy, M. Riet, G.
Charlet, B. Zhu, and D. W. Peckham, “Generation and transmission of 21.4-Gbaud PDM 64-
QAM using a high-power DAC driving s single I/Q modulator,” in Proc. of OFC’2011,
Paper PDPB2 (2011).

10

[11] D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical
fibres,” Nat. Photonics 7(5), 354–362 (2013).
[12] P. J. Winzer, "Making spatial multiplexing a reality", Nat. Photon. 8, 345 (2014)
[13] B. Zhu, T. F. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. F. Yan, J. M. Fini, E.
M. Monberg, and F. V. Dimarcello, “112-Tb/s Space-division multiplexed DWDM
transmission with 14-b/s/Hz aggregate spectral efficiency over a 76.8-km seven-core fiber,”
Opt. Express 19(17), 16665–16671 (2011).
[14] S. Randel, R. Ryf, A. Sierra, P. J. Winzer, A. H. Gnauck, C. A. Bolle, R.-J. Essiambre,
D. W. Peckham, A. McCurdy, and R. Lingle, "6×56-Gb/s mode-division multiplexed
transmission over 33-km few-mode fiber enabled by 6×6 MIMO equalization," Opt. Express
19, 16697-16707 (2011).
[15] S. Matsuo, Y. Sasaki, T. Akamatsu, I. Ishida, K. Takenaga, K. Okuyama, K. Saitoh,
and M. Kosihba, "12-core fiber with one ring structure for extremely large capacity
transmission," Opt. Express 20, 28398-28408 (2012).
[16] R. Ryf, N. K. Fontaine, M. A. Mestre, S. Randel, X. Palou, C. Bolle, A. H. Gnauck, S.
Chandrasekhar, X. Liu, B. Guan, R. Essiambre, P. J. Winzer, S. Leon-Saval, J. Bland-
Hawthorn, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Grüner-Nielsen, R. V. Jensen,
and R. Lingle, "12 x 12 MIMO Transmission over 130-km Few-Mode Fiber," in Frontiers in
Optics 2012/Laser Science XXVIII, OSA Technical Digest (online) (Optical Society of
America, 2012), paper FW6C.4.
[17] J. Poynting, "The wave motion of a revolving shaft, and a suggestion as to the angular
momentum in a beam circularly polarised light," Proc. R. Soc. Lond. A Ser. A vol. 82, pp.
560-567, 1909.
[18] R. Beth, "Mechanical detection and measurement of the angular momentum of light,"
Phys. Rev. vol. 50, pp. 115-125, 1936.
[19] L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital
angular-momentum of light and the transformation of Laguerre–Gaussian laser modes,"
Phys. Rev. A 45, 8185‒8189 (1992).
[20] S. Barnett and L. Allen, "Orbital angular momentum and non paraxial light beams,"
Opt. Commun. 110, 670‒678 (1994).
[21] A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and
applications,” Adv. Opt. Photon.3, 161–204 (2011).
[22] J. M. Vaughan and D. V. Willetts, “Temporal and interference fringe analysis of
TEM01 laser modes,” J. Opt. Soc. Am. 73, 1018–1021 (1983).

11

[23] M. Mirhosseini, O. S. Magaña-Loaiza, C. Chen, B. Rodenburg, M. Malik, and R. W.
Boyd, "Rapid generation of light beams carrying orbital angular momentum," Opt. Express
21, 30196-30203 (2013).
[24] E. Karimi, S. A. Schulz, I. D. Leon, V. Qassim, J. Upham and R. W. Boyd, “Generating
optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,”
Light: Science & Applications 3, e167 (2014).
[25] N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro,
“Light propagation with phase discontinuities: generalized laws of reflection and refraction,”
Science 334, 333–337 (2011).
[26] N. R. Heckenberg, R. McDuff, C. P. Smith, and A. White, "Generation of optical phase
singularities by computer-generated holograms," Opt. Lett., vol. 17, pp. 221-223, 1992.
[27] P. Genevet, J. Lin, M. A. Kats, and F. Capasso, “Holographic detection of the orbital
angular momentum of light with plasmonic photodiodes,” Nat Commun 3, 1278 (2012).
[28] M. Malik, M. O’Sullivan, B. Rodenburg, M. Mirhosseini, J. Leach, M. P. J. Lavery, M.
J. Padgett, and R. W. Boyd, "Influence of atmospheric turbulence on optical
communications using orbital angular momentum for encoding," Opt. Express 20, 13195-
13200 (2012)
[29] G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pasko, S. M. Barnett, and S.
Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular
momentum,” Opt. Express 12, 5448-5456 (2004).
[30] J. H. Shapiro, S. Guha, and B. I. Erkmen, “Ultimate channel capacity of free-space
optical communications,” J. Opt. Netw 4, 501–516 (2005)
[31] A. E. Willner, J. Wang, and H. Huang, “Applied physics. A different angle on light
communications,” Science 337 (6095), 655–656 (2012).

12

Chapter 2 100 Tb/s Free-Space Optical Link Using OAM
combined with WDM and PDM
2.1 Introduction
Recently, OAM beams have showed the potential application of being used as data
carriers in an optical communication link, based on the fact that they form an orthogonal
basis [1,2]. Specifically, multiple independent data streams, each carried by a beam with the
same wavelength and polarization but a different OAM charge, were spatially multiplexed at
the transmitter and demultiplexed at the receiver, and the system capacity and spectral
efficiency (SE) can be dramatically improved [3-6].
While OAM-based communication links have been reported, these demonstrations have
used two domains instead of three, including 1) OAM multiplexing and PDM, in which 16
OAM beams and 2 polarizations are used to achieve a 2.56-Tbit/s free-space link on a single
wavelength [7], 2) OAM multiplexing and WDM, by which a 2-Tbit/s data link via 2 OAM
modes on 25 wavelengths was demonstrated in free space [8], and a 1.6 Tbit/s transmission
using 2 OAM modes on 10 wavelengths in a vortex fibre [9].
Different domains such as wavelength and polarization have each been used to
multiplex/demultiplex independent data channels in optical communication systems [10, 11].
Giving that distinction of OAM beams is independent to the wavelength and polarization
(with a paraxial approximation), it would be beneficial if all three domains could be used
simultaneously in a single communication link. The total data transmission capacity could be
dramatically increase [12].

13

In this chapter, we describes the combination of OAM multiplexing, PDM and WDM
simultaneously in a single free space optical communication link. We demonstrate the
multiplex/demultiplexing of 1008 data channels (each carrying 100-Gbit/s QPSK signal) by
utilizing 12 OAM beams, each with 2 polarizations and each containing 42 WDM channels.
This free space data link provids an aggregated capacity of 100.8 Tbit/s (12×2×42×100
Gbit/s) and a spectral efficiency of 22.3 bit/s/Hz. In addition, the limitations on the total
number of multiplexed channels are discussed.
2.2 Concept and experiment
The concept of a data link using three-dimensional multiplexing is presented in Fig. 2.1.
A linearly polarized OAM beam can be generated by applying a spiral phase hologram to a
Gaussian beam. Analytically, it can be derived as:
( , , ) exp[ (2 ( ))] ( , )exp( ) x
c
E r t x i t t U r z i     
λ
(2-1)
where x (or y) indicating x (or y) polarization. r is the radial distance from the centre axis of
the beam, θ is the azimuthal angle, t and z represent time and propagation distance. λ and ℓ
stand for wavelength and OAM charge, respectively. U ( r , t ) is the complex amplitude profile
determined by r and z. ∅ ( t ) is the phase of the light and can be used to encode information.
Clearly, the three parameters ℓ, x and λ, which correspond to OAM, wavelength and
polarization domain, respectively, are independent of each other, thereby allowing 3-
dimensional multiplexing.

14

Figure 2.1 Concept of using 3-dimensional multiplexing to increase the multiplexed data channels.
(a), (b) and (c) are performed successively to achieve OAM, polarization and wavelength
multiplexing, respectively. (The arrows indicate the helical phase-change direction. Each arrow
starting from white colour and ending with black colour represents a phase change from 0 to 2π.)
As an example, OAM beams with one polarization and the same wavelength (λ1), but
carrying different data channels (Data 1, 2, 3 on OAM ℓ1, OAM ℓ2 and OAM ℓ3,
respectively), can be spatially multiplexed/demultiplexed in one beam, as shown in Fig.
2.1(a). In addition, the same set of OAM beams on the orthogonal polarization can be used
Data 1
Data 2
Data 3
Gaussian
Gaussian
Gaussian
OAM ℓ
1
OAM ℓ
2
OAM ℓ
3
λ
1
λ
2
λ
3
OAM
charge
ℓ
1
ℓ
2
ℓ
3
Phase pattern
OAM multiplexed
λ
1
λ
2
λ
3
OAM
charge
Data 1, 2, 3
OAM MUX
Wavelength MUX
X-pol
OAM ℓ
1
, ℓ
2
, ℓ
3
on x-pol
OAM ℓ
1
, ℓ
2
, ℓ
3
on y-pol
OAM ℓ
1
, ℓ
2
, ℓ
3
Data 1, 2, 3
Data 4, 5, 6
Data 1, 2, 3
Data 4, 5, 6
Polarization MUX
OAM
charge
Y-pol
Data 1-6
Data 7-12
Data 13-18
X-pol
Y-pol
Data 1-18
OAM & Polarization multiplexed
OAM & Polarization &
Wavelength multiplexed
λ
1
λ
1
λ
1
λ
1
λ
1
OAM ℓ
1
, ℓ
2
, ℓ
3
ℓ
1
ℓ
2
ℓ
3
X-pol
Y-pol
ℓ
1
ℓ
2
ℓ
3
(a)
(b)
(c)
X-pol
Y-pol
-5 -4 -3 -2 -1 0 1 2 3 4 5
x 10 -3
-5
-4
-3
-2
-1
0
1
2
3
4
5
x 10 -3

-5 -4 -3 -2 -1 0 1 2 3 4 5
x 10 -3
-5
-4
-3
-2
-1
0
1
2
3
4
5
x 10 -3
-3
-2
-1
0
1
2
3
-5 -4 -3 -2 -1 0 1 2 3 4 5
x 10 -3
-5
-4
-3
-2
-1
0
1
2
3
4
5
x 10 -3

15

to carry another set of data (Data 4-6). These two sets are then polarization-multiplexed, as
shown in Fig. 2.1(b). Furthermore, using two more wavelengths (λ2 and λ3), the same set of
polarization- and OAM-multiplexed beams can be used to transport more independent data
streams (Data 7-12 on λ2, Data 13-18 on λ3), as shown in Fig.2.1(c). The 3-dimensional
multiplexed beam is then:
33
11
0
,
exp[ (2 ( ))] ( , )exp( )
l
MUX
x y l l
c
E x i t t U r z i


  



  
(2-2)

Figure 2.2 Experimental setup of 42 channel WDM transmitter, each channel carrying 100 Gbit/s
QPSK data. (a): optical spectrum of multiplexed 42 CW lasers. (b) optical spectrum of 42
wavelengths, each one carrying 100 Gbit/s QPSK signal. (c) and (d): optical spectrum of even
channels and odd channels, respectively, separated by a optical interleaver. LD: laser diode. AWG:
array waveguide grating. EDFA: erbium doped fiber amplifer. PC: polarization controller. OC: optical
coupler.

16

In this experiment, a WDM transmitter was built, comprising 100 GHz-spaced 42
wavelengths (1536.34-1568.5 nm), each modulated with 100 Gbit/s QPSK data, as shown in
Fig. 2.2. Forty-two distributed feedback (DFB) lasers starting from the wavelength of
1536.34nm to 1568.5 nm with 100-GHz (~0.8 nm) spacing are multiplexed using an array
waveguide grating (AWG). A narrow-linewidth (~100 kHz) tunable laser is used as the light
source instead of the DFB laser under measurement due to the requirement for coherent
detection. Each of the DFB lasers is adjusted by a polarization controller (PC) to make sure
that they are in the same polarization state. After passing through an erbium-doped fiber
amplifier (EDFA), the continuous-wave (CW) lasers are modulated by two 50 Gbit/s
pseudorandom binary sequence (PRBS) via an I/Q modulator to produce the 100 Gbit/s
QPSK signal. In order to decorrelate the data of neighbouring WDM channels, even and odd
channels are separated by a 100/200 GHz optical interleaver, one branch of which is
relatively delayed by ~250 symbols (~5 ns) and is then recombined with the other branch
again using a 3-dB coupler. The amplified WDM signal is split, decorrelated and fed to
SLMs for OAM generation.
Procedures for creating 12 OAM beams each with 2 polarizations, are set forth in
Fig.2.3 (a1-a4) and (b1-b4). First, we used a spatial light modulator (SLM) encoded with a
specially designed phase pattern to convert a Gaussian beam to a superposition of three
OAM beams [13]. Specifically, SLM1 generates OAM+4, OAM+10 and OAM+16, while
SLM2 generates OAM+7, OAM+13 and OAM+19. Secondly, these two outputs are
multiplexed together using a beam splitter (BS), thereby creating the multiplexing of 6 OAM
beams including ℓ=+4, +7, +10, +13, +16 and +19. Third, the multiplexed 6 OAM beams are
split into two copies. One copy is reflected 5 times (3 times by the mirrors and twice by the 2

17

BSs) to create another 6 OAM beams with inverse charges, and delayed by ~60 symbols to
decorrelate the data on the two copies. These two copies are then combined again to achieve
12 multiplexed OAM beams with ℓ=±4, ±7, ±10, ±13, ±16 and ±19. Fourth, these 12 OAM
beams are split again via a BS. One of them is polarization-rotated by 90 degrees and
delayed by ~33 symbols, and then recombined with the other copy using a polarization beam
splitter (PBS), thereby creating the multiplexing of 24 OAM beams (with ℓ=±4, ±7, ±10,
±13, ±16, ±19 on two polarizations).

Figure 2.3 (a1-a4) Block diagram of OAM multiplexing and polarization multiplexing. (MR: mirror,
SLM: spatial light modulation, BS: non-polarization beam splitter, PBS: polarization beam splitter,
HWP: half wave plate.) (b1-b4) Procedures of creating multiplexed 12 OAM beams, each with 2
polarizations. (a1) and (b1): The generation of OAM with ℓ=+4, +10 and +16 using one SLM and the
generation of OAM with ℓ=+7, +13 and +19 using another SLM. (a2) and (b2): Multiplex OAM
beams with ℓ=+4, +10 and +16 with ℓ=+7, +13 and +19. (a3) and (b3): Create OAM beams with ℓ=-
4, -7, -10, -13, -16 and +19 using wavefront phase conjugation (reflected by mirrors) and multiplex
them. (a4) and (b4): Create the same set of OAM beams in another polarization state, and multiplex
them.

The recorded images of multiplexed OAM beams in each step are shown in Fig.2.4.
The intensity profile of wavefronts in Fig.2.4(a3) and (b3) each has a 6-fold rotational

18

symmetric shape instead of a ring-shape, which is because each of them contains three OAM
beams with a charge interval of 6. We note that the data carried by different OAM beams are
mutually uncorrelated except for those originating from the same SLM, such as OAM beams
with ℓ=+4, +10, and +16, or OAM beams with ℓ=+7, +13 and +19.

Figure 2.4 Designed holograms and images of multiplexed OAM beams. (a1): Gaussian beam. (a2):
Phase hologram for generating 3 OAM beams (ℓ=+4, +10 and +16) (a3): The generated OAM beam
including ℓ=+4, +10 and +16. (b1): Gaussian beam. (b2): Phase hologram for generating 3 OAM
beams (ℓ=+7, +13 and +19) (b3): Generated OAM beams (ℓ=+7, +13 and +19). (c): Multiplexed
OAM beams with ℓ=+4, +7, +10, +13, +16, and +19 (d): Multiplexed OAM beams with ℓ=±4, ±7,
±10, ±13, ±16 and ±19 (e): Polarization-multiplexed OAM beams including ℓ=±4, ±7, ±10, ±13, ±16
and ±19 on both x- and y- polarization.
Demultiplexing is the inverse process of multiplexing. Polarization demultiplexing is
first achieved by using a polarizer, which can select only x- or y-polarization and block the
other one. A half-wave plate (HWP) is inserted after the polarizer to optimize the
polarization of the incoming light for the third spatial light modulator (SLM), which is
loaded with a spiral phase pattern that is inverse to the OAM beam to be demultiplexed. As a
result, the OAM beam to be demultiplexed is converted to a Gaussian beam, while all other
beams remain in OAM state with a non-zero charge. The converted Gaussian beam can be
coupled to a single mode fibre, which functions as a mode filter, through a 3-mm collimator

19

and a 300 mm lens. A tunable bandpass filter with a bandwidth of 1 nm is used to select a
wavelength from the WDM signal. Each channel is demultiplexed by adjusting the polarizer,
the phase pattern and the tunable filter. Note that all channels can be demultiplexed
simultaneously, if the polarizer, the third SLM and the bandpass filter are replaced with a
polarization-dependent beam splitter, an OAM mode sorter (30) and an AWG, respectively.
Then the selected channel is sent to a coherent receiver composed of a 90-degree optical
hybrid, balanced detectors and analog-to-digital converters (ADCs) with a bandwidth of 32
GHz. The signals after analog-to-digital conversion are recorded on a hard drive for digital
signal processing and signal analysis.
2.3 Data transmission results
We first characterize the crosstalk of the OAM multiplexing/demultiplexing system on
a single wavelength. Here, crosstalk is defined as the ratio of the power received only from
the demultiplexed channel (measured when all other beams are blocked) to the power
received from all other channels except the demultiplexed channel (measured when only this
beam is blocked). The measured power distributions are depicted in Fig. 2.5. The measured
crosstalk varies between -15.9 dB and -25.2 dB, with an average of ~-19 dB. We note that
the crosstalk measurement in Fig. 2.5 cannot reflect crosstalk among the three OAM beams
that originate from the same Gaussian beam, such as OAM+4, OAM+10 and OAM+16, or
OAM+7, OAM+13 and OAM+19. This type of crosstalk is characterized separately by
sending only one of the three OAM beams through the system and then measuring the power
that leaks to the other two, as shown in Tables 1(a) and 1(b), respectively. The measurement
shows that crosstalk among each of the three OAM beams is <-32 dB, which is expected to
have a negligible degradation on 100-Gbit/s QPSK signal.

20

Figure 2.5 Measured power distribution after OAM demultiplexing.

Table 3.1 (a) Crosstalk among OAM+4, OAM+10 and OAM+16 (dB)

OAM+4 OAM+10 OAM+16
OAM+4 NA -33.6 -32.9
OAM+10 -34.1 NA -34.9
OAM+16 -36.6 -33.6 NA

Table 3.1 (b) Crosstalk among OAM+7, OAM+13 and OAM+19 (dB)

OAM+7 OAM+13 OAM+19
OAM+7 NA -32.9 -44.2
OAM+13 -34.6 NA -32.2
OAM+19 -45.1 -44.9 NA

Fig. 2.6 shows the measured optical spectra of the received signal when demultiplexing
OAM+10 in x-polarization from: 1) OAM+6, OAM+10, OAM+16; and 2) all other beams.

21

Therefore, the difference between these two curves also reflects crosstalk for OAM+10 beam
at each wavelength. The measurement indicates that the crosstalk has a negligible
dependence on wavelength within the measured range.

Figure 2.6 Measured optical spectra of a single beam (OAM+10 in x-polarization). Blue solid:
demultiplexing OAM+10 when sending OAM+4, OAM+10 and OAM+16. Red dot: demultiplexing
OAM+10 when sending all other modes except OAM+4, OAM+10 and OAM+16.
Fig. 2.7 plots the measured bit-error rate (BER) as a function of optical signal-to-noise
ratio (OSNR) for a demultiplexed channel with the largest crosstalk. The BER is measured
when: 1) all channels are on (i.e., including all crosstalk); 2) only one group of OAM beams
(3 from the same SLM) is on (i.e., without OAM crosstalk); 3) only one group of OAM
beams is on while the neighboring wavelength channels are off (i.e., without OAM crosstalk,
without WDM crosstalk); and 4): back-to-back. At a BER of 3.8×10−3, the results show that
WDM crosstalk produces a power penalty of ~0.3 dB and crosstalk from other OAM modes
produces an additional penalty of ~1.7 dB. We believe that the power penalty due to OAM
crosstalk can be partially attributed to the non-ideal OAM generation at the transmitter, for
which the SLM has a limited light utilization efficiency (~86%). The crosstalk could
therefore potentially be reduced by using a higher-efficiency SLM. We then adjust the OAM

22

Figure 2.7 BER as a function of OSNR for the demultiplexed channel with the worst crosstalk.

Figure 2.8 Measured BER and OSNR for all 1008 channels (504 channels in x-pol and the other 504
channels in y-pol).
8 10 12 14 16 18
6
5
4
3
2
1
Back to back
No mode XT, no wavelength XT
No mode XT, with wavelength XT
With mode XT, with wavelength XT
-log10(BER)
OSNR (dB)
3.8e-3

23

demultiplexer, the polarizer and the filter to demultiplex each of 1008 channels and measure
the BER and OSNR, as plotted in Fig. 2.8. With the presence of all the crosstalk, each
individual channel achieves a BER below 3.8×10
−3
.

2.4 Discussion
In general, a QPSK-encoded optical communication system is crosstalk-limited. A
crosstalk of ~-19 dB is expected to have a 0.5 dB power penalty on OSNR to achieve the
same BER for an optical QPSK system [14]. In a 3-dimensional multiplexed free-space
optical link presented here, the major crosstalk comes from:
1) Crosstalk from PDM. The polarization multiplexing in free space relies on the
polarization beam splitter (PBS). The measured crosstalk from x-pol to y-pol (and from y-
pol to x-pol) of the PBS is ~33 dB.
2) Crosstalk from WDM. The crosstalk of WDM also relies on the components used,
including the AWG and the interleaver, which are used to multiplex wavelengths and to
decorrelate the data on adjacent channels, respectively. The AWG has a crosstalk of -30 dB
from adjacent channels and -35 dB from non-adjacent channels. The adjacent channel
isolation of the interleaver is -25 dB.
3) Crosstalk from OAM multiplexing. Theoretically, pure OAM modes with different
charges are completely orthogonal while the beam we generated is hardly a pure OAM beam
because the SLMs have a limited light utilization efficiency (<100%). (Typically, a phase
pattern superposed with a blazed grating can be used to separate the zeros order beam (light

24

without modulation) apart from the first order diffraction beam (phase modulated light) (2).
However, the diffraction angle of a grating is wavelength dependent, which prevents the
combining of OAM multiplexing with WDM). The unmodulated light remains a Gaussian
beam, which can be coupled into a single mode fibre together with the untwisted OAM beam.
In the experiment, the measured average crosstalk for each OAM beam (12 OAM×2
polarization) at a single wavelength is ~-19dB, which approaches the crosstalk limit for
QPSK signal. Further increase on the number of multiplexed OAM modes, each carrying
WDM channels, requires the improvement of SLM or more efficient OAM
multiplexing/demultiplexing techniques. The number of WDM channels can potentially be
extended, while it is still limited by the spectral window of the SLM (1400nm-1550nm), the
optical amplifiers and other components
In this proof-of-concept demonstration, we use bulk SLMs and BSs for OAM
generation and multiplexing. However, these devices could potentially be replaced by novel
integrated devices (e.g., [15], [16]), which could be more compact and practical for future
systems. In order to enable more efficient polarization demultiplexing at the receiver without
the use of a polarization rotator, one could potentially use a polarization-independent mode
sorter [17] followed by coupling into an optical fiber and a polarization-diversity coherent
receiver. In addition, if an array waveguide grating is used instead of the tunable filter, each
channel can be demultiplexed simultaneously without dropping the power of other channels.
The results for this paper are for a 1-m free-space link on an optical bench. For longer
distances, limitations include the following: (a) atmospheric turbulence could cause system
degradation and require adaptive optics compensation techniques [18], and (b) the beam
divergence for higher OAM charges would require a larger receiver aperture [19].

25

2.5 Summary
In this chapter, we investigate the orthogonality of OAM with other multiplexing
domains and present a free-space data link that uniquely combines OAM-, polarization-, and
wavelength-division multiplexing. Specifically, we demonstrate the
multiplexing/demultiplexing of 1008 data channels carried on 12 OAM beams, 2
polarizations and 42 wavelengths. Each channel is encoded with 100 Gbit/s quadrature
phase-shift keying, providing an aggregate capacity of 100.8 Tbit/s (12×2×42×100 Gbit/s).

26

2.6 References
[1] L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw and J. P. Woerdman, Orbital angular
momentum of light and the transformation of Laguerre–Gaussian laser modes, Phys. Rev. A
45, 8185–8189 (1992)
[2] Graham Gibson, Johannes Courtial, Miles J. Padgett, Mikhail Vasnetsov, Valeriy
Pas’ko,Stephen M. Barnett, Sonja Franke-Arnold, Free-space information transfer using
light beams carrying orbital angular momentum. Opt. Express 12, 5448–5456 (2004).
[3] Y. Awaji, N. Wada, and Y. Toda, Demonstration of spatial mode division multiplexing
using Laguerre–Gaussian mode beam in telecom-wavelength in Proceedings of the IEEE
Photonics Conference paper WBB2, PHO 2010, Denver (IEEE Photonics Society, 2010).
[4] J. H. Shapiro, S. Guha, and B. I. Erkmen, Ultimate channel capacity of free-space optical
communications. J. Opt. Netw 4, 501–516 (2005).
[5] T. Su, et al. Demonstration of free space coherent optical communication using
integrated silicon photonic orbital angular momentum devices. Optics Express 20, 9396–
9402 (2012)
[6] A. E. Willner, J. Wang and H. Huang, A Different Angle on Light Communications,
Science 337, 655-656 (2012).
[7] J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S.
Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital
angular momentum multiplexing,” Nat. Photon. 6, 488–496 (2012).
[8] I. Fazal, et al. 2 Tbit/s free-space data transmission on two orthogonal orbital-angular-
momentum beams each carrying 25 WDM channels, Opt. Lett. 37, 4753-4755 (2012)..
[9] N. Bozinovic, et al. Orbital Angular Momentum (OAM) Based Mode Division
Multiplexing (MDM) over a Km-length Fiber, in European Conference and Exhibition on
Optical Communication (ECOC), paper Th.3.C.6 (2012).
[10] A. M. Yao and M. J. Padgett, Orbital angular momentum: origins, behavior and
applications, Adv. Opt. Photon. 3, 161-204 (2011).
[11] B. Zhu, et al., Space-, Wavelength-, Polarization-Division Multiplexed Transmission
of 56-Tb/s over a 76.8-km Seven-Core Fiber, in Proceedings of the Optical Fiber
Communication Conference paper PDPB7, OFC/NFOEC2011, Los Angeles (Optical
Society of America, 2011).
[12] H. Huang, G. Xie, Y. Yan, N. Ahmed, Y. Ren, Y. Yue, D. Rogawski, M. J. Willner,
B. I. Erkmen, K. M. Birnbaum, S. J. Dolinar, M. P. J. Lavery, M. J. Padgett, M. Tur, and A.
E. Willner, "100 Tbit/s free-space data link enabled by three-dimensional multiplexing of
orbital angular momentum, polarization, and wavelength," Opt. Lett. 39, 197-200 (2014).

27

[13] H. Takara, et al. 1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) Crosstalk-managed
Transmission with 91.4-b/s/Hz Aggregate Spectral Efficiency, in Proceedings of European
Conference and Exhibition on Optical Communication, paper Th.3.C, ECOC2012.
[14] Y. Yan, et al. Spatial-Mode Multicasting of a Single100-Gbit/s Orbital Angular
Momentum (OAM) Mode onto Multiple OAM Modes, in European Conference and
Exhibition on Optical Communication, OSA Technical Digest (online), (Optical Society of
America, 2012), paper Th.2.D.1.
[15] X. Cai, J. Wang, M. J. Strain, B. J.-Morris, J. Zhu, M. Sorel, J. L. O’ Brien, M. G.
Thompson, S. Yu, Integrated Compact Optical Vortex Beam Emitters. Science 338, 363–366
(2012).
[16] K. Fontaine, C. R. Doerr, and L. Buhl, "Efficient Multiplexing and Demultiplexing
of Free-space Orbital Angular Momentum using Photonic Integrated Circuits," in Optical
Fiber Communication Conference, OSA Technical Digest (Optical Society of America,
2012), paper OTu1I.2.
[17] Martin P. J. Lavery, David J. Robertson, Gregorius C. G. Berkhout, Gordon D.
Love, Miles J. Padgett, and Johannes Courtial, "Refractive elements for the measurement of
the orbital angular momentum of a single photon," Opt. Express 20, 2110-2115 (2012)
[18] Brandon Rodenburg, Martin P. J. Lavery, Mehul Malik, Malcolm N. O’Sullivan,
Mohammad Mirhosseini, David J. Robertson, Miles Padgett, and Robert W. Boyd,
"Influence of atmospheric turbulence on states of light carrying orbital angular momentum,"
Opt. Lett. 37, 3735-3737 (2012).
[19] J. H. Shapiro, S. Guha, and B. I. Erkmen, Ultimate channel capacity of free-space
optical communications. J. Opt. Netw 4, 501–516 (2005).

28

Chapter 3 Crosstalk mitigation in an OAM-Multiplexed free-
space communication link using MIMO DSP

3.1 Introduction
Optical transmission links can employ SDM by multiplexing multiple coaxially
propagating OAM beams [1, 2, 3]. Idealy, OAM beams with different azimuthal states are
mutually orthogonal, and this orthogonalty can be maintained after the propagation in
homogeneous media such as free space. However, it has been found that OAM orthogonality
may be disturbed when they propagate in an inhomogeneous medium such as the turbulent
atmospheric [4, 5]. As a result, different OAM beams can not be completely distinguished
from one another after demultiplexing, and the channel interference may happen when each
channel carries an independent data stream.
Adaptive optics has been previously used to correct turbulence effects on OAM modes
[6, 7]. An alternative option might be to shift the complexity of the optical setup to the
digital domain and use MIMO digital signal processing (DSP) to mitigate the crosstalk in
such an OAM-multiplexed system. MIMO DSP has been widely used in RF communications
and also has been demonstrated in few-mode fiber (FMF) communications to correct the
channel interference caused by mode coupling effects [8-12]. Different than the scenario in
the FMF where modes may be randomly coupled to each other, experiments show that
different OAM beams (with the same beam size) are almost equally affected by the
turbulence, meaning that the power of each beam is almost uniformly spread to the
neighboring channels [5].

29

In this chapter, we discuss the implementation of a 4×4 adaptive MIMO equalizer in a
4-channel OAM multiplexed free space optical link using heterodyne detection [13, 14].
Four OAM modes, each carrying 20 Gbit/s QPSK data, are collinearly multiplexed,
propagated through a laboratory turbulence emulator to introduce crosstalk, and then
demultiplexed. Experimental results indicate that MIMO equalization could be used in an
OAM-multiplexed communication link to mitigate the crosstalk, and improve both error
vector magnitude (EVM) and the bit-error-rate (BER).
3.2 Turbulence Effects and Turbulence Emulator
In general, the distinction of each OAM state is highly dependent on the phase front of
each OAM beam. It is known that inhomogeneities in the temperature and pressure of the
atmosphere lead to random variations in the refractive index along the transmission path.
These refractive index inhomogeneities can degrade the phase front of each single OAM
channel. A turbulence-distorted OAM mode can be decomposed into multiple OAM modes.
Under dynamic turbulent atmospheric conditions, these degradations are slowly time-
varying processes with a time scale on the order of milliseconds (much slower than the
signaling period), which might severely limit the distance and number of OAM beams that
can be accommodated in free-space optical links [15].
To experimentally study the turbulence effects, we build a turbulence emulator using a
thin phase screen plate that is mounted on a rotation stage, as shown in Fig.3.1(a). The plate
is machined with pseudo-random phase distribution obeying Kolmogorov spectrum statistics,
which is characterized by a specific effective Fried coherence length r
0
[16, 17]. The benefit
of using an emulator instead of the true turbulence is that we can quantitize and control the

30

strength of the simulated turbulence by varying the plate with a different r
0
, changing the
size of the beam that is incident on the plate or the number of passes through the plate. The
frequency of the turbulence emulator can be adjusted by changing the incident position of
the beam or the rotation speed [5]. To verify the reliability and accuracy of the emulated
turbulence, we measured the intensity distribution and power spectrum of the beam after
passing through the emulator. The measured probability density function of the beam
intensity and the average strehl ratio imply that the emulated turbulence has a similar
statistics to the theoretical prediction. Fig. 3.1(b) shows the measured average power
(normalized) l = 3 beam under different emulated turbulence conditions. It can be seen that
the majority of the power is still in the transmitted OAM mode under weak turbulence, but it
spreads to neighboring modes as the turbulence strength increases [5]. The spreaded power
spectrum indicates that strong channel crosstalk could happen if multiple data-carrying
OAM beams are transmitted simultenalsy.

Figure 3.1. (a) Turbulence emulator. (b). Measured power distribution of an OAM beam after passing
through turbulence with different strength [5].

3.3 Crosstalk Mitigation Using MIMO DSP
The block diagram of experimental setup is shown in Fig.3.2. A CW laser at 1550 nm
with a linewidth of ~80 kHz is modulated by two 10-Gbit/s pseudo random binary sequence
Atmospheric Turbulence
Rotating Phase Plate
An ideal
OAM beam
A distorted
OAM beam
Weak Turbulence Strong Turbulence
(a) (b)

31

(2
15
-1) using an IQ modulator to provide 20 Gbit/s QPSK signal. The modulated beam is
then split into four copies, each of which is delayed using different length of fiber to
decorrelate the data sequence. Giving that the fiber delay is less than the coherence length of
the laser, we note that this setup may not accurately represent the case in which the
incoherent laser sources are used for each data channel. To describe the incoherent scenario,
one could use the power coupling models [18], and the power transfer matrix instead of a
complex amplitude matrix among each mode could be estimated and be used to mitigate the
crosstalk. In Fig. 3.2, each of these four beams is collimated in free space, and then
converted to a different pure OAM mode (i.e., channel i is carried on OAM beam with a
state of ℓi) using a computer-generated phase hologram. The four OAM beams are spatially
multiplexed using 3 beam splitters, and coaxially propagate in free space for ~1m. Note that
for such an optical link under the laboratory condition, there is almost no mode distortion
caused by propagation. Instead, we introduce wavefront distortions on the propagated OAM
beams through a turbulence emulator described in section 3.2. We note that the turbulence
provided by the emulator varies periodically as the phase plate rotates, however, the period
(>10 ms) is far greater than the signal recording time, therefore has a negligible effects on
the experiment. The equivalent effective Fried coherence length r
0
of the phase plate is ~5
mm (corresponding to an effective atmospheric structure constant of 9.8×10
-10
). Considering
that the beam diameter d when passing through the emulator is ~3.4 mm (ℓ=±3) and ~1.9
mm (ℓ=±1), respectively, the emulated turbulence is a weak turbulence, with a d/r0 of less
than 0.68 [5]. After propagation through the emulator, the received beam is split into four
copies using three cascaded BSs. Each copy is incident on a phase hologram with a
corresponding demultiplexing spiral charge (i.e., channel i is demultiplexed using OAM
charge of -ℓi). As a result, in each arm of the demultiplexer, one of the four multiplexed

32

OAM mode is down-converted to a Gaussian beam, which can be coupled into a single
mode fiber. We note that this setup has an extra 6-dB loss due to the cascaded BSs, which
could potentially be reduced by using different methods for demultiplexing [19-21].

Figure 3.2: Block diagram for the experimental setup [13]. OAM: orbital angular momentum. PC:
polarization controller. BPF: bandpass filter. SMF: single mode fiber. EDFA: erbium doped fiber
amplifier. OC: optical coupler. LO: local oscillator. ADC: analog to digital converter. PD: photo
detector. BS: free space beam splitter.
After demultiplexing, each channel is combined with a local oscillator (LO) using a 3
dB optical coupler, and detected by a photodiode (PD). The four LOs are derived from the
same narrow linewidth laser, the wavelength of which is set to ~10 GHz away from the
signal wavelength. Note that heterodyne detection only requires one PD and one analog-to-
digital convertor (ADC) to recover both I and Q components for each QPSK channel [22].
After O/E conversion, the four signals from the four PDs are simultaneously sampled by a 4-
channel real time scope with a sampling rate of 40 GS/s on each channel, and recorded for
offline digital signal processing. The offline processing procedures is depicted in Fig.3.3(a).
Each of the four sequences is converted to the frequency domain and then band-pass filtered,
followed by a 10-GHz frequency shift to baseband, as shown in Fig. 3(b1)-(b3), respectively.
Then the signals are converted back to time domain and down-sampled to 2 samples per
symbol.
EDFA
I/Q
Mod.
Laser
BPF
PC
QPSK Generation
QPSK
2 x 10 Gbit/s
ℓ=0
ℓ=ℓ 1
ℓ=ℓ 1
ℓ=0
ADC
ADC
ADC
ADC
Offline processing
LO OAM generation
Spatial MUX
Free-space
transmission
2X1
Heterodyne Detection
SMF
SMF
SMF
1X4
Turbulence
Emulator
BS
BS
BS
SMF coupling
2X1
2X1
2X1
PD
PD
PD
PD
DEMUX
1X4
ℓ=0
ℓ=ℓ 2
ℓ=0
ℓ=ℓ 3
ℓ=0
ℓ=ℓ 4
ℓ=ℓ 2
ℓ=0
ℓ=ℓ 3
ℓ=0
ℓ=ℓ 4
ℓ=0

33

Figure 3.3: (a) Procedures of offline signal processing for heterodyne and MIMO equalization. (b1)-
(b3): signal spectrum of channel using heterodyne detection. (b1) spectrum of the sampled signal. (b2)
spectrum after bandpass filtering. (b3): spectrum after frequency shifting.
The MIMO DSP used here is similar to that has been used in FMF for solving the mode
coupling [12]. The adaptive equalizer could blindly estimate the coefficients of each finite-
impulse filter (FIR) and mitigate the interference. For a 4×4 MIMO system, the equalizer
includes 16 FIR filters. The output of the equalizer can be expressed as [12]:
j ij i
i
y

wx (3-1)
where 𝐖 𝑖𝑗
(i, j=1,2,3,4) is the coefficient vector of the FIR filter with a vector length of N,
𝐗 𝑖 is the input signal vector of the ith channel, and 𝑦 𝑗 is the output of the FIR filter. The
notation * represents the convolution between two vectors. Note that here we only
investigate the static turbulence, i.e., the turbulence and the resultant crosstalk do not vary
during each data recording. All the FIR coefficients are initialized as identity, and then
updated until the coefficients are convergent based on constant modulus algorithm (CMA)
[23, 24]:
CH4 CH3 CH2 CH1
FFT
Bandpass Filtering for Heterodyne
Frequency Offset Estimation
Frequency Shift
IFFT
Resampling
4 ×4 Adaptive MIMO Equalizer
Carrier Phase Recovery
Decision & BER Counter
-20 -10 0 10 20
-30
-20
-10
0
10
Received Signal from ADC
Frequency (GHz)
Power (dBm)
0 5 10 15 20
-30
-20
-10
0
10
Extraction
Frequency (GHz)
Power (dBm)
-10 -5 0 5 10
-30
-20
-10
0
10
Fliped
Frequency (GHz)
Power (dBm)
Power (dBm) Power (dBm) Power (dBm)
(a)
(b1)
(b2)
(b3)

34

( 1) ( )
conj
ij ij i i i
k k u e y       w w x (3-2)
where u is the step size,
2
||
i ref i
e P y  is the error signal of the adaptive estimation, and
P
ref
is the normalized reference power of the QPSK signal. Fig. 3.4 shows the convergent tap
weights of the 16 FIR filters after 10000 iterations of updating using the CMA algorithm.
The number of taps in each filter is set to 15, which is enough to cover the differential time
delays among each data sequence.
3.4 Results and Discussions

Figure 3.4 The convergent tap weights (FIR filter coefficients) of the equalizer using CMA algorithm.
(a)-(d) shows the absolute value of complex taps weights of four FIR filters to equalize ch. 1, ch. 2, ch.
3 and ch. 4, respectively.
As an example, Fig. 3.4 (a) illustrates the tap weights of 4 FIR filters (
11
w ,
21
w ,
31
w
and
41
w ) that are used to generate the equalized output for channel 1. The total time
0 5 10 15
0
0.5
1
0 5 10 15
0
0.5
1
0 5 10 15
0
0.5
1
0 5 10 15
0
0.5
1

data1
data2
data3
data4
0 5 10 15
0
0.5
1
0 5 10 15
0
0.5
1
0 5 10 15
0
0.5
1
0 5 10 15
0
0.5
1

data1
data2
data3
data4
0 5 10 15
0
0.5
1
0 5 10 15
0
0.5
1
0 5 10 15
0
0.5
1
0 5 10 15
0
0.5
1

data1
data2
data3
data4
|w
11
|
|w
21
|
|w
31
|
|w
41
|
0 5 10 15
0
0.5
1
0 5 10 15
0
0.5
1
0 5 10 15
0
0.5
1
0 5 10 15
0
0.5
1

data1
data2
data3
data4
|w
12
|
|w
22
|
|w
32
|
|w
42
|
Taps number Taps number
Taps number Taps number
Taps weight
Taps weight
Taps weight
Taps weight
0 5 10 15
0
0.5
1
0 5 10 15
0
0.5
1
0 5 10 15
0
0.5
1
0 5 10 15
0
0.5
1

data1
data2
data3
data4
|w
13
|
|w
23
|
|w
33
|
|w
43
|
0 5 10 15
0
0.5
1
0 5 10 15
0
0.5
1
0 5 10 15
0
0.5
1
0 5 10 15
0
0.5
1

data1
data2
data3
data4
|w
14
|
|w
24
|
|w
34
|
|w
44
|

35

consumption for estimating all the tap weights is ~ 0.5 sec by using a regular laptop. We
note that the current system is not fast enough to track a dynamically changing turbulence.
The calculation time could potentially be reduced by optimizing the algorithm such that less
iterations are required [25], and by implementing the algorithm on a more efficient
computing hardward, e.g., field programmable gate arrays [26].

Figure 3.5 Recovered constellations of 20 Gbit/s QPSK signal in each of the four channel (with and
without MIMO equalization)
The obtained FIR filter coefficients are used to equalize the crosstalk among QPSK
channels carried on four OAM modes based on equation (1). After equalization, the FFT-
based frequency offset estimation and carrier phase recovery algorithms are applied to
recover the signal constellations. Fig. 3.5 illustrates the recovered constellations of all four
20 Gbit/s QPSK signals with and without MIMO equalization in each channel for a single
turbulence realization. Without equalization, channels 2 and 4 corresponding to OAM
modes with ℓ=+3 and -3, respectively, suffer from a larger crosstalk than the other two
channels (carried on ℓ=±1). This is because ℓ=±3 beams have a slightly larger beam size and

36

a correspondingly larger d/r0 value due to the divergence. Consequently, ℓ=±3 beams
experience a stronger distortion [5]. With the assist of MIMO DSP, the EVM (an indicator of
signal performance [27]) of four channels is improved from 0.24, 0.46, 0.33 and 0.46 to 0.14,
0.14, 0.15 and 0.21, respectively.

Figure 3.6. (a) The measured BER as a function of OSNR for the 20 Gbit/s QPSK signal in channel
4 with ℓ=8. (b) The measured EVM of the recovered QPSK signal under 29 different emulated
turbulence realizations (d/r0 is ~0.68) [13].
We also demonstrate MIMO equalization using another four OAM modes (ℓ=+2, +4,
+6 and +8). Fig. 3.6(a) shows the calculated BER as a function of OSNR for the channel
carried on ℓ=+8 (the channel that experienced the most crosstalk). Without MIMO
equalization, the measured BER for this channel are above 3.8×10
-3
(the threshold that can
be corrected by forward error correction (FEC) coding). We extrapolate this curve to cross
the FEC threshold at the OSNR of ~26.8 dB. While after MIMO equalization, the estimated
required OSNR at BER of 3.8×10
-3
is ~22.3 dB.
We then rotate the phase plate randomly to test the system under different turbulence
realizations. Fig. 3.6(b) shows the measured average EVM values of the four multiplexed
channels under 29 different turbulence realizations. We note that the benefit of using MIMO
equalization varies for different realizations. For example, the EVM in the 4th realization is
21 22 23 24 25 26 27
6
5
4
3
2
1
without MIMO
with MIMO
-log10(BER)
OSNR (dB)
FEC threshold
0 5 10 15 20 25 30
0.0
0.2
0.4
0.6
0.8
Without MIMO equalization
With MIMO equalization
EVM
Turbulence realizations

37

reduced only by ~0.1. This is because signal performance is affected by both OSNR and the
crosstalk. The equalizer only compensates for the crosstalk, while the OSNR varies in each
realization, and can not be compensated by the linear equalization.
3.5 Summary
In this chapter, we briefly discussed the atmospheric turbulence effects on multiplexed
OAM beams, and demonstrated the method of using MIMO DSP to mitigate the channel
crosstalk caused by the turbulence. The experimental results imply that under a weak
turbulence, MIMO equalizer can be used to partially correct the turbulence caused problems,
and reduce the BER and EVM of the transmitted signal.

38

3.6 Reference
[1] Graham Gibson, Johannes Courtial, Miles Padgett, Mikhail Vasnetsov, Valeriy
Pas'ko, Stephen Barnett, and Sonja Franke-Arnold, "Free-space information transfer using
light beams carrying orbital angular momentum," Opt. Express 12, 5448-5456 (2004).
[2] J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S.
Dolinar, M. Tur, and A. E. Willner, Terabit free-space data transmission employing orbital
angular momentum multiplexing, Nature Photonics 6, 488 (2012)
[3] Nenad Bozinovic, Yang Yue, Yongxiong Ren, Moshe Tur, Poul Kristensen, Hao
Huang, Alan E. Willner, Siddharth Ramachandran, Terabit-Scale Orbital Angular
Momentum Mode Division Multiplexing in Fibers, Science 340, 1545 (2013).
[4] Mehul Malik, Malcolm O’Sullivan, Brandon Rodenburg, Mohammad Mirhosseini,
Jonathan Leach, Martin P. J. Lavery, Miles J. Padgett, and Robert W. Boyd, "Influence of
atmospheric turbulence on optical communications using orbital angular momentum for
encoding," Opt. Express 20, 13195-13200 (2012)
[5] Yongxiong Ren, Hao Huang, Guodong Xie, Nisar Ahmed, Yan Yan, Baris I.
Erkmen, Nivedita Chandrasekaran, Martin P. J. Lavery, Nicholas K. Steinhoff, Moshe Tur,
Samuel Dolinar, Mark Neifeld, Miles J. Padgett, Robert W. Boyd, Jeffrey H. Shapiro, and
Alan E. Willner, "Atmospheric turbulence effects on the performance of a free space optical
link employing orbital angular momentum multiplexing," Opt. Lett. 38, 4062-4065 (2013).
[6] Brandon Rodenburg, Mohammad Mirhosseini, Mehul Malik, Omar S Magaña-
Loaiza, Michael Yanakas, Laura Maher, Nicholas K Steinhoff, Glenn A Tyler and Robert W
Boyd, Simulating thick atmospheric turbulence in the lab with application to orbital angular
momentum communication, New J. Phys. 16 033020 (2014).
[7] Yongxiong Ren, Guodong Xie, Hao Huang, Changjing Bao, Yan Yan, Nisar Ahmed,
Martin P. J. Lavery, Baris I. Erkmen, Samuel Dolinar, Moshe Tur, Mark A. Neifeld, Miles J.
Padgett, Robert W. Boyd, Jeffrey H. Shapiro, and Alan E. Willner, "Adaptive optics
compensation of multiple orbital angular momentum beams propagating through emulated
atmospheric turbulence," Opt. Lett. 39, 2845-2848 (2014)
[8] D. J. Richardson, J. M. Fini and L. E. Nelson, Space-division multiplexing in optical
fibres, Nat. Photon. 7, 354 (2013).
[9] Roland Ryf, Sebastian Randel, Alan H. Gnauck, Cristian Bolle, Alberto Sierra, Sami
Mumtaz, Mina Esmaeelpour, Ellsworth C. Burrows, René-Jean Essiambre, Peter J. Winzer,
David W. Peckham, Alan H. McCurdy, and Robert Lingle, "Mode-Division Multiplexing
Over 96 km of Few-Mode Fiber Using Coherent 6 × 6 MIMO Processing," J. Lightwave
Technol. 30, 521-531 (2012)

39

[10] Abdullah Al Amin, An Li, Simin Chen, Xi Chen, Guanjun Gao, and William Shieh,
"Dual-LP11 mode 4x4 MIMO-OFDM transmission over a two-mode fiber," Opt. Express
19, 16672-16679 (2011)
[11] Peter J. Winzer and Gerard J. Foschini, "MIMO capacities and outage probabilities in
spatially multiplexed optical transport systems," Opt. Express 19, 16680-16696 (2011).
[12] Sebastian Randel, Roland Ryf, Alberto Sierra, Peter J. Winzer, Alan H. Gnauck,
Cristian A. Bolle, René-Jean Essiambre, David W. Peckham, Alan McCurdy, and Robert
Lingle, "6×56-Gb/s mode-division multiplexed transmission over 33-km few-mode fiber
enabled by 6×6 MIMO equalization," Opt. Express 19, 16697-16707 (2011).
[13] Hao Huang, Yinwen Cao, Guodong Xie, Yongxiong Ren, Yan Yan, Changjing Bao,
Nisar Ahmed, Mark A. Neifeld, Samuel J. Dolinar, and Alan E. Willner, "Crosstalk
mitigation in a free-space orbital angular momentum multiplexed communication link using
4×4 MIMO equalization," Opt. Lett. 39, 4360-4363 (2014).
[14] H. Huang, G. Xie, Y. Ren, Y. Yan, C. Bao, N. Ahmed, M. Ziyadi, M. R. Chitgarha,
M. Neifeld, S. Dolinar, A. Willner, “4 × 4 MIMO equalization to mitigate crosstalk
degradation in a four-channel free-space orbital-angular-momentum-multiplexed system
using heterodyne detection.,” in Proceedings of the European Conference and Exhibition on
Optical Communication paper Th.1.C.4, London (Optical Society of America, 2013).
[15] G. A. Tyler and R. W. Boyd, “Influence of atmospheric turbulence on the
propagation of quantum states of light carrying orbital angular momentum,” Opt. Lett. 34,
142-144 (2009).
[16] P. Polynkin, A. Peleg, L. Klein, T. Rhoadarmer, and J. Moloney, “Optimized
multiemitter beams for free-space optical communications through turbulent atmosphere,”
Opt. Lett. 32, 885-887 (2007).
[17] L. Andrews, R. Phillips, and A. R. Weeks, “Propagation of a Gaussian beam wave
through a random phase screen,” Wave Random Media 7, 229-244 (1997).
[18] Kasyapa Balemarthy, Arup Polley, and Stephen E. Ralph, "Electronic Equalization of
Multikilometer 10-Gb/s Multimode Fiber Links: Mode-Coupling Effects," J. Lightwave
Technol. 24, 4885-4894 (2006).
[19] J. Leach, M. Padgett, S. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the
orbital angular momentum of a single photon,” Phys. Rev. Lett.88(25), 257901 (2002).
[20] M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the
orbital angular momentum eigenstates of light,” Nat. Commun.4, 2781 (2013).
[21] Steven Golowich, Nenad Bozinovic, Poul Kristensen, and Siddharth Ramachandran,
"Complex mode amplitude measurement for a six-mode optical fiber," Opt. Express 21,
4931-4944 (2013).

40

[22] Ze Dong, Xinying Li, Jianguo Yu, and Jianjun Yu, "Generation and transmission of 8
× 112-Gb/s WDM PDM-16QAM on a 25-GHz grid with simplified heterodyne detection,"
Opt. Express 21, 1773-1778 (2013).
[23] M. J. Ready and R. P. Gooch "Blind equalization on radius directed adaptation",
Proc. of Internaltional Conference on Acoustics, Speech, and Signal Processing (ICASSP-
90), vol.3, 1699 (1990).Albuquerque, NM
[24] David S. Millar and Seb J. Savory, "Blind adaptive equalization of polarization-
switched QPSK modulation," Opt. Express 19, 8533-8538 (2011).
[25] J. Benesty, P. Duhamel, “Fast constant modulus adaptive algorithm,” IEEE Radar
and Signal processing, 138 379–387 (1991).
[26] Andreas Leven, Noriaki Kaneda, and Stephen Corteselli, "Real-Time Implementation
of Digital Signal Processing for Coherent Optical Digital Communication Systems", IEEE J.
Select. Topics Quantum Electron. 16, 1227 (2010).
[27] R. Schmogrow, B. Nebendahl, M. Winter,A.Josten, D. Hillerkuss, S. Koenig, J.
Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, J. Leuthold, "Error
vector magnitude as a performance measure for advanced modulation formats", IEEE
Photon. Technol. Lett. 24, 61-63 (2012).

41

Chapter 4 Spatial FFT and the application for OAM
demultiplexing

4.1 Introduction
Orbital-angular-momentum (OAM) multiplexing has emerged as a potential method for
transmitting multiple data channels over the same spatial medium [1]. One of the key
challenges of implementing OAM multiplexing in a communication system is the efficient
demultiplexer at the receiver, just as is the case for a wavelength demultiplexer in a WDM
system. Many different approaches have been proposed and demonstrated, including but not
limited to 1) using an inverse helical phase hologram to down-convert the OAM into a
Gaussian beam, 2) a geometric optical transformation-based mode sorter [2], 3) free-space
interferometers [3] and 4) photonic integrated circuits [4, 5]. In the first approach, only the
power of down-converted Gaussian-like beam can be collected using a single mode fiber
coupling, and the other beams are wasted without being detected. Therefore, the power
efficiency is ≤1/N, where N is the number of multiplexed beams. The interferometer
approach also has a scalability limitation since the number of elements required increase
rapidly as the growth of the multiplexed beams. The OAM demultiplexer using photonic
integrated circuits could be very compact in size, but the demuliplexing of only a small
number (<4) of OAM beams was demonstrated. The geometric transformation based method
seems particularly attractive due to its relative good performance. Such a “mode-sorter”
device has been demonstrated, in which refractive elements uniquely perform a log-polar
transformation and focusing, thereby converting angular momentum into a spatial separation
at the output focal plane [2]. Simultenaously demultiplexing of >50 OAM modes has been
demonstrated using such a device [6]. However, the OAM modes with adjacent vortex

42

charges still have ~20% power overlap with each other after processed by the mode sorter
[2]. One approach to reduce the overlapping is to modify the transformation to create
multiple identical transverse cycles and join them properly, which results in a larger
separation between the spots. The spatial overlapping has been reduced to <7% by creating
three transverse cycles, and can be further reduced if more copies are used [7].
On the other hand, we realize that although the adjacent OAM modes after the mode
sorter partly overlap with each other in the spatial domain, their “orthogonality” is still
preserved, in the similar sense of orthogonal frequency division multiplexing (OFDM) in the
frequency domain [8]. A typical method for OFDM demodulation is Fast Fourier Transform
(FFT), which could efficiently recover the information on each spectrum-overlapped sub-
channel [8]. A laudable goal would be apply the same concept of OFDM and FFT in the
spatial domain to assist demultiplexing spatially overlapped OAM beams.
In this chapter, we demonstrate OAM demultiplexing using a mode sorter followed by
an optical FFT in the spatial domain. The spatial FFT is achieved using a spatial light
modulator (SLM) that performs a complex filtering function, which is equivalent to the
transfer function of simplified optical FFT. The experimentally observed separation
efficiency among four OAM modes with l=+1, +2, +3 and +4 is <-11.8 dB. Simulation
results implies that a even lower crosstalk of <-18.6 dB can be achieved by using FFT [9].
4.2 Mode sorter using geometric transformation
The principle of the OAM mode filter is based on double-passing through an OAM
mode sorter. The mode sorter, as recently reported by Berkhout et al [2], essentially
comprises a log-polar transformer [10] and a convex lens, the combination of which

43

separates different OAM states into spatial positions. The log-polar transformer maps from
the polar coordinates to the perpendicular coordinates. Specifically, it maps a position (x, y)
in the input plane to a position (u, v) in the output plane, where u = − 𝑎 ln ( √ x
2
+ y
2
/ 𝑏 ) and
v = 𝑎 ⁡ tan
− 1
( y x ⁄ ) , 𝑎 and b are scaling constants [2]. As a result, an OAM “ring” is unfolded
and converted into a rectangular-shaped plane wave in the forward propagation. As a result
of the transformation in the forward pass, the multiplexed OAM beams at the input plane, as
described in Fig. 4.1 by a set of concentric rings in terms of the beam intensity, are mapped
into a set of spatially overlapped rectangular-shaped plane waves. Note that each plane wave
after the transformation has a tilt, whose value depends on the vortex charge of the
corresponding input OAM beam. A lens can then focus these differently tilted plane waves
into spatially distinct elongated spots at its focal plane. Therefore, OAM beams with
different states are mapped into different positions and spatial distinguished.

Figure 4.1 Concept of an OAM demultiplexer (mode sorter) using optical geometrical transformation.
Assuming that the rectaular beam unfolded from the ring has a span of d in the x-
direction, and it is focused by a lens with a focal length of f, the beam profile at the focal
ℓ=1, 2, 3, 4
Log-polar
Transformation
MUXed OAM
beams
60 80 100 120 140 160 180 200 220
0
0.5
1
1.5
“OFDM”
ℓ=1, 2, 3, 4
x
y
z
lens
Sinc
Rect
Ring

44

plane is just the fourier transform of the input beam [11]. Therefore, each rectangular beam
shall be focused into a spot with a “sinc” distribution in the x-direction. The distance from
the peak to the first null point is 𝜆𝑓 / 2 𝜋𝑑 based on the fourier transform. Mean while, if we
consider two neighboring OAM modes with a modes spacing of ℓ, we can obtain two
rectangular shaped beam with a different phase tilt of 2 𝜋 . According to the ray optics, this
two tilt wave will be focus into two “sinc” spots with an inter spot separation of 𝜆𝑓 / 2 𝜋𝑎 , as
shown in Fig. 4.2(a). Clearly, this two spots have certain amont of power overlap, and the
received crosstalk from the two neighboring modes (on the left and on the right) is ~20% if
an ideal edge spatial filter is used to separate them. The measured crosstalk in a experiment
of sorting ℓ =-5 to +5 is shown in Fig. 4.2(b) [2].

Figure 4.2 (a) Simulation results shows that OAM beams with l=1 and l=2 have an overlapped power
distribution after the demultiplexing using a mode sorter. (b) Measured power overlap using the mode
sorter [2].
4.3 Analogy of OFDM in Frequency and Spatial Domain
OFDM is a special type of frequency division multiplexing in communications systems.
The basic ideal of OFDM is to split a high speed serial data stream into multiple subchannels
each with a lower symbol rate (serial-to-parallel conversion). The subchannels are then
-1.5 -1 -0.5 0 0.5 1
x 10
-3
0
1
2
3
4
5
6
x 10
6
-5 -4 -3 -2 -1 0 1 2 3 4 5
x 10
-3
-5
-4
-3
-2
-1
0
1
2
3
4
5
x 10
-3
ℓ=1
Power
X position
ℓ=2
ℓ=1
ℓ=2

45

frequency multiplexed, with a frequency spacing Δf that is equal to the 1/T, where T is the
symbol period. In such a case, all the subchannels are orthogonal to each other, meaning that
there is no channel interference, although the spectra of neiboring subchannels overlap with
each other. Two of the major benefits of OFDM is: 1) much lower symbol rate in each
subchannel indicates a better tolerance to the channel impairments. 2) no guard band
between each channel is required, leading to a higher spectral efficiency.
If we make a comparison between the case of OFDM and the output of the mode
sorter, it is not hard to find that the latter is an analogy of OFDM, but in the spatial-
frequency domain, as shown in Fig.4.3. Each OAM beam is transformed and focused into a

Figure 4.3 An analogy between OFDM and the way that each OAM beam spot is
arranged at the output of a mode sorter.
Orthogonal spatial
division multiplexing
Spatial
position
f1 f2 f3 f4
l1 l2 l3 l4
t
t
t
Δf
T
t
f1
f2
f3
f4
Δf=1/T
FT
Time domain Frequency domain
phase
x
Intensity
2 π
4 π
6 π
8 π
FT
Spatial domain
Frequency domain
Δu
d
Orthogonal frequency
division multiplexing
(OFDM)
Δf=λf/d

46

“sinc” spot that is closely arranged to each other. This conclusion implies that a special
filtering method can be used here to further separate the power from each multiplexed OAM
beam.
4.4 Spatial FFT

Figure 4.4 (a) Analogy between all optical FFT in the frequency domain and spatial domain [9, 12]. (b)
The amplitude and phase response of the designed spatial filter that functions as FFT calculator.

Giving that subchannels are closely frequency-multiplexed and their spectra overlap,
using a simple bandpass filter to extract an individual channel could cause channel
interference. A more efficient way for subchannel demultiplexing of OFDM signal is the
FFT algorithm, and typical approach is to implementing FFT in the low-cost digital signal
processing components. Hillerkuss et al proposed a method of optical FFT using cascaded
dealy-line-interferometers, as shown in Fig.4.4. [12]. Optical computation of FFT using
passive optical circuits could be more power efficient, and can process the signal with a
much larger bandwidth than doing it in the electrical domain. 26 Tbit/s optical OFDM data
transmission has been successfully demonstrated enabled by the optical FFT [13]. Similarly,
we can design such a spatial interferometer to function as an optical FFT processor to help
Spatial
sampling
1
2Δx
π/2
ℓ=1
ℓ=2
ℓ=3
ℓ=4
1
4Δx
1
4Δx
All optical FFT in spatial domain
0 1 2 3
0.0
0.4
0.8
1.2
X position (mm)
Amplitude
-6
-4
-2
0
2
4
6
Phase

47

with OAM demultiplexing, as shown in Fig. 4.4(a). Further more, the interferometer is
nothing but a more complex filter with both amplitude and phase responses. Up to now, we
can conclude the ideal is to design a spatial filter with a special amplitude and phase
response, such that the filter function as FFT processor, and therefore can demultiplex each
of the subchannel successfully [14]. Fig. 4.4 (b) shows an example of spatial filter response
that can process 4 sub-channels.
4.5 OAM demultiplexing using FFT

Figure 4.5 Concept of using spatial FFT to separate overlapped beams at the output of the mode sorter.
The spatial FFT can be achieved using a spatial light modulator.

Fig 4.5 (a) illustrate the concept of using spatial FFT to further separate the overlapped
beams after the mode sorter. An SLM with a programmed phase hologram would diffract the
beam and the first-order diffraction beam would be the desired one with FFT filtering. The
simulated results of demultiplexing OAM modes with ℓ=0, ±1, ±2 and ±3, using a mode

48

sorter followed by spatial FFT is shown in Fig.4.6(a). Simulations indicate that the crosstalk
from between 0 and ±1 could be reduced down to less than -26 dB. However, we also
observed that the crosstalk goes higher as the increase of the ℓ value. This is due to the fact
that the optical gemoetrical transformation essentially assumes the k vector of the incident
beam being perpendicular to the surface of sorter plane. It is known that a higher order OAM
beam has a k vector with a larger component on the transverse direction, and could
experience a larger error as compared to the perfect log-polar transformation. This error
degrates the orthogonality of each “carrier”, and leads to the increase of crosstalk after FFT.

Figure 4.6 Simulation (a) and experimental (b) results when demultiplexing OAM with l=1,
2, 3 and 4.
We also experimentally demonstrated the OAM demultiplexing using spatial FFT for
OAM beams with ℓ=1, 2, 3 and 4. The four multiplexed OAM beams are transformed and
mapped into four elongated spots in the focal plane that are partially overlapped in the form
of “OFDM”. The following spatial FFT is achieved by programming an SLM loaded with a
hologram that performs spatial filtering in x direction. The hologram is designed to have an
amplitude and phase response as shown in figure 4.4(b). The SLM is placed at the focal
Simulation

50 100 150 200 250 300
50
100
150
200
250
0
2000
4000
6000
8000
10000
12000
14000
16000
50 100 150 200 250 300
50
100
150
200
250
50 100 150 200 250 300
50
100
150
200
250
50 100 150 200 250 300
50
100
150
200
250

-5 0 5
x 10
-3
-5
-4
-3
-2
-1
0
1
2
3
4
5
x 10
-3
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
x 10
6
Experiment
X position
-20
-10
0
1
2
3
4
1
2
3
4
Sent OAM
Crosstalk (dB)
Received OAM
-20
-10
0
1
2
3
4
1
2
3
4
Sent OAM
Crosstalk (dB)
Received OAM
X position
(b6)
(c6)
ℓ=1 ℓ=2 ℓ=3 ℓ=4
ℓ=1 ℓ=2 ℓ=3 ℓ=4
Before FFT
Before FFT

49

plane of the mode sorter. We then use a focal lense to collimate the beam and convert the
light into “time-domain”. A spatial window is used to perfom the gating function, as is the
case in time domain FFT. We then focus the beam again to measure the crosstalk, as shown
in Fig. 4.6(b). The measurement shows that crosstalk between the adjacent modes can be
reduced to <-11.8 dB. We believe the major reason of the discrepancy between thte
simulation and the experiment is that the SLM has limited quantization resolution, and it
does not function as an ideal FFT filter.
We further simulate the performance of OAM demultiplexing using spatial FFT for
seven OAM beams with l= -3, -2, -1, 0, 1, 2, 3. The simulated channel crosstalk is shown in
Fig.4.7. It indicates that the crosstalk can be maintained below -20 dB for an l state of +/-3.
A larger l value is suffering from a higher crosstalk due to the error of the geometrical
transformation.

Figure 4.7 Simulated results when use the designed filter as FFT calculator to demultiplex overlapped
beams after the mod sorter.

50

4.6 Summary
In this chapter, we first review the convential mode sorter and its limitations. Then we
discussed the concept of spatial OFDM and FFT, and their application for improving the
efficiency of mode sorter. We demonstrate separation of 4 OAM beams with l=1, 2, 3 and 4
using a mode sorter combined with a spatial FFT. The observed crosstalk between the
adjacent modes is <-11.8 dB. A lower crosstalk of <-18.6 dB is anticipated by simulation
results.

51

4.7 Reference
[1] Graham Gibson, Johannes Courtial, Miles Padgett, Mikhail Vasnetsov, Valeriy
Pas'ko, Stephen Barnett, and Sonja Franke-Arnold, "Free-space information transfer using
light beams carrying orbital angular momentum," Opt. Express 12, 5448-5456 (2004)
[2] Gregorius C. G. Berkhout, Martin P. J. Lavery, Johannes Courtial, MarcoW.
Beijersbergen, and Miles J. Padgett, Efficient Sorting of Orbital Angular Momentum States
of Light, Physical Review Letters 105, 153601 (2010).
[3] J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett,
Interferometric Methods to Measure Orbital and Spin, or the Total Angular Momentum of a
Single Photon, Phys. Rev. Lett. 92 (1) (2004)
[4] T. Su, R. P. Scott, S. S. Djordjevic, N. K. Fontaine, D. J. Geisler, X. Cai, and S. J. B.
Yoo, "Demonstration of free space coherent optical communication using integrated silicon
photonic orbital angular momentum devices," Opt. Express 20, 9396-9402 (2012)
[5] N. K. Fontaine, C. R. Doerr, and L. Buhl, "Efficient Multiplexing and
Demultiplexing of Free-space Orbital Angular Momentum using Photonic Integrated
Circuits," in Optical Fiber Communication Conference, OSA Technical Digest (Optical
Society of America, 2012), paper OTu1I.2.
[6] M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A.
Tyler, A. Wilner, and M. J. Padgett, “Efficient measurement of orbital angular momentum
over 50 states,” New J. Phys. 15 013024 (2013)
[7] M. Mirhosseini, M. Malik, Z. Shi, R. W. Boyd, Efficient separation of the orbital
angular momentum eigenstates of light, Nat Commun. 4, 2781 (2013)
[8] W. Shieh, H. Bao, and Y. Tang, "Coherent optical OFDM: theory and design," Opt.
Express 16, 841-859 (2008)
[9] H. Huang, G. Xie, N. Ahmed, Y. Ren, Y. Yan, M. P. J. Lavery, M. Padgett, S.
Dolinar, and A. E. Willner, "Experimental Demonstration of Orbital Angular Momentum
Demultiplexing using an Optical FFT in the Spatial Domain," in CLEO: 2014, OSA
Technical Digest (online) (Optical Society of America, 2014), paper SM3J.6.
[10] Martin P. J. Lavery, David J. Robertson, Gregorius C. G. Berkhout, Gordon D. Love,
Miles J. Padgett, and Johannes Courtial, "Refractive elements for the measurement of the
orbital angular momentum of a single photon," Opt. Express 20, 2110-2115 (2012)
[11] J. W. Goodman, Introduction to Fourier Optics, McGraw-Hill Physical and Quantum
Electronics Series (Roberts, 2005).

52

[12] D. Hillerkuss, M. Winter, M. Teschke, A. Marculescu, J. Li, G. Sigurdsson, K.
Worms, S. Ben Ezra, N. Narkiss, W. Freude, and J. Leuthold, "Simple all-optical FFT
scheme enabling Tbit/s real-time signal processing," Opt. Express 18, 9324-9340 (2010)
[13] D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T.
Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J.
Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F.
Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M.
Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate
super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat.
Photonics5(6), 364–371 (2011).
[14] C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of
arbitrary optical vector beams,” New J. Phys. 9, 3, 1-20 (2007).

53

Chapter 5 Wavefront Characterization for Orbital Angular
Momentum Modes Using Homodyne Detection

5.1 Introduction
OAM modes have applications in many fields, including classical and quantum optical
communications, imaging, as well as trapping and spinning of small particles [1-5], almost
all of which require a high beam quality and a low wavefront distortion. For example, in
near-field optical communications, OAM modes, each carrying an independent data stream,
can be multiplexed and demultiplexed efficiently, providing a higher transmission capacity
and spectral efficiency [5]. However, unwanted wavefront distortions, e.g., due to turbulence
along the path or imperfect optics, degrade the multiplexing and demultiplexing efficiency.
Therefore, it could be very helpful to characterize the wavefronts of OAM modes, and obtain
distortion information that could potentially be useful in distortion compensations.
In general, wavefront characterization of an OAM mode requires the measurement of
both the intensity and phase profile in the transverse plane. Commonly used approaches of
phase extraction for a laser beam include phase-stepping interferometry [6-8], in which
moving optical components provides a variable phase reference, and the Fourier-transform
method [9], in which the fringe pattern from off-axis interference is utilized to estimate the
phase. Phase measurements of singularities in a vortex beam have been reported with the
latter technique [10, 11]. Another method, reported recently, measures the positions of the
focal spots behind an array of lenslets, resulting in a piecewise-linear approximation of the

54

phase profile of the incoming beam with a spatial resolution determined by the lenslet size
[12, 13].
In this chapter, we describe a method of characterizing the wavefront of OAM modes
using homodyne detection. We measured the amplitude and phase profile of OAM beams
with an azimuthal index of -2, -4, -6 and -8 [14]. Wavefront correlations between the
measured results and the pure LG modes are calculated.
5.2 Principle and experiment

Figure 5.1 Principle of OAM beam phase reconstruction based on the quadrature phase-shift
interference.
The principle of homodyne detection is similar to that is used in coherent detection to
recover the time-varying amplitude and phase of modulated signal. The OAM beam to be
measured is mixed with a local oscillator (LO) beam through a free space 90-dgree optical
hybrid. The OAM beam and the LO beam coaxially interfere (with the same spatial
frequency, i.e., homodyne) with each other through 50:50 beam splitters, as shown in Fig.
5.1. A and B each stand for the complex amplitude of an OAM beam and a reference beam
(i.e., a plane wave), respectively. These two beams are launched into the optical hybrid, in
π/2
cos[ ( , )] xy 
sin[ ( , )] xy 
Reference
beam
OAM
beam
A
B

55

which the OAM beam interferes with a reference beam on one path and with the π/2 phase-
shifted reference beam on the other path. Fringe patterns C and D from two outputs can be
expressed as follows [8]:
2 2 2
2 cos( )
AB
A B A B A B        (5-1)
2 2 2
exp( / 2) 2 sin( )
AB
A B j A B A B         (5-2)
Here |A| and Φ
A
are the amplitude and phase profiles of the OAM beam, respectively;
|B| and Φ
B
are that of the reference beam. All variables here are functions of the transverse-
plane coordinate with respect to the propagation direction of the beams. The beam
intensities, including |A|
2
, |B|
2
, |A+B|
2
and |A+Bexp(jπ/2)|
2
can be measured by a camera.
Consequently, cos(Φ
A
-Φ
B
) and sin(Φ
A
-Φ
B
) can be determined, and the phase profile of the
OAM beam also can be expressed as:
222
222
exp( / 2)
arctan
AB
A B j A B
A B A B


  
   
   

(5-3)
where Φ
B
is a constant if the reference beam is considered a plane wave.
In the experiment, only a single physical interferometer path is used, and two
quadrature interferences are conducted sequentially, with a variable phase retarder placed on
the path of the reference beam, as shown in Fig. 5.2. A continuous wave laser at 1550 nm is
injected into a collimator, the output of which has a beam diameter of ~3 mm. The
collimated Gaussian beam is then split by a beam splitter (BS) into two copies, one of which
is launched onto a spatial light modulator (SLM) loaded with a fork phase hologram to

56

generate OAM beams [1, 5], while the other copy is redirected as the reference beam. Since
the SLM is polarization-dependent, a half-wave plate is inserted before the SLM to optimize
the polarization of the incoming beam.

(a)

(b)
Figure 5.2 (a) Experiment setup. SLM: spatial light modulator. BS: beam splitter. HWP: half wave
plane. Col.: collimator. LCR: liquid crystal retarder. CL: convex lens. MR: mirror. A forked phase
hologram for generating OAM-4 is inserted. (b) The liquid crystal phase retarder and its phase-voltage
response.
Before interfering with the OAM beam, the reference beam is expanded by a telescope
using two convex lenses, such that it is much larger than the transverse extent of the
incoming OAM beam. A liquid crystal phase retarder (LCR) is inserted in the path of the

57

reference beam to control the phase shift of the reference beam. Switching the output voltage
of the liquid crystal controller between 0 and 1.76 V corresponds to a phase shift of 0 and
π/2, respectively. Then the OAM beam and the reference beam are properly combined
coaxially by a second beam splitter to obtain the interference. An infrared camera is used to
measure the intensity profile of the OAM beam, the reference beam, and the fringe patterns
with 0 and π/2 phase-shifts in sequence. If a dual-path interferometer is used, the two
quadrature-interferograms can be recorded with a single-shot measurement, and the
measurement speed can be improved [8]. Accordingly, the phase profiles of the OAM beams
can be retrieved based on equation (3). As an example, Fig. 5.3 shows the measured
intensities to characterize the wavefront of OAM-4 beam. It can be seen that with a π/2
phase-shift in the reference beam, the fringe pattern between OAM-4 and the reference beam
rotates by ~π/8. This occurs because an OAM-4 beam has a phase term of exp(i4φ),
therefore, the azimuth angle and phase change of the wavefront follow a ratio of 1:4.

Figure 5.3. Measured intensity profiles (a) OAM-4 beam. (b) Reference beam. (c) and (d): Fringe
patterns without and with a π/2 phase-shift

58

Figure 5.4. Measured and simulated wavefronts of generated OAM beams. (a1)~(a4): Measured
intensity profiles of OAM
-2
, OAM
-4
, OAM
-6
and OAM
-8
. (b1)~(b4): Measured phase profiles of
OAM
-2
, OAM
-4
, OAM
-6
and OAM
-8
.(c1)~(c4):. Simulated phase profiles.
Figure 5.4 (a1)-(a4) and (b1)-(b4) illustrate the measured intensity profiles and the
recovered phase fronts of experimentally generated OAM modes, including OAM-2, OAM-
4, OAM-6 and OAM-8 using the proposed setup. As references, fig. 5.4 (c1)-(c4) illustrate
the simulated phase fronts of corresponding LG modes [1]. Compared to the simulated
results, the experimentally recovered phase is blurry at the vortex center and in the region
beyond the OAM circle. This is mainly due to the fact that the OAM beams have a relative
low power in these regions. This, in combination with the limited dynamic range of the
camera and its noise, yields a very low signal-to-noise ratio measurement. Additionally, the
blurry region at the center of the beam is larger for a higher-order OAM beam, which has a
larger ring-shaped intensity distribution, as can be seen in Fig. 5.4 (a1)-(a4). It is also noted

59

that the measured phase fronts twist along the azimuthal direction faster than the simulated
results. The major reason we believe is that the reference beam (a plane wave) in the
experiment is approximated by an expanded Gaussian beam which has a curved phase front.
This curved phase front is transferred to the measured results and it enhances the twisting of
the phase.

Figure.5.5 Wavefront correlation between the generated OAM modes and the theoretical LG modes as
functions of azimuthal index.

Here, the OAM modes were generated by irradiating a fundamental Gaussian mode
onto a forked diffraction grating. Consequently, the resulting beams are not pure LG0l
modes (i.e., LG
p,l
with p=0) but rather a superposition of an infinite number of LG modes,
{LG
p,l
, p≥0}, having the same azimuthal index but different radial index values [15]. To
study this issue we calculated the correlation between the measured wavefronts of the
generated OAM modes and those of pure LG modes with the same azimuthal index but a
radial index of 0, as illustrated in Fig. 5.5 (squares). Clearly, the correlation is less than unity
and decreases with the azimuthal index, as more power is carried by radially higher-order

60

(p>0) LG modes. This result is in accord with simulations, in which we multiplied a helical
phase term exp(ilφ) with a Gaussian beam and took a Fourier transform to investigate the
far-field spatial profiles and their correlations with far-field images of the corresponding
LG0l modes, as also shown in Fig. 5.5 (open circles). A similar trend of a monotonically
decreasing correlation as a function of azimuthal index (l) is observed , although the
measured dots consistently fall below the simulated results. We attribute a major part of this
discrepancy to the limited phase changes that the SLM can apply. The phase modulation
depth of our SLM was only ~1.6π, while a modulation depth of ≥2π is required for the
generation of high-quality LG beams [16]. Simulated correlation results for different
modulation depths appear in Fig. 5.5. Indeed, the simulated curve with a modulation depth
of 1.6π provides a better fit to the measured dots. The rest of the differences can be attributed
to measurement errors, including the limited dynamic range of the camera, and stages
vibrations. A higher-dynamic range camera and anti-vibration stages can be used to
potentially improve the measurement accuracy.
5.3 Summary
In this chapter, we discussed the wavefront characterization for OAM beams using
homodyne detection. The phase fronts and intensity profiles of OAM-2, OAM-4, OAM-6
and OAM-8 are recovered. Wavefront correlations between the experimental results and the
pure Laguerre-Gaussian modes are calculated to evaluate the measurement. The measured
results are in reasonable agreement with the anticipated results based on simulations.

61

5.4 References
[1] A. Yao and M. Padgett, "Orbital angular momentum: origins, behavior and
applications," Adv. Opt. Photon. 3, 161-204 (2011).
[2] Mair, A. Vaziri, G. Weihs and A. Zeilinger, “Entanglement of the orbital angular
momentum states of photons,” Nature 412, 313 (2001).
[3] Graham Gibson, Johannes Courtial, Miles Padgett, Mikhail Vasnetsov, Valeriy Pas'ko,
Stephen Barnett, and Sonja Franke-Arnold, "Free-space information transfer using light
beams carrying orbital angular momentum," Opt. Express 12, 5448-5456 (2004)
[4] M. Padgett, R. Bowman, “Tweezers with a twist.” Nature Photon. 5, 343–348 (2011).
[5] J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S.
Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital
angular momentum multiplexing”, Nat. Photon. 6, 488 (2012).
[6] K. Creath, "Phase-shifting interferometry techniques," in Progress in Optics, E. Wolf,
ed. (Elsevier, New York, 1988), Vol. 26, pp. 357-373.
[7] Joenathan, "Phase-measuring interferometry: new methods and error analysis," Appl.
Opt. 33, 4147-4155 (1994).
[8] Kevin L. Baker, Eddy A. Stappaerts, Scott C. Wilks, Peter E. Young, Donald T. Gavel,
Jack W. Tucker, Dennis A. Silva, and Scot S. Olivier, "Open- and closed-loop aberration
correction by use of a quadrature interferometric wave-front sensor," Opt. Lett. 29, 47-49
(2004)
[9] Mitsuo Takeda, Hideki Ina, and Seiji Kobayashi, "Fourier-transform method of fringe-
pattern analysis for computer-based topography and interferometry," J. Opt. Soc. Am. 72,
156-160 (1982)
[10] T. Ando, N. Matsumoto, Y. Ohtake, Y. Takiguchi, and T. Inoue, "Structure of
optical singularities in coaxial superpositions of Laguerre Gaussian modes," J. Opt. Soc.
Am. A 27, 2602-2612 (2010).
[11] Rockstuhl, A. A. Ivanovskyy, M. S. Soskin, M. G. Salt, H. P. Herzig, R. Dändliker,
“High-resolution measurement of phase singularities produced by computer-generated
holograms,” Optics Communications, 242, 163-169 (2004).
[12] F. A. Starikov, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V.
Maslov, A. V. Ogorodnikov, S. A. Sukharev, V. P. Aksenov, I. V. Izmailov, F. Yu. Kanev,
V. V. Atuchin, and I. S. Soldatenkov, "Wavefront reconstruction of an optical vortex by a
Hartmann-Shack sensor," Opt. Lett. 32, 2291-2293 (2007).

62

[13] F. A. Starikov, G. G. Kochemasov, M. O. Koltygin, S. M. Kulikov, A. N.
Manachinsky, N. V. Maslov, S. A. Sukharev, V. P. Aksenov, I. V. Izmailov, F. Yu. Kanev,
V. V. Atuchin, and I. S. Soldatenkov, "Correction of vortex laser beam in a closed-loop
adaptive system with bimorph mirror," Opt. Lett. 34, 2264-2266 (2009).
[14] H. Huang, Y. Ren, N. Ahmed, Y. Yan, Y. Yue, A. Bozovich, J.-Y. Yang, K.
Birnbaum, J. Choi, B. Erkmen, S. Dolinar, M. Tur and A. Willner, "Demonstration of OAM
Mode Distortions Monitoring using Interference-Based Phase Reconstruction," in CLEO:
2011-Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical
Society of America, 2011), paper CF3C.4.
[15] M. A. Clifford, J. Arlt, J. Courtial, K. Dholakia, “High-order Laguerre-Gaussian
Laser Modes for Studies of Cold Atoms”, Optics Communications 156, 300 (1998).
[16] Moreno, C. Iemmi, A. Marquez, J. Campos, M. J. Yzuel, "Modulation diffraction
efficiency of spatial light modulators," 10th Euro-American Workshop on Information
Optics (WIO), pp.1-4 (2011).

63

Chapter 6 Reconfigurable optical add/drop multiplexer for
an OAM-Multiplexed Optical Communication
system

6.1 Introduction
Multiplexing different data channels together at a transmitter and demultiplexing them
at a receiver has been the staple of dramatically increasing capacity in optical
communication systems for decades, such as in wavelength-division-multiplexing (WDM).
However, significant enhancement in usability for a multi-user network was enabled by the
development of “loss-less” and reconfigurable WDM add/drop multiplexing nodes such that
a single wavelength channel can be dropped and/or added at a given network node [1, 2]. In
general, add/drop multiplexing is quite useful in multi-channel communication networks in
which a user at an intermediate point may want to access an individual channel without
disturbing/detecting the non-selected channels [3].
Recently, there have been advances in a type of multiplexing different than WDM, that
being the combining of multiple independent spatially co-propagating data channels each on
a different orbital angular momentum (OAM) modes [4-6]. A laser beam carrying OAM
includes a phase term of exp(ilφ) in its wavefront, where φ indicates the azimuth angle and l
determines the OAM value. Specifically, each laser beam with a different OAM value is
orthogonal to each other, therefore different OAM modes can be multiplexed together at a
transmitter and demultiplexed at a receiver. The simultaneous propagation of multiple OAM
modes on a single wavelength increases system capacity and spectral efficiency (i.e.,
bit/s/Hz).

64

To date, communications using multiple OAM modes have been relatively static point-
to-point links, such that data on all the modes is transmitted as a unit from transmitter to
receiver [7-11]. A laudable goal would be to follow the path of the WDM community and
demonstrate reconfigurable add/drop multiplexing in an OAM-based network environment
in order to help advance the usefulness of OAM modes in multi-user applications.
In this chaper, we demonstrate reconfigurable optical add/drop multiplexing of multiple
100-Gbit/s channels in an OAM mode division multiplexing data link. We program a spatial
light modulator (SLM) to down-convert a selected OAM mode into a Gaussian mode, so that
it is spatially separated with the other OAM modes. A specially designed grating is used to
redirect the down-converted Gaussian beam apart from the passthrough OAM modes.
Simultaneously, another Gaussian beam carrying a new data stream is added. Then all
channels are up-converted back to the original OAM modes. The OSNR penalty due to the
add/drop operation for all channels at a BER of 2×10
-3
is <2 dB.

Figure 6.1 Concept of an add/drop multiplexer in a WDM system and a OAM-multiplexed system.
...

1

2

n

3
...

1

2

n

3

2

2
/
/
Add
Drop
Wavelength Add/Drop
Multiplexer
Spatial Add/Drop Multiplexer for
OAM beams
OAM charge
Wavelength Wavelength
Add/
drop
OAM charge
l
1
l
2
l
3
l
N
l
1
l
2
'
l
3
l
N
l
2
'
l
2
add
drop

65

Figure 6.2. (a) Concept of OAM channel add/drop multiplexing. The add/drop operation includes
three steps: down-conversion, add/drop and up-conversion. (b) Concept of OAM down-conversion.
(c) Concept of OAM up-conversion.
6.2 Concept and principle
Figure 6.2 depicts the principle of the OAM based add/drop multiplexing, which can be
described in three steps: 1) down-conversion, 2) add/drop, 3) up-conversion. For a set of
multiplexed OAM beams (e.g., OAM with ℓ= ℓ1, ℓ2 and ℓ3 carrying data channels 1, 2 and
3, respectively), eah of them has a doughnut-like ring-shaped intensity distribution.
Therefore, multiplexing of different OAM modes results in a group of concentric rings that
are spatially collocated. Each selected channel (e.g., OAM ℓ
2
) can be spatially separated by
applying a spiral phase pattern with a charge of -ℓ
2
to all beams, thereby down-converting
channel 2 (OAM with ℓ=ℓ
2
) beam to a Gaussian beam ( OA M
l = 0
, l = l
2
− l
2
= 0), while all
other channels remain as OAM beams with their charges modified by − l
2
, i.e., ⁡ l
1
− l
2
,
⁡ l
3
− l
2
for channels 1 and 3, respectively. Due to the different intensity power distributions
of the Gaussian beam from OAM beams, the target channel can be spatially separated..
Charge
No.
l
1
l
2
l
3
l
1
-l
2
0 l
3
-l
2
0
l
1
l
2
l
3
l
1
-l
2
0 l
3
-l
2
0
Dropped channel
Phase
hologram
grating
Down-conversion
Input
Output
Multiplexed OAM
modes
Up-conversion
Add/drop
Drop
Add
Down-conversion Up-conversion
(a)
(b) (c)
Charge
No.
Charge
No.
Charge
No.

66

(a)

(b)
Figure 6.3 (a) Principle of add/drop operation and the design of the phase hologram grating (b)
Incident angle of the added beam as a function of the incident angle of the pass-through beams (or the
dropped beam).
In the add/drop stage, the down-converted laser beams are reflected by a specially
designed circular phase pattern that has different gratings in the center and in the outer ring
area, which will be used to reflect Gaussian modes and the other ring-shaped OAM modes,
d
φ
Drop
Add
r
1
r
2
r
3
1
1’
2
2’
3
3’
α
2
β
1
α
1
β
2
Phase hologram
grating
x
β
3
α
3
d
φ
x
Δ
0 20 40 60 80
0
20
40
60
80
Incident angle of input beams (degree)
Incident angle of the
added beam (degree)

grating period=40 um
grating period=80 um
grating period=200 um
Incident angle of input beams

67

respectively. By controlling the difference between two grating areas of the phase pattern,
the Gaussian mode can be redirected apart from the passthrough channels. Simultaneously,
another Gaussian beam that carrying a new data stream can be added to the passthrough
OAM modes by taking advantage of the two different gratings, as shown in Fig. 5.2.
Following selective manipulation, a process that is the inverse of the down-conversion,
named up-conversion, is applied to recover the charges of all OAM modes. As an example,
if we apply a spiral phase pattern with a charge of -2 to all modes for down-conversion,
another pattern with a charge of -2 is used during up-conversion. As a result, the spatially
multiplexed OAM channels are recovered, with their data being selectively processed, as
shown in Fig. 6.2.
The detail of the phase pattern design is shown in Fig. 6.3. The inner region (
1
rr  )
and the outer region (
2
rr  ) of the phase pattern are two different blazed phase gratings,
which can be described as:
𝜑 ( 𝑥 ) = {
⁡ ⁡ ⁡ m od (
2 𝜋𝑥
𝑑 , ⁡ ⁡ ⁡ 2 𝜋 ) , ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ 𝑟 < 𝑟 1
⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ 0 , ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ 𝑟 1
≤ 𝑟 < 𝑟 2
⁡
m od (
2 𝜋𝑥
− 𝑑 , ⁡ ⁡ ⁡ 2 𝜋 ) , ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ 𝑟 ≥ 𝑟 2
(6-1)
where 𝑟 is the distance from the centre point of the SLM, x indicates the position along the
vertical axis. 𝑑 is the grating period, and 𝑚 𝑜𝑑 is the modulus function. The inner circle
( 𝑟 < 𝑟 1
) and outer region ( 𝑟 ≥ 𝑟 2
) are used to diffract the dot beam (down-converted beam)
and circle beam (OAM beams), respectively. The blazed phase gratings in the two regions
have a different diffraction angle; thereby they redirect the down-converted beam at a
different angle to the OAM beam.

68

There are three different light paths: path (1, 1’), path (2, 2’) and path (3, 3’),
corresponding to the passthrough channel, the dropped channel and the added channel,
respectively. Note that light path (1, 1’) is diffracted by outer region grating with a period of
d, while light path (2, 2’) and (3, 3’) are reflected by outer region grating with a period of –d:
 
 
 
11
22
33
(1,1') sin sin
(2, 2') sin sin
(3, 3') sin sin
For light path d
For light path d
For light path d
  
  
  

  
  
(6-2)
where α1, β1, α2, β2, α3, β3 are the incident and the first-order diffraction angle of the
passthrough channels, the dropped channel and the added channel, respectively.
Accordingly, the incident angle of passthrough beams are the same as the beam to be
dropped (α1=α2). In order to make sure that the added beam is collinear with the
passthrough beams, the diffraction angle of the passthrough channel should be the same as
that of the added beam (β1=β3). Therefore, the incident angle of the added beam needs to
satisfy:
21
arcsin(sin 2 / ) d     (6-3)
Figure 6.3(b) depicts the incident angle of the added beam as a function of the incident
angle of the input beams for different grating periods. A smaller grating period generates a
larger incident angle difference between the added beam and the input beams, while the
minimum period is limited by the pixel size of the SLMs.
6.3 Experiment and results
Figure 6.4(a) shows the detailed experimental setup. A 1550 nm external cavity laser is
modulated by two 50-Gbit/s binary sequences using an I/Q modulator to generate a 100-

69

Gbit/s QPSK signal. The signal from the QPSK transmitter is divided into three copies, each
of which is decorrelated by a ~500-symbol delay using single mode fibers (SMF) with
different lengths. The three channels are sent to three collimators, respectively, each of
which converts the output of the SMF to a collimated Gaussian beam in free space. Then,
they are fed to three LCoS-based SLMs (SLM1, 2, and 3) to generate three different OAM
beams (OAM-5, OAM+2, OAM+8), respectively. Note that we use three OAM beams with
a charge spacing of >6 to reduce the spatial overlap between the down-converted beam and
the other OAM beams. The SLMs each has a pixel size of 20 um and each pixel has an 8-bit
quantified phase modulation resolution. Polarization controllers and a polarizer are used to
maximize the diffraction efficiency of the SLM. These three OAM beams are multiplexed
together using two beam splitters. The multiplexed OAM beams are taken as the inputs of
the add/drop multiplexer..

Figure 6.4. (Left): Experimental setup of OAM mode add/drop multiplexing. (Right): the phase
holograms on SLM4, SLM5 and SLM6 for add/drop operation. For example, to add/drop OAM+2,
SLM4 is loaded with a phase pattern of -2 for down-conversion, and SLM6 is loaded with a spiral
phase pattern of +2 for up-conversion. The phase pattern on SLM5 is the same for adding/dropping
different OAM modes. (ECL: external cavity laser. PC: polarization controller. EDFA: Erbium doped
fiber amplifier. OC: optical coupler. SLM: spatial light modulator. Pol. Polarizer. Col.: collimator.
BS: beam splitter. HWP: half wave plate. BPF: bandpass filter. )
EDFA BPF
Add/drop
I/Q
Mod.
PC
2 x 50 Gbit/s
EDFA
Coherent
receiver
ECL
1x3
OC
Delay
SLM1
BS
PC
PC
Col
SLM2
Col
Pol.
Pol.
Lens SLM7
Mirror
Col
HWP
Lens
BS
SLM3
Col
Pol.
Lens
Lens
SLM4
SLM5
SLM6
Lens
PC
From add channel
Dropped channel
MUX
DEMUX
QPSK Transmitter
-0.015 -0.01 -0.005 0 0.005 0.01 0.015
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
-0.015 -0.01 -0.005 0 0.005 0.01 0.015
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
-0.015 -0.01 -0.005 0 0.005 0.01 0.015
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
-0.015 -0.01 -0.005 0 0.005 0.01 0.015
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
-0.015 -0.01 -0.005 0 0.005 0.01 0.015
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
-0.015 -0.01 -0.005 0 0.005 0.01 0.015
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
SLM4
SLM6
SLM5
+5
-5
-2
+2
-8
+8
A/D
OAM-5
A/D
OAM+2
A/D
OAM+8

70

The add/drop function block is achieved by using three other SLMs. SLM4, with a
spiral phase pattern of –k, and SLM6, with a phase pattern of +k, function as the down-
converter and up-converter, respectively. (k =-5, +2, +8 for adding/dropping on OAM-5,
OAM+2, and OAM+8, respectively). SLM5 is loaded with the designed phase pattern,
including two different regions, as shown in the bottom left inset of Fig. 6.4. The grating
parameters are optimized according to the size of the input beams. The radii of the inner
region and outer region used here are 2.5 mm and 3.5 mm, respectively. Both gratings (inner
cts the dropped channel away
from the pass-through channels so that it can be selectively collected by a collimator and
coupled into the SMF for further detection. Another Gaussian beam with the same beam
waist to the down-converted Gaussian beam is launched onto the grating in the center area of
SLM5 and is added to the pass-through beams after reflection by the grating. All channels
are individually demultiplexed by SLM7 and detected by a coherent receiver to analyze the
constellations and the BER. To reconfigurably add/drop a different OAM channel, we can
change the pattern on the SLM4 to down-convert a different channel and, accordingly, the
pattern on SLM 6 for up-conversion. The insets in Fig. 6.4 show the phase holograms on
SLM4, SLM5 (bottom left), and SLM 6 (top right) for the add/drop operation. For example,
to add/drop OAM+2, SLM4 is loaded with a phase pattern of -2 for down-conversion and
SLM6 is loaded with a spiral phase pattern of +2 for up-conversion. The phase pattern on
SLM5 is the same for adding/dropping different OAM modes.
Figure 6.5(a) illustrates the camera-recorded images of OAM-5, OAM+2, OAM+8 and
the image of three multiplexed OAM beams. First, we demonstrate the add/drop of a channel
carried on OAM+2. Fig. 6.5(b) shows the images in each step of adding/dropping the

71

channel carried by OAM+2. Fig. 6.5(c1) and (c2) show the measured BER curves for the
added/dropped channels on OAM+2 and pass-through channels on OAM-5 and OAM+8,
respectively.

Figure 6.5. Experimental results: (a1-a4) Images of the generated three OAM beams and their
multiplexed intensity profile. (b1-b5) Images in each step of adding/dropping the channel on OAM+2.
(c1, c2): BER curves for the added/dropped channels (c1) and the pass-through channels (c2). (d1-d3):
Recovered constellations of the added and the dropped channels.
The OSNR penalties at a BER of 2 × 10
-3
for the added and dropped channel on
OAM+2 is ~2 dB and ~0.8 dB, respectively. The observed penalty for two pass-through
channels is ~1.5 dB. The penalties are mainly caused by the crosstalk among each channel,
which could potentially be reduced by using more efficient SLMs with a higher resolution.
The penalty of the added channel is relatively higher than the other channels because part of
Multiplexed OAM
(ℓ=-5,+2 and +8)
ℓ=+2 ℓ=-5 ℓ=+8
Down
conversion
Up-
conversion
(b) Add/drop of OAM+2
After
dropping
Dropped
channel
After
adding
(a) OAM mode multiplexing
a1) a2) a3) a4)
b1) b2) b3) b4) b5)
8 10 12 14 16 18
5
4
3
2
B2B
OAM+2 (added)
OAM+2 (dropped)
-log10(BER)
OSNR (dB)
FEC limit
8 10 12 14 16 18
5
4
3
2
B2B
OAM +8 (pass)
OAM -5 (pass)
-log10(BER)
OSNR (dB)
FEC limit
c1) c2)
B2B
Dropped
channel
Added
channel
d1) d2) d3)
-log
10
(BER)
-log
10
(BER)

72

the dropped beam, e.g., the tailed rings after down-conversion, spatially overlaps with the
other OAM beams. This part of energy (with an OAM charge of 0) is not dropped. In
contrast, it remains with the other beams, and affects the added channel (also with an OAM
charge of 0) the most. To show the reconfigurability of the scheme, we also demonstrate the
add/drop of OAM-5 and OAM+8 from the three multiplexed OAM beams by switching the
phase hologram loaded on the SLMs accordingly. Fig. 6.5(d) shows the recovered QPSK
constellations of dropped and added channel. Fig. 6.6(a) shows the images at each step of
adding/dropping OAM-5 and the BER for all channels. Fig. 6.6(b) shows the results of
adding/dropping OAM+8. A similar OSNR penalty is observed for the added/dropped
channels and the pass-through channels.

Figure 6.6 (a) Experimental results for adding/dropping OAM-5. (a1-a4) Images recorded by a camera.
(a5) BER curves for each channel. (b) Experimental results for adding/dropping OAM+8. (b1-b4)
Images (b5) BER curves.
Down-conv.
Up-conv.
(a) add/drop of OAM-5 (b) Add/drop of OAM+8
Drop Add Down-conv.
Up-conv.
Drop
Add
8 10 12 14 16 18
5
4
3
2
OAM+8
OAM+2
B2B
OAM-5 (added)
OAM-5 (dropped)
-log10(BER)
OSNR (dB)
FEC limit
8 10 12 14 16 18
5
4
3
2
OAM+2
OAM-5
B2B
OAM+8(added)
OAM+8(dropped)
-log10(BER)
OSNR (dB)
FEC limit
a1) a2) a3) a4) b1) b2) b3) b4)
a5) b5)
-log
10
(BER)
-log
10
(BER)

73

6.4 Summary
In this chapter, we designed an optical add/drop multiplexer for orbital angular
momentum (OAM) multiplexed data links by taking advantage of the ring-shaped intensity
profile of OAM beams. We demonstrated adding/dropping a single OAM beam from three
multiplexed OAM beams using liquid-crystal-on-silicon-based diffraction optical elements.
For multiplexed OAM beams carrying 100 Gbit/s quadrature phase-shift-keying data, a
power penalty of < 2dB is observed to achieve a bit-error rate of 2.0 × 10
-3
for each channel
of the add/drop multiplexer.

74

6.5 References
[1] S. Frisken, "Advances in Liquid Crystal on Silicon Wavelength Selective Switching," in
Optical Fiber Communication Conference and Exposition and The National Fiber Optic
Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America,
2007), paper OWV4.
[2] J. Homa, K. Bala, "ROADM Architectures and Their Enabling WSS Technology,"
Communications Magazine, IEEE , vol.46, no.7, pp.150-154, July 2008
[3] J. Ertel, R. Helbing, C. Hoke, O. Landolt, K. Nishimura, P. Robrish, and R. Trutna,
"Design and Performance of a Reconfigurable Liquid-Crystal-Based Optical Add/Drop
Multiplexer," J. Lightwave Technol. 24, 1674- (2006).
[4] H. Huang, G. Xie, Y. Yan, N. Ahmed, Y. Ren, Y. Yue, D. Rogawski, M. Tur, B.
Erkmen, K. Birnbaum, S. Dolinar, M. Lavery, M. Padgett, and A. E. Willner, "100 Tbit/s
Free-Space Data Link using Orbital Angular Momentum Mode Division Multiplexing
Combined with Wavelength Division Multiplexing," in Optical Fiber Communication
Conference/National Fiber Optic Engineers Conference 2013, OSA Technical Digest
(online) (Optical Society of America, 2013), paper OTh4G.5.
[5] Graham Gibson, Johannes Courtial, Miles Padgett, Mikhail Vasnetsov, Valeriy Pas'ko,
Stephen Barnett, and Sonja Franke-Arnold, "Free-space information transfer using light
beams carrying orbital angular momentum," Opt. Express 12, 5448-5456 (2004).
[6] J. H. Shapiro, S. Guha, and B. I. Erkmen, Ultimate channel capacity of free-space optical
communications. J. Opt. Netw 4, 501–516 (2005).
[7] Y. Awaji, N. Wada, and Y. Toda, Demonstration of spatial mode division multiplexing
using Laguerre–Gaussian mode beam in telecom-wavelength in Proceedings of the IEEE
Photonics Conference paper WBB2, PHO 2010, Denver (IEEE Photonics Society, 2010).
[8] X. Cai, J. Wang, M. J. Strain, B. J.-Morris, J. Zhu, M. Sorel, J. L. O’ Brien, M. G.
Thompson, S. Yu, Integrated Compact Optical Vortex Beam Emitters. Science 338, 363–366
(2012).
[9] P. Boffi, P. Martelli, A. Gatto and M. Martinelli, “Mode-division multiplexing in fibre-
optic communications based on orbital angular momentum”, J. Opt. 15 075403 (2013).
[10] J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S.
Dolinar, M. Tur, and A. E. Willner, Terabit free-space data transmission employing orbital
angular momentum multiplexing, Nature Photonics 6, 488 (2012).
[11] Nenad Bozinovic, Yang Yue, Yongxiong Ren, Moshe Tur, Poul Kristensen, Hao
Huang, Alan E. Willner, Siddharth Ramachandran, Terabit-Scale Orbital Angular
Momentum Mode Division Multiplexing in Fibers, Science 340, 1545 (2013).

75

[12] Y. Yue, N. Ahmed, H. Huang, Y. Yan, Y. Ren, D. Rogawski, and A. E. Willner,
"Reconfigurable Orbital-Angular-Momentum-Based Switching among Multiple 100-Gbit/s
Data Channels," in Optical Fiber Communication Conference/National Fiber Optic
Engineers Conference 2013, OSA Technical Digest (online) (Optical Society of America,
2013), paper OM2G.1.
[13] Xi Chen, An Li, Jia Ye, Abdullah Al Amin, and William Shieh, "Demonstration of
Few-Mode Compatible Optical Add/Drop Multiplexer for Mode-Division Multiplexed
Superchannel," J. Lightwave Technol. 31, 641-647 (2013).
[14] M. D. Feuer, L. E. Nelson, K. S. Abedin, X. Zhou, T. F. Taunay, J. F. Fini, B. Zhu, R.
Isaac, R. Harel, G. Cohen, and D. M. Marom, "ROADM System for Space Division
Multiplexing with Spatial Superchannels," in Optical Fiber Communication
Conference/National Fiber Optic Engineers Conference 2013, OSA Technical Digest
(online) (Optical Society of America, 2013), paper PDP5B.8.
[15] H. Huang, Y. Yue, Y. Yan, N. Ahmed, Y. Ren, and A. E. Willner, "Orbital-angular-
momentum-based Reconfigurable and “Lossless” Optical Add/Drop Multiplexing of
Multiple 100-Gbit/s Channels," in Optical Fiber Communication Conference/National Fiber
Optic Engineers Conference 2013, OSA Technical Digest (online) (Optical Society of
America, 2013), paper OTh4G.4.
[16] J. W. Goodman, Introduction to Fourier Optics, McGraw-Hill Physical and Quantum
Electronics Series (Roberts, 2005).
[17] C. Schmidt-Langhorst, R. Ludwig, D. Groß, L. Molle, M. Seimetz, R. Freund, and C.
Schubert, "Generation and Coherent Time-Division Demultiplexing of up to 5.1 Tb/s Single-
Channel 8-PSK and 16-QAM Signals," in Optical Fiber Communication Conference and
National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of
America, 2009), paper PDPC6.
[18] David A. B. Miller, "Reconfigurable add-drop multiplexer for spatial modes," Opt.
Express 21, 20220-20229 (2013).

76

Chapter 7 Tunable Filter for Orbital-Angular-Momentum
Multiplexed Optical Channels

7.1 Introduction
In a multiplexed communications system including multiple independent data channels,
one of the important function blocks is the tunable filtering. For example, tunable bandpass
filters in a WDM system are frequently used to select a certain wavelength channel from
multiple wavelength-multiplexed channels, or to remove out-of-band ASE noise. Similarly, a
spatial mode filter that performs efficient filtering and demultiplexing of multiple OAM
beams would be useful in an OAM- multiplexed system in order to extract the desired
information. Presently, few basic elements exist to enable OAM systems. It might be
interesting to further demonstrate a tunable optical filter that can selectively output one
OAM mode from multiple input multiplexed OAM modes, and keep its OAM characteristics
[10].
In this chapter, we demonstrated a tunable mode-passing/blocking filter for spatially
multiplexed OAM beams using a log-polar transformation-based mode sorter and a spatial
light modulator (SLM). Multiple multiplexed OAM beams are mapped to different positions
on the screen of the SLM and are reflected back to the sorter. The programmable SLM can
selectively control the passing or blocking of each OAM beam, therefore the mode filter is
tunable in terms of the passing modes or blocking modes. Mode filtering or blocking of one
or multiple OAM modes from four OAM modes (ℓ=-9, -4, +4 and +9) is demonstrated. The

77

performance of the filter including the beam quality, insertion loss and filter resolution are
discussed in the end.
7.2 Concept and Principle

Figure 7.1 Concept of a tunable OAM mode filter, which is similar to a tunable wavelength filter.
Similar to the tunable filter in the wavelength domain, as shown in Fig. 7.1, an OAM
mode filter is expected to be able to transmit (i.e., a “band-pass filter”)or block (i.e., a band-
block filter) the selected OAM modes from multiple spatially multiplexed OAM modes.
After filtering, the output data channels are required to maintain their input OAM property.
This can be achieved by passing the beams through an OAM mode sorter for twice (one
forward and one backward). The mode-sorter, as we described in chapter 5, performs a
coordinate transformation (from log-polar coordinate to cartsian coordinate), such that each
of OAM beam with a ring shape is transformed into a plane wave with a different phase tilt.
A following lens then can focus them into different locations due to the phase tilt. On the
other hand, the beams can be reflected by a mirror that is placed perpendicular to the
propagating direction at the focal plane of the lens, and pass through the mode sorter again in
OAM
λ
WDM channels
λ1 λ3 λ2 λ2
MDM (OAM) channels
OAM
l1 l3 l2
Wavelength
tunable filter
OAM mode
tunable filter
λ4 λ4
l4
λ
λ1 λ3
l1 l3 l2 l4

78

the opposite direction, as shown in Fig. 7.2(c). Since the mirror is at the focal plane, the
reflected beams with the elongated shape are collimated by the convex lens and are
converted to rectangular plane waves with different tilts. Following that, the geometric
transformer performs inverse transformation (from Cartesian to log-polar coordinates) and
converts the tilt plane waves back into vortex beams with a ring-shaped intensity.
Furthermore, if the mirror at the focal plane of the lens is replaced with a programmable
mirror array, we can selectively control the passing or blocking of each OAM mode, and the
tunable OAM mode filtering function can be achieved. Fig. 7.2(c) shows an example of a
“band blocking” filter (blocking OAM beam with ℓ = ℓ
3
).

Figure 7.2 Principle of the OAM mode filter. (a) A log-polar geometrical transformation transforms
an OAM beam to a rectangular shaped plane wave, and vice versa. (b) Multiplexed OAM beams are
mapped to different positions at the focal plane of the convex lens (CL) after passing through the
mode sorter. (c) The reflected beams (after filtering) are converted back to ring-shapes while back-
propagating through the mode sorter.
Programmable
mirror array
Beam
Splitter
Output
Multiplexed OAM
beams
( ℓ1, ℓ2, ℓ4)
Input
Multiplexed OAM
beams
geometrical
transformation
From OAM ℓ1
From OAM ℓ2
From OAM ℓ3
From OAM ℓ4
f
Input
CL
CL
(b)
(c)
geometrical
transformation
f
Tilted plane wave
Log-polar
coordinates
(a)
Cartesian
coordinates
OAM ring
geometrical
transformation
(ℓ1, ℓ2, ℓ3, ℓ4)

79

7.3 Experiment and results
The schematic overview of the OAM filter setup is shown in Fig. 7.3. The light from a
laser source is collimated and then launched onto a liquid crystal on silicon-based diffractive
spatial light modulator. The SLM is loaded with a designed phase hologram to generate
multiple superimposed OAM modes [13]. The generated OAM beams are sent to the OAM
mode filter as the inputs. The mode transformer in the filter is achieved by using two
reflective optical elements [9], each of which has an aperture size of 8 mm. A convex lens
with a focal length of 1m is placed right after the mode transformer to focus the beams. At
the focus plane, we use a reflective SLM instead of the mirror array to reflect the beams. The
SLM surface is divided into different regions, each of which encompasses the spot
corresponding to a specific OAM mode. Each region of the SLM can be programmed to
either reflect the beam back to the lens or to diffract the beam away from the other beams,
effectively blocking it. All reflected beams back-propagate through the optical system and
are converted back into the desired selection of superimposed OAM beams. We use a beam
splitter to separate the backward propagating beam from the input beams. We note that the
charge of the OAM beams after double passing through the mode sorter are inversed. Due to
the additional reflection of the beam splitter, the final output beams are expected to have the
same vortex charges as the input OAM beams.
We first tested the OAM mode filter by sending a single OAM beam as the input. The
filter is set to pass all the input beams. Therefore, an OAM beam with the same vortex
charge is expected to be obtained at the output port of the filter. Simulation results in Fig. 7.4
illustrate the beam profile evolution when we send in OAM with ℓ=+4. Fig. 7.4 (a), (b), (c)
and (d) (corresponding to the position ○ a , ○ b , ○ c and ○ d , respectively, of the setup in Fig.7.3)

80

shows the simulated beam profile of the input beam, the beam after transformation, the beam
at the focal plane, and the output beam, respectively. We compare the input beam and the
output beam by calculateding their intensity correlation and wavefront (including both
intensity and phase front) correlation coefficient, which is ~0.98 and ~0.97, respectively.
These two numbers indicate that the ring-shaped intensity and the helical phase of the beam
can be maintained fairly well after filtering.

Figure 7.3 Schematic overview of the OAM filter setup. SLM: spatial light modulator. BS: non-
polarization beam splitter.

Fig. 7.5 shows the experimentally observed intensity profiles and interferograms of
both the input and output beams. We send the OAM beam with ℓ=+4, -4, +9 and -9,
respectively. The interferograms are obtained by interfering the target beam with a plane
wave (approximated by an expanded Gaussian beam) from the same laser source. The
interferograms in the second and the fourth column imply that the output beams have the
same vortex charge as the input OAM beams.
SLM2
Mode transformer
BS
1
2
3
4
1550 nm
laser
Output
mode analysis
Fiber collimator
PC
control
Filter
SLM1
Mirror
a b c
d
Lens
Lens
Lens

81

Figure 7.4. The simulated beam profiles at each position of the setup. (a), (b), (c) and (d) correspond
to ○ a , ○
b
, ○
c
and ○
d
in Fig.7.3, respectively. (a): the intensity (left) and phase front (right) of the
input beam. (b): “ring” is unfolded to a rectangular shape after the mode transformation. (c):
rectangular shaped beam is focused. (d) intensity (left) and phase (right) of the beam at the filter
output.

Figure 7.5 Observed intensities and interferograms of both the input and the output beams of the
OAM filter in the experiment. Only one OAM beam is sent to the filter each time. The filter is set to
pass all the modes.

Since the reflector (mirror array or SLM) is required to be placed right at the focal
plane of the lens, a position shift away from the focal plane may cause distortions on the
LG intensity
200 400 600 800 1000
100
200
300
400
500
600
700
800
900
1000
LG phase

200 400 600 800 1000
100
200
300
400
500
600
700
800
900
1000
Far field phase
200 400 600 800 1000
100
200
300
400
500
600
700
800
900
1000
Far field phase

200 400 600 800 1000
100
200
300
400
500
600
700
800
900
1000 -3
-2
-1
0
1
2
3
-3
-2
-1
0
1
2
3
LG intensity
200 400 600 800 1000
100
200
300
400
500
600
700
800
900
1000
LG phase

200 400 600 800 1000
100
200
300
400
500
600
700
800
900
1000
Far field phase
200 400 600 800 1000
100
200
300
400
500
600
700
800
900
1000
Far field phase

200 400 600 800 1000
100
200
300
400
500
600
700
800
900
1000 -3
-2
-1
0
1
2
3
-3
-2
-1
0
1
2
3
-π
π
LG intensity
200 400 600 800 1000
100
200
300
400
500
600
700
800
900
1000
LG phase

200 400 600 800 1000
100
200
300
400
500
600
700
800
900
1000
Far field phase
200 400 600 800 1000
100
200
300
400
500
600
700
800
900
1000
Far field phase

200 400 600 800 1000
100
200
300
400
500
600
700
800
900
1000 -3
-2
-1
0
1
2
3
-3
-2
-1
0
1
2
3
(a)
(d)
LG intensity
200 400 600 800 1000
100
200
300
400
500
600
700
800
900
1000
LG phase

200 400 600 800 1000
100
200
300
400
500
600
700
800
900
1000
Far field phase
200 400 600 800 1000
100
200
300
400
500
600
700
800
900
1000
Far field phase

200 400 600 800 1000
100
200
300
400
500
600
700
800
900
1000 -3
-2
-1
0
1
2
3
-3
-2
-1
0
1
2
3
-π
π
(b)
(c)
ℓ=+4
ℓ=-4
ℓ=+9
ℓ=-9
Intensity Interferogram Intensity Interferogram
Filter input Filter output

82

output beams of the filter. The simulation result in Fig. 7.6 indicates that the wavefront
correlation coefficient between the input and output beam varies almost symmetrically with
the reflector shift along the beam propagating axis.

Figure 7.6. Simulated wavefront correlation between the input (ℓ=+4 and +9, respectively) and output
beam as a function of the reflector (mirror array or SLM) position on the beam propagating axis (0 is
the focal plane position).
We then send multiple multiplexed OAM modes as the filter input, and analyze the
output beams by a second aligned mode sorter. Fig. 7.7(a) shows the superimposed intensity
profile of the input beams, including OAM with ℓ=±4 and ±9. After the first passage through
the mode sorter, four OAM beams are mapped to four elongated spots at the focal plane, as
shown in Fig.7.7(b). Fig. 7.7(c) shows the image of the beams at the output of the filter
without blocking any beam. A further log-polar transformation maps the output beams into
four spots again, as shown in Fig. 7.7(d).
The experimental results of the tunable filtering functions are shown in Fig. 7.8. Figure
7.8 (a1)-(a3) shows the scenario when all four modes pass through the filter. Through the
programming of the SLM at the focal plane of the first mode sorter where all the input
modes are spatially separated, we selectively block the channels carried on corresponding
OAM modes, as shown in the left column of Fig. 7.8. We demonstrated a “band-block” filter

83

which blocks the OAM beam with ℓ=-9 and ℓ=-4, as shown in Fig. 7.8(b) and (c),
respectively. We analyzed the power of each mode at the focal plane of the second mode
sorter using a camera, and the power of OAM beam with ℓ=-9 and ℓ=-4 are suppressed by
~17 dB and ~15.5 dB, respectively, as shown in Fig. 7.8(b3) and (c3). The filter we proposed
is also “bandwidth” tunable. We demonstrated the blocking-filtering of two OAM modes
with ℓ=±4 instead of one, as shown in Fig. 7.8(d1)-(d3). At the filter output, the power of the
OAM beams with ℓ=+9 and -9 are suppressed by ~14.5 dB and ~16 dB, respectively. We
also present the “band-pass” filtering of OAM-4 and OAM+4, respectively, by blocking the
three other modes using the SLM, as shown in Fig. 7.8(e1) and (f1), respectively. Fig. 7.8(e3)
and (f3) indicate that the output of the filter has majority of the power from a single OAM
mode, such as OAM with ℓ=-4 and ℓ=+4, respectively. The suppression ratio of the other
modes are >15 dB.

Figure 7.7 (a) Input of the OAM filter, including OAM beams with ℓ=±4, ±9. (b) Intensity distribution
after the first mode sorter. (c) The output of the OAM filter without blocking any mode. (d) The
intensity distribution after the second mode sorter
In this proof-of-concept experiment, we demonstrated the filtering of four OAM modes
(ℓ=±4 and ±9) with a minimum vortex charge spacing of five. However, the minimum OAM
mode charge spacing that can be distinguished by the filter (i.e., filtering resolution) is
fundamentally limited by the crosstalk errors of the mode sorter. In the present form of the
-9 +9
-4 +4
-9
+9
-4 +4
a) b)
c) d)

84

mode sorter, the transformed light spots of the neighboring modes slightly overlap, and ~20%
of the energy of an OAM mode is leaked to the other modes after the mode sorter [9]. We
note that this crosstalk of the mode sorter can be reduced to ~5% by modifying the
transformation to give multiple transverse cycles [14, 15], and the filtering resolution can be
also potentially improved accordingly. In addition, current design of the filter has 6 dB
power loss (3 dB for the forward beam and 3 dB for the backward beam) due to the use of
the beam splitter. In principle, instead of propagating the beams through the same mode
sorter twice (back and force), we could potentially use an additional mode sorter to convert
the elongated beams back to the OAM beams. Consequently, the BS and the introduced 6-
dB loss could be saved

Figure 7.8. (a1): Four OAM modes are mapped to four spots after the first pass of OAM mode sorter.
(a2) all four channel pass. (b1-b3): block OAM
-9
. (c1-c3): block OAM
-4
. (d1-d3):blcok two modes:
OAM
-9
and OAM
+9
. (e1-e3): pass OAM
-4
. (f1-f3): pass OAM
+4
. The grids indicate the grating patterns
that are used on the SLM to block selected OAM channels.
7.4 Summary
In this chapter, we discussed a tunable mode filter for spatially multiplexed laser beams
carrying orbital angular momentum. The filter comprises an optical geometric
-9 +9
-4 +4
-9 -4 +4 +9
-20
-15
-10
-5
0
Power(dBm)
-20
-15
-10
-5
0
Power(dBm)
-20
-15
-10
-5
0
Power(dBm)
-20
-15
-10
-5
0
Power(dBm)
-20
-15
-10
-5
0
Power(dBm)
-9 -4 +4 +9
-9 -4 +4 +9
-9 -4 +4 +9
-9 -4 +4 +9
(a1)
(b1)
(c1)
(a2)
(b2)
(c2)
(b3)
(c3)
(d1)
(e1)
(f1)
(d2)
(e2)
(f2)
(d3)
(e3)
(f3)
1st pass of
mode sorter
Output of
mode analyzer
Power
spectrum
1st pass of
mode sorter
Output of
mode analyzer
Power
spectrum

85

transformation-based OAM mode sorter and a spatial light modulator (SLM). The
programmable SLM can selectively control the passing/blocking of each input OAM beam
We experimentally demonstrate tunable filtering of one or multiple OAM modes from four
multiplexed input OAM modes with vortex charge of ℓ=-9, -4, +4 and +9. The measured
output power suppression ratio of the propagated modes to the blocked modes exceeds 14.5
dB.

86

7.5 References
[1] Alison M. Yao and Miles J. Padgett, "Orbital angular momentum: origins, behavior and
applications," Adv. Opt. Photon. 3, 161-204 (2011).
[2] Graham Gibson, Johannes Courtial, Miles Padgett, Mikhail Vasnetsov, Valeriy Pas'ko,
Stephen Barnett, and Sonja Franke-Arnold, "Free-space information transfer using light
beams carrying orbital angular momentum," Opt. Express 12, 5448-5456 (2004).
[3] J. H. Shapiro, S. Guha, and B. I. Erkmen, Ultimate channel capacity of free-space optical
communications, J. Opt. Netw 4, 501 (2005).
[4] P. Boffi, P. Martelli, A. Gatto, and M. Martinelli, Optical vortices: An innovative
approach to increase spectral efficiency by fiber mode-division multiplexing, in Proc. SPIE,
2013, vol. 8647, p. 864705.
[5] L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman, “Orbital angular
momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A
45, 8185 (1992).
[6] Jian Wang, Jeng-Yuan Yang, Irfan Fazal, Nisar Ahmed, Yan Yan, Hao Huang,
Yongxiong Ren, Yang Yue, Sam Dolinar, Moshe Tur, and Alan E. Willner, “Terabit free-
space data transmission employing orbital angular momentum multiplexing”, Nature
Photonics 6, 488 (2012).
[7] Nenad Bozinovic, Yang Yue, Yongxiong Ren, Moshe Tur, Poul Kristensen, Hao Huang,
Alan E. Willner, Siddharth Ramachandran, Terabit-Scale Orbital Angular Momentum Mode
Division Multiplexing in Fibers, Science 340, 1545 (2013).
[8] G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett,
“Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15),
153601 (2010).
[9] Martin P. J. Lavery, David J. Robertson, Gregorius C. G. Berkhout, Gordon D. Love,
Miles J. Padgett, and Johannes Courtial, "Refractive elements for the measurement of the
orbital angular momentum of a single photon," Opt. Express 20, 2110-2115 (2012).
[10] Hao Huang, Yongxiong Ren, Guodong Xie, Yan Yan, Yang Yue, Nisar Ahmed, Martin
P. J. Lavery, Miles J. Padgett, Sam Dolinar, Moshe Tur, and Alan E. Willner, "Tunable
orbital angular momentum mode filter based on optical geometric transformation," Opt. Lett.
39, 1689-1692 (2014).
[11] Olof Bryngdahl, "Geometrical transformations in optics," J. Opt. Soc. Am. 64, 1092-
1099 (1974).
[12] Y. Saito, S. Komatsu, and H. Ohzu, “Scale and rotation invariant real time optical
correlator using computer generated hologram”, Opt. Commun. 47, 8 (1983).

87

[13] J. Leach, M. R. Dennis, J. Courtial and M. J. Padgett, Vortex knots in light, New J.
Phys. 7 55 (2005).
[14] Malcolm N. O’Sullivan, Mohammad Mirhosseini, Mehul Malik, and Robert W. Boyd,
"Near-perfect sorting of orbital angular momentum and angular position states of light," Opt.
Express 20, 24444-24449 (2012).
[15] M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital
angular momentum eigenstates of light,” Nat. Commun.4, 2781 (2013).

88

Chapter 8 Analog Signal Transmission in a High-Contrast-
Gratings based Hollow-Core- Waveguide

8.1 Introduction
Waveguide structures are used for many elements and components inside photonic integrated
circuits (PICs). For on-chip photonic links, it is important to maintain the linearity of the
transmitted signals, especially for analog signals [1, 2]. However, it is extremely difficult to
achieve this goal by using regular integrated waveguides due to their large loss, dispersion
and nonlinearity. Hollow-core-waveguides (HWs) have been shown to exhibit extremely low
nonlinearity as well as low loss and high thermal stability, all of which are important
characteristics for analog elements [3]. Moreover, high-contrast gratings (HCGs) can
provide extremely large reflectivity over a broad bandwidth, and they have been used to
confine the light wave in the hollow core. It seems that the hollow core waveguide using
HCG may have the potential to further reduce the propagation loss [4].
For an HCG with optimized design, the light propagation in the hollow region excites
modes in the grating bars. The first two excited modes can cancel one another outside the
gratings, which leads to extremely high reflectivity [5]. Recently, it is indicated that HCG
waveguides may exhibit extremely low nonlinearity under a wide variety of waveguide
parameters [6]. However, both loss and chromatic dispersion can vary significantly with the
variation of waveguide parameters and might affect the operation of an analog link or
subsystem [7]. Therefore, it might be desirable to characterize the HCG-HW for their
suitability in microwave analog applications.

89

In this paper, we analyze the analog signal performance of hollow-core waveguides that
use an HCG [8]. The link SFDR of the third-order intermodulation distortion (IM3), second-
order harmonic distortion (SHD) and the third-order harmonic distortion (THD) are
calculated. After propagating 100 m in a HCG-HW with optimally designed parameters,
there is very little degradation with respect to the back-to-back case of either third-order
intermodulation distortion spur-free dynamic range (IM3 SFDR) or third-order harmonic
distortion (THD) SFDR [9]. The simulation results also indicate that a HCG-HW analog link
potentially can operate at modulation frequencies of up to 80 GHz, and in an optical
bandwidth of > 50 nm, while maintaining an IM3 SFDR of > 100 dB·Hz2/3. The impact of
parameter variations of an HCG-HW on the linearity of transmitted analog signals also is
investigated. With ±10nm and ±20nm variations on all parameters, the propagation length in
an HCG-HW is limited to ~28 m and ~6 m, respectively, in order to maintain an IM3 SFDR
of >100 dB·Hz2/3
8.2 Waveguide parameters
The two-dimensional structure of an HCG-HW is shown in Fig. 1. High contrast silicon
gratings with refractive indices of 3.476 are surrounded by air, which has a low refractive
index, thereby providing a very high reflectivity (> 99.9%) [10]. Two layers of HCG, placed
parallel to each other, function as two mirrors and light can be confined effectively within
the hollow core. Therefore, it is expected that low nonlinearity and loss can be achieved by
this structure, since most of the energy of the light is confined and transmitted in the air
(hollow-core). It is noted that four parameters have significant effects on the performances
of an HCG-
the distance between the two layers of HCGs. The other three parameters are related to the

90

grating structure, as shown in Fig. 1. An HCG-HW that has been optimized for low loss, i.e.,
achieve a propagation loss as low as 0.0052 dB/m [6]. Fig. 2 (a) depicts the loss contour
within the range of 1 dB/m for an HCG- -HW with >
50 nm variations in its grating thickness and its air gap can still provide a loss of < 1 dB. Fig.
2(b) also shows that a chromatic dispersion of < 100 ps/(nm•km) can be achieved over a
wavelength range of 100 nm and the dispersion can be even lower if the core size is
increased.

Figure 8.1. Two-dimensional structure of an HCG-HW. k indicates the propagation direction of the
confined lightwave.

(a) (b)
Figure 8.2. (a) Calculated waveguide loss (dB/m) at 1550 nm for an HCG-HW with a 15 μm core size
as a function of grating period and air gap. (b) Chromatic dispersion of HCG-HW as a function of
wavelength. D: core size of the HCG-HW.

91

8.3 Link modeling
The schematic configuration of the analysis model is shown in Fig. 8.3. A continuous
wave (CW) at 1550 nm is generated by a laser source with a linewidth of 1 kHz and a
relative intensity noise (RIN) of -165 dB/Hz. The output power of the CW laser is 20 dBm.
Then the CW is double side modulated by analog signals (two sine waves with frequencies
very close to each other, e.g., 40 GHz and 41 GHz ), using a quadrature-biased Mach-
Zehnder modulator (MZM) with a Vπ of 5V. The modulated optical signal is then launched
into the HCG-HW for signal transmission. After optical-to-electrical conversion by a PIN
photodetector with a responsivity of 0.7 A/W, the output signal is analyzed in terms of
harmonic and intermodulation distortions. The common parameters used in the modeling are
organized into Table1.
TABLE 8.1
HCG-HW optical link common parameters
CW Laser
Laser Power 20 dBm
Laser Noise (RIN) -165 dB/Hz
Wavelength 1550 nm
Electro-optical
Modulator
V
π
5 V
Modulator
Impedance
50 Ω
Insertion Loss 3 dB
Fundamental
frequencies (f
1
, f
2
)
f
1
=40,
f
2
=41
GHz
Waveguide
structure
Core size 15 m 
Period 750 nm
Air gap 430 nm
Thickness 340 nm
Length 100 m
PIN Photo
detector
Detector load 50 Ω
Detector
responsivity
0.7 A/W
Dark current 1 nA
Noise
bandwidth
BW 1 Hz

92

Figure 8.3. Schematic of an analog link using HCG-HW. (a) and (b) describe the spectra of the input
RF signal and the output RF signal after transmission in HCG-HW, respectively.
SFDR is an important common measure of the linearity of an analog link [1, 2]. It is
defined as the RF input power range, the lower bound of which is the noise floor (in a 1Hz
bandwidth) and the upper bound of which is the value that produces distortion terms with
output power equal to the noise floor [9, 11]. For sub-octave applications, the third order
intermodulation distortion is of primary concern, while for broadband RF photonic links,
both second-order and third-order harmonic distortions also should be taken into account
[11].
Analytically, the third order intermodulation (IM3) SFDR can be expressed as [12, 13]:
3 10
2
( 3 10 log )
3
IM O
SFDR IP noisefloor BW     (8-1)
Where IP3o indicates the output third-order interception point, which is an imaginary
point where the fundamental and third order intermodulation response curves intersect [13].
The noise floor in the equation indicates the power level of the output noise in 1-Hz
bandwidth. The equation for SHD SFDR and THD SFDR are similar except that the IP3O is
replaced by the intercept point between the fundamental and SHD responses, and between
f
f
1
f
2
P
HCG-HW
CW
Laser
MZM
Photo-
Detector
Signal
Analysis
RF
Signal f
1
f
2
f
(a)
(b)

93

the fundamental and THD responses, respectively. The coefficient outside of parenthesis is
also different; it is 1/2 for the second order distortions (SHD) and 2/3 for the third order
(THD, IM3) distortions because of the different slopes of the distortion responses. From
Equation (1) it is clear that SFDR is determined by two factors: interception point IP3o
which is decided by system linearity and noise floor (comprising RIN noise, shot noise,
thermal noise and optical amplifiers added noise)
Transmission media imperfections, such as loss, chromatic dispersion and
nonlinearities, degrade the SFDR of an analog optical link in different ways [12-15]. While
dispersion and loss can notably increase when changing the structure parameters, as shown
in Fig. 2, the optical nonlinearities of the HCG-HW are maintained at a fairly low value
(nonlinear coefficient < 10-7 W-1km-1) over a wide range of structure parameters [7], and
therefore they hardly affect the analog signals.
The output power of a quadrature-biased (on positive slope), zero-chirp MZM fed by a
CW laser is related to the applied RF signal VRF(t) by a nonlinear relationship [16]:








 
















  
 
  
V
t V
V
t V
t P
RF RF
) (
sin 1
2
3 ) (
cos 1 ) (
mod
(8-2)
Thus, even in the absence of dispersion, the retrieved RF signal, being proportional to
the photodetector output current/voltage, and therefore to , is already afflicted by distortions.
Due to the odd symmetry of the sine function SHD is minimized but THD is maximized.
The introduction of dispersion seriously aggravates the situation, particularly for signals
with high modulation frequencies [15]. To explain, we first note that the sine function in

94

equation (2) transforms every RF tone to multiple sidebands around the optical carrier, while
the square-law photodetector retrieves the RF tones as a sum of beating terms, originating
from pairs of optical sidebands, having the same frequency spacing. This summation
critically depends on the relative phases of the various contributions, which are directly
affected by dispersion. Thus, distortion terms that were missing from are no longer zero.
Similarly, originally weak terms may grow in magnitude.

Figure 8.4. Power of RF carrier and distortions as functions of dispersion. Modulation frequency:
f1=40GHz, f2=41GHz. The propagation distance is 100 m.
Fig. 8.4 shows that dispersion induces a periodic change in the intensity of the
fundamental RF carrier and distortion terms (including IM3, SHD and THD) with a
modulation frequency of approximately 40 GHz (f1 = 40 GHz, f2 = 41 GHz). The period of
each curve is determined by its frequency. Since the frequency of IM3 (2f1 - f2) is very
close to that of the RF carrier (f1), they have similar periodicities. Therefore, the IM3 SFDR
is relatively more tolerant to the variations in dispersion than SHD (2f1) and THD (3f1). The
latter two are more sensitive to dispersion because they have double and triple frequency
spacing, respectively. As expected, at the zero dispersion point, i.e., at the output of the
modulator without transmission, SHD is minimized while THD is maximized. Therefore,
0 100 200 300 400
-80
-60
-40
-20
0
Intensity (dBm)
Dispersion (ps/nm/km)
B
C
D
E
F
G
RF carrier
SHD
THD
IM3
IM2 (f1+f2)
IM2 (f1-f2)

95

with the increase of dispersion in a range of less than a half period (in this case < 100
ps/nm/km), SHD increases faster and THD decreases even faster, as can be seen in Fig. 4.
The second order intermodulation distortions (IM2), including f1+f2 term and f1-f2 term, are
also analyzed. IM2 (f1+f2) is a little stronger than SHD, while they has a very similar
dependence on the dispersion due to the fact that f1+f2 ≈2f1 ≈2f2. The other one, IM2 (f1-
f2), is much lower than other distortion terms during the analyzing range (i.e., dispersion is
less than 400 ps/nm/km), and is therefore not considered in the later discussion.

Figure 8.5 SFDR reduction as a function of link loss. The 3rd-order includes IM3 SFDR and THD
SFDR. The 2nd-order indicates the SHD SFDR.
The optical transmission loss may also induce notable reduction of the SFDR [9].
Equation (1) shows that the SFDR is determined by the IP3o and the power of noise.
Provided that the nonlinearity of HCG-HW is negligibly low, IP3o is linearly related to the
optical transmission loss, i.e., every 1 dB of optical loss results in a 2 dB reduction on the
output power of the electrical signal (including RF carrier and distortions) after
optical/electrical conversion according to the square law detection. However, the consequent
reduction of the noise floor might not be always linear, depending on the source of the noise
RIN noise
dominated
Shot noise dominated
Thermal noise
dominated
3
rd
-order
2
nd
-order

96

that is dominant at the output. Generally, in an optical link without an optical amplifier, the
noise sources include mainly RIN noise, thermal noise and shot noise. Their relationships to
the optical power incident to the photodetector (Popt) are as follows [12]:
2
~
~
RIN opt
Shot opt
Thermal
PP
PP
PT
(8-3)
where T indicates the temperature. From the equations above it can be seen that every 1 dB
of optical loss causes 2 dB and 1 dB reductions on the power of RIN noise and shot noise
(dark current is low enough and not considered here), respectively, and has no effect on the
thermal noise since it is only related to the temperature T [11]. Different reductions in the
power of output signal and noise floor will finally result in changes in SFDR. Fig. 5 shows
the dependence of the second order and the third order SFDR on optical transmission loss.
For an optical link with the parameters listed in Table 1, a loss of 0-10 dB has almost no
effect on the SFDRs because the system is dominated by RIN noise. Shot noise becomes the
dominant noise when the loss is in the range of 10-20 dB. In this case, each loss of 1 dB
might cause reductions in second-order SFDR and third-order SFDR 0.5 and 0.67 dB,
respectively. For a loss of more than 20 dB, thermal noise is most significant, and the
reduction in the SFDRs caused by the optical loss should be doubled compared to the case in
which shot noise is dominant.
Since the nonlinearity of HCG-HW is negligibly low [4], the dispersion and optical
losses are the main contributors to changes in the SFDR of the link. In this chapter, we
mainly focus on the effects of dispersion and loss on the analog link’s SFDR.

97

8.4 Results and discussion

Figure 8.6. Power of RF carrier and distortions as functions of RF input power. According to the
definition, SFDRs can be obtained by measuring the interval between two intersections, as shown in
the figure. The link using 100 m HCG-HW with optimized parameters can achieve a SHD SFDR of
105.7 dB•Hz
1/2
, THD SFDR of 113.3 dB•Hz
2/3
and an IM3 SFDR of 109.9 dB•Hz
2/3
at 40 GHz.
Using the model described above, we first investigate the performance of a HCG-HW
with optimized structure parameters, which are: core size 15 m, air gap 430 nm, grating
thickness 340nm and period of 750 nm. Fig. 6 shows the intensity of RF carrier and
distortions (IM3 and SHD) as functions of RF input power. SFDRs can be obtained by
measuring intercepting points of the noise floor and each distortions terms, as shown in Fig.
6. Operating at 1550 nm, the IM3 and SHD SFDRs in a 100 m HCG-HW link are 109.9
dB·Hz
2/3
and 105.7 dB·Hz
1/2
, respectively, at a modulation frequency of 40 GHz. The
modulation frequency of around 40 GHz is used because the HCG-HW is relatively linear
and we cannot see any notable distortions from the spectrum of the output analog signal with
a lower frequency. The THD SFDR, which is also shown in this figure, is calculated as
113.3 dB·Hz
2/3
. It is noted that the achieved IM3 SFDR of the analog link using HCG-HW is
as high as that of a back-to-back analog link using a MZM [9], which shows the great
linearity of the HCG-HW.
-150 -100 -50 0 50
-150
-100
-50
0
RF input power (dBm)
Distotion output power (dBm)

data1
data2
data3
data4
data5
data6
data7
data8
data9 Noise floor
SHD SFDR

98

Figure 8.7. (a) SFDRs as function of modulation frequency. IM3 SFDR and THD SFDR have little
change when the modulation rate is increased. However, SHD SFDR decreases significantly due to
the chromatic dispersion of the HCG-HW. (b) SFDRs as functions of wavelength. HCG-HW shows
an optical bandwidth of 50 nm with IM3 SFDR > 100 dB•Hz
2/3
and SHD SFDR > 85 dB•Hz
1/2

Broadening the operational RF bandwidth of an analog link is of great importance. Fig.
8.7(a) depicts the SFDRs as functions of the modulation rate, i.e., the frequency of the
driving analog signal. When we change the modulation rate from 1 GHz to 80 GHz, IM3
SFDR remains almost constant at 109.9 dB·Hz
2/3
, while SHD SFDR decreases as the
modulation frequency increases, but, as shown in Fig. 8.7(a), it is still greater than 90
dB·Hz
1/2
at 80 GHz. THD SFDR is also quite independent of the modulation frequency,
except for a small increase at the end, as shown in Fig. 8.7(a). As we know that dispersion
induced phase shift (delay) is proportional to the signal bandwidth, therefore, increasing the
modulation frequency in an analog link strengthens the effects of chromatic dispersion. As
indicated in section III concerning the dependence of SFDR on the dispersion (Fig. 8.3), IM3
and THD SFDR are more tolerant to dispersion than SHD SDFR. At the zero point of the
modulation rate, the SHD SFDR drops rapidly with modulation frequency. THD SFDR has a
little improvement since the IM3 distortion is partly canceled due to the dispersion. These
results also indicate that HCG-HW is promising for both sub-octave and broadband on-chip
analog applications.
0 20 40 60 80
80
100
120
140
160

SFDR (dB)
Modulation Rate (GHz)
IM3 SFDR
SHD SFDR
THD SFDR
1.52 1.54 1.56 1.58
40
60
80
100
120
Loss=0.005dB/m
Zero Dispersion
Loss=0.57dB/m

SFDR (dB)
Wavelength ( m)
IM3 SFDR
SHD SFDR
THD SFDR
Loss=0.60dB/m

99

Optical bandwidth is also worthy of consideration for many applications, such as
wavelength division-multiplexing (WDM). The SFDR dependence on operating wavelength
is shown in Fig. 8.7(b). It can be seen that both THD and IM3 SFDR achieve the largest
value at 1550 nm, where the waveguide has the minimum loss. However, the maximum
value of SHD SFDR occurs at 1525 nm, which is the zero dispersion wavelength (ZDW) of
HCG-HW. This again can be explained by the fact that SHD is dramatically affected by
dispersion and waveguide dispersion changes with the wavelength. All three SFDRs
decrease rapidly when the wavelength is out of C band because the waveguide loss becomes
larger, as indicated in Fig. 8.7(b). However, an optical bandwidth of ~50 nm with an all
SFDRs greater than 85 (dB·Hz
1/2
for SHD and dB·Hz
2/3
for IM3 and THD) is still achieved.

Figure 8.8 (a) SFDRs as functions of grating period. (b) Calculated propagating loss as a function of
grating period and air gap. The dotted arrow indicates the trace of changing period while keep the air
gap at 470 nm. Two peaks of SFDR occur at period of around 690 nm and 750 nm, which correspond
to two low-loss areas.
The results in section A show that an optimally designed HCG-HW can potentially
provide a good transmission medium for analog signals. However, from the waveguide
structure shown in Fig. 8.1 we can see that there are different parameters that are highly
related to the waveguide design, and it would be of great importance to investigate the
dependence of the quality of the transmitted analog signal on each structure parameter. First,
Period ( m)
Air Gap ( m)

0.68 0.7 0.72 0.74 0.76 0.78
0.3
0.35
0.4
0.45
0.5
Loss (dB/m)
0
0.2
0.4
0.6
0.8
A
B
C
A
B
C
680 700 720 740 760 780
40
60
80
100
120
0.29dB/m
0.005dB/m
Loss=0.003dB/m
Zero
Dispersion
0.46dB/m
0.60dB/m

SFDR (dB)
Period (nm)
IM3 SFDR
SHD SFDR
THD SFDR

100

we calculate SFDR by varying a single grating parameter (grating period or air gap) each
time, as shown in Fig. 8.8 and Fig. 8.9.

Figure 8.9. (a) SFDR as function of grating air gap. (b) Calculated propagating loss as a function of
grating period and air gap. The dotted arrow indicates the trace of changing air gap while keep the
period at 750 nm. IM3 and THD SFDR are almost flat within the low loss region between 370 nm to
470 nm of air gap. SHD SFDR drops ~10 dB with air gap due to the dispersion
SFDRs as functions of grating period are shown in Fig. 8.8(a). The propagation loss of
HCG-HW as a function of period and air gap is also depicted in Fig. 8.8 (b) to help explain
the curves. The dotted line in Fig. 8.8 (b) is the trace of varying grating period while keeping
the air gap at 430 nm without changing. The maximum value of IM3 SFDR and THD SFDR
are achieved at grating period of ~ 690 nm, where the waveguide has minimum loss. Note
that there are two peaks (Point A and point C in Fig. 8.8 (a)) at grating period of around 690
nm and 750 nm for all SFDR curves, corresponding to two low-loss areas (Point A and
point C in Fig. 8.8 (b)) respectively in the loss contour map on the right, with a dip in the
middle (Point B). The effect of waveguide dispersion can be found from the SHD SFDR
curve more obviously than the other two. Basically the WG dispersion increases as the
period increases, thus the SHD SFDR peak at 690 nm is lower than that at 750 nm. The
largest value of SHD SFDR is achieved at the grating period of ~ 758 nm, where the
waveguide has zero dispersion. At the grating period of beyond point A and point C, all
Period ( m)
Air Gap ( m)

0.68 0.7 0.72 0.74 0.76 0.78
0.3
0.35
0.4
0.45
0.5
Loss (dB/m)
0
0.2
0.4
0.6
0.8
350 400 450 500
40
60
80
100
120
Loss=0.0004dB/m
Zero Dispersion
0.64dB/m
0.45dB/m

SFDR (dB)
Air gap (nm)
IM3 SFDR
SHD SFDR
THD SFDR
A
B
C
A
B
C

101

SFDRs drop very rapidly due to the increase of waveguide loss, as can be seen from Fig. 8.8
(b).
Fig. 8.9 (a) shows SFDRs as functions of grating air gap. IM3 SFDR and THD SFDR
are almost flat and kept at the maximum value of 109.9 dB•Hz2/3 within the range of
between 370 nm and 470 nm, while SHD SFDR has a ~10 dB drop with the increase of
grating air gap due to its sensitivity on dispersion. Similarly, point A, B and C in Fig. 8.9 (a)
are corresponding to point A, B and C in the loss contour map, as shown in Fig. 8.9 (b). The
dotted line indicates the trace of changing air gap while keeping the period at 750 nm.
Again, the rapid increase of waveguide loss beyond the air gap range of between 370 nm and
470 nm results in sharp declines of all three SFDRs, as shown in Fig. 8.9 (a).

Figure 8.10. Parameter cube of the HCG-HW. The optimal point indicates the HCG-HW with the
optimized parameters, i.e., core size (D) of 15 μm, air gap (a
g
) of 430 nm, grating thickness (t
g
) of 340
nm and period (Λ) of 750 nm
For a waveguide with submicron gratings, the accuracy of fabrication is an important
factor that should be taken into account. In the last section we discuss the waveguide
performance variations caused by changing a single structure parameter. In a more realistic
case, all three grating parameters (air gap, period and thickness) might change
simultaneously and affect waveguide performances significantly. In order to characterize the
Air gap
Thickness
Period
Optimal point
± 10 or ± 20 nm variation points

102

fabrication tolerance of HCG-HW, we generate a “parameter cube” with Period, Thickness
and Air gap as its three axes of the coordinate, as shown in Fig.8.10. The center of the cube
is considered as the operating point with optimized parameters, i.e., air gap (a
g
) of 430 nm,
grating thickness (t
g
) of 340 nm and period (Λ) of 750 nm. Each of these three parameters
might have a variation of +/-10nm or +/-20nm, thus there are eight combinations of three
parameters, which can be indicated by eight vertices, respectively, among which the worst
one (with the smallest SFDR) could be considered as the lower bound of all points inside the
cube. This is reasonable, because within the 10nm and 20nm range, the loss, dispersion and
nonlinear of HCG-HW change monotonously. Then we calculate the SFDR as a function of
the length of the waveguide in the cases of optimized point, ±10 nm variation and ±20 nm
variation, as shown in Fig. 8.10, which can give us a comprehensive picture of the
performance of HCG-HW in terms of fabrication tolerance.
Figure 8.11 and Fig. 8.12 show IM3 SFDR and SHD SFDR as a function of
propagation distance, respectively. The results indicate that an HCG-HW with the optimal
design performs fairly well. However, the waveguide performance can be affected
significantly by the parameter changes. With a fabrication variation of ±10 nm, the
propagation distance is limited to ~28 m to achieve an IM3 SFDR of >100 dB•Hz2/3. The
distance is further decreased to ~6 m when there is a ±20 nm variation on the waveguide
parameters. Similar trends can be observed in Fig. 8.12. To maintain a SHD SFDR of >100
dB•Hz1/2, the propagation length is limited to ~22 m and ~6.5 m, with a parameter variation
of ±10 nm and ±20 nm, respectively.
Focusing on the analog signaling performance, we make a simple comparison between
a HCG-HW and a low-loss silicon ridge waveguide [17, 18], as shown in Fig. 8.11 and Fig.

103

8.12. The SFDRs of a low-loss silicon ridge waveguide as functions of transmission distance
are calculated. It seems that even with a ±20 nm variation in all three grating parameters,
HCG-HWs still perform better than silicon-ridge waveguides.

Figure 8.11 IM3 SFDR as a function of propagating length in an HCG-HW.

Figure 8.12 SHD SFDR as a function of propagating length in an HCG-HW.

8.5 Summary
In this chapter, we investigate the performance of an HCG-HW for the transmission of
analog signals. The simulation results indicate that an HCG-HW with optimized parameters
has a RF bandwidth of up to 80 GHz and a operating wavelength range of >50 nm, with an
0.01 0.1 1 10 100 1,000
20
40
60
80
100
120
Waveguide Length (m)
IM3 SFDR (dB.Hz
2/3
)

Optimized design
10nm variation
20nm variation
Si ridge WG
0.01 0.1 1 10 100 1,000
20
40
60
80
100
120
140
160
Waveguide Length (m)
SHD SFDR (dB.Hz
1/2
)

Optimized design
10 nm variation
20 nm variation
Si ridge WG

104

IM3 SFDR of greater than 100 dB•Hz
2/3
. Analysis also indicates that HCG-HW performance
is dependent on the waveguide structure parameters. To maintain a IM3 SFDR of >100
dB•Hz
2/3
, the analog signal propagation distance is limited to ~6 m due to a ±20 nm variation
on all three parameters.

105

8.6 References
[1] C. H. Cox. III, Analog Optical Links: Theory and Practice, Cambridge University Press,
2004, pp. 201-205.
[2] W. S. C. Chang, RF Photonic Technology in Optical Fiber Links, Cambridge
University Press, 2002, pp. 25-32.
[3] P. Roberts, “Ultimate low loss of hollow-core photonic crystal fibers,” Optics Express,
vol. 13, no. 1, pp.236-244, Jan. 2005.
[4] Y. Zhou, V. Karagodsky, B. Pesala, F. G. Sedgwick and C. J. Chang-Hasnain, “A novel
ultra-low loss hollow-core waveguide using subwavelength high-contrast gratings,” Optics
Express, vol. 17, no. 3, pp.1508-1517, 2009.
[5] V. Karagodsky, F. G. Sedgwick and C. J. Chang-Hasnain, “Theoretical analysis of
subwavelength high contrast grating reflectors,” Optics Express, vol. 18, no. 16, pp.16973-
16988, 2010.
[6] Y. Yue, L. Zhang, J. Wang, Y. Xiao-Li, B. Shamee, V. Karagodsky, F. G. Sedgwick, W.
Hofmann, R. G. Beausoleil, C. J. Chang-Hasnain and A. E. Willner, “A ‘Linear’ High-
Contrast Gratings Hollow-Core Waveguide and Its System Level Performance,” presented at
the Optical Fiber Commun. Conf. (OFC), San Diego, CA, 2010, paper OTuI5.
[7] Y. Yue, L. Zhang, F. G. Sedgwick, B. Shamee, W. Yang, J. Ferrara, C. Chase, R. G.
Beausoleil, C. J. Chang-Hasnain and A. E. Willner, “Chromatic Dispersion Variation and Its
Effect on High-Speed Data Signals due to Structural Parameter Changes in a High-Contrast-
Grating Waveguide,” presented at the IEEE Photonics Society Annual Meeting, Denver, CO,
2010, paper ThB2.
[8] H. Huang, Y. Yue, L. Zhang, X. Wang, C. Chase, D. Parekh, F. Sedgwick, M. Tur, M.
C. Wu, C. J. Chang-Hasnain and A. Willner, “Analog Signal Performance of a Hollow-Core-
Waveguide using High-Contrast- Gratings,” presented at the Optical Fiber Commun. Conf.
(OFC), Los Angeles, CA, 2011, paper OThA3.
[9] W. B. Bridges and J. H. Schaffner, “Distortion in linearized electrooptic modulators”,
IEEE Transations on Microwave Theory and Techniques, vol. 43, no.9, pp. 2184-2197, Sep.
1995.
[10] Bala Pesala, Vadim Karagodsky and Connie Chang-Hasnain, “Ultra-Compact Low
Loss Photonic Components using High-Contrast Gratings,” presented in ICOP 2009-
International Conference on Optics and Photonics CSIO, Chandigarh, India, 2009.
[11] C. H. Cox III, E. I. Ackerman, G. E. Betts and J. L. Prince, “Limits on the Performance
of RF-Over-Fiber Links and Their Impact on Device Design,” IEEE Transactions On
Microwave Theory And Techniques, vol. 54, no. 2, pp. 906-920, Feb. 2006.

106

[12] G. Katz, S. Arnon, P. Goldgeier, Y. Hauptman and N. Atias, “Cellular over optical
wireless networks,” IEE Proceedings - Optoelectronics, vol. 153, no. 4, pp.195-198, Aug.
2006.
[13] J. A. MacDonald, M. V. Kubak and A. Katz, “Wideband dynamic range improvement
of microwave photonic links,” presented in IEEE Conference, Avionics Fiber-Optics and
Photonics, Minneapolis, MN, September 20-22, 2005, pp.67-68, paper ThB3.
[14] G. J. Meslener, “Chromatic Dispersion Induced Distortion of Modulated
Monochromatic Light Employing Direct Detection,” IEEE Journal of Quantum Electronics,
vol. 20, no. 10, pp. 1208-1216, Oct. 1984.
[15] C. S. Oh and W. Gu, “Fiber Induced Distortions in a Subcarrier Multiplexed
Lightwave System,” IEEE Journal On Selected Areas In Communications, vol. 8, no. 7, pp.
1296-1303, Sep. 1990.
[16] Ganesh K . Gopalakrishnan, William K . Burns, and Catherine H. Bulmer, Microwave-
Optical Mixing in LiNbO3 Modulators, IEEE Transactions on Microwave Theory and
Techniques, vol. 41, No. 12, pp 2383-2391, Dec. 1993.
[17] R. Pafchek, R. Tummidi, J. Li, M. A. Webster, E. Chen and T. L. Koch, “Low-loss
silicon-on-insulator shallow-ridge TE and TM waveguides formed using thermal oxidation,”
Applied Optics, vol. 48 no. 5, pp.958-963, 2009.
[18] M. A. Webster, R. M. Pafchek, G. Sukumaran and T. L. Koch, "Low-loss quasi-planar
ridge waveguides formed on thin silicon- on-insulator", Applied Physics Letters, vol.87, no.
23, 2005

107

Chapter 9 100-Gbit/s Amplitude and Phase Modulation
Characterization of a Single-Drive EO Polymer
Mach-Zehnder Modulator

9.1 Introduction
Electro-optic modulators with a high bandwidth are crucial components of high-speed
transmitters for fiber optic networks. As one of the candidates, Electro-optical (EO) polymer
modulators have been researched for many years due to their fast EO response, which
enables a broadband modulation rate of > 100 GHz [1, 2]. Currently, it is clear that the
communications community has much interest in 100-Gbit/s data channels as well as the
significant potential for 400-Gbit/s and 1-Tbit/s channels in the near future [3, 4]. Although
dual-polarization quadrature-phase-shift-keying (DP-QPSK), 4x25 Gbaud/s, is emerging as a
common method to achieve 100-Gbit/s channels, there is still an increasing interest in ever-
higher baud rates. One key threshold has been the desire to achieve 100-Gbaud/s data
modulation from an optical modulator in order to open up the possibility of serial electronic
100-Gbit/s data channels at 100-Gbaud/s on a single polarization, 400-Gbit/s using DP-
QPSK, and 1 Tbit/s using dual-polarization and 32 quadrature-amplitude-modulation (QAM)
[5-7]. Beyond the need for higher bit-rates, 100-Gbit/s modulators may play an important
role in systems that cannot readily handle dual-polarizations or multilevel modulation, and
for many short-reach applications in which serial 100-Gbit/s transmission might be a cost-
effective solution. Advances in high-speed RF electronics and photo-detectors have enabled
full electronic time-division-multiplexed (ETDM) systems in the >100 Gbit/s range [8-11].
One of the limitations of these systems has typically been the limited bandwidth of the

108

optical modulator [1], resulting in the need for additional optical or electronic equalization
techniques to correct for output data distortions [8, 10].
To date, modulator development with a very high modulation bandwidth has produced:
(a) a traveling-wave EO polymer modulator with a frequency response of beyond 100 GHz
[1, 12], (b) a monolithically integrated 100-GHz traveling-wave electro-absorption
modulator (TWEAM) [13] showing 50-Gbit/s on-off-keyed (OOK) data, and (c) a thin-
LiNbO3-substrate modulator, with which the non-return-to-zero (NRZ)-DPSK at 83 Gbaud/s
and the DP-NRZ-DQPSK at 90 Gbaud/s have been demonstrated [14, 15].
In this chapter, we summarize our test results on 100-GHz EO polymer Mach-Zehnder
Modulators (MZMs), including a dual-drive and a single-drive version [16, 17]. For the
dual-drive modulator, we experimentally characterize its frequency response and broadband
data modulation. Generation of NRZ-DPSK at 80 Gbit/s and NRZ-OOK of up to 91.6 Gbit/s
is demonstrated using ETDM. Chirp tuning is shown by changing the phase and amplitude
of the driving signal on each arm. With the single-drive modulator, both NRZ-OOK and
NRZ-DPSK with error-free measurements of up to 100 Gbaud/s are obtained without the
assistance of equalization. A chirp factor of as low as -0.0219 is also achieved at 100-Gbit/s
for OOK modulation
9.2 Modulator Structure
The 100-GHz single-drive EO polymer MZM, as shown in Fig. 9.1, has a single RF
input, which is then split into two electrodes, each covers one arme of the MZI. It was
fabricated with a standard inverted-rib waveguides fabrication process [18, 19]. It includes
multiple layers: bottom electrode, lower cladding, core layer and upper cladding. On a 6-

109

inch wafer, bottom electrodes were sputtered and patterned, then a layer of UV15LV was
spun, UV exposed and thermal cured as bottom cladding. Inverted-rib waveguides were then
fabricated on the commercial epoxy bottom clad. Following the bottom clad and the rib
waveguides, the core layer of B74/APC was deposited and thermal-cured. Then the top clad
was spun and thermal-cured after a surface treatment of the core layer. After poling at 140
o
C, 900V, RF electrodes were then fabricated on the surface of the polymer stack using an
electroplating process. The dimensions of the RF electrodes were precisely controlled to
fulfill the modeling for velocity match and maintain broad EO bandwidth. In addition, the
push-pull poling technique is performed at 164 0C and 700V bias voltage, which could
ensure the zero-chirp and a lower Vπ [20, 21].

Figure 9.1 (a) Package of the 100 GHz EO polymodulator with W1 RF connector. (b) Electrode
structure of the single drive MZM.
9.3 Measuremens
This single-drive EO polymer MZM has an effective Vπ of ~3.5V, which is about one
half of that of the dual-drive version due to the push-pull polling. Again, a network analyzer,
which is capable of measurements of up to 110 GHz, is used to characterize the frequency
response first. The measured S21 parameter is shown in Fig.9.2. The -3-dB and -7-dB

110

bandwidths are around 65 GHz and 110 GHz, respectively, showing the capability of
broadband data modulation.

Figure 9.2 (Left) S21 test setup. (Right) Frequency response of the single-drive EO MZM, with a -
3dB bandwidth of ~60GHz and -7dB bandwidth of > 110 GHz. VNA: vector network analyzer. LD:
laser diode. PD: photo detector.
The insertion loss as a function of optical wavelength of the input signal is measured, as
shown in Fig. 9.3(a). The minimum insertion loss is ~7.5 dB at 1570 nm. Similar to the dual-
drive version, the single-drive modulator is biased through a current source and the bias
tuning of this modulator is based on the electro-thermal effect with a response speed of >1
kHz. In general, the bias-induced phase shift is proportional to the square of the incident
current to the electrode. The measured transmission power as a function of the square of
incident current is shown in Fig. 9.3(b). It can be seen that the measured results fit very well
to a standard sine function, indicating that there is almost no performance degradation due to
the bias control within a regular operating range. In addition, negligible bias drift over time
is observed during the testing. The maximum point and the minimum point are biased at
approximately 54 mA and 83 mA, respectively.
0 20 40 60 80 100
-40
-30
-20
-10
0
10
Frequency (GHz)
Rel. Power (dB)
VNA
LD
Modulator
PD
DUT

111

Figure 9.3 (a) Insertion loss of this MZM as a function of the input signal’s optical wavelength.
(b)Transmission power as a function of the square of the applied bias current on this MZM

Figure 9.4 Experimental setup for 100-Gbit/s serial data modulations. PPG: pulse pattern generator.
MUX: multiplexer. EA: electrical amplifier. PC: polarization controller. VOA: variable optical
attenuator. OC: optical coupler. EDFA: Erbium-doped fiber amplifier. PD: photo-detector. BERT: bit-
error-ratio tester.
Figure 9.4 shows the experimental setup for 100-Gbit/s serial data modulation with the
single-drive modulator. Similarly, the pulse pattern generator is driven by a 50-GHz RF
clock source to provide two 50-Gbit/s data channels (i.e., data and inverted data). Both
channels are fed into an electrical multiplexer to generate a 100-Gbit/s data channel through
ETDM. A state-of-the-art broadband amplifier (SHF804TL) with a 3-dB bandwidth of 55
GHz and usable gain bandwidth of > 80 GHz can amplify the data to an output voltage of
~3.2 V at 100-Gbit/s, which is close to the Vπ of the MZM. The amplified data is directly
1500 1530 1560 1590 1620
0
4
8
12
16
IL (dB)
Wavelength (nm)
Measured power
Sine function (Fit curve)
0 2000 4000 6000 8000
0.0
0.5
1.0
1.5
2.0
2.5
Transmitted power (mW)
Square of bias current (mA
2
)
Equation y=y0+A*sin(pi*(
x-xc)/w)
Adj. R-Square 0.99831
Value
B xc 672.8988
B w 4155.42573
B A 1.11381
B y0 1.2214
2:1 MUX
100 Gbit/s
4:1
Clk divider
λ
Sig
PPG
12.5-GHz
Clock
50-GHz Clock
PD
VOA
PC
100-GHz MZM
EA
EDFA
Optical
sampler
DPSK
demodulator
Bypass for OOK
BERT
Oscilloscope/
Chirp Analyzer

112

used to drive the MZM, which is biased using a current source, (i.e., with ~18.4 mA for
OOK and ~80.7 mA for DPSK). The wavelength of the input continuous-wave (CW) laser is
1550.14 nm, with an optical power of 16-dBm. The modulated optical signal is then sent into
a 65-GHz sampling scope for measurements.

Figure 9.5 (a): Measured eye-diagram of 100-Gbit/s ETDM signal. (b): Measured eye-diagram of the
generated 100-Gbit/s optical OOK signal.
The eye diagrams of the 100-Gbit/s ETDM data (after MUX) and optically modulated
OOK data (after MZM) are shown in Fig. 9.5(a) and (b). Please note that no equalization
technique is used here. As the results illustrates, the 100-Gbit/s optical eye is clean and open
except for the some inter-symbol interference (ISI) effects. To distinguish the bandwidth
limitation from the sampling scope, fig.9.6(a) and (b) shows the waveform of 100 Gbit/s
OOK signal measured by a 65 GHz sampling scope and a complex spectrum analyzer (CSA),
respectively. Note that the CSA is capable of measuring an optical signal of up to 800 GHz.
The pattern-dependent amplitude variation in Fig. 9.6(b) is smaller, which indicates that the
actual quality of the generated 100-Gbit/s signal should be slightly better than that shown in
Fig. 9.5(b). The generated OOK signal at 100Gbit/s is also better than the results achieved in

113

dual-drive modulator testing because only one driving signal is required for the single drive
modulator and a higher output voltage is provided by the RF amplifier.

Figure 9.6. Waveforms of 100Gbit/s OOK signal measured by electrical sampling scope (65GHz
bandwidth) and a complex spectrum analyzer.
The measured average chirp factor using CSA is as low as -0.0219 with the bias current
of 18.4 mA. To verify the generated signal, the constellations of both generated NRZ-OOK
and NRZ-DPSK signals at 92 Gbit/s are also measured by the CSA. The constellations
illustrate that the OOK signal and DPSK signal are generated successfully. Additionally, the
measured traces are almost parallel with the x-axis, indicating a very small chirp on the
generated OOK and DPSK signals.
To measure the BER, the generated 100-Gbit/s NRZ-OOK signal is down-sampled to
12.5 Gbit/s by using an optical sampler (i.e., a nonlinear optical loop mirror) driven by a
12.5-GHz RF clock [22]. The eye diagrams of the eight down-sampled NRZ-OOK
tributaries are shown in Fig. 9.7, respectively. It is noted that the relatively thick “1” level of
the eye is due to the existing ISI effect. Each tributary is O/E converted by a photo-detector

114

with a bandwidth of 50 GHz and then processed for BER measurements. Error-free
performance (i.e., BER of 1×10
-9
) is achieved for all eight tributaries.

Figure 9.7 100-Gbit/s NRZ-OOK after down-sampling. (Left: eyediagrams. Right: BER
performances)

Figure 9.8 DPSK demodulator at 12.5 Gbit/s using a polarization-based interferometer.
PC
DPSK demodulator
80ps
DGD
PC
12.5 Gbit/s
DPSK
12.5 Gbit/s
OOK
Pol.
8:1
Down-sampling
DPSK
demodulation
Receiver
100 Gbit/s
DPSK
X-pol
y-pol

115

Moreover, the generated 100-Gbit/s NRZ-DPSK signal is also down-sampled and then
sent to a 12.5-Gbit/s polarization-based DPSK demodulator, as shown in Fig. 9.8. The
interfererometer is created using a 80 ps differential group delay element followed by a
polarizer [23]. The incoming DPSK signal should be polarized with an angle of 45 degree to
the x- and y-axis. The eye-diagram for each tributary is shown in Fig. 9.9. We note that the
demodulated eye diagrams shown here are the “half eyes” of the balanced eye diagrams
since a polarizer is employed in the setup and only one end of a balanced detector is used.
The measured BER curves are plotted with 2-dB better performance for OOK over DPSK. If
balanced detection is utilized, a 3-dB improvement is expected for DPSK. The lower DPSK
performance is mainly attributed to the single ~Vπ peak-to-peak drive signal instead of the
ideal 2Vπ.

Figure 9.9 100-Gbit/s NRZ-DPSK after down-sampling. (Left: eyediagrams. Right: BER
performances)

116

9.4 Summary
In this chapter, a single drive 100 GHz EO polymer modulator is characterized.
Tunable chirp at 40 Gbit/s and broadband modulation of up to 91.6 Gbit/s are shown using
the dual-drive EO MZM. With the single-drive version, both NRZ-OOK and NRZ-DPSK at
100 Gbit/s are generated and a BER of 1×10
-9
is achieved after down-sampling, without the
need for equalization. Negligible chirp and chirp tuning is shown for the dual-drive
modulator. S21 measurements show the potential for >100-Gbit/s serial modulation for both
single- and dual-drive modulators.

117

9.5 Reference
[1] Datong Chen, Harold R. Fetterman, Antao Chen, William H. Steier, Larry R. Dalton,
Wenshen Wang, and Yongqiang Shi, “Demonstration of 110 GHz electro-optic polymer
modulators,” Appl. Phys. Lett., vol.70, Issue 25, 3335 (1997)
[2] R. Dinu, D. Jin, G. Yu, B. Chen, D. Huang, H. Chen, A. Barklund, E. Miller, C. Wei,
and J. Vemagiri, "Environmental Stress Testing of Electro-Optic Polymer Modulators," J.
Lightwave Technol. 27, 1527-1532 (2009).
[3] R. H. Derksen, M. Moller, C. Schubert, "100-Gbit/s Full-ETDM Transmission
Technologies," IEEE Compound Semiconductor Integrated Circuit Symposium, 2007
(CSIC), pp. 89-92, Oct. 2007.
[4] M. Camera, B. -E. Olsson, G. Bruno, "Beyond 100 Gbit/s: System implications towards
400G and 1T," Symposia S6 Towards 1000 Gb/s, 36th European Conference and Exhibition
on Optical Communication (ECOC), Sept. 2010.
[5] J. Berthold, "Toward 100G networking and beyond," in Proceedings of 37th European
Conference and Exhibition on Optical Communication (ECOC), 2011, paper: Tu.3.K.1,
Sept. 2011.
[6] P. Winzer, "Beyond 100G Ethernet," IEEE Communications Magazine, vol.48, no.7,
pp.26-30, July 2010.
[7] D. Van den Borne, V. Sleiffer, M. S. Alfiad, S. L. Jansen, "Towards 400G and beyond:
How to design the next generation of ultra-high capacity transmission systems," 16th
Optoelectronics and Communications Conference (OECC), 2011, pp.429-432, July 2011.
[8] G. Raybon, P. Winzer, and C. Doerr, "1-Tb/s (10×107 Gb/s) Electronically Multiplexed
Optical Signal Generation and WDM Transmission," J. Lightwave Technol. 25, 233-238
(2007).
[9] S. Jansen, R. Derksen, C. Schubert, X. Zhou, M. Birk, C. Weiske, M. Bohn, D. van den
Borne, P. Krummrich, M. Moller, F. Horst, B. Offrein, H. de Waardt, G. Khoe, and A.
Kirstadter, "107-Gb/s Full-ETDM Transmission over Field Installed Fiber Using Vestigial
Sideband Modulation," in Optical Fiber Communication Conference and Exposition and The
National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical
Society of America, 2007), paper OWE3.
[10] P. J. Winzer, G. Raybon, C. R. Doerr, M. Duelk, and C. Dorrer, "107-Gb/s Optical
Signal Generation Using Electronic Time-Division Multiplexing," J. Lightwave Technol. 24,
3107- (2006)
[11] A. Kanno, T. Sakamoto, A. Chiba, T. Kawanishi, M. Sudo, K. Higuma, J. Ichikawa,
"95-Gb/s NRZ-DPSK modulation with full-ETDM technique," 36th European Conference
and Exhibition on Optical Communication (ECOC), 2010, paper Mo.2.F.5, Sept. 2010.

118

[12] J. Mallari, C. Wei, D. Jin, G. Yu, A. Barklund, E. Miller, P. O'Mathuna, R. Dinu, A.
Motafakker-Fard, and B. Jalali, "100Gbps EO Polymer Modulator Product and Its
Characterization Using a Real-Time Digitizer," in Optical Fiber Communication
Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OThU2.
[13] M. Chacinski, et. al., “Monolithically Integrated 100 GHz DFB-TWEAM”, J.
Lightwave Technol. 27, 3410-3415 (2009).
[14] A. Kanno, T. Sakamoto, A. Chiba, T. Kawanishi, K. Higuma, M. Sudou, and J.
Ichikawa, "166 Gb/s PDM-NRZ-DPSK Modulation Using Thin-LiNbO3-Substrate
Modulator," in Optical Fiber Communication Conference, OSA Technical Digest (CD)
(Optical Society of America, 2010), paper JWA40.
[15] A. Kanno T. Sakamoto A. Chiba M. Sudo K. Higuma J. Ichikawa T. Kawanishi,
"90 Gbaud NRZ-DP-DQPSK Modulation with Full-ETDM Technique using High-Speed
Optical IQ Modulator", IEICE Transactions on Electronics Vol.E94-C No.7 pp.1179-1186.
[16] S. R. Nuccio, R. Dinu, B. Shamee, D. Parekh, C. Chang-Hasnain, and A. Willner,
"Modulation and Chirp Characterization of a 100-GHz EO Polymer Mach-Zehnder
Modulator," in National Fiber Optic Engineers Conference, OSA Technical Digest (CD)
(Optical Society of America, 2011), paper JThA030.
[17] H. Huang, J. Yang, Y. Yue, Y. Ren, S. R. Nuccio, R. Dinu, D. Parekh, C. J. Chang-
Hasnain, and A. Willner, "100-Gbit/s Amplitude and Phase Modulation Characterization of a
Single-Drive, Low-Vπ Polymer Mach-Zehnder Modulator," in Optical Fiber Communication
Conference, OSA Technical Digest (Optical Society of America, 2012), paper OW4F.5.
[18] D. Jin, D. Huang, B. Chen, H. Chen, L. Zheng, A. Barklund, G. Yu, E. Miller, M.
Moolayil, B. Li, R. Dinu, “Low half-wave voltage modulators using nonlinear optical
polymers,” Proc. SPIE, Vol. 6653, September 2007.
[19] S. K. Kim; H. Zhang; D.H. Chang; C. Zhang; C. Wang; W.H. Steier; H.R. Fetterman,
“Electrooptic polymer modulators with an inverted-rib waveguide structure,” Photonics
Technology Letters, IEEE, Vol. 15, Issue 2, 2003, Pages 218 – 220.
[20] G. Yu, J. Mallari, H. Shen, E. Miller, C. Wei, V. Shofman, D. Jin, B. Chen, H. Chen,
and R. Dinu, "40GHz Zero Chirp Single-ended EO Polymer Modulators with Low Half-
wave Voltage," in CLEO:2011 - Laser Applications to Photonic Applications, OSA
Technical Digest (CD) (Optical Society of America, 2011), paper CTuN5.
[21] W. Wang; Y. Shi; D. J. Olson, W. Lin; J. H. Bechtel, "Push-pull poled polymer Mach-
Zehnder modulators with a single microstrip line electrode," Photonics Technology Letters,
IEEE , vol.11, no.1, pp.51-53, Jan. 1999
[22] A. Bogoni, P. Ghelfi, M. Scaffardi, L. Poti, "All-optical regeneration and
demultiplexing for 160-gb/s transmission systems using a NOLM-based three-stage
scheme," IEEE Journal of Selected Topics in Quantum Electronics, vol.10, no.1, pp. 192-
196, Jan.-Feb. 2004

119

[23] C. W. Chow; H. K. Tsang, "Polarization-independent DPSK demodulation using a
birefringent fiber loop," IEEE Photonics Technology Letters, vol.17, no.6, pp.1313-1315,
June 2005.

120

Chapter 10 Sub-Channel Data Updating for Multiple
Channels of a 16-QAM Signal using a Single PPLN
Waveguide

10.1 Introduction
High-order advanced modulation formats have attracted significant interest due to their
capability of achieving higher spectral efficiency through data modulation on both amplitude
and phase so that each symbol carries more information [1, 2]. On the other hand, data
grooming with a flexible granularity is potentially desirable in a dynamic and heterogeneous
network to meet the demands of variable traffic [3]. Typically, a 16-quadrature amplitude
modulation (QAM) signal carries 4 bits of information in each symbol and can be considered
as two independent quadrature phase-shift-keying (QPSK) sub-channels at the same baud
rate. Therefore, a laudable goal would be to process independent sub-channels of a 16-QAM
signal separately, e.g., data erasing and updating, for data grooming applications.
The processing of sub-channels in a signal with higher-order modulation format has
been reported in the literature, including multiplexing of three on-off-keying (OOK) data
streams into a 8-PSK signal [4] and two QPSK channels into a star 16-QAM signal using
cross-phase modulation [5]. Multiplexing of four OOK signals into a rectangular 16-QAM
has been proposed using a nonlinear optical loop mirror [6]. Extracting a DPSK channel
from a QPSK signal and a QPSK from 8-PSK signal were also demonstrated using four-
wave mixing [7, 8]. However, sub-channel manipulation of a rectangular QAM signal in the
optical domain, to the best of our knowledge, has not been addressed.

121

In this chapter, we experimentally demonstrate sub-channel data erasing/updating for a
single channel 16-QAM signal [9]. We further show the parallel processing capability by
simultaneously updating four wavelength-division-multiplexed (WDM) 16-QAM channels.
For a single channel 16-QAM signal at 40 Gbit/s, an optical signal-to-noise ratio (OSNR)
penalty of ~2 dB for return-to-zero (RZ) operation and 4 dB for non-return-to-zero (NRZ)
operation is observed at a bit-error-rate (BER) of 2×10-3 (forward error correction (FEC)
threshold). For the parallel processing of four WDM NRZ-16-QAM signals, the average
OSNR penalty at BER of 2×10-3 is ~4.5 dB.
10.2 Concept and principle of subchannel data erasing and
updating
In general, each symbol of a 16-QAM signal carries 4 bits of information. One of the
commonly used encoding approach is that, 2 bits of information determins which quadrature
the symbol appears in the constellation, and the other 2 bits determins the position within the
quadrature. Therefore, a data channel with a 16-QAM modulation format can be considered
as two independent sub-channels, i.e., a QPSK signal (QPSK 1) and an offset QPSK signal
(QPSK 2), as shown in Fig. 10.1.
The concept of sub-channel data erasing and updating is shown in Fig.10.2. the data
carried by one sub-channel can be erased if the phase of QPSK 1 is canceled by phase-
subtraction between the 16-QAM signal and a synchronized QPSK 1 signal, which
potentially could be extracted from the same 16-QAM signal, leaving the other sub-channel
as an off-set QPSK signal, as shown in Fig. 10.2(a). Furthermore, a new 16-QAM signal can
be obtained if a different QPSK signal (QPSK 3) is induced by phase addition between the

122

Figure 10.1 A 16-QAM signal includes two independent QPSK sub-channels

offset QPSK and the new QPSK, i. e., data updating, as shown in Fig. 10.2(b). As a result,
data on one sub-channel is rewritten, while the information on the other sub-channel is
maintained. Following the concept described above, Fig. 10.2(c) shows the principle of
phase addition/subtraction based on the sum-/difference-frequency generation (SFG/DFG) in
a PPLN waveguide [10]. Three signals (S1, S2 and S3, corresponding to 16-QAM, QPSK 3
and QPSK 1, respectively) are fed into the PPLN waveguide. SFG between S1 and S2
happens first, followed by the DFG with S3. Consequently, an idler will be generated,
following the linear phase relationship expressed as Φ
idler
=Φ
S1
+Φ
S2
-Φ
S3
. Specifically, if S2 is
a continuous wave (CW) with a constant phase, and S3 is a QPSK signal that carries the
same information as the sub-channel QPSK 1, the phase of the generated idler would be Φ
S1
-
Φ
S3
. Accordingly, this sub-channel will be erased with the other sub-channel (QPSK2)
remaining as an offset QPSK. On the other hand, if S2 carries a new QPSK signal (QPSK 3),
its phase will be added into the offset QPSK (QPSK 2) and a new 16-QAM signal with one
sub-channel being updated can be obtained. It is noted that the updated signal is carried on a
different wavelength after processing, therefore the changing of the filter at the receiver
QPSK 1 + QPSK 2
I
Sub-channel 1 “X X ”
I Q
Q
Sub-channel 2 “X X”
I
Q
16-QAM
“X X X X” 4 bits
QPSK 1
QPSK 2

123

might be required, or an additional wavelength conversion stage could be used to convert it
back to the original wavelength.

Figure 10.2 Concept and principle (a) Concept of data erasing. (b) Concept of data updating. The
symbol ‘+ ’ and ‘ –’ indicate phase addition and subtraction, respectively. (c) Principle of data
updating using cascaded ① SFG and ②DFG in a PPLN waveguide. QPM: quasi-phase matching.
SFG/DFG: sum-/difference-frequency generation

124

10.3 Experiment and Results

Figure 10.3 Experimental setup. LD: laser diode. PC: polarization controller. EDFA: erbium doped
fiber amplifier. OC: optical coupler. BPF: band-pass filter. ODL: optical delay line. OSA: optical
spectral analyzer. LO: local oscillator. ADC: analog to digital converter. DSP: digital signal
processing.
The experimental setup is illustrated in Fig.10.3. The 16-QAM is generated through a
serial modulation method, in which two IQ modulators driven by four independent 10-Gbit/s
binary data channels modulate a continuous-wave (CW) laser (LD1). The first IQ modulator
generates a typical QPSK channel (QPSK 1), and the second IQ modulator generates an
offset QPSK channel (QPSK 2). In this proof-of-concept experiment, the second IQ
modulator is replaced with a unbalanced delay-line interferometer (DLI), which is able to
generate a 16-QAM signal by vector addition between two QPSK signals, with one of them
attenuated by 6-dB. Two other CW lasers (LD2 and LD3) are also coupled into the first IQ
modulator, and then properly delayed to emulate the known QPSK 1 channel and the

125

unknown QPSK 3 channel, respectively. Three tunable delay lines are used to synchronize
three signals in the time domain. After amplification to ~15 dBm, all three channels are
coupled into a PPLN waveguide with a length of ~4 cm. The idler is filtered out from the
output signals and sent to a coherent receiver for BER measurement.

Figure 10. 4 Optical spectrum and constellations. (a)-(c): Back-to-back QPSK signals and NRZ 16-
QAM signal. (d): offset QPSK with the other sub-channel erased. (e): updated NRZ 16-QAM. (f):
updated RZ 16-QAM.
The spectrum at the output of the PPLN waveguide is shown in Fig. 10.4. An idler with
a conversion efficiency of approximately -12 dB is obtained. Fig. 10.4(a)-(c) displays the
measured constellations of the QPSK 1 and new QPSK 3, as well as the 16-QAM signal
before coupling into the PPLN waveguide. First, we verify the information-erasing process
using a CW instead of a new QPSK signal for S2. After SFG/DFG, an offset QPSK signal is
obtained as the idler, as shown in Fig. 10.4(d). One of the sub-channels (the old QPSK, i.e.,
QPSK 1) of the 16-QAM signals has been successfully erased. We further change S2 into a
QPSK signal (the new QPSK, i.e., QPSK 3). A new NRZ 16-QAM signal with one QPSK
sub-channel being updated is obtained, as shown in Fig. 10.4(e). We also demonstrate
16-QAM New QPSK Old QPSK
QPM
Idler
1.5nm/div
10dB/div
Updated
16-QAM
NRZ
RZ
(a) (b) (c)
(d)
(e)
(f)
Offset QPSK

126

simultaneous information updating and format conversion into a RZ 16-QAM signal by
pulse carving S3 through a Mach-Zehnder modulator, as shown in Fig. 10.4 (f).

Figure 10.5 BER performance as a function of the received OSNR
Figure 10.5 shows the measured BER curves of the back-to-back and updated 16-QAM
signals in both RZ and NRZ formats at 10 Gbaud/s. The observed power penalty at a BER of
2×10
-3
is ~2 dB for RZ 16-QAM and ~4 dB for NRZ 16-QAM. RZ format performs better
than NRZ due to that RZ has a higher peak power and consequently a higher conversion
efficiency than NRZ with the same average power. Fig. 5(a) shows the BER performance as
a function of the relative time offset among three input signals with an OSNR of 20 dB. The
time offset tolerance to achieve BER of < 2×10
-3
is ~20 ps for two QPSK signals and ~15 ps
for a NRZ 16-QAM signal. It can be seen from the optical spectrum that besides the desired
idler (i.e., λ
b
+λ
c
-λ
a
), there are also some other idlers with a lower efficiency from unwanted
interaction. The efficiency of both the desired and undesired idlers (e.g, 2λ
b
-λ
a
) as functions
of the frequency spacing between pump a and b (see fig. 3) are plotted in Fig. 5(b) (λ
c
-λ
b
is
fixed at 1.6 nm). The undesired interaction efficiency increase dramatically when the
16 18 20 22 24 26 28
2
3
4
5
Received OSNR (dB)
-log10(BER)

B2B NRZ 16-QAM
Updated NRZ 16-QAM
Updated RZ 16-QAM
FEC threshod

127

frequency of pump a approaches pump b, since their phase matching condition is more
closely satisfied.

(a) (b)
Figure 10.6 (a) BER versus relative time offset among three input signals (OSNR = 20 dB). (b).
Conversion efficiencies as functions of frequency spacing between pump a and pump b. (λc-λb=1.6
nm).
To show the capability of parallel processing, we demonstrate simultaneously
processing of four-channel WDM 16-QAM signals in a single stage, provided that these four
16-QAM signals share the same data on one of their sub-channels. The shared sub-channel
(QPSK1) could be erased and subsequently updated by phase subtraction/addition. The
observed optical spectrum is shown in Fig. 10. 7. Two amplified QPSK signals (QPSK1 and
QPSK3) at 1548.09 nm and 1550.14 nm with a power of ~18.2 dBm, together with four
NRZ 16-QAM signals with 50 GHz wavelength spacing (1544.74 nm, 1545.14 nm, 1545.54
nm and 1545.94 nm), all around 15.4-dBm, are coupled into the PPLN waveguide. As
expected, four idlers are generated, corresponding to four updated NRZ 16-QAM signals, the
constellations of each signal are shown in Fig.10.7. The BER of each channel are also
measured and plotted in Fig. 10.8. Due in part to the crosstalk between adjacent channels,
the WDM signal processing performance is not as good as a single channel, but all four
-20 0 20
1
1.5
2
2.5
3
3.5
Time offset (ps)
-log10(BER)

S3(QPSK3)
S2(QPSK1)
S1(16-QAM)
0 1 2 3
-50
-40
-30
-20
Frequency spacing of pump a & b (nm)
Conver. efficien. (dB)

b+c-a
2b-a

128

channels can still achieve a BER below 2×10
-3
. An average OSNR penalty of ~4.5 dB at a
BER of 2×10
-3
is observed for the data erasing/updating operations.

Fig.10.7 Optical spectral of WDM NRZ 16-QAM information updating and the constellations for
each updated channel.

Fig. 10. 8 BER performance as a function of the received OSNR for each WDM channel.
10.4 Summary
In this chapter, we described sub-channel data updating of high-order modulation
format signals using cascaded sum- and difference-frequency generation (SFG/DFG) in a
single PPLN waveguide. One QPSK sub-channel of a 16-QAM signal at 40 Gbit/s is
successfully updated, with an OSNR penalty of ~2 dB for RZ and ~4 dB for NRZ at a BER
Ch4
Ch3 Ch1
Ch2
16QAM
New QPSK Old QPSK
Updated
16QAM
1 2 3 4
QPM
4 3 2 1
1.5nm/div
10dB/div
15 20 25 30
2
3
4
5
6
Received OSNR (dB)
-10log(BER)

Ch1 B2B
Ch1 updated
Ch2 B2B
Ch2 updated
Ch3 B2B
Ch3 updated
Ch4 B2B
Ch4 updated
FEC threshod

129

of 2×10
-3
. Simultaneous processing of four wavelength-multiplexed 16-QAM signals with an
average OSNR penalty of 4.5 dB at a BER of 2×10
-3
is also demonstrated.
10.5 Reference
[1] A. H. Gnauck, P. J. Winzer, S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Peckham,
"Spectrally Efficient Long-Haul WDM Transmission Using 224-Gb/s Polarization-
Multiplexed 16-QAM," J. Lightwave Technol. 29, 373-377 (2011)
[2] T. Omiya, K. Toyoda, M. Yoshida, and M. Nakazawa, "400 Gbit/s Frequency-Division-
Multiplexed and Polarization-Multiplexed 256 QAM-OFDM Transmission over 400 km
with a Spectral Efficiency of 14 bit/s/Hz," in Optical Fiber Communication Conference,
OSA Technical Digest (Optical Society of America, 2012), paper OM2A.7.
[3] Nobuyuki Kataoka, Naoya Wada, Kyosuke Sone, Yasuhiko Aoki, Hideyuki Miyata,
Hiroshi Onaka, and Ken-ichi Kitayama, "Field Trial of Data-Granularity-Flexible
Reconfigurable OADM With Wavelength-Packet-Selective Switch," J. Lightwave Technol.
24, 88- (2006)
[4] Ken Mishina, Satoru Kitagawa, and Akihiro Maruta, "All-optical modulation format
conversion from on-off-keying to multiple-level phase-shift-keying based on nonlinearity in
optical fiber," Opt. Express 15, 8444-8453 (2007)
[5] X. Wu, J. Wang, H. Huang, and A. E. Willner, "Experimental Optical Multiplexing of
Two 20-Gbit/s QPSK Data Channels from Different Wavelengths onto a Single 40-Gbit/s
Star 16-QAM using Fiber Nonlinearities," in CLEO:2011 - Laser Applications to Photonic
Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper
CThH4.
[6] Guoxiu Huang, Yuji Miyoshi, Akihiro Maruta, Yuki Yoshida, and Ken-Ichi Kitayama,
"All-Optical OOK to 16-QAM Modulation Format Conversion Employing Nonlinear
Optical Loop Mirror," J. Lightwave Technol. 30, 1342-1350 (2012).
[7] Guo-Wei Lu and Tetsuya Miyazaki, "Optical phase erasure based on FWM in HNLF
enabling format conversion from 320-Gb/s RZDQPSK to 160-Gb/s RZ-DPSK," Opt.
Express 17, 13346-13353 (2009)
[8] Guo-Wei Lu, Ekawit Tipsuwannakul, Tetsuya Miyazaki, Carl Lundström, Magnus
Karlsson, and Peter A. Andrekson, "Format Conversion of Optical Multilevel Signals Using
FWM-Based Optical Phase Erasure," J. Lightwave Technol. 29, 2460-2466 (2011)
[9] H. Huang, J. Yang, X. Wu, S. Khaleghi, M. Tur, C. Langrock, M. M. Fejer, and A.
Willner, "All-Optical Sub-Channel Data Erasing and Updating for a 16-QAM Signal using a
Single PPLN Waveguide," in CLEO: Science and Innovations, OSA Technical Digest
(online) (Optical Society of America, 2012), paper CM2B.3.

130

[10] H. Tan, G. P. Banfi, and A. Tomaselli, “Optical frequency mixing through cascaded
second-order processes in β-barium borate,” Appl. Phys. Lett.,vol. 63, no. 18, pp. 2472–
2474, Nov. 1993.

131

Bibliography

I. P. Kaminow, T. Li, and A. E. Willner, Optical Fiber Telecommunications 5th Edition.
Elsevier, (2008).
I. P. Kaminow, C. R. Doerr, C. Dragone, T. Koch, U. Koren, A. A. M. Saleh, A. J. Kirby, C.
M. Ozveren, B. Schofield, R. E. Thomas, R. A. Barry, D. M. Castagnozzi, V. W. S. Chan, B.
R. Hemenway, D. Marquis, S. A. Parikh, M. L. Stevens, E. A. Swanson, S. G. Finn, and R.
G. Gallager, “A wideband all-optical WDM network,” Journal on Selected Areas in
Communications 14, 780-799 (1996).
P. J. Winzer and R.-J. Essiambre, “Advanced modulation formats for high-capacity optical
transport networks,” J. Lightwave Technol. 24, 4711-4720 (2007).
X. Zhou and J. Yu, “Multi-level, multi-dimensional coding for high-speed and high-spectral-
efficiency optical transmission,” J. Lightwave Technol. 27, 3641-3653 (2009).
S. Okamoto, K. Toyoda, T. Omiya, K. Kasai, M. Yoshida, and M. Nakazawa, “512 QAM
(54 Gbit/s) coherent optical transmission over 150 km with an optical bandwidth of 4.1
GHz,” in Proc. of ECOC’2010, Paper PD2-3 (2010).
M. Sjödin, P. Johannisson, H. Wymeersch, P. A. Andrekson, and M. Karlsson, "Comparison
of polarization-switched QPSK and polarization-multiplexed QPSK at 30 Gbit/s," Opt.
Express 19, 7839-7846 (2011)
D. Qian, Ming-Fang Huang, Ezra Ip, Yue-Kai Huang, Yin Shao, Junqiang Hu, and Ting
Wang, "High Capacity/Spectral Efficiency 101.7-Tb/s WDM Transmission Using PDM-
128QAM-OFDM Over 165-km SSMF Within C- and L-Bands," J. Lightwave Technol. 30,
1540-1548 (2012).
W. Shieh, H. Bao, and Y. Tang, "Coherent optical OFDM: theory and design," Opt. Express
16, 841-859 (2008).
D. Hillerkuss, R. Schmogrow, M. Meyer, Stefan Wolf, Meinert Jordan, Philipp Kleinow,
Nicole Lindenmann, Philipp C. Schindler, Argishti Melikyan, Xin Yang, Shalva Ben-Ezra,
Bend Nebendahl, Michael Dreschmann, Joachim Meyer, Francesca Parmigiani, Periklis
Petropoulos, Bojan Resan, Andreas Oehler, Kurt Weingarten, Lars Altenhain, Tobias
Ellermeyer, Michael Moeller, Michael Huebner, Juergen Becker, Christian Koos, Wolfgang
Freude, and Juerg Leuthold, "Single-Laser 32.5 Tbit/s Nyquist WDM Transmission," J. Opt.
Commun. Netw. 4, 715-723 (2012)
A. H. Gnauck, P. J. Winzer, A. Konczykowska, F. Jorge, J.-Y. Dupuy, M. Riet, G. Charlet,
B. Zhu, and D. W. Peckham, “Generation and transmission of 21.4-Gbaud PDM 64-QAM
using a high-power DAC driving s single I/Q modulator,” in Proc. of OFC’2011, Paper
PDPB2 (2011).

132

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical
fibres,” Nat. Photonics 7(5), 354–362 (2013).
P. J. Winzer, "Making spatial multiplexing a reality", Nat. Photon. 8, 345 (2014)
B. Zhu, T. F. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. F. Yan, J. M. Fini, E. M.
Monberg, and F. V. Dimarcello, “112-Tb/s Space-division multiplexed DWDM transmission
with 14-b/s/Hz aggregate spectral efficiency over a 76.8-km seven-core fiber,” Opt. Express
19(17), 16665–16671 (2011).
S. Randel, R. Ryf, A. Sierra, P. J. Winzer, A. H. Gnauck, C. A. Bolle, R.-J. Essiambre, D.
W. Peckham, A. McCurdy, and R. Lingle, "6×56-Gb/s mode-division multiplexed
transmission over 33-km few-mode fiber enabled by 6×6 MIMO equalization," Opt. Express
19, 16697-16707 (2011).
S. Matsuo, Y. Sasaki, T. Akamatsu, I. Ishida, K. Takenaga, K. Okuyama, K. Saitoh, and M.
Kosihba, "12-core fiber with one ring structure for extremely large capacity transmission,"
Opt. Express 20, 28398-28408 (2012).
R. Ryf, N. K. Fontaine, M. A. Mestre, S. Randel, X. Palou, C. Bolle, A. H. Gnauck, S.
Chandrasekhar, X. Liu, B. Guan, R. Essiambre, P. J. Winzer, S. Leon-Saval, J. Bland-
Hawthorn, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Grüner-Nielsen, R. V. Jensen,
and R. Lingle, "12 x 12 MIMO Transmission over 130-km Few-Mode Fiber," in Frontiers in
Optics 2012/Laser Science XXVIII, OSA Technical Digest (online) (Optical Society of
America, 2012), paper FW6C.4.
J. Poynting, "The wave motion of a revolving shaft, and a suggestion as to the angular
momentum in a beam circularly polarised light," Proc. R. Soc. Lond. A Ser. A vol. 82, pp.
560-567, 1909.
R. Beth, "Mechanical detection and measurement of the angular momentum of light," Phys.
Rev. vol. 50, pp. 115-125, 1936.
L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular-
momentum of light and the transformation of Laguerre–Gaussian laser modes," Phys. Rev. A
45, 8185‒8189 (1992).
S. Barnett and L. Allen, "Orbital angular momentum and non paraxial light beams," Opt.
Commun. 110, 670‒678 (1994).
A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and
applications,” Adv. Opt. Photon.3, 161–204 (2011).
J. M. Vaughan and D. V. Willetts, “Temporal and interference fringe analysis of TEM01
laser modes,” J. Opt. Soc. Am. 73, 1018–1021 (1983).

133

M. Mirhosseini, O. S. Magaña-Loaiza, C. Chen, B. Rodenburg, M. Malik, and R. W. Boyd,
"Rapid generation of light beams carrying orbital angular momentum," Opt. Express 21,
30196-30203 (2013).
E. Karimi, S. A. Schulz, I. D. Leon, V. Qassim, J. Upham and R. W. Boyd, “Generating
optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,”
Light: Science & Applications 3, e167 (2014).
N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light
propagation with phase discontinuities: generalized laws of reflection and refraction,”
Science 334, 333–337 (2011).
N. R. Heckenberg, R. McDuff, C. P. Smith, and A. White, "Generation of optical phase
singularities by computer-generated holograms," Opt. Lett., vol. 17, pp. 221-223, 1992.
P. Genevet, J. Lin, M. A. Kats, and F. Capasso, “Holographic detection of the orbital angular
momentum of light with plasmonic photodiodes,” Nat Commun 3, 1278 (2012).
M. Malik, M. O’Sullivan, B. Rodenburg, M. Mirhosseini, J. Leach, M. P. J. Lavery, M. J.
Padgett, and R. W. Boyd, "Influence of atmospheric turbulence on optical communications
using orbital angular momentum for encoding," Opt. Express 20, 13195-13200 (2012)
G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pasko, S. M. Barnett, and S. Franke-
Arnold, “Free-space information transfer using light beams carrying orbital angular
momentum,” Opt. Express 12, 5448-5456 (2004).
J. H. Shapiro, S. Guha, and B. I. Erkmen, “Ultimate channel capacity of free-space optical
communications,” J. Opt. Netw 4, 501–516 (2005).
A. E. Willner, J. Wang and H. Huang, “A different angle on light communications,” Science
337, 655–656 (2012).
Y. Awaji, N. Wada, and Y. Toda, “Demonstration of spatial mode division multiplexing
using Laguerre–Gaussian mode beam in telecom-wavelength,” in Proceedings of the IEEE
Photonics Conference paper WBB2, PHO 2010, Denver (IEEE Photonics Society, 2010).
T. Su, R. P. Scott, S. S. Djordjevic, N. K. Fontaine, D. J. Geisler, X. Cai, and S. J. B. Yoo,
“Demonstration of free space coherent optical communication using integrated silicon
photonic orbital angular momentum devices”, Optics Express 20, 9396–9402 (2012)
J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar,
M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular
momentum multiplexing,” Nat. Photon. 6, 488–496 (2012).
I. Fazal, et al. 2 Tbit/s free-space data transmission on two orthogonal orbital-angular-
momentum beams each carrying 25 WDM channels, Opt. Lett. 37, 4753-4755 (2012)..

134

N. Bozinovic, et al. Orbital Angular Momentum (OAM) Based Mode Division Multiplexing
(MDM) over a Km-length Fiber, in European Conference and Exhibition on Optical
Communication (ECOC), paper Th.3.C.6 (2012).
H. Huang, G. Xie, Y. Yan, N. Ahmed, Y. Ren, Y. Yue, D. Rogawski, M. J. Willner, B. I.
Erkmen, K. M. Birnbaum, S. J. Dolinar, M. P. J. Lavery, M. J. Padgett, M. Tur, and A. E.
Willner, "100 Tbit/s free-space data link enabled by three-dimensional multiplexing of
orbital angular momentum, polarization, and wavelength," Opt. Lett. 39, 197-200 (2014).
Y. Yan, et al. Spatial-Mode Multicasting of a Single100-Gbit/s Orbital Angular Momentum
(OAM) Mode onto Multiple OAM Modes, in European Conference and Exhibition on
Optical Communication, OSA Technical Digest (online), (Optical Society of America, 2012),
paper Th.2.D.1.
X. Cai, J. Wang, M. J. Strain, B. J.-Morris, J. Zhu, M. Sorel, J. L. O’ Brien, M. G.
Thompson, S. Yu, Integrated Compact Optical Vortex Beam Emitters. Science 338, 363–366
(2012).
K. Fontaine, C. R. Doerr, and L. Buhl, "Efficient Multiplexing and Demultiplexing of Free-
space Orbital Angular Momentum using Photonic Integrated Circuits," in Optical Fiber
Communication Conference, OSA Technical Digest (Optical Society of America, 2012),
paper OTu1I.2.
Martin P. J. Lavery, David J. Robertson, Gregorius C. G. Berkhout, Gordon D. Love, Miles J.
Padgett, and Johannes Courtial, "Refractive elements for the measurement of the orbital
angular momentum of a single photon," Opt. Express 20, 2110-2115 (2012)
Brandon Rodenburg, Martin P. J. Lavery, Mehul Malik, Malcolm N. O’Sullivan,
Mohammad Mirhosseini, David J. Robertson, Miles Padgett, and Robert W. Boyd,
"Influence of atmospheric turbulence on states of light carrying orbital angular momentum,"
Opt. Lett. 37, 3735-3737 (2012).
Nenad Bozinovic, Yang Yue, Yongxiong Ren, Moshe Tur, Poul Kristensen, Hao Huang,
Alan E. Willner, Siddharth Ramachandran, Terabit-Scale Orbital Angular Momentum Mode
Division Multiplexing in Fibers, Science 340, 1545 (2013).
Yongxiong Ren, Hao Huang, Guodong Xie, Nisar Ahmed, Yan Yan, Baris I. Erkmen,
Nivedita Chandrasekaran, Martin P. J. Lavery, Nicholas K. Steinhoff, Moshe Tur, Samuel
Dolinar, Mark Neifeld, Miles J. Padgett, Robert W. Boyd, Jeffrey H. Shapiro, and Alan E.
Willner, "Atmospheric turbulence effects on the performance of a free space optical link
employing orbital angular momentum multiplexing," Opt. Lett. 38, 4062-4065 (2013).
Brandon Rodenburg, Mohammad Mirhosseini, Mehul Malik, Omar S Magaña-Loaiza,
Michael Yanakas, Laura Maher, Nicholas K Steinhoff, Glenn A Tyler and Robert W Boyd,
Simulating thick atmospheric turbulence in the lab with application to orbital angular
momentum communication, New J. Phys. 16 033020 (2014).

135

Yongxiong Ren, Guodong Xie, Hao Huang, Changjing Bao, Yan Yan, Nisar Ahmed, Martin
P. J. Lavery, Baris I. Erkmen, Samuel Dolinar, Moshe Tur, Mark A. Neifeld, Miles J.
Padgett, Robert W. Boyd, Jeffrey H. Shapiro, and Alan E. Willner, "Adaptive optics
compensation of multiple orbital angular momentum beams propagating through emulated
atmospheric turbulence," Opt. Lett. 39, 2845-2848 (2014)
Roland Ryf, Sebastian Randel, Alan H. Gnauck, Cristian Bolle, Alberto Sierra, Sami
Mumtaz, Mina Esmaeelpour, Ellsworth C. Burrows, René-Jean Essiambre, Peter J. Winzer,
David W. Peckham, Alan H. McCurdy, and Robert Lingle, "Mode-Division Multiplexing
Over 96 km of Few-Mode Fiber Using Coherent 6 × 6 MIMO Processing," J. Lightwave
Technol. 30, 521-531 (2012)
Abdullah Al Amin, An Li, Simin Chen, Xi Chen, Guanjun Gao, and William Shieh, "Dual-
LP11 mode 4x4 MIMO-OFDM transmission over a two-mode fiber," Opt. Express 19,
16672-16679 (2011)
Peter J. Winzer and Gerard J. Foschini, "MIMO capacities and outage probabilities in
spatially multiplexed optical transport systems," Opt. Express 19, 16680-16696 (2011).
Hao Huang, Yinwen Cao, Guodong Xie, Yongxiong Ren, Yan Yan, Changjing Bao, Nisar
Ahmed, Mark A. Neifeld, Samuel J. Dolinar, and Alan E. Willner, "Crosstalk mitigation in a
free-space orbital angular momentum multiplexed communication link using 4×4 MIMO
equalization," Opt. Lett. 39, 4360-4363 (2014).
H. Huang, G. Xie, Y. Ren, Y. Yan, C. Bao, N. Ahmed, M. Ziyadi, M. R. Chitgarha, M.
Neifeld, S. Dolinar, A. Willner, “4 × 4 MIMO equalization to mitigate crosstalk degradation
in a four-channel free-space orbital-angular-momentum-multiplexed system using
heterodyne detection.,” in Proceedings of the European Conference and Exhibition on
Optical Communication paper Th.1.C.4, London (Optical Society of America, 2013).
G. A. Tyler and R. W. Boyd, “Influence of atmospheric turbulence on the propagation of
quantum states of light carrying orbital angular momentum,” Opt. Lett. 34, 142-144 (2009).
P. Polynkin, A. Peleg, L. Klein, T. Rhoadarmer, and J. Moloney, “Optimized multiemitter
beams for free-space optical communications through turbulent atmosphere,” Opt. Lett. 32,
885-887 (2007).
L. Andrews, R. Phillips, and A. R. Weeks, “Propagation of a Gaussian beam wave through a
random phase screen,” Wave Random Media 7, 229-244 (1997).
Kasyapa Balemarthy, Arup Polley, and Stephen E. Ralph, "Electronic Equalization of
Multikilometer 10-Gb/s Multimode Fiber Links: Mode-Coupling Effects," J. Lightwave
Technol. 24, 4885-4894 (2006).
J. Leach, M. Padgett, S. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital
angular momentum of a single photon,” Phys. Rev. Lett.88(25), 257901 (2002).

136

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital
angular momentum eigenstates of light,” Nat. Commun.4, 2781 (2013).
Steven Golowich, Nenad Bozinovic, Poul Kristensen, and Siddharth Ramachandran,
"Complex mode amplitude measurement for a six-mode optical fiber," Opt. Express 21,
4931-4944 (2013).
Ze Dong, Xinying Li, Jianguo Yu, and Jianjun Yu, "Generation and transmission of 8 × 112-
Gb/s WDM PDM-16QAM on a 25-GHz grid with simplified heterodyne detection," Opt.
Express 21, 1773-1778 (2013).
M. J. Ready and R. P. Gooch "Blind equalization on radius directed adaptation", Proc. of
Internaltional Conference on Acoustics, Speech, and Signal Processing (ICASSP-90), vol.3,
1699 (1990).Albuquerque, NM
David S. Millar and Seb J. Savory, "Blind adaptive equalization of polarization-switched
QPSK modulation," Opt. Express 19, 8533-8538 (2011).
J. Benesty, P. Duhamel, “Fast constant modulus adaptive algorithm,” IEEE Radar and Signal
processing, 138 379–387 (1991).
Andreas Leven, Noriaki Kaneda, and Stephen Corteselli, "Real-Time Implementation of
Digital Signal Processing for Coherent Optical Digital Communication Systems", IEEE J.
Select. Topics Quantum Electron. 16, 1227 (2010).
R. Schmogrow, B. Nebendahl, M. Winter,A.Josten, D. Hillerkuss, S. Koenig, J. Meyer, M.
Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, J. Leuthold, "Error vector
magnitude as a performance measure for advanced modulation formats", IEEE Photon.
Technol. Lett. 24, 61-63 (2012).
G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett,
Efficient Sorting of Orbital Angular Momentum States of Light, Phys. Rev. Lett. 105,
153601 (2010).
J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett,
Interferometric Methods to Measure Orbital and Spin, or the Total Angular Momentum of a
Single Photon, Phys. Rev. Lett. 92 (1) (2004)
M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A.
Wilner, and M. J. Padgett, “Efficient measurement of orbital angular momentum over 50
states,” New J. Phys. 15 013024 (2013)
H. Huang, G. Xie, N. Ahmed, Y. Ren, Y. Yan, M. P. J. Lavery, M. Padgett, S. Dolinar, and
A. E. Willner, "Experimental Demonstration of Orbital Angular Momentum Demultiplexing
using an Optical FFT in the Spatial Domain," in CLEO: 2014, OSA Technical Digest (online)
(Optical Society of America, 2014), paper SM3J.6.

137

J. W. Goodman, Introduction to Fourier Optics, McGraw-Hill Physical and Quantum
Electronics Series (Roberts, 2005).
D. Hillerkuss, M. Winter, M. Teschke, A. Marculescu, J. Li, G. Sigurdsson, K. Worms, S.
Ben Ezra, N. Narkiss, W. Freude, and J. Leuthold, "Simple all-optical FFT scheme enabling
Tbit/s real-time signal processing," Opt. Express 18, 9324-9340 (2010)
D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis,
R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M.
Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P.
Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M.
Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s
−1
line-rate super-
channel transmission utilizing all-optical fast Fourier transform processing,” Nat.
Photonics5(6), 364–371 (2011).
C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary
optical vector beams,” New J. Phys. 9, 3, 1-20 (2007).
Mair, A. Vaziri, G. Weihs and A. Zeilinger, “Entanglement of the orbital angular momentum
states of photons,” Nature 412, 313 (2001).
M. Padgett, R. Bowman, “Tweezers with a twist.” Nature Photon. 5, 343–348 (2011).
K. Creath, "Phase-shifting interferometry techniques," in Progress in Optics, E. Wolf, ed.
(Elsevier, New York, 1988), Vol. 26, pp. 357-373.
Joenathan, "Phase-measuring interferometry: new methods and error analysis," Appl. Opt.
33, 4147-4155 (1994).
Kevin L. Baker, Eddy A. Stappaerts, Scott C. Wilks, Peter E. Young, Donald T. Gavel, Jack
W. Tucker, Dennis A. Silva, and Scot S. Olivier, "Open- and closed-loop aberration
correction by use of a quadrature interferometric wave-front sensor," Opt. Lett. 29, 47-49
(2004)
Mitsuo Takeda, Hideki Ina, and Seiji Kobayashi, "Fourier-transform method of fringe-
pattern analysis for computer-based topography and interferometry," J. Opt. Soc. Am. 72,
156-160 (1982)
T. Ando, N. Matsumoto, Y. Ohtake, Y. Takiguchi, and T. Inoue, "Structure of optical
singularities in coaxial superpositions of Laguerre Gaussian modes," J. Opt. Soc. Am. A 27,
2602-2612 (2010).
Rockstuhl, A. A. Ivanovskyy, M. S. Soskin, M. G. Salt, H. P. Herzig, R. Dändliker, “High-
resolution measurement of phase singularities produced by computer-generated holograms,”
Optics Communications, 242, 163-169 (2004).
F. A. Starikov, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V.
Ogorodnikov, S. A. Sukharev, V. P. Aksenov, I. V. Izmailov, F. Yu. Kanev, V. V. Atuchin,

138

and I. S. Soldatenkov, "Wavefront reconstruction of an optical vortex by a Hartmann-Shack
sensor," Opt. Lett. 32, 2291-2293 (2007).
F. A. Starikov, G. G. Kochemasov, M. O. Koltygin, S. M. Kulikov, A. N. Manachinsky, N.
V. Maslov, S. A. Sukharev, V. P. Aksenov, I. V. Izmailov, F. Yu. Kanev, V. V. Atuchin, and
I. S. Soldatenkov, "Correction of vortex laser beam in a closed-loop adaptive system with
bimorph mirror," Opt. Lett. 34, 2264-2266 (2009).
H. Huang, Y. Ren, N. Ahmed, Y. Yan, Y. Yue, A. Bozovich, J.-Y. Yang, K. Birnbaum, J.
Choi, B. Erkmen, S. Dolinar, M. Tur and A. Willner, "Demonstration of OAM Mode
Distortions Monitoring using Interference-Based Phase Reconstruction," in CLEO: 2011-
Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society
of America, 2011), paper CF3C.4.
M. A. Clifford, J. Arlt, J. Courtial, K. Dholakia, “High-order Laguerre-Gaussian Laser
Modes for Studies of Cold Atoms”, Optics Communications 156, 300 (1998).
Moreno, C. Iemmi, A. Marquez, J. Campos, M. J. Yzuel, "Modulation diffraction efficiency
of spatial light modulators," 10th Euro-American Workshop on Information Optics (WIO),
pp.1-4 (2011).
S. Frisken, "Advances in Liquid Crystal on Silicon Wavelength Selective Switching," in
Optical Fiber Communication Conference and Exposition and The National Fiber Optic
Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America,
2007), paper OWV4.
J. Homa, K. Bala, "ROADM Architectures and Their Enabling WSS Technology,"
Communications Magazine, IEEE , vol.46, no.7, pp.150-154, July 2008
J. Ertel, R. Helbing, C. Hoke, O. Landolt, K. Nishimura, P. Robrish, and R. Trutna, "Design
and Performance of a Reconfigurable Liquid-Crystal-Based Optical Add/Drop Multiplexer,"
J. Lightwave Technol. 24, 1674- (2006).
H. Huang, G. Xie, Y. Yan, N. Ahmed, Y. Ren, Y. Yue, D. Rogawski, M. Tur, B. Erkmen, K.
Birnbaum, S. Dolinar, M. Lavery, M. Padgett, and A. E. Willner, "100 Tbit/s Free-Space
Data Link using Orbital Angular Momentum Mode Division Multiplexing Combined with
Wavelength Division Multiplexing," in Optical Fiber Communication Conference/National
Fiber Optic Engineers Conference 2013, OSA Technical Digest (online) (Optical Society of
America, 2013), paper OTh4G.5.
P. Boffi, P. Martelli, A. Gatto and M. Martinelli, “Mode-division multiplexing in fibre-optic
communications based on orbital angular momentum”, J. Opt. 15 075403 (2013).
Y. Yue, N. Ahmed, H. Huang, Y. Yan, Y. Ren, D. Rogawski, and A. E. Willner,
"Reconfigurable Orbital-Angular-Momentum-Based Switching among Multiple 100-Gbit/s
Data Channels," in Optical Fiber Communication Conference/National Fiber Optic
Engineers Conference 2013, OSA Technical Digest (online) (Optical Society of America,
2013), paper OM2G.1.

139

Xi Chen, An Li, Jia Ye, Abdullah Al Amin, and William Shieh, "Demonstration of Few-
Mode Compatible Optical Add/Drop Multiplexer for Mode-Division Multiplexed
Superchannel," J. Lightwave Technol. 31, 641-647 (2013).
M. D. Feuer, L. E. Nelson, K. S. Abedin, X. Zhou, T. F. Taunay, J. F. Fini, B. Zhu, R. Isaac,
R. Harel, G. Cohen, and D. M. Marom, "ROADM System for Space Division Multiplexing
with Spatial Superchannels," in Optical Fiber Communication Conference/National Fiber
Optic Engineers Conference 2013, OSA Technical Digest (online) (Optical Society of
America, 2013), paper PDP5B.8.
H. Huang, Y. Yue, Y. Yan, N. Ahmed, Y. Ren, and A. E. Willner, "Orbital-angular-
momentum-based Reconfigurable and “Lossless” Optical Add/Drop Multiplexing of
Multiple 100-Gbit/s Channels," in Optical Fiber Communication Conference/National Fiber
Optic Engineers Conference 2013, OSA Technical Digest (online) (Optical Society of
America, 2013), paper OTh4G.4.
C. Schmidt-Langhorst, R. Ludwig, D. Groß, L. Molle, M. Seimetz, R. Freund, and C.
Schubert, "Generation and Coherent Time-Division Demultiplexing of up to 5.1 Tb/s Single-
Channel 8-PSK and 16-QAM Signals," in Optical Fiber Communication Conference and
National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of
America, 2009), paper PDPC6.
David A. B. Miller, "Reconfigurable add-drop multiplexer for spatial modes," Opt. Express
21, 20220-20229 (2013).
P. Boffi, P. Martelli, A. Gatto, and M. Martinelli, Optical vortices: An innovative approach
to increase spectral efficiency by fiber mode-division multiplexing, in Proc. SPIE, 2013, vol.
8647, p. 864705.
Hao Huang, Yongxiong Ren, Guodong Xie, Yan Yan, Yang Yue, Nisar Ahmed, Martin P. J.
Lavery, Miles J. Padgett, Sam Dolinar, Moshe Tur, and Alan E. Willner, "Tunable orbital
angular momentum mode filter based on optical geometric transformation," Opt. Lett. 39,
1689-1692 (2014).
Olof Bryngdahl, "Geometrical transformations in optics," J. Opt. Soc. Am. 64, 1092-1099
(1974).
Y. Saito, S. Komatsu, and H. Ohzu, “Scale and rotation invariant real time optical correlator
using computer generated hologram”, Opt. Commun. 47, 8 (1983).
J. Leach, M. R. Dennis, J. Courtial and M. J. Padgett, Vortex knots in light, New J. Phys. 7
55 (2005).
Malcolm N. O’Sullivan, Mohammad Mirhosseini, Mehul Malik, and Robert W. Boyd,
"Near-perfect sorting of orbital angular momentum and angular position states of light," Opt.
Express 20, 24444-24449 (2012).

140

C. H. Cox. III, Analog Optical Links: Theory and Practice, Cambridge University Press,
2004, pp. 201-205.
W. S. C. Chang, RF Photonic Technology in Optical Fiber Links, Cambridge
University Press, 2002, pp. 25-32.
P. Roberts, “Ultimate low loss of hollow-core photonic crystal fibers,” Optics Express, vol.
13, no. 1, pp.236-244, Jan. 2005.
Y. Zhou, V. Karagodsky, B. Pesala, F. G. Sedgwick and C. J. Chang-Hasnain, “A novel
ultra-low loss hollow-core waveguide using subwavelength high-contrast gratings,” Optics
Express, vol. 17, no. 3, pp.1508-1517, 2009.
V. Karagodsky, F. G. Sedgwick and C. J. Chang-Hasnain, “Theoretical analysis of
subwavelength high contrast grating reflectors,” Optics Express, vol. 18, no. 16, pp.16973-
16988, 2010.
Y. Yue, L. Zhang, J. Wang, Y. Xiao-Li, B. Shamee, V. Karagodsky, F. G. Sedgwick, W.
Hofmann, R. G. Beausoleil, C. J. Chang-Hasnain and A. E. Willner, “A ‘Linear’ High-
Contrast Gratings Hollow-Core Waveguide and Its System Level Performance,” presented at
the Optical Fiber Commun. Conf. (OFC), San Diego, CA, 2010, paper OTuI5.
Y. Yue, L. Zhang, F. G. Sedgwick, B. Shamee, W. Yang, J. Ferrara, C. Chase, R. G.
Beausoleil, C. J. Chang-Hasnain and A. E. Willner, “Chromatic Dispersion Variation and Its
Effect on High-Speed Data Signals due to Structural Parameter Changes in a High-Contrast-
Grating Waveguide,” presented at the IEEE Photonics Society Annual Meeting, Denver, CO,
2010, paper ThB2.
H. Huang, Y. Yue, L. Zhang, X. Wang, C. Chase, D. Parekh, F. Sedgwick, M. Tur, M. C.
Wu, C. J. Chang-Hasnain and A. Willner, “Analog Signal Performance of a Hollow-Core-
Waveguide using High-Contrast- Gratings,” presented at the Optical Fiber Commun. Conf.
(OFC), Los Angeles, CA, 2011, paper OThA3.
W. B. Bridges and J. H. Schaffner, “Distortion in linearized electrooptic modulators”, IEEE
Transations on Microwave Theory and Techniques, vol. 43, no.9, pp. 2184-2197, Sep. 1995.
Bala Pesala, Vadim Karagodsky and Connie Chang-Hasnain, “Ultra-Compact Low Loss
Photonic Components using High-Contrast Gratings,” presented in ICOP 2009-International
Conference on Optics and Photonics CSIO, Chandigarh, India, 2009.
C. H. Cox III, E. I. Ackerman, G. E. Betts and J. L. Prince, “Limits on the Performance of
RF-Over-Fiber Links and Their Impact on Device Design,” IEEE Transactions On
Microwave Theory And Techniques, vol. 54, no. 2, pp. 906-920, Feb. 2006.
G. Katz, S. Arnon, P. Goldgeier, Y. Hauptman and N. Atias, “Cellular over optical wireless
networks,” IEE Proceedings - Optoelectronics, vol. 153, no. 4, pp.195-198, Aug. 2006.

141

J. A. MacDonald, M. V. Kubak and A. Katz, “Wideband dynamic range improvement of
microwave photonic links,” presented in IEEE Conference, Avionics Fiber-Optics and
Photonics, Minneapolis, MN, September 20-22, 2005, pp.67-68, paper ThB3.
G. J. Meslener, “Chromatic Dispersion Induced Distortion of Modulated Monochromatic
Light Employing Direct Detection,” IEEE Journal of Quantum Electronics, vol. 20, no. 10,
pp. 1208-1216, Oct. 1984.
C. S. Oh and W. Gu, “Fiber Induced Distortions in a Subcarrier Multiplexed Lightwave
System,” IEEE Journal On Selected Areas In Communications, vol. 8, no. 7, pp. 1296-1303,
Sep. 1990.
Ganesh K . Gopalakrishnan, William K . Burns, and Catherine H. Bulmer, Microwave-
Optical Mixing in LiNbO3 Modulators, IEEE Transactions on Microwave Theory and
Techniques, vol. 41, No. 12, pp 2383-2391, Dec. 1993.
R. Pafchek, R. Tummidi, J. Li, M. A. Webster, E. Chen and T. L. Koch, “Low-loss silicon-
on-insulator shallow-ridge TE and TM waveguides formed using thermal oxidation,”
Applied Optics, vol. 48 no. 5, pp.958-963, 2009.
M. A. Webster, R. M. Pafchek, G. Sukumaran and T. L. Koch, "Low-loss quasi-planar ridge
waveguides formed on thin silicon- on-insulator", Applied Physics Letters, vol.87, no. 23,
2005.
Datong Chen, Harold R. Fetterman, Antao Chen, William H. Steier, Larry R. Dalton,
Wenshen Wang, and Yongqiang Shi, “Demonstration of 110 GHz electro-optic polymer
modulators,” Appl. Phys. Lett., vol.70, Issue 25, 3335 (1997)
R. Dinu, D. Jin, G. Yu, B. Chen, D. Huang, H. Chen, A. Barklund, E. Miller, C. Wei, and J.
Vemagiri, "Environmental Stress Testing of Electro-Optic Polymer Modulators," J.
Lightwave Technol. 27, 1527-1532 (2009).
R. H. Derksen, M. Moller, C. Schubert, "100-Gbit/s Full-ETDM Transmission
Technologies," IEEE Compound Semiconductor Integrated Circuit Symposium, 2007
(CSIC), pp. 89-92, Oct. 2007.
M. Camera, B. -E. Olsson, G. Bruno, "Beyond 100 Gbit/s: System implications towards
400G and 1T," Symposia S6 Towards 1000 Gb/s, 36th European Conference and Exhibition
on Optical Communication (ECOC), Sept. 2010.
J. Berthold, "Toward 100G networking and beyond," in Proceedings of 37th European
Conference and Exhibition on Optical Communication (ECOC), 2011, paper: Tu.3.K.1,
Sept. 2011.
P. Winzer, "Beyond 100G Ethernet," IEEE Communications Magazine, vol.48, no.7, pp.26-
30, July 2010.

142

D. Van den Borne, V. Sleiffer, M. S. Alfiad, S. L. Jansen, "Towards 400G and beyond: How
to design the next generation of ultra-high capacity transmission systems," 16th
Optoelectronics and Communications Conference (OECC), 2011, pp.429-432, July 2011.
G. Raybon, P. Winzer, and C. Doerr, "1-Tb/s (10×107 Gb/s) Electronically Multiplexed
Optical Signal Generation and WDM Transmission," J. Lightwave Technol. 25, 233-238
(2007).
S. Jansen, R. Derksen, C. Schubert, X. Zhou, M. Birk, C. Weiske, M. Bohn, D. van den
Borne, P. Krummrich, M. Moller, F. Horst, B. Offrein, H. de Waardt, G. Khoe, and A.
Kirstadter, "107-Gb/s Full-ETDM Transmission over Field Installed Fiber Using Vestigial
Sideband Modulation," in Optical Fiber Communication Conference and Exposition and The
National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical
Society of America, 2007), paper OWE3.
P. J. Winzer, G. Raybon, C. R. Doerr, M. Duelk, and C. Dorrer, "107-Gb/s Optical Signal
Generation Using Electronic Time-Division Multiplexing," J. Lightwave Technol. 24, 3107-
(2006)
A. Kanno, T. Sakamoto, A. Chiba, T. Kawanishi, M. Sudo, K. Higuma, J. Ichikawa, "95-
Gb/s NRZ-DPSK modulation with full-ETDM technique," 36th European Conference and
Exhibition on Optical Communication (ECOC), 2010, paper Mo.2.F.5, Sept. 2010.
J. Mallari, C. Wei, D. Jin, G. Yu, A. Barklund, E. Miller, P. O'Mathuna, R. Dinu, A.
Motafakker-Fard, and B. Jalali, "100Gbps EO Polymer Modulator Product and Its
Characterization Using a Real-Time Digitizer," in Optical Fiber Communication
Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OThU2.
M. Chacinski, et. al., “Monolithically Integrated 100 GHz DFB-TWEAM”, J. Lightwave
Technol. 27, 3410-3415 (2009).
A. Kanno, T. Sakamoto, A. Chiba, T. Kawanishi, K. Higuma, M. Sudou, and J. Ichikawa,
"166 Gb/s PDM-NRZ-DPSK Modulation Using Thin-LiNbO3-Substrate Modulator," in
Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of
America, 2010), paper JWA40.
A. Kanno T. Sakamoto A. Chiba M. Sudo K. Higuma J. Ichikawa T. Kawanishi, "90
Gbaud NRZ-DP-DQPSK Modulation with Full-ETDM Technique using High-Speed Optical
IQ Modulator", IEICE Transactions on Electronics Vol.E94-C No.7 pp.1179-1186.
S. R. Nuccio, R. Dinu, B. Shamee, D. Parekh, C. Chang-Hasnain, and A. Willner,
"Modulation and Chirp Characterization of a 100-GHz EO Polymer Mach-Zehnder
Modulator," in National Fiber Optic Engineers Conference, OSA Technical Digest (CD)
(Optical Society of America, 2011), paper JThA030.
H. Huang, J. Yang, Y. Yue, Y. Ren, S. R. Nuccio, R. Dinu, D. Parekh, C. J. Chang-Hasnain,
and A. Willner, "100-Gbit/s Amplitude and Phase Modulation Characterization of a Single-

143

Drive, Low-Vπ Polymer Mach-Zehnder Modulator," in Optical Fiber Communication
Conference, OSA Technical Digest (Optical Society of America, 2012), paper OW4F.5.
D. Jin, D. Huang, B. Chen, H. Chen, L. Zheng, A. Barklund, G. Yu, E. Miller, M. Moolayil,
B. Li, R. Dinu, “Low half-wave voltage modulators using nonlinear optical polymers,” Proc.
SPIE, Vol. 6653, September 2007.
S. K. Kim; H. Zhang; D.H. Chang; C. Zhang; C. Wang; W.H. Steier; H.R. Fetterman,
“Electrooptic polymer modulators with an inverted-rib waveguide structure,” Photonics
Technology Letters, IEEE, Vol. 15, Issue 2, 2003, Pages 218 – 220.
G. Yu, J. Mallari, H. Shen, E. Miller, C. Wei, V. Shofman, D. Jin, B. Chen, H. Chen, and R.
Dinu, "40GHz Zero Chirp Single-ended EO Polymer Modulators with Low Half-wave
Voltage," in CLEO:2011 - Laser Applications to Photonic Applications, OSA Technical
Digest (CD) (Optical Society of America, 2011), paper CTuN5.
W. Wang; Y. Shi; D. J. Olson, W. Lin; J. H. Bechtel, "Push-pull poled polymer Mach-
Zehnder modulators with a single microstrip line electrode," Photonics Technology Letters,
IEEE , vol.11, no.1, pp.51-53, Jan. 1999
A. Bogoni, P. Ghelfi, M. Scaffardi, L. Poti, "All-optical regeneration and demultiplexing for
160-gb/s transmission systems using a NOLM-based three-stage scheme," IEEE Journal of
Selected Topics in Quantum Electronics, vol.10, no.1, pp. 192- 196, Jan.-Feb. 2004
C. W. Chow; H. K. Tsang, "Polarization-independent DPSK demodulation using a
birefringent fiber loop," IEEE Photonics Technology Letters, vol.17, no.6, pp.1313-1315,
June 2005
A. H. Gnauck, P. J. Winzer, S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Peckham,
"Spectrally Efficient Long-Haul WDM Transmission Using 224-Gb/s Polarization-
Multiplexed 16-QAM," J. Lightwave Technol. 29, 373-377 (2011)
T. Omiya, K. Toyoda, M. Yoshida, and M. Nakazawa, "400 Gbit/s Frequency-Division-
Multiplexed and Polarization-Multiplexed 256 QAM-OFDM Transmission over 400 km
with a Spectral Efficiency of 14 bit/s/Hz," in Optical Fiber Communication Conference,
OSA Technical Digest (Optical Society of America, 2012), paper OM2A.7.
Nobuyuki Kataoka, Naoya Wada, Kyosuke Sone, Yasuhiko Aoki, Hideyuki Miyata, Hiroshi
Onaka, and Ken-ichi Kitayama, "Field Trial of Data-Granularity-Flexible Reconfigurable
OADM With Wavelength-Packet-Selective Switch," J. Lightwave Technol. 24, 88- (2006)
Ken Mishina, Satoru Kitagawa, and Akihiro Maruta, "All-optical modulation format
conversion from on-off-keying to multiple-level phase-shift-keying based on nonlinearity in
optical fiber," Opt. Express 15, 8444-8453 (2007)
X. Wu, J. Wang, H. Huang, and A. E. Willner, "Experimental Optical Multiplexing of Two
20-Gbit/s QPSK Data Channels from Different Wavelengths onto a Single 40-Gbit/s Star 16-
QAM using Fiber Nonlinearities," in CLEO:2011 - Laser Applications to Photonic

144

Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper
CThH4.
Guoxiu Huang, Yuji Miyoshi, Akihiro Maruta, Yuki Yoshida, and Ken-Ichi Kitayama, "All-
Optical OOK to 16-QAM Modulation Format Conversion Employing Nonlinear Optical
Loop Mirror," J. Lightwave Technol. 30, 1342-1350 (2012).
Guo-Wei Lu and Tetsuya Miyazaki, "Optical phase erasure based on FWM in HNLF
enabling format conversion from 320-Gb/s RZDQPSK to 160-Gb/s RZ-DPSK," Opt.
Express 17, 13346-13353 (2009)
Guo-Wei Lu, Ekawit Tipsuwannakul, Tetsuya Miyazaki, Carl Lundström, Magnus Karlsson,
and Peter A. Andrekson, "Format Conversion of Optical Multilevel Signals Using FWM-
Based Optical Phase Erasure," J. Lightwave Technol. 29, 2460-2466 (2011)
H. Huang, J. Yang, X. Wu, S. Khaleghi, M. Tur, C. Langrock, M. M. Fejer, and A. Willner,
"All-Optical Sub-Channel Data Erasing and Updating for a 16-QAM Signal using a Single
PPLN Waveguide," in CLEO: Science and Innovations, OSA Technical Digest (online)
(Optical Society of America, 2012), paper CM2B.3.
H. Tan, G. P. Banfi, and A. Tomaselli, “Optical frequency mixing through cascaded second-
order processes in β-barium borate,” Appl. Phys. Lett.,vol. 63, no. 18, pp. 2472–2474, Nov.
1993.

Abstract (if available)

Abstract As a fundamental property of light, orbital angular momentum (OAM) can be carried by helically phased laser beams. A light beam carrying OAM could have different azimuthal states. Each state is usually identified by an integer l indicating that phase twisting rate. Similar to any orthogonal mode groups, coaxially propagating OAM beams with different states are orthogonal due to the helical phase structure. The orthogonality of OAM beams allows the multiplexing/demultiplexing of multiple data channels in a single data link, in which each channel is identified by a different OAM state. OAM multiplexing shows potential to enhance the capacity and spectral efficiency of data transmission systems. ❧ In this dissertation, we briefly discussed the background of OAM, and the applications of OAM for optical communications. In the first three chapters, we focus on the system level demonstrations using OAM multiplexing, including a free-space data link with a capacity of 100.8 Tbit/s and an efficient OAM demultiplexing technique that can further reduce the crosstalk of adjacent OAM channels. One of the challenges of free space OAM communication is the atmospheric turbulence. In chapter 4 and 5, we demonstrated a method to measure the wavefront of OAM beams, and a potential approach to mitigate the channel crosstalk caused by atmospheric turbulence. An advanced communication system is not just point –to-point static data transmission, but also requires reconfigurability. Basic function elements in an OAM multiplexed system, including a reconfigurable add/drop multiplexer and tunable mode filter is demonstrated in chapter 6 and 7, respectively. Waveguides and modulators are critical for optical communications. We simulated the performance of a low-loss hollow-core waveguide for analog signal transmission, and characterized a 100-GHz EO polymer modulator using broadband data modulation. In the last section, we described a subsystem in which subchannels of a 16-QAM signal can be erased or updated optically.

Linked assets

University of Southern California Dissertations and Theses

Conceptually similar

PDF

Orbital angular momentum based spatially multiplexed optical and millimeter-wave communications

PDF

Using beams carrying orbital angular momentum for communications and remote sensing

PDF

High capacity optical and RF/mm-wave communications utilizing orbital angular momentum multiplexing

PDF

Applications of orbital angular momentum in high-capacity free-space optical communications

PDF

Optical communications, optical ranging, and optical signal processing using tunable and reconfigurable technologies

PDF

Optical and mm-wave orbital-angular-momentum beam generation and its applications in communications

PDF

Integrated silicon waveguides and specialty optical fibers for optical communications system applications

PDF

All-optical signal processing toward reconfigurable optical networks

PDF

Using spatial modes for data transmission through the air and through the air-water interface

PDF

High-capacity optical communications using structured light in random and disturbed media

PDF

Spatial modes for optical communications and spatiotemporal beams

PDF

Free-space optical communications and probing through turbulent links using structured light

PDF

High-speed and reconfigurable all-optical signal processing for phase and amplitude modulated signals

PDF

Reconfigurable high‐speed optical signal processing and high‐capacity optical transmitter

PDF

optical communication systems and space-time wave packet generation using frequency combs and spatial modes

PDF

Optical signal processing for enabling high-speed, highly spectrally efficient and high capacity optical systems

PDF

Reconfigurable optical signal processing for efficient spectrum utilization in high-speed optical communication systems

PDF

Reconfigurable high speed optical signal processing for optical communication and modulation format manipulation

PDF

Reconfigurable and flexible high-speed optical signal processing and spectrally shared optical subsystems

PDF

Advanced modulation, detection, and monitoring techniques for optical communication systems

Asset Metadata

Creator Huang, Hao (author)

Core Title Multiplexing techniques and reconfigurable networking functions for optical communications using orbital angular momentum beams

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 01/26/2017

Defense Date 11/06/2014

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag OAI-PMH Harvest,optical communications,vortex beam

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Willner, Alan E. (committee chair)

Creator Email haoh@usc.edu,hi.haoh@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-529422

Unique identifier UC11298541

Identifier etd-HuangHao-3136_rev.pdf (filename),usctheses-c3-529422 (legacy record id)

Legacy Identifier etd-HuangHao-3136_rev.pdf

Dmrecord 529422

Document Type Dissertation

Format application/pdf (imt)

Rights Huang, Hao

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA