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

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

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Content HIGH-SPEED AND RECONFIGURABLE ALL-OPTICAL SIGNAL PROCESSING FOR PHASE AND AMPLITUDE MODULATED SIGNALS by Salman Khaleghi A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulllment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (ELECTRICAL ENGINEERING) August 2013 Copyright 2013 Salman Khaleghi To my parents Sima Kheirabadi and Hassan Khaleghi And my family for their everlasting love, support and understanding. ii Acknowledgments Of all the sections of this dissertation, this is the most dicult but most pleasant one to write. As this document marks the end of a journey in engineering school, I hope that what I have learned from each of the people I thank here continues to stay close to my heart. I would like to acknowledge Prof. Alan E. Willner, who has been a great advisor and mentor; he is a professor whose wisdom and vision goes beyond the technical areas of science and engineering. I want to thank Prof. Willner for all he has taught me throughout my graduate studies, from the simplest lessons { perhaps the \orderly messy" expression { to the most scholarly and technical, and for his encouragement, inspiration, patience, and valuable hints and advice. I owe my now-much-broader understanding to his vision, wisdom, and research insight. I am sure I will benet from what he has taught me in the future, as I have thus far. I want to extend my appreciation to Prof. Andrea Armani, Prof. Alexander Sawchuk, and Prof. Joseph Touch for serving on my dissertation committee. I would also like to thank Prof. Keith Chugg and Prof. William Steier for their guidance during my qualifying examination. I wish to thank Prof. Joe Touch for his invaluable technical and non- technical guidance and support at the Information Sciences Institute (ISI). I would also like to thank Prof. Moshe Tur for his guidance and support during his visits to USC. It is with great pleasure that I also thank Prof. Jawad Salehi for his mentorship and support and for sharing his insight, which established the path for my Ph.D. in the eld of optical communications in the last year of my undergraduate education. I also wish iii to express my appreciation to Dr. Kambiz Jamshidi, who mentored me in starting along this path. I want to thank them both for their support and the inspiring lessons they taught me at that critical time of transitioning to graduate school. My warmest thanks go to the many members of the Optical Communications Lab (OCLab) at USC for all these years of insightful discussions and collaboration. I would like to thank Dr. Irfan Fazal and Dr. Jeng-Yuan Yang for sharing with me their invaluable insight into life and research at OCLab. I would also like to extend my appreciation to the then-senior members of the OCLab, Dr. Lin Zhang, Dr. Scott Nuccio, Prof. Jian Wang, and Dr. Omer Faruk Yilmaz, for their friendship as well as mentorship. I wish to thank other OCLab members, Dr. Louis Christen, Dr. Bo Zhang, Dr. Xiaoxia Wu, Bishara Shamee, Dr. Yang Yue, Hao Huang, Asher Voskoboinik, Yan Yan, Nisar Ahmed, Amanda Bozovich, Yongxiong Ren, Morteza Ziyadi, Wajih Daab, Amirhossein Mohajerin-Ariaei, Guodong Xie, Ahmed Almaiman, and Changjing Bao, for valuable discussions and their help. Thank you all! I enjoyed all the days and sleepless nights we spent in the lab and I wish you all the best in your careers. Speaking of OCLab members, I would like to particularly thank Mohammadreza Chitgarha, with whom I collaborated on most of the experiments in the lab over the past few years and who was also my \co-conspirator" in some adventures at USC. Many times at around 3:00 a.m. we shared the joy of obtaining some of our greatest results and \scientic discoveries" in the lab. I would like to thank him for valuable discussions of ideas, active collaboration, and what I have learned from him. It is also a great pleasure to extend my appreciation to Prof. Alexander Sawchuk, Dr. Iman Adibi, Dr. Safar Hatami, and my brother Sina for their help, support, and guidance when I needed it the most. I also want to thank the wonderful sta of the electrical engineering department at USC, Tim Boston, Diane Demetras, Anita Fung, and Gerrielyn Ramos, who have been a phenomenal help during my Ph.D. years. I would like to extend my greatest thanks to the USC Viterbi School of Engineering for the Dean's Fellowship Award toward my Ph.D. iv I want to thank all my friends, especially those in Los Angeles, who made this journey a great life experience. Finally, but very importantly, I want to thank my parents for their unconditional love and support during these years. As time goes by, I continue to better understand and appreciate their devotion and wisdom. I am thankful to my father, Prof. Hassan Khaleghi, who taught me and my siblings what it means to seek and do the right thing and to nd satisfaction in pursuing what makes an impact, and to my mother, Sima Kheirabadi, for her love, understanding, support, and dedication in raising us to become who we are. This dissertation is the fruit of their sacrices. I would also like to thank my siblings. Sina, being the older brother, was always a pioneer in his wonderful accom- plishments; most of what I have achieved so far would not have been possible without his continuous help, support, guidance, and inspiration. My thanks also go to Soroush and our dear sister Saba for their understanding, wisdom, and encouragement all these years. I would like to thank my sisters-in-law, Sanam and Sepideh, for their support and warmest generosity. I missed their weddings because of what will come in the rest of this dissertation! v Table of Contents Dedication ii Acknowledgments iii List of Tables ix List of Figures x Abstract xviii Chapter 1: Introduction 1 1.1 Basic Enabling Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Modulation Formats and Coherent Detection . . . . . . . . . . . . . . . . 6 1.3 Nonlinear Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3.1 Four Wave Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3.2 Three Wave Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3.2.1 cSFG-DFG . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.3.2.2 cSHG-DFG . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.3.3 SPM and XPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.4 Materials and Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Chapter 2: Overview of Basic Enabling Operations 18 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2 Wavelength Multicasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.3 Multiplexing and Demultiplexing . . . . . . . . . . . . . . . . . . . . . . . 21 2.3.1 Active Optical Multiplexing . . . . . . . . . . . . . . . . . . . . . . 21 2.3.2 Passive Optical Multiplexing . . . . . . . . . . . . . . . . . . . . . 24 2.4 Tunable Optical Delays . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Chapter 3: Recongurable Conversion/Dispersion-Based Optical Tapped-Delay- Lines 28 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.2 Concept and Principle: All-Optical Tapped-Delay-Line . . . . . . . . . . . 30 vi 3.2.1 Optical Multicasting (Fan-out) . . . . . . . . . . . . . . . . . . . . 34 3.2.2 Phase Tuning and Optical Delays . . . . . . . . . . . . . . . . . . . 34 3.2.3 Optical Multiplexing . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.3 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.3.1 Complex-Coecient TDL using Optical Multiplexing . . . . . . . . 39 3.3.2 Bipolar-Coecient TDL using Electrical Multiplexing . . . . . . . 42 3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Chapter 4: Characterization of the Optical-Tapped-Delay Line 44 4.1 Characterization of Phase Tuning using Fine Wavelength Oset . . . . . . 44 4.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.1.2 Concept and Theoretical Analysis . . . . . . . . . . . . . . . . . . 46 4.1.3 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.1.4 Experimental Results and Discussion . . . . . . . . . . . . . . . . . 50 4.2 Finite Impulse Response Filter Characterization . . . . . . . . . . . . . . 54 4.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.2.2 Theoretical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.2.3 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.2.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Chapter 5: Applications of the Recongurable Optical Tapped-Delay-Line 63 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 5.2 Correlation and Pattern Recognition . . . . . . . . . . . . . . . . . . . . . 63 5.2.1 Correlation using Optical Multiplexing . . . . . . . . . . . . . . . . 64 5.2.2 Correlation using Electrical Multiplexing . . . . . . . . . . . . . . 69 5.3 Equalization of Chromatic Dispersion . . . . . . . . . . . . . . . . . . . . 69 5.3.1 Optical TDL Equalizer with Optical Multiplexing . . . . . . . . . 69 5.3.2 Optical TDL Equalizer with Electrical Multiplexing . . . . . . . . 72 5.4 Optical Discrete Fourier Transform . . . . . . . . . . . . . . . . . . . . . . 74 5.4.1 All-Optical OFDM Generation and Demodulation . . . . . . . . . 74 5.4.2 Adjustable Bit-Rate Optical DFT . . . . . . . . . . . . . . . . . . 75 5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Chapter 6: Recongurable Optical QAM Converter/Encoder 78 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 6.2 Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 6.3 Formulation and Experimental Setup . . . . . . . . . . . . . . . . . . . . . 81 6.4 Experimental Results and Discussion . . . . . . . . . . . . . . . . . . . . . 84 6.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Chapter 7: Tunable WDM Optical Tapped-Delay-Line for Simultaneous and Inde- pendent Data Processing 88 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 7.2 Concept of WDM Tapped-Delay-Line and Theory . . . . . . . . . . . . . 90 vii 7.3 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 7.4 Experimental Results and Discussion . . . . . . . . . . . . . . . . . . . . . 95 7.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Chapter 8: System Design Guidelines When Utilizing Chirp-Inducing Wavelength Converters in a Fiber Transmission System 100 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 8.2 Frequency Chirp in Wavelength Converters . . . . . . . . . . . . . . . . . 102 8.3 Modeling and Simulation using Arbitrary Chirp Prole . . . . . . . . . . . 106 8.4 Analysis of Chirp Penalties . . . . . . . . . . . . . . . . . . . . . . . . . . 108 8.4.1 Average Normalized Chirp Parameters . . . . . . . . . . . . . . . . 109 8.4.2 Interaction of Chirp, Dispersion and SPM . . . . . . . . . . . . . . 109 8.5 Simulation Results and Discussion . . . . . . . . . . . . . . . . . . . . . . 111 8.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Chapter 9: Conclusions 116 Bibliography 121 viii List of Tables Table 4.1 Optical FIR capability to accommodate dierent baud rates using tunable delays. DL = 15.6 ps/nm . . . . . . . . . . . . . . . . 60 Table 8.1 Interaction of chirp, ber dispersion and self phase modulation . 112 ix List of Figures Figure 1.1 Recent advances and enabling technologies for optical signal pro- cessing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Figure 1.2 (a) Example of optically-assisted processing: optical correlators could help to recognize packet headers and reduce the look-up time for network routing applications [47]. (b) Example of pattern search in large data: optical correlators can recognize patterns at Tbit/s speeds to identify regions of interest and leave the accurate processing to electronics that run at Gbit/s speeds. . . . . . . . . 3 Figure 1.3 Nonlinearities and optical wave parameters used for data encod- ing and signal processing. . . . . . . . . . . . . . . . . . . . . . . 4 Figure 1.4 Advanced modulation formats using amplitude and phase domains, with independent polarization and wavelength multiplexing. . . . 6 Figure 1.5 Third-order (3) nonlinear processes: (a) degenerate and (b) non- degenerate four wave mixing (FWM) schemes for generation of (phase conjugate) signal copy. ZDW: zero dispersion wavelength. 10 Figure 1.6 Cascaded second-order (2) nonlinear processes: (a) cascaded sum and dierence frequency generations (cSFG-DFG) and (b) second harmonic generation and DFG (cSHF-DFG) for wave- length conversion in a PPLN device. QPM: quasi-phase matching. 12 Figure 1.7 Nonlinear phase shift results in (i) self phase modulation (SPM), that causes spectral broadening, and (ii) cross phase modulation (XPM), that creates cross-talk on a certain channel from the other channels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Figure 1.8 Having multiple mixing terms may be desirable (e.g., simultane- ous generation of mixing terms) or unwanted (e.g., when it would waste part of the spectrum and create cross-talk on desired signals). 16 x Figure 2.1 Various nonlinear schemes for optical multicasting: (a) degen- erate FWM, requiring N probe pumps for N-fold multicasting [9], (b) multi-pump FWM, requiring (N + 1)=2 pumps forN-fold multicasting [14], and (c) supercontinuum generation followed by periodic ltering, requiring a short-pulse pump source [106]. . . . 19 Figure 2.2 Concept of active optical multiplexing and demultiplexing using nonlinearities: WDM channels that utilize short-duration data pulses are time aligned such that their data pulses minimally overlap, and optically multiplexed to one wavelength channel in a nonlinear element. For demultiplexing, a sampling pump source is time-aligned and multiplied by the signal in a nonlinear device. 22 Figure 2.3 Nonlinear optical loop mirror (NOLM): (a) Principle of opera- tion of the NOLM (signal B is split and sent into two direc- tions, one with low nonlinearities and one with high nonlineari- ties, the two are then added to create interference.) (b) Equiv- alent logic/application function of the NOLM. (c) Multiplexing of sixteen 40 Gbit/s OOK WDM signals to a 640-Gbit/s wave- length channel, and demultiplexing of the 640-Gbit/s OOK signal to its 10-Gbit/s tributaries, using the NOLM [110]. HNLF: highly nonlinear ber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Figure 2.4 Nonlinear optical demultiplexing of 640-to-10-Gbit/s in a chalco- genide waveguide: device structure, experimental spectrum and eye diagram [41]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Figure 2.5 Concept of passive optical multiplexing to achieve 5.12 Tbit/s data speed on a single wavelength channel (1.28 Tbaud polarization- multiplexed DQPSK signal) [46]. . . . . . . . . . . . . . . . . . . 25 Figure 2.6 Continuously tunable parametric optical delay using the conversion- dispersion technique: (a) concept, (b) 22 ns delay for 43-Gbit/s OOK signal with 2.5 ps pulses [68], (c) 7.3 s delay using dis- cretely time-oset continuous delay units [31]. . . . . . . . . . . . 25 Figure 3.1 Generic block diagram of a tapped-delay-line (TDL): input signal is tapped at dierent time intervals, taps (copies) are weighted each by its own coecient and then summed to produce the output. 31 xi Figure 3.2 Optical implementation of a TDL based on nonlinearities and conversion-dispersion-based delays: N copies of the input optical signal are generated at dierent frequencies using cascaded non- linear wave mixings of SFG followed by DFG. The amplitude of each signal copy depends on its CW laser pump power. Copies are sent into a chromatic dispersive medium to introduce the tap delays. Delayed and weighted signal copies are sent to a second nonlinear medium to be multiplexed and create the output signal. !: frequency separation between signal copies, 2 : group veloc- ity dispersion parameter, L: length of the dispersive medium, PPLN: periodically poled lithium niobate. . . . . . . . . . . . . . 32 Figure 3.3 Time and spectral domain diagram of the signals in various stages, as the signals propagate through the optical TDL. . . . . . . . . . 33 Figure 3.4 Mathematical vector representation of TDL operation. In each tap the delayed input is multiplied by a complex coecient which could rotate and scale it. The output y(t) is a vector summation of the weighted taps. . . . . . . . . . . . . . . . . . . . . . . . . . 35 Figure 3.5 Measured spectrum of the output of the fan-out stage (PPLN-1) with four taps, in which the signal is constant (CW pump laser). Schematic LCoS lter responses, showing tap-phase tuning. Out- put spectra of the multiplexing stage (PPLN-2) when phases of the tap coecients result in destructive (right top) and construc- tive (right bottom) addition of taps. . . . . . . . . . . . . . . . . 35 Figure 3.6 Experimental set-up for an optical TDL for equalization and cor- relation. (a) Multicasting and delay, (b) optical multiplexing, and (c) electrical multiplexing. Spectra of the rst and the sec- ond PPLN waveguide outputs are shown for a 3-tap optical TDL with various tap amplitudes. PPLN: Periodically poled lithium niobate waveguide, LCoS: liquid crystal on silicon, PC: polariza- tion controller, BPF: bandpass lter, ATT: attenuator, DLI: delay line interferometer, BERT: bit error rate tester, BPD: balanced photodiode, MZM: Mach-Zehnder modulator. . . . . . . . . . . . 40 Figure 4.1 The principle of operation of the complex-coecient optical tapped- delay-line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Figure 4.2 (a) Experimental setup for the tunable optical TDL using optical multicasting, conversion/dispersion delays, and optical multiplex- ing. (b) Output spectra of PPLN #1 and PPLN #2. . . . . . . . 50 xii Figure 4.3 (a) Constructive or destructive interference could create a peak or null at the output, used for phase characterization. (b) Inter- ference fringes caused by ne detuing of pump frequencies for dierent amounts of dispersion. . . . . . . . . . . . . . . . . . . . 51 Figure 4.4 (a) Measured phase induced by frequency ne-tuning for various tap to QPM wavelength distances. (b) Fine-tuning of tap located at 4.1 nm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Figure 4.5 (a) Required frequency detuning for 2 phase shift on a tap versus tap-to-QPM wavelength distance for various DCF lengths. (b) Spectrum showing tap delay variation. . . . . . . . . . . . . . . . 53 Figure 4.6 Theoretical relative delay error versus phase applied by ne-tuning of pump wavelengths for D = 34 ps/nm disperison at dierent delays (wavelength separation). . . . . . . . . . . . . . . . . . . . 53 Figure 4.7 Input 31-Gbaud QPSK signal constellation diagram, and the out- put of a 2-tap correlator with tap coecients [1 1] and [1 -1]. . . 54 Figure 4.8 Conceptual block diagram of the tunable complex-coecient opti- cal FIR lter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Figure 4.9 (a) Experimental setup: multicaster, delay, phase control, and multiplexer. (b) A generic LCoS lter amplitude/phase prole for applying phases on the pumps. . . . . . . . . . . . . . . . . . 59 Figure 4.10 Wave mixing spectra for (a) fan-out stage, and (b) multiplexing stage. (c), (d) Experimental and theoretical amplitude/phase response of26.7-GHz FSR length-3 FIR lters. . . . . . . . . . 61 Figure 4.11 Wave mixing spectra for (a) fan-out stage, and (b) multiplexing stage. (c), (d) Experimental and theoretical amplitude/phase response of 40-GHz FSR length-4 FIR lters. . . . . . . . . . . . 62 Figure 5.1 Concept of a TDL-based correlator. (a) TDL coecients are determined by the search pattern. Input data stream slides through the TDL resulting in high correlation peak when full pattern matching occurs. (b) Complex coecient taps allow for vector addition of adjacent symbols to create correlation peaks, enabling correlation on phase-shift-keyed signals. . . . . . . . . . . . . . . 64 Figure 5.2 All-optical TDL correlation results for (a) 40-Gbit/s OOK, (b) 40-Gbit/s BPSK, (c) 80-Gbit/s QPSK signals, and (d) 27-Gbit/s BPSK signal. (e) Coherent detection of 20 Gbaud BPSK and QPSK correlator output. . . . . . . . . . . . . . . . . . . . . . . . 65 xiii Figure 5.3 All-optical Correlation, BER performances: 4-bit BPSK pattern correlation, and 2-bit correlation (patterns \ 0" and \ ") resulting in dierential demodulation of BPSK signal with the optical TDL, and comparison to conventional DLI DPSK demod- ulator performance. AMI: alternate-mark-inversion, DB: duobi- nary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 Figure 5.4 Experimental results for the tunable correlator with electrical multiplexing. Nonlinear fan-out (multicasting) spectrum, cor- relator output eye diagram, correlator's output waveform, and electrically thresholded output waveform for (a) 40-Gbit/s OOK pattern \1111", (b) 40-Gbit/s OOK pattern \1x1x1", and (c) 30-Gbit/s OOK pattern \1111". \x" denotes a \don't care" bit. . 68 Figure 5.5 Experimental spectra for dierent conditions of operation for the all-optical TDL equalizer, showing tunability to dierent bit rates and modulation formats. . . . . . . . . . . . . . . . . . . . . . . . 70 Figure 5.6 (a) Measured power penalty at 10 9 BER versus chromatic dis- persion applied on the input signal for equalization, demonstrat- ing TDL reconguration to accommodate dierent bit-rates and modulation formats. (b) Eye diagrams after direct detection in balanced photodiodes before and after equalization for 3- and 4- tap equalizers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Figure 5.7 (a) BER measurements on dispersed 80-Gbit/s RZ-DQPSK sig- nals before and after equalization using the all-optical TDL. (b) Eye diagrams of dispersed signal before and after equalization for 80-Gbit/s RZ-DQPSK signal. . . . . . . . . . . . . . . . . . . . . 72 Figure 5.8 TDL equalizer with electrical multiplexing. Multicasting spec- tra (top) for two equalizers with uniform and non-uniform tap- spacing, along with plots of measured tap coecients versus tap delays (bottom). Equalizers #1 and #2 are used to compensate 0 to 40 ps/nm and 50 to 90 ps/nm chromatic dispersion, respectively. 73 Figure 5.9 (a) BER measurements of the dispersed back-to-back signal and after TDL equalization with electrical multiplexing. (b) OSNR penalty at 10 3 BER and corresponding eye diagrams for the equalized and dispersed signals. . . . . . . . . . . . . . . . . . . . 74 Figure 5.10 Concept of optical orthogonal frequency modulation (OFDM) transmitter and receiver. . . . . . . . . . . . . . . . . . . . . . . . 75 xiv Figure 5.11 Tunable optical OFDM demodulation using optical DFT enabled by the optical tapped-delay-line: (a) concept, and (b) multicast- ing and multiplexing spectra and output eye diagrams of all four subcarriers in a four 40-Gbaud QPSK subcarrier OFDM signal [26]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Figure 6.1 Conceptual block diagram of an optical QAM format converter using nonlinear signal processing. . . . . . . . . . . . . . . . . . . 80 Figure 6.2 Experimental setup and schematic wave-mixing spectra. PC: Polarization Controller, BPF: Bandpass Filter, ATT: Attenua- tor, LO: Local Oscillator. . . . . . . . . . . . . . . . . . . . . . . . 82 Figure 6.3 (a) Spectra of the 1st and the 2nd PLLN waveguides outputs for 31 Gbaud input signal with half rate sampling pump. (b) Output constellations. (c) Spectra for 20 Gbaud signals, and (d) output constellations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Figure 6.4 (a) Output spectra of nonlinear stages for QPSK to 64-QAM conversion. Constellation diagrams showing dierent encodings for (b) 31-Gbaud and (c) 20-Gbaud signals. . . . . . . . . . . . . 85 Figure 6.5 BER measurements versus OSNR for experiments with (a) a sam- pling pump, and (b) with a CW pump. . . . . . . . . . . . . . . . 86 Figure 7.1 Concept of independent processing of WDM channels in a WDM optical tapped-dely-line (e.g., format conversion on channel A, equalization on channel B, and correlation on channel C. . . . . . 90 Figure 7.2 Implementation of a 2-tap OTDL as the building block of the WDM-OTDL: (a) Block diagram, and (b) equivalent system func- tion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Figure 7.3 The principle of operation of the WDM-OTDL: (i) Taps are cre- ated by simultaneous wavelength conversion of all WDM channels in nonlinear elements. (ii) Tap delays are induced after a dis- persive element, because the original signals and the wavelength converted taps are at dierent wavelength. (iii) Tap coecients are applied by an inline liquid crystal on silicon (LCoS) lter). (iv) Owing to pump reusing, weighted taps add coherently. (iv) Number of taps is the number of nonlinear wavelength converting stages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 Figure 7.4 Experimental setup for two experiments: (i) 4-channel WDM- OTDL using an HNLF as the wavelength conversion medium, and (ii) 8-channel operation using a PPLN waveguide instead of the HNLF. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 xv Figure 7.5 Four 26-Gbaud BPSK/QPSK WDM channels using an HNLF as the rst nonlinear stage and a PPLN as the second: (a) Optical spectra after the HNLF and the PPLN device, showing rst and second set of taps, respectively. (b) Input and output constel- lation diagrams for various modulation formats and independent functions on the channels. (c) OSNR penalty of each tap (con- version) and format conversion for BPSK to QPSK and QPSK to 16-QAM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 Figure 7.6 Sensitivity of the system to phase and power variations for QPSK to 16-QAM conversion on channel 4. . . . . . . . . . . . . . . . . 97 Figure 7.7 Eight 20 Gbaud QPSK WDM channels using a PPLN waveguide in the rst stage: (a) Spectra after the rst and the second nonlin- ear stages. (b) A 2-tap equalizer for a signal that is distorted by 200 ps/nm chromatic dispersion. (c) Simultaneous 2-symbol pat- tern search on the eight WDM channels, resulting in a throughput of 416 Gbit/s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Figure 8.1 (a) Experimental Setup for SOA-MZI wavelength converter for RZ-OOK signals. (b) Principle of operation of the SOA-MZI wavelength converter based on dierential cross phase modulation [67] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 Figure 8.2 Generation of various frequency chirp proles, especially at the edges of the signal, depending on the wavelength converter design. 105 Figure 8.3 Concept of arbitrary chirp waveform generator simulations to pro- vide input for device optimization to achieve improved system performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Figure 8.4 Simulation technique, various chirp proles used for simulation and sample experimental chirp waveforms measurements. . . . . . 106 Figure 8.5 Concept of normalized chirp, dened as the chirp prole times the intensity prole. . . . . . . . . . . . . . . . . . . . . . . . . . . 108 Figure 8.6 Mapping of average normalized chirp on leading and trailing edges on a scatter diagram (chirp diagram). . . . . . . . . . . . . . . . . 110 Figure 8.7 Power penalty on the chirp diagram for (a-c) low nonlinearity ber transmission (80 km SMF with13 dBm input power) and (d-f) high nonlinearity ber transmission (25 80 km SMF with 3 dBm input power) . . . . . . . . . . . . . . . . . . . . . . . . 113 xvi Figure 8.8 (a) Various chirp peak locations, (b) low nonlinearities regime: power penalty versus residual dispersion, (c) high nonlinearities regime: power penalty versus residual dispersion . . . . . . . . . . 114 Figure 8.9 (a) Various chirp proles, (b) low nonlinearities regime: power penalty versus residual dispersion, (c) high nonlinearities regime: power penalty versus residual dispersion . . . . . . . . . . . . . . 114 xvii Abstract Technology has empowered people in all walks of life to generate, store, and communicate enormous amounts of data. Recent technological advances in high-speed backbone data networks, together with the growing trend toward bandwidth-demanding applications such as data and video sharing, cloud computing, and data collection systems, have created a need for higher capacities in signal transmission and signal processing. Optical communication systems have long beneted from the large bandwidth of optical signals (beyond tera-hertz) to transmit information. Through the use of optical signal processing techniques, this Ph.D. dissertation explores the potential of very-high- speed optics to assist electronics in processing huge amounts of data at high speeds. Optical signal processing brings together various elds of optics and signal processing { nonlinear devices and processes, analog and digital signals, and advanced data mod- ulation formats { to achieve high-speed signal processing functions that can potentially operate at the line rate of ber optic communications. Information can be encoded in amplitude, phase, wavelength, polarization, and spatial features of an optical wave to achieve high-capacity transmission. Many advances in the key enabling technologies have led to recent research in optical signal processing for digital signals that are encoded in one or more of these dimensions. Optical Kerr nonlinearities have femto-second response times that have been exploited for fast processing of optical signals. Various optical non- linearities and chromatic dispersions have enabled key sub-system applications such as wavelength conversion, multicasting, multiplexing, demultiplexing, and tunable optical delays. xviii In this Ph.D. dissertation, we employ these recent advances in the enabling technolo- gies for high-speed optical signal processing to demonstrate various techniques that can process phase- and amplitude-encoded optical signals at the line rate of optics. We use nonlinear media, such as highly nonlinear ber, periodically poled lithium niobate, and semiconductor optical ampliers, for nonlinear mixing of optical signals. We propose and experimentally demonstrate a novel, fully tunable optical tapped-delay-line that is a key building block for signal processing functions. Applications such as nite impulse response ltering, equalization, correlation (pattern recognition), discrete Fourier trans- form, digital-to-analog conversion, and exible optical signal conversion and generation are shown. The phase- and amplitude-preserving nature of the demonstrated techniques, together with their wide-tuning range, allows for processing of optical signals that carry dierent modulation formats with dierent data rates. The recongurability may apply to future optical networks that carry heterogeneous trac with dierent modulation formats and baud rates. xix Chapter 1 Introduction Technology has enabled people in all walks of life to generate, store and communicate enormous amounts of data. Recent technological advances in high-speed backbone data networks, together with the growing trend of bandwidth-demanding applications such as data and video sharing, cloud computing, and data collection systems, have created a need for higher capacities in signal transmission and signal processing. For instance, on YouTube alone, in every minute, over 10 years of video is being watched and over 72 hours new content is being uploaded [127], with about 25% of the trac coming from mobile devices. This trac is expected to increase, because higher-capacity network infrastructures provide a platform that motivates the development of new applications and vice versa. Owing to their relatively large bandwidth, optical interconnects and communications have been considered as a potential solution to help electronics deliver high data capacities [102]. It is well-known that a lens does a Fourier transform [10]; however, lenses have not been used inside computers to perform digital signal processing because either the input or output should be in the optical domain to begin with and it is may be dicult to justify converting the signal from the electronics to optics and back to electronics for performing a Fourier transform. Nonetheless, optical signal processing has recently been revisited due to recent advances in ve dierent areas of optical communications technologies that directly impact optical signal processing. These enabling technologies 1 Coherent detection for high-speed systems Photonic integrated circuits (PIC) Access to four optical domains (amplitude, phase, polarization, wavelength) Advances in materials and devices (more efficient nonlinearities) High-speed electronics (advanced DSP) Recent Enabling Technologies Motivating Optical Signal Processing Figure 1.1: Recent advances and enabling technologies for optical signal processing. could make a compelling argument for why certain functions could be executed optically, as noted in Figure 1.1. Advanced optical modulation techniques and coherent detection together with the use of high-speed electronics (digital signal processing) can encode and access information on the four optical domains of amplitude, phase, polarization and wavelength per a spatial mode. Importantly, advances in materials and devices which have resulted in devices with higher nonlinearities and higher eciencies, and photonic integrated circuits (PICs) technologies, are the key for any practical utilization of optical signal processing in the future [71]. Another simple application can be an optical tapped-delay-line which is the funda- mental building block for optical signal processing and will be discussed in details in this tutorial . On the other hand, electronic signal processing may better suit the applications that require massive memories with random access. A key motivation for using optical signal processing is that optical techniques do not need to \touch" or switch every individual \bit", as electronic transistors do. Optical ampliers, for instance, can amplify Tbit/s signals without touching the signal at the bit level. Another example is basic wavelength conversion using a laser pump and a nonlinear device, where the data information can be transferred from one carrier wavelength to another at a very fast speed (nonlinearities have femtosecond response times) as optical signals y through the device [7]. As another popular example, a mirror based on micro- electro-mechanical systems (MEMS) technology can be tilted to reroute trac from one 2 Optically-Assisted Network Routing Optical Pattern Localization/ Recognition Electronic Pattern Recognition User Interface Tbit/s Large Data Gbit/s Mbit/s Rejects 99.9% Rejects 99.9% (a) Pattern Search in Large Data (b) Figure 1.2: (a) Example of optically-assisted processing: optical correlators could help to recognize packet headers and reduce the look-up time for network routing applications [47]. (b) Example of pattern search in large data: optical correlators can recognize patterns at Tbit/s speeds to identify regions of interest and leave the accurate processing to electronics that run at Gbit/s speeds. output port to another without processing it at the bit-level [44][32]. In the case of an optical correlator for searching for a data pattern in an incoming optical signal, the correlator can add optical bits to create a large peak and an electronic thresholder can be used at a much slower speed to signal whenever an optical matching peak occurs [75][47]. Another simple application can be an optical tapped-delay-line which is the fundamental building block for optical signal processing and will be discussed in detail in this tutorial [33][64]. On the other hand, electronic signal processing may better suit applications that require massive amounts of memory with random access. 3 Polarizations Amplitude Phase Frequency Four Wave Mixing (FWM) Nonlinear Signal Processing Various dimensions to encode, process and manipulate information on an optical signal 3 rd Order Susceptibility, χ (3) Three Wave Mixing: Sum and Difference Frequency Generation (SFG and DFG) 2 nd Order Susceptibility, χ (2) Self Phase Modulation (SPM) Cross Phase Modulation (XPM) Figure 1.3: Nonlinearities and optical wave parameters used for data encoding and signal processing. Alternatively, another application can be \optically assisted" signal processing, as opposed to pure electrical or optical signal processing. Optically assisted signal process- ing can use optics for what it does well and electronics for what it does best. Optics can perform few functions very fast and electronics is best for doing accurate complex computations with buers and memory. Figure 1.2(a), for example, depicts the concept of an optically assisted network routing technique using optical correlation on headers of Internet data packets [47]. Currently, most Internet trac is destined to a few popular websites. The calculation in [6] shows that utilizing optical correlators only to help iden- tify packets headed toward these popular destinations could assist in routing the packets and reducing latency because only a fraction of trac is left to be fully processed elec- tronically. In a similar manner, optically assisted signal processing can be used to search for a target pattern in large amounts of data, as shown in Figure 1.2(b). The massive data information can be encoded on an optical carrier at Tbit/s speed to be sent into an optical correlator for pattern recognition. The optical correlator can then identify regions of interest where a match may occur, which may be once every thousand bits. Therefore, the output can be at Gbit/s speeds, which can then be searched and processed electronically with high accuracy before being made available to the user. 4 Optical signal processing exploits various physical phenomena and devices. First are the nonlinear optical processes that comprise a substantial portion of optical signal processing. The femtosecond response time of nonlinearities in optical materials can be used to process and manipulate data signals. Third-order susceptibility (3) could give rise to nonlinear Kerr-eects such as four wave mixing (FWM), self phase modulation (SPM), and cross phase modulation (XPM) (Figure 1.3). Second-order susceptibility (2) results in three wave mixing in the form of sum frequency generation (SFG), dier- ence frequency generation (DFG) and second harmonic generation (SHG), and devices can be designed to produce cascading of such mixings in the same nonlinear element [115][1][69]. Second, various optical materials and devices have been utilized for optical signal processing, including highly nonlinear bers (HNLFs) [88], semiconductor opti- cal ampliers (SOAs) [70], silicon waveguides [39][71], chalcogenide waveguides [41][84], periodically poled lithium niobate (PPLN) waveguides [69], and photonic crystals [66]. Third, in order to encode and manipulate information, optics can exploit the four dimen- sions of amplitude, phase, wavelength and polarization, which dierentiates optical pro- cessing from electronic processing. Fourth are the functions that can be performed with these nonlinear devices, including wavelength conversion, optical multiplexing and demultiplexing, multicasting, equalization, correlation, fast/discrete Fourier transform (FFT/DFT), digital-to-analog (D/A) and analog-to-digital (A/D) conversions, regener- ation, optical logic gates (AND, OR, XOR, etc.), all-optical tunable delays, and more. In comparing optics and electronics for signal processing, one should consider the advantages of both and consider the potential uses of each. One can avoid optical-to- electrical-to-optical (OEO) conversion and perform processing at the very high-speed line rate of optics, if the signals are already in the optical domain. Due to the spectral eciency of optical signals, in one symbol time, one can optically process many bits of information. Electronics, on the other hand, is a very mature technology with easy memory access and massive integration capabilities for accurate signal processing. 5 X-polarization Y-polarization Re Im Im Re Channel 2 Re Im Im Re Channel 1 Wavelength ( λ) Figure 1.4: Advanced modulation formats using amplitude and phase domains, with independent polarization and wavelength multiplexing. Although both digital and analog optical signals can be processed all-optically, this tutorial will focus on optical signal processing of digital data modulated on optical waves. In Section 1.1, we will discuss the main technologies that can enable high-capacity optical signal processing from a systems perspective. 1.1 Basic Enabling Technologies In this section, we overview some of the basic enabling technologies that make possible the all-optical processing of digital signals. We rst discuss advanced modulation formats that allow for encoding multiple information bits onto one symbol time. We continue this section by reviewing some ultra-fast nonlinear processes that are widely utilized in optical signal processing applications. Finally, we provide an overarching summary of some optical materials and devices commonly used for optical signal processing from a systems point of view. 1.2 Modulation Formats and Coherent Detection Information bits can be imprinted on the amplitude and/or phase of an optical wave [108][36]. Coherent homodyne detection can be used to recover the amplitude and phase, which can then be used to decode the information bits. In general, n bits of information 6 can form M = 2 n states. Each of these M states can be mapped to an amplitude and phase symbol in the complex plane, as depicted in Figure 1.4. Furthermore, wavelength division multiplexing (WDM) and polarization multiplexing (PM) (X and Y polariza- tions) can also be utilized to multiplex signals into other dimensions of an optical wave and increase the spectral eciency (i.e., the number of transmitted bits per second per one Hz of bandwidth). As shown in the signal constellation diagrams in Figure 1.4, one can choose dierent symbols with distinct amplitudes, distinct phases, or a combi- nation of dierent amplitudes and phases. These three cases result in amplitude shift keying (ASK), phase shift keying (PSK) and quadrate amplitude modulation (QAM), respectively. On channel 2 in Figure 1.4, for instance, a 16-QAM signal is encoded on the X-polarization of the optical wave and an 8-PSK signal is encoded independently on the Y-polarization. Because these symbols are in the complex domain, instead of using amplitude and phase, one can alternatively dene a symbol using real (Re) and imaginary (Im) parts of the symbol. In communications theory, the former is known as the in-phase (I) and the latter as the quadrature (Q) component of the data symbol. Traditionally, optical communication systems that use direct detection can distin- guish between dierent levels of amplitude (intensity) but not phase. Thus, on-o- keyed (OOK) optical signals (x i 2 f0; 1g) can easily be received with direct detec- tion, but PSK signals need to be dierentially encoded to be received via direct detection. Signals carrying dierential modulation formats such as dierential binary- phase-shift-keying (DPSK) (x i 2f1; +1g) and dierential quadrate-phase-shift-keying (DQPSK) (x i 2fe j=4 ; e j3=4 ; e j5=4 ; e j7=4 g) need to be sent to an optical delay-line- interferometer (DLI) with one symbol time delay between its two arms to convert distinct phase levels of the input signal to distinct amplitude levels that can be detected directly in a photodiode. Whether amplitude or phase of the optical carrier are varied to write data bits onto the optical wave, during a symbol time, the shape of the amplitude can be at (non-return-to-zero, NRZ) or pulse-like (i.e., return-to-zero, RZ), resulting in NRZ- and RZ-D(Q)PSK signals as well as NRZ- and RZ-OOK signals [108]. 7 With recent advances in high-speed A/D converters, optical coherent detection has received increasing interest. Optical coherent receivers can recover the amplitude and phase of a polarization multiplexed signal with the aid of a local oscillator (LO) that can be a continuous-wave (CW) laser [52]. In an optical coherent receiver, the input data signal with electric eld amplitude E S (t) is split and combined with the LO with electric eld E LO and 90 -phase-shifted copies of it, and is then sent into two balanced photodiodes (BPDs). The BPDs are bandwidth-limited square-law devices and thus give a radio frequency (RF) current proportional to i I /jE S (t) +E LO j 2 jE S (t)E LO j 2 ; (1.1) i Q /jE S (t)jE LO j 2 jE S (t) +jE LO j 2 : (1.2) Thus, the output currents are i I /jE LO jjE S (t)j (1.3) cos((! S ! LO )t + (\E S (t)\E LO )); i Q /jE LO jjE S (t)j (1.4) cos((! S ! LO )t + (\E S (t)\E LO ) 2 ): In the BPDs, the signal and LO powers cancel out such that the output currents only contain the beating term between the signal and the LO. The beating in BPDs also generates a term at twice the carrier frequency of the optical signal, which falls far outside the RF bandwidth of the photodiodes. In a simplied model of the coherent receivers, if the signal and the LO are fully phase and frequency synchronized (i.e., 8 ! S =! LO and\E LO = 0), then the alternate-current (AC) part of the two PD currents are proportional to i I;AC /jE S (t)j cos(\E S (t)); (1.5) i Q;AC /jE S (t)j sin(\E S (t)): (1.6) Therefore, the data signal has been shifted from the optical carrier frequency to the base-band where the information in the I and Q components can be recovered electroni- cally. Two high-speed A/D converters can sample these currents to fully recover all the information of the signal using DSP techniques. In the more general case for the detection of polarization multiplexed signals, a polar- ization diversity coherent receiver is used, which employs polarization beam splitters, 90-degree optical hybrids, and BPDs to recover in-phase and quadrature components for both X- and Y-polarizations [52]. DSP algorithms can track and correct for LO fre- quency and phase mismatches (carrier recovery), and can undo the degrading eects of chromatic dispersion (CD), polarization mode dispersion (PMD), polarization dispersion loss (PDL) and some nonlinearities [53]. 1.3 Nonlinear Processes Nonlinear photonic interactions have been exploited to manipulate and process infor- mation of an optical data signal. Kerr nonlinearities have femtosecond response times and can mix and vary optical signals over bandwidths beyond THz; therefore, they have long been considered as an enabling technology for all-optical signal processing [88]. In this section, we provide an overview of some nonlinear processes that are widely used for optical signal processing. In general, \wave mixing" is a process during which multiple optical waves at dierent frequencies interact with each other and generate an idler sig- nal at a new frequency. These wave-mixing interactions are generally governed by a set 9 * * * ZDW ω signal ω pump ω conv ω signal ω pump1 ω conv1 ω conv3 ω pump2 ω conv2 Degenerate FWM Non-Degenerate FWM ZDW ω ω (a) (b) Figure 1.5: Third-order (3) nonlinear processes: (a) degenerate and (b) nondegenerate four wave mixing (FWM) schemes for generation of (phase conjugate) signal copy. ZDW: zero dispersion wavelength. of two rules: (i) conservation of energy, and (ii) phase matching conditions, which is a form of conservation of momentum [115][1]. We overview the (2) and (3) nonlinear processes. The third-order nonlinear pro- cesses ( (3) ), can result in four wave mixing (FWM), self phase modulation (SPM) and cross phase modulation (XPM) [1]. (2) nonlinearities can mix two waves and create mixing products such as second harmonic generation (SHG), sum frequency generation (SFG), dierence frequency generation (DFG), and a cascading of such mixing terms [69]. 1.3.1 Four Wave Mixing Four wave mixing (FWM) is the wave mixing process whereby three input waves mix under the phase-matching conditions in a nonlinear medium to produce a fourth wave. Figure 1.5 depicts the schematic spectra of two dierent types of FWM, namely degen- erate and non-degenerate FWM. In degenerate FWM (Figure 1.5(a)), a continuous wave (CW) pump at angular frequency ! pump and a data signal at frequency ! signal are com- bined and sent into a (3) nonlinear medium such as highly nonlinear ber (HNLF). If the pump is located around the zero-dispersion-wavelength (ZDW) of the nonlinear 10 medium, then the phase matching conditions are met and the conservation of energy rule determines the frequency of the newly generated (converted) wave as follows: ! conv = 2! pump ! signal : (1.7) Similarly, the electric eld of the converted signal is proportional to E conv (t)/ (E pump ) 2 E signal (t); (1.8) in which, \ " denotes the complex conjugate of the eld. Thus, the converted signal is a \wavelength converted" and \phase-conjugate" copy of the original data signal. In this tutorial, we generally tend to drop the time dependency term for the CW pumps in order to emphasize and distinguish between data-modulated signals and CW pumps. In the degenerate FWM, if the data-modulated signal is used as the pump, then the converted signal is proportional to the square of the signal eld. Therefore, it neither conserves the phase information of the original signal, nor preserves the intensity shape. In the non-degenerate FWM scheme, shown in Figure 1.5(b), two pumps at frequen- cies ! pump1 and ! pump2 located around the ZDW of the medium, and the input signal at ! signal are combined and sent into the nonlinear device. If the medium has a at dispersion slope around the ZDW, phase-matching conditions hold for FWM between these pumps and signals, resulting in the generation of the following mixing products: ! conv1 = 2! pump1 ! signal ; (1.9) ! conv2 = ! pump1 +! pump2 ! signal ; (1.10) ! conv3 = ! signal +! pump2 ! pump1 ; (1.11) 11 ω dummy ω pump ω SFG χ (2) DFG ω signal ω conv QPM ω pump ω SHG ω signal ω conv * χ (2) DFG Cascaded SFG and DFG Cascaded SHG and DFG (a) (b) ω ω χ (2) SFG χ (2) SHG QPM Figure 1.6: Cascaded second-order (2) nonlinear processes: (a) cascaded sum and dier- ence frequency generations (cSFG-DFG) and (b) second harmonic generation and DFG (cSHF-DFG) for wavelength conversion in a PPLN device. QPM: quasi-phase matching. with the electric eld amplitudes proportional to E conv1 (t)/ (E pump1 ) 2 E signal (t); (1.12) E conv2 (t)/ E pump1 E pump2 E signal (t); (1.13) E conv3 (t)/ E signal (t)E pump2 E pump1 : (1.14) Thus, multiple wave-mixing interactions occur simultaneously in the two-pump scheme resulting in both phase-conjugating and non-phase-conjugating wavelength con- versions. In (1.12){(1.14), it is worth mentioning that, because FWM involves two frequencies being added and one subtracted, if the input pumps happen to be in the same frequency band (e.g., C-band), then the generated wavelength converted signals also generally tend to appear in the same band. 1.3.2 Three Wave Mixing (2) nonlinear media can mix two optical waves (e.g., at! 1 and! 2 ) under phase-matching conditions and generate a third wave at the sum frequency (! SFG = ! 1 +! 2 ) and dierence frequency (! DFG =! 1 ! 2 ). In the case of one input pump, instead of sum frequency the second harmonic term ! SHG = 2! 1 is generated. As can be noted, if the two input signals are in the same frequency band (e.g.,1550 nm), the SHG/SFG 12 term is at775 nm, which is in a dierent frequency band. In many (2) nonlinear signal processing demonstrations, there has been an interest in keeping the generated signals in the same frequency band as the input signals by means of cascading SFG and DFG (cSFG-DFG) or SHG and DFG (cSHG-DFG), as shown in Figures 1.6(a) and (b), respectively. Periodically poled lithium niobate (PPLN) devices can serve as a medium for (2) nonlinear interactions. Due to their suitable nonlinear mixing eciency, relatively low propagation loss, and ease of fabrication, these devices may allow the implementation of some advanced all-optical signal-processing functions at bandwidths beyond THz [69]. Instead of true phase-velocity matching, the quasi-phasematching (QPM) technique is used in PPLN waveguide designs, in which a periodic sign change in the nonlinear susceptibility of the medium compensates for the velocity mismatch of the interacting waves [69]. From a systems point of view, the QPM wavelength in PPLN devices is very similar to ZDW in HNLFs in the sense that pumps generally need to be placed symmetrically around the QPM wavelength in order for the wave mixings to occur. 1.3.2.1 cSFG-DFG As depicted in Figure 1.6(a), when a data signal (! signal ) and a pump (! pump ) that are symmetrically located around the QPM wavelength are sent into a PPLN device, they produce the sum frequency product at ! SFG = ! signal +! pump = 2! QPM , whose amplitude is proportional to E SFG (t) / E signal (t)E pump . If another dummy pump (! dummy ) is also sent into the PPLN device together with the pump and the signal, then the SFG signal can mix with ! dummy through the DFG process and create a con- verted signal at frequency! conv =! SFG ! dummy , with eld amplitude proportional to 13 E conv (t)/E SFG (t)E dummy . Therefore, the converted signal results from the mixing of the three input signals and its center frequency and eld amplitude are determined by ! conv = ! signal +! pump ! dummy ; (1.15) E conv (t)/ E signal (t)E pump E dummy : (1.16) 1.3.2.2 cSHG-DFG Instead of using two pumps for SFG, one can only inject a pump that has the same frequency as the QPM frequency, to produce SHG at frequency ! SHG = 2! pump with eld amplitude E SHG / (E pump ) 2 . The SHG term can then mix with the signal to produce a phase-conjugate wavelength-converted signal at ! conv = 2! pump ! signal ; (1.17) E conv (t)/ (E pump ) 2 E signal (t): (1.18) The mathematical relations of cSFG-DFG and cSHG-DFG resemble non-degenerate and degenerate FWM, respectively. Therefore, as illustrated in Figures 1.5 and 1.6, these cascaded (2) processes can be viewed as quasi-FWM processes. It is important to note that wavelength conversion schemes that are based on these wave mixing interactions maintain the data that is modulated on the amplitude and phase of input signal. 1.3.3 SPM and XPM The intensity of optical signals can modulate the refractive index of the medium in which they are propagating. This instantaneous change in the refractive index instantaneously 14 Nonlinear Medium (e.g., HNLF) γ ~ χ (3) XPM (offset filtering to convert phase to amplitude) Spectral broadening due to SPM ω signal ω pump ω signal ω pump ω ω Figure 1.7: Nonlinear phase shift results in (i) self phase modulation (SPM), that causes spectral broadening, and (ii) cross phase modulation (XPM), that creates cross-talk on a certain channel from the other channels. changes the optical path length and causes a \nonlinear phase shift" on the signals. The nonlinear phase shift is given by [1] NL (t) = L eff 0 @ P signal (t) + 2 X i6=signal P i (t) 1 A ; (1.19) in which is the nonlinear parameter, L eff is the eective length of the medium, and P i denotes the power of the i-th co-propagating wavelength channel. For any given signal with powerP signal (t), the phase modulation induced by nonlinear phase shift has two parts: (i) SPM as a result of L eff P signal (t), and (ii) XPM because of 2 L eff P i6=signal P i (t). Figure 1.7 depicts an example where an amplitude modulated data signal and a CW pump are injected into a nonlinear medium. SPM causes spectral broadening on the signal, while the CW pump experiences XPM from the data signal. Thus, the information of the data signal is transferred to the CW pump through XPM and can be recovered by appropriately-oset side-band ltering. The SPM can be utilized for supercontinuum generation, for instance [89]. Because nonlinear phase shift is induced as a result of the power variations of the input signals, XPM and SPM processes are generally more suitable for applications that involve amplitude-modulated signals (e.g. OOK). 15 AB A*B A B ω AB* CW Example: FWM γ ~ χ (3) B* B 2 A* A B CW Pump    ω Figure 1.8: Having multiple mixing terms may be desirable (e.g., simultaneous generation of mixing terms) or unwanted (e.g., when it would waste part of the spectrum and create cross-talk on desired signals). 1.4 Materials and Devices Various materials and devices have been utilized for optical signal processing, and the choice of a nonlinear device is a trade-o between many gures of merit, such as high nonlinear eciency, wide and at bandwidth, low loss, data format transparency (to maintain phase and amplitude modulation), simultaneous wave mixings for simultaneous operations, low dispersion for phase matching, and low two photon absorption [35]. Materials such as silica, lithium niobate, silicon, bismuth oxide, chalcogenide, semi- conductors and multiple quantum well are used to create nonlinear optical devices suit- able for signal processing. Various devices such as HNLF, rib waveguides, PPLN waveg- uides, nanowire waveguides, semiconductor optical ampliers (SOAs) that use these materials might perform well in the implementation of certain functions. For exam- ple, large conversion bandwidth and simultaneous wave mixing in low-dispersion HNLFs can be exploited for supercontinuum generation; however, on the other hand, due to a wide phase matching bandwidth, HNLF may produce a lot of extra parasitic mixing terms that may (i) occupy bandwidth, and (ii) create cross-talk on the desired signal. This concept is shown in Figure 1.8, where a FWM scheme in HNLF is utilized to create multiplications of signalsA andB and their phase conjugates. As shown in the spectral diagram, the extra mixing products that appear due to high eciency and easy phase matching in a low dispersion HNLF can \ll up" the bandwidth through generation of unwanted signals proportional to A , B , and B 2 , for example [107]. 16 1.5 Conclusions In this chapter, we overviewed the key technologies that are commonly exploited for opti- cal signal processing. Nonlinear optical interactions in the form of FWM, SFG, DFG, SHG, XPM, and SPM were reviewed form a systems perspective. We also overviewed optical signal modulation and demodulation techniques using direct detection and coher- ent detection. Finally, we presented a systems-level approach to choosing proper nonlin- ear materials for optical signal processing techniques. 17 Chapter 2 Overview of Basic Enabling Operations 2.1 Introduction In this chapter, we will review a few basic operations that comprise the fundamental blocks for realizing the advanced signal processing functions that are presented in the following chapters. We overview signal multicasting, multiplexing and demultiplexing, and tunable all-optical delays. Wavelength multicasting is a process that creates multiple replicas of a data signal onto selective predetermined wavelengths [106]. Optical signal multiplexing combines multiple data signals that may be on dierent amplitudes, phases, wavelength channels, polarizations, or time slots into one data channel [99][85][103]. Optical demultiplexing refers to the processes that can decompose a data signal into its constituting tributaries [88][99]. Finally, tunable all-optical delays provide the means for delaying an optical signal over a nite continuous range [97]. 18 Requires N probe pumps for N-fold multicasting ω Signal Requires (N+1)/2 pumps for N-fold multicasting Signal ω Signal Requires a short-pulse pump and a periodic filter ω Degenerate FWM (a) Multi-pump FWM (b) Supercontinuum Generation (c) Input Signal An Output Copy 8-fold Multicasting, 320 Gbit/s OOK 16-fold Multicasting, 40 Gbit/s OOK Input Signal An Output Copy 8 dB/div 8 nm/div AFTER HNLF-2 1590 1510 1550 Wavelength (nm) λ SMP BEFORE HNLF-2 HNLF-2 Supercontinuum Generation 24-fold 40-Gbit/s OOK Multicasting 8 dB/div 8 nm/div Ch1 Ch1 Ch5 Ch9 Ch13 Ch17 Ch21 Ch24 Ch5 Ch9 Ch13 Ch17 Ch21 Ch24 1590 1510 1550 Wavelength (nm) 24-fold Multicasting, 40 Gbit/s OOK Figure 2.1: Various nonlinear schemes for optical multicasting: (a) degenerate FWM, requiring N probe pumps for N-fold multicasting [9], (b) multi-pump FWM, requir- ing (N + 1)=2 pumps for N-fold multicasting [14], and (c) supercontinuum generation followed by periodic ltering, requiring a short-pulse pump source [106]. 2.2 Wavelength Multicasting Optical wavelength multicasting utilizes nonlinearities to create multiple copies of the input data signal at dierent output wavelengths [30][13]. Various materials, nonlinear processes, numbers of pumps and pump congurations can be exploited for multicasting. Figure 2.1 depicts conceptual spectra and sample experimental results on some of these multicasting techniques [106]. In Figure 2.1(a), to create N signal copies, the input data signal at frequency ! signal is sent to a nonlinear device together with N pumps at frequencies ! pump;i (i = 1;:::;N) to create N copies of the input signal at 2! signal ! pump;i through degenerate FWM. Figure 2.1(a), shows the output spectrum and the input/output eye diagrams for 16-fold multicasting of a 40-Gbit/s optical data signals in a silicon waveguide [9]. Although this technique can preserve the information on amplitude-modulated signals (e.g., OOK), it may distort the pulse shapes, amplitude levels, and phases because the optical elds of the output copies are proportional to the square of the input signal eld. In this scheme, each signal copy can be independently 19 controlled by the CW pump laser that generates it. This feature may be useful for opti- cal signal processing applications that require independent control over the amplitude, wavelength and the number of output copies. Figure 2.1(b), shows another method that utilizes non-degenerate FWM. In this manner, N=2 CW pumps are required to generate N copies of the data signal [14][118]. In this scheme, some output signals are phase-conjugate, and because fewer CW pumps are used, the power or wavelength of the generated copies can hardly be varied without aecting the power or wavelength of other signal copies. On the other hand, in non- degenerate FWM, the output eld is proportional to the eld of the input signal (or its conjugate); thus, the pulse shape and phase information can generally be preserved. Therefore, the phase-modulated signals are better supported using this scheme compared to degenerate FWM. Experimental results of one such demonstration are shown in Figure 2.1(b), where a 320-Gbit/s OOK signal is multicast to 8 copies using 4 CW pump lasers and HNLF [14]. Supercontinuum generation can also be utilized for signal multicasting, as shown in Figure 2.1(c) [106]. Supercontinuum in created when dierent nonlinear processes such as SPM, FWM, and Raman scattering can interact with each other to cause a signicant spectral broadening [89]. Typically, high-power narrow pulsewidths are required to gen- erate the supercontinuum. The supercontinuum can be ltered with a periodic optical lter to create simultaneous and multiple copies of the original data signal. Figure 2.1(c), shows experimental results on 24-fold multicasting of 40-Gbit/s OOK signals [106]. The diagram on the left shows the superimposed spectra of the input and output of the HNLF that creates the supercontinuum, and the one on the right shows the periodically ltered spectrum and some sample output eye diagrams. It has been shown that this method can also support phase-modulated signals for low input power levels [116]. Although this method can provide multiple copies of the input signal without the need for CW pumps, it can hardly allow for independent control over the properties of the outputs. 20 Beside these three techniques, several other methods and nonlinearities have also been exploited for multicasting purposes. These include methods that are based on XPM [11], cSFG-DFG in PPLN waveguides [123], cross gain modulation and cross absorption modulation in SOAs, where the input signal modulates the gain or absorption of the semiconductor medium which then transfers to the CW lasers that propagate through the same medium [111]. 2.3 Multiplexing and Demultiplexing Various techniques have been considered for optical multiplexing of WDM data channels to an optical time division multiplexed (OTDM) channel and demultiplexing a low-speed tributary from a high-speed OTDM signal. These include the use of XPM in HNLFs [86], FWM in HNLFs and waveguides [103][35], and cSFG-DFG in PPLN devices [12]. OTDM signals can simultaneously use advanced modulation formats to increase data capacity [46]. Passive techniques that utilize optical power combiners and polarization beam com- biners have also been used to multiplex low-baud-rate, short-pulse data signals to high- speed OTDM signals [46]. 2.3.1 Active Optical Multiplexing Figure 2.2 depicts the time domain schematic for the optical multiplexing of dierent WDM data signals to a high baud-rate OTDM signal followed by a demultiplexing stage. Each WDM data signal occupies a portion of the symbol time, such that after optical time alignment they can be interleaved in a nonlinear element with negligible interference. For example, 16 input data channels at 40-Gbit/s have been multiplexed to a 640-Gbit/s channel through XPM in a HNLF followed by another nonlinear stage for down-sampling (demultiplexing) the 640-Gbit/s signal to its 10-Gbit/s tributaries [110]. Although the 21 Δ τ n-1 Δ τ 1 e.g., 640-Gbit/s Single Wavelength Channel t λ 1 λ 2 λ n t t λ 0 t λ d WDM Input Signals e.g., 40 Gbit/s Optical Time Alignments Multiplexing to Single λ (Nonlinear Element) Demultiplexing Output Signal e.g., 10 Gbit/s Sampling Pump e.g., Demultiplexed 10-Gbit/s Tributary Figure 2.2: Concept of active optical multiplexing and demultiplexing using nonlineari- ties: WDM channels that utilize short-duration data pulses are time aligned such that their data pulses minimally overlap, and optically multiplexed to one wavelength channel in a nonlinear element. For demultiplexing, a sampling pump source is time-aligned and multiplied by the signal in a nonlinear device. data format used in the following examples may be OOK, the technique can also work on phase-modulated signals [46]. A nonlinear optical loop mirror (NOLM) has long been used as a method for signal multiplexing and demultiplexing. As shown in Figure 2.3(a), in principle, the NOLM is an interferometer in which the interfering signals propagate in counter directions; in one direction, the signal may be aected by nonlinear interactions with other signals [1]. In an NOLM, when the nonlinearites are low, the input signal (signalB) comes out as fully destructive in the output of the NOLM; however, when signalsA 1 toA n create XPM on signal B, then signal B's phase is changed in that direction of the loop; therefore, the output of the NOLM becomes more constructive. The interferometer basically transfers the XPM-induced phase to intensity. Figure 2.3(b) shows the conceptual equivalent logic function of the NOLM. The physical interactions of XPM and interferometry can be viewed as follows. When the multiplexing of signals A 1 to A n is nonzero, signal B comes out of the NOLM as \1", and when signalsA 1 toA n are zero, signalB is blocked (\0"). The NOLM can be used for both multiplexing and demultiplexing. Figure 2.3(c) shows schematic and experimental results for multiplexing of 16 OOK WDM channels 22 … MUX Signal A 1 Signal A 2 … Signal A n Signal B DEMUX 50/50 50/50 HNLF Signal A 1 Signal A 2 … Signal A n Signal B Low Nonlinearity Output Output: • Mux • Demux • AND • OR Nonlinear Optical Loop Mirror (NOLM) (a) Equivalent Logic Function (b) Input Signal B Output t Input Signal A 1 Input Signal A 2 CW Laser Sampling Pulses t t t t t t 0 2 4 Time (ps) 16 WDM 40-Gbit/s Time Aligned Channels 0 2 4 Time (ps) 640-Gbit/s Multiplexed Output 0 2 4 Time (ps) 640-Gbit/s Multiplexed Output 0 6.25 12.5 Time (ps) A 10-Gbit/s Demultiplexed Output Multiplexing Demultiplexing (c) Figure 2.3: Nonlinear optical loop mirror (NOLM): (a) Principle of operation of the NOLM (signalB is split and sent into two directions, one with low nonlinearities and one with high nonlinearities, the two are then added to create interference.) (b) Equivalent logic/application function of the NOLM. (c) Multiplexing of sixteen 40 Gbit/s OOK WDM signals to a 640-Gbit/s wavelength channel, and demultiplexing of the 640-Gbit/s OOK signal to its 10-Gbit/s tributaries, using the NOLM [110]. HNLF: highly nonlinear ber. at 40-Gbit/s to a single channel at 640-Gbit/s. Signal B here is a CW pump that gets modulated after the NOLM due to the XPM by the 16 time-interleaved WDM channels. Subsequently, this 640 Gbit/s channel can be sent to an NOLM as signal A 1 , while 23 ω demux ω control ω signal FWM for Demultiplexing ω Time Output 10Gbit/s Eye Diagram (10 ps/div) 10 GHz Control Pulses 640 Gbit/s Signal 10 Gbit/s Demux’ed Signal 640-to-10-Gbit/s OTDM Demultiplexing in Chalcogenide Waveguide OTDM Demultiplexing in Chalcogenide Waveguide (a) Figure 2.4: Nonlinear optical demultiplexing of 640-to-10-Gbit/s in a chalcogenide waveg- uide: device structure, experimental spectrum and eye diagram [41]. signal B is a sampling short-pulse pump with a 10 GHz repetition rate, resulting in demultiplexing (down-sampling) of the 640-Gbit/s signal to 10-Gbit/s [110]. FWM in chalcogenide waveguides have also been utilized for OTDM demultiplexing, as shown in Figure 2.4. 10-GHz repetition rate control pulses demultiplex a 640-Gbit/s OTDM signal down to 10-Gbit/s. The spectra after the FWM and the ltered output are shown in Figure 2.4, together with the eye diagram of an extracted 10-Gbit/s tributary [41]. 2.3.2 Passive Optical Multiplexing High baud rate OTDM signals can be generated at the transmitter by modulating a short- pulse low-repetition rate pump source with data signals and then passively delaying and combining them into proper time slots and polarizations. As shown in Figure 2.5, a 10- GHz repetition rate short-pulse laser is modulated to create a 20-Gbit/s DQPSK signal. The signal is then passively split, delayed and combined to create a multiplexed signal at a 128-times-higher baud rate (1.28 Tbaud). The 2.56-Tbit/s signal is then split and multiplexed in a polarization beam combiner to double the data bit rate to 5.12 Tbit/s (2 polarizations, 2 bit/sybmol DQPSK, 1.28 Tbaud) [46]. 24 Passive Optical Multiplexing from 10-Gbaud to 1.28 Tbaud Figure 2.5: Concept of passive optical multiplexing to achieve 5.12 Tbit/s data speed on a single wavelength channel (1.28 Tbaud polarization-multiplexed DQPSK signal) [46]. Δτ Δτ Δτ λ 1 λ 2 λ 1 λ 2 λ in λ in λ in λ in t λ in t t Δ τ ≈ D × Δλ Wavelength Converter Dispersive Element Wavelength Converter Dispersion Compensator t t t t t t 7.3 μs delay using discrete + continuous delays 22 ns delay for 43 Gbit/s OOK, 2.5 ps pulses (b) (c) (a) Figure 2.6: Continuously tunable parametric optical delay using the conversion- dispersion technique: (a) concept, (b) 22 ns delay for 43-Gbit/s OOK signal with 2.5 ps pulses [68], (c) 7.3 s delay using discretely time-oset continuous delay units [31]. 2.4 Tunable Optical Delays Many signal processing functions require the addition of delayed and weighted copies of an input signal. A tapped-delay-line or a nite impulse response (FIR) lter utilizes 25 delayed copies of the input signal to process digital as well as analog signals. Digital applications may include equalization, correlation, discrete Fourier transform, modula- tion format conversion and synchronization [87][117][63]. Analog applications include a wide range of D/A and A/D conversions, microwave delays for phased array anten- nas, FIR ltering and matched ltering, and other microwave photonic applications [15][114][45][101][19][119]. Traditionally, delays have been created by sending a signal through a xed optical path [76]. Having tunable optical delays, can create possibilities of devising optical signal processing techniques capable of accommodating the heterogeneous data trac of future networks, baud-rate-adjustable signal processing and arbitrary lter designs. One way to realize continuously tunable optical delays is to use the relative delay induced between two wavelength channels as a result of chromatic dispersion (CD) [97]. This technique's principle of operation is explained in Figure 2.6(a). The incoming signal at a certain wavelength ( in ) is sent into a nonlinear element to create a wavelength- converted copy at either 1 or 2 , ( = 1 2 ). The wavelength-converted signal is then sent to a dispersive element (e.g., dispersion compensating ber, DCF), which has two eects: (i) pulses spread out due to intrachannel CD, and (ii) each wavelength travels at a dierent speed due to inter-channel CD. Therefore, if the original signal is converted to 1 , it will experience a relative delay of DL in comparison to if it was converted to 2 . Then, the signal is converted back to the original wavelength; however, depending of the length of the dispersive element (L), its dispersion (D) and the pulse duration of the signal, the signal may have been spread over time due to CD. If necessary, this broadening caused by intra-channel dispersion can be compensated for in a dispersion compensating module. Therefore, by using this method, one can tune the signal delay by selecting a wavelength on to which the signal is temporarily converted. In other words, the delay can be tuned by tuning a pump laser. Delay resolutions as low as 100 fs and up, and delays up to 3.6 s have been shown using the conversion-dispersion technique [80][78]. Typically, large amounts of dispersion 26 are required for large delays, which may cause signicant pulse broadening that requires compensation; however, for smaller delays that are within a bit time, smaller dispersion values are required and thus the pulse broadening may be negligible and dispersion compensation may not be necessary. Two dierent results on tunable delays are shown in Figure 2.6(b)(c). In Figure 2.6(b), a 0 to 22 ns delay has been shown on 43-Gbit/s OOK signals with 2.5 ps short pulses [68]. Wideband operation is enabled by using spectral inversion to compensate for intra-channel CD on the signals. Figure 2.6(c) shows the tuning results of a demonstra- tion that uses a combination of discrete (xed) delays and continuously tunable optical delays to achieve a 0 to 7.3 s delay [31]. In other experiments, a 1.56 s delay was achieved on RZ-DPSK signals at 40-Gbit/s [3] and a 3.6 s delay was shown using one continuously tunable scheme for 100-Gbit/s RZ-DQPSK signals [78] [107]. 2.5 Conclusions In this chapter, we overviewed various technologies that enable optical processing of amplitude- and phase-modulated signals. We provided prior art in the eld of optical signal processing spanning a wide range of functions such as optical multicasting, multi- plexing, demultiplexing and tunable optical delays. Although various devices and tech- niques have been utilized in the literature to demonstrate these functions, we only gave a few examples that may help with the implementation of more advanced sub-systems. 27 Chapter 3 Recongurable Conversion/Dispersion-Based Optical Tapped-Delay-Lines In this chapter, we demonstrate a recongurable high-speed optical tapped delay line (TDL), enabling several fundamental real-time signal processing functions such as corre- lation (for pattern search) and equalization. Weighted taps are created and added using optical multicasting and multiplexing schemes that utilize the nonlinear wave mixings in the periodically poled lithium niobate (PPLN) waveguides. Tunable tap delays are real- ized using the conversiondispersion technique. In the demonstrated TDL, the amplitude and phase of tap coecients can be varied, enabling signal processing on amplitude- and phase-encoded optical signals [64]. 3.1 Introduction High-data-rate all-optical signal processing has been one of the main research goals in photonics. Signal processing using nonlinear optics has been of great interest due to its inherent ultrafast, THz bandwidth and its potentially phase-preserving nature [1], [71], [100]. Many important functions for signal processing have been implemented using 28 various forms of photonic nonlinear interactions [54], [49], [12]. Future optical signal processing systems can benet from nonlinear optics for wavelength conversion [49], add-drop multiplexing of digital signals [12], and quantization [54]. A key building block of many digital signal processing applications is the tapped-delay-line (TDL), in which an incoming data stream is tapped at dierent time intervals, given amplitude weights, and then added together [87]. A TDL can be congured to provide a variety of important signal processing functions, including (i) nite impulse response (FIR) ltering, (ii) signal correlation and convolution, (iii) digital-to-analog conversion, (iv) equalization, and (v) discrete Fourier transform (DFT) [87], [47]. In signal processing, TDLs have been implemented electronically, providing these key functions in a recongurable fashion but on the binary electrical signals [38]. Utilization of the extremely large bandwidth of photonic technologies would require implementation of TDLs all-optically. An optical method can potentially advance the performance of signal processing when the signal to be processed is at high speed or is a combination of many lower-speed signals [33], [15]. The optical data signal ows through the TDL module without the need to actively operate/switch on each bit individually. Moreover, optical signal processing can also benet from the ability to manipulate and process opti- cal eld amplitude and phase in order to increase the capacity and speed of processing. For optical TDLs, critical issues include the following abilities: (a) continuously tune tap delays from a fraction of a bit time to multiple bit times, (b) nely tune the relative tap delays since fractions of a bit time at 10's of Gbaud can easily be on the order of a few ps, and (c) accommodate dierent modulation data formats (e.g., on-o keying, OOK, and phase-shift-keying, PSK). Recent work on optical TDLs includes xed ber-based TDLs [76], cascaded Mach- Zehnder interferometers [33], [94], and hybrid optical and electrical approaches that take advantage of microwave photonics techniques [15], [114]. These approaches are generally xed or are tunable over nite or discrete ranges, or tend not to have independent control over the amplitude, phase, and delay of each tap. We propose and demonstrate an optical 29 TDL that utilizes recent advances in the elds of optical multicasting, multiplexing and conversion-dispersion delays [97] to realize a tunable and recongurable optical TDL. In this section, we report a recongurable all-optical TDL that is continuously tun- able in all aspects (amplitude, phase, delay and number of the taps) and thus can be programmed in the eld to perform a desired function (e.g, equalization or correlation). Our approach takes advantage of ultrafast optical nonlinear eects to create and com- bine the taps, as well as all-optical tunable conversion-dispersion-based delays. We show real-time optical equalization and correlation at line-rates as high as 80-Gbit/s using the optical TDL with two to four taps. We demonstrate TDL schemes with (i) optical mul- tiplexing (enabling processing of amplitude and phase), and (ii) electronic multiplexing (for amplitude modulated (OOK) signals). The optically multiplexed TDL-based equal- izer is used to compensate the chromatic dispersion on dierential binary-phase-shift- keyed (DPSK) and dierential quadrature phase-shift-keyed (DQPSK) signals. Optical TDL equalizer with half a symbol time tap spacing is demonstrated at 40-Gbaud and 27-Gbaud data rates. Optical TDL-based correlation for pattern detection have been realized to search for 3- and 4-symbols-long patterns in OOK, binary-phase-shift-keyed (BPSK), and quadrature phase-shift-keyed (QPSK) signals. Electrical multiplexing is utilized to realize correlation and equalization with bipolar taps, resulting in an electrical output signal. 3.2 Concept and Principle: All-Optical Tapped-Delay- Line The generic form of a tunable tapped-delay-line is shown in Figure 3.1. For a TDL with N taps, taken at times T i , and weighted by complex-coecientsjh i j\h i , the relation between the input signalx(t) and the outputy(t) is determined byy(t) = P N1 k=0 h i x(t T i ). Therefore, the function of the TDL is simply controlled by the number of taps (N), the tap delays (T i ), and the complex tap coecients (h i ). 30 Delay T 1 Delay T 2 Delay T N-1 × × × + + + • • • • • • • • • × + |h 0 |e j ס h 0 |h 1 |e j ס h 1 |h 2 |e j ס h 2 |h N-1 |e j ס h N-1 Delay T 0 Input, x(t) y(t), Output Figure 3.1: Generic block diagram of a tapped-delay-line (TDL): input signal is tapped at dierent time intervals, taps (copies) are weighted each by its own coecient and then summed to produce the output. The principle of operation of our proposed optical TDL is depicted in Figures 3.2 and 3.3. First, a nonlinear optical mixer and multiple dummy tunable pump lasers can mul- ticast (fan-out) N replicas of the data signal, with each replica located at a dierent center frequency. A liquid crystal on silicon (LCoS) programmable lter can be used to apply the tap phases. Subsequently, these replicas travel through a chromatic dispersive element at various speeds incurring a dierent time delay. Finally, these N replicas are multiplexed together by another high-speed nonlinear mixer creating an output signal that is \processed" by the tapped-delay-line. The taps can be precisely tuned in terms of amplitude, phase and relative time delay by varying the pump lasers. Various schemes have been used in the literature for multicasting, conversion- dispersion delays, and optical multiplexing. For optical multicasting, dierent media and nonlinearities have been utilized, including four-wave-mixing (FWM) in semicon- ductor optical ampliers (SOAs) [30], silica-based highly nonlinear bers (HNLFs) [13] and silicon nanowires [9]. Cascaded sum-frequency-generation followed by dierence- frequency-generation (cSFG-DFG) in periodically poled lithium niobate (PPLN) waveg- uides have also been used for multicasting [105]. 31 N Æ 1 Optical Multiplexing Nonlinear Element (PPLN) Frequency-Dependent Optical Delay (Chromatic Dispersion) Input Signal N+1 lasers Laser Tunable Optical Tapped-Delay-Line SHG Mixing Signal Copies Power Frequency ( Ȧ ) § Delay Frequency ( Ȧ ) § 1 Æ N Optical Multicasting Output Signal Power § Delayed Copies Frequency ( Ȧ ) V arious Tap Coefficients Input Signal Output Signal Ȧ S Ȧ D2 Ȧ D3 Ȧ P1 Ȧ C1 Ȧ D1 Ȧ C3 Ȧ C2 Ȧ MUX Ȧ D2 Ȧ D3 Ȧ P2 Ȧ C1 Ȧ D1 Ȧ C3 Ȧ C2 DFG Mixing SHG Mixing DFG Mixing Phase Filter (LCoS Filter) ןȟɘȾ ʹ Copy 3 Time § …101100… Copy 2 § …101100… Copy 1 § …101100… Copy 3 Time § …10 1100… Copy 2 § …101 100… Copy 1 § …1011 00… Nonlinear Element (PPLN) Figure 3.2: Optical implementation of a TDL based on nonlinearities and conversion- dispersion-based delays: N copies of the input optical signal are generated at dierent frequencies using cascaded nonlinear wave mixings of SFG followed by DFG. The ampli- tude of each signal copy depends on its CW laser pump power. Copies are sent into a chromatic dispersive medium to introduce the tap delays. Delayed and weighted signal copies are sent to a second nonlinear medium to be multiplexed and create the output signal. !: frequency separation between signal copies, 2 : group velocity dispersion parameter, L: length of the dispersive medium, PPLN: periodically poled lithium nio- bate. We utilize chromatic-dispersion-based delays to realize tap delays [97], [68], [2], [29]. The chromatic-dispersion-based delays exploit the wavelength-dependent speed of light in a dispersive medium coupled with tunable wavelength conversion to achieve continuously tunable delays. Using HNLF for wavelength conversion, distortion-free 22 ns delay is demonstrated for 2.6-ps-wide optical signals [68], and 105-ns delay is shown for 10- Gbit/s optical signals [2]. Conversion-dispersion delays have also been realized using PPLN waveguides as their wavelength converters [29]. Fine tuning resolution of <500 fs is reported for conversion-dispersion-based optical delays [80]. Prior work on nonlinear optical multiplexing have been based on FWM [103], cross- phase modulation (XPM) [109], and supercontinuum generation [109], [99] in HNLFs. 32 ω t P ω t P ω t P ω t P 1  N Optical fan-out Frequency-dependent optical delay (chromatic dispersion) N  1 Optical multiplexing Input signal and pump lasers Generation of signal copies Relatively delayed signal copies and re-used pumps Multiplexed signal Input signal Output signal Delay ∝ Δ ω β 2 L N+1 CW laser pumps CW laser pump Tunable optical tapped-delay-line Power Frequency (ω) ≈ SFG mixing DFG mixing Power ≈ DFG mixing SFG mixing Delay Frequency (ω) ≈ c Delay T 1 Delay T 2 Delay T N-1 × × × + + + • • • • • • • • • × + |h 0 |e j ∠h 0 a ω S ω D2 ω D3 ω P1 ω C1 ω D1 ω C3 ω C2 Frequency (ω) ω MUX ω D2 ω D3 ω P2 ω C1 ω D1 ω C3 ω C2 |h 1 |e j ∠h 1 |h 2 |e j ∠h 2 |h N-1 |e j ∠h N-1 b Delay T 0 y(t) Output ∠h 0 |h 0 | |x(t-T 0 )| ∠x(t-T 1 ) + ∠h 1 |h 1 |. |x(t-T 1 )| |h 2 |. |x(t-T 2 )| ∠x(t-T 2 ) +∠h 2 3 rd tap 2 nd tap 1 st tap |h 0 |. |x(t-T 0 )| ∠x(t-T 0 ) ∠x(t-T 0 ) +∠h 0 Input x(t) y(t) Output h 1 x(t-T 1 ) h 2 x(t-T 2 ) Figure 3.3: Time and spectral domain diagram of the signals in various stages, as the signals propagate through the optical TDL. Cascaded SFG-DFG processes in PPLN waveguides have also been used as the medium to time multiplex eight lower rate 20-Gbit/s OOK signals to a 160-Gbit/s signal [85], and add/drop multiplexing at 640-Gbit/s data rates [12]. In our optical TDL approach, PPLN waveguides are chosen as the nonlinear optical wave-mixer for multicasting (fan-out) and multiplexing stages. FWM interactions in HNLF bers could produce extra mixing products that might be undesirable since they occupy bandwidth and could cause crosstalk. The wave mixing interactions (cSFG-DFG) are governed by conservation of energy and phase-matching conditions [69], as discussed in the following. 33 3.2.1 Optical Multicasting (Fan-out) In the fan-out stage, copies of an amplitude- and/or phase-encoded incoming signal (at ! S ) are generated using cSFG-DFG processes [1], [69]. The signal at! S and a continuous- wave (CW) pump laser at ! P 1 , that are located symmetrically around the quasi-phase matching (QPM) frequency! QPM of the PPLN waveguide, mix through SFG process to produce a signal copy at ! S +! P 1 = 2! QPM . The SFG term then mixes with multiple dummy pump lasers at frequencies ! Di through DFG nonlinear process to create signal copies at 2! QPM ! Di . Thus, the generated output signal copies will be at frequencies ! Ci =! S +! P 1 ! Di (Figure 3.2, schematic spectrum on the left). Given the electric eld of the signal A S (t), CW DFG dummy pump lasers A Di (t), and the CW SFG pump laser A P 1 (t), the amplitude of the generated signal copy is A Ci (t)/A Di A P 1 A S (t), in whichA Di denotes the complex conjugate ofA Di . Therefore, the amplitude of each signal copy is proportional to the amplitude of the dummy pump laser that generated it. Therefore, variable weight taps can be realized by varying the dummy lasers' powers. 3.2.2 Phase Tuning and Optical Delays The signal copies and their corresponding dummy pumps are ltered and sent into an amplitude- and phase-programmable lter (based on LCoS technology [40]) in which (i) the signal copies (! Ci 's) and their dummy pumps (! Di 's) are ltered, and (ii) a phase shift LCoS i is applied to each dummy pump laser ! Di , as depicted in Figure 3.5. Eventually after multiplexing, these applied phases turn out to be the tap phases. The output is then sent into a dispersive medium of length L and propagation constant (!). Therefore, the elds of the delayed signal copies,A DCi (t), and the delayed dummy pumps, A DDi , become: 34 Re Im Re Im Re Im Re Im y(t) Output ס h 0 |h 0 | |x(t-T 0 )| h 1 x(t-T 1 ) h 0 x(t-T 0 ) 3 rd tap 2 nd tap 1 st tap |h 0 |. |x(t-T 0 )| ס x(t-T 0 ) ס x(t-T 0 ) + ס h 0 h 1 x(t-T 1 ) h 2 x(t-T 2 ) h 1 x(t-T 1 ) h 2 x(t-T 2 ) h 2 x(t-T 2 ) Figure 3.4: Mathematical vector representation of TDL operation. In each tap the delayed input is multiplied by a complex coecient which could rotate and scale it. The output y(t) is a vector summation of the weighted taps. 1,540 1,551 1,562 Wavelength (nm) 1,540 1,551 1,562 Wavelength (nm) LCoS Amplitude (dB) LCoS Phase (deg.) -50 dB 0 dB 0° 1 ס 0° 1,540 1,551 1,562 -60 -40 -20 0 ω S ω P1 Power (dBm) Wavelength (nm) 1,540 1,551 1,562 -60 -40 -20 0 ω P2 ω MUX Power (dBm) Wavelength (nm) 1,540 1,551 1,562 -60 -40 -20 0 ω P2 ω MUX Power (dBm) Wavelength (nm) Constructive Coherent Addition PPLN-2 Output + + + = Destructive Coherent Addition PPLN-2 Output PPLN-1 Output 1 ס 90° 1 ס 180° 1 ס -90° 1 ס 0° 1 ס 0° 1 ס 0° 1 ס 0° + + + = 0 4 ס 0° LCoS Amplitude (dB) LCoS Phase (deg.) -50 dB 0 dB -90° 90° 0° 180° 0°0°0° LCoS Filter Response LCoS Filter Response Dummy Pumps Signal Copies Signal Pump1 Figure 3.5: Measured spectrum of the output of the fan-out stage (PPLN-1) with four taps, in which the signal is constant (CW pump laser). Schematic LCoS lter responses, showing tap-phase tuning. Output spectra of the multiplexing stage (PPLN-2) when phases of the tap coecients result in destructive (right top) and constructive (right bottom) addition of taps. A DCi (t)/A Di A P 1 = 1 f f A S (!)e j(!)L g (3.1) A DDi /A Di e j(! Di )L e j LCoS i (3.2) In which f A S (!) ==fA S (t)g is the Fourier transform ofA S (t),e j(!)L is the transfer function of the dispersive medium at frequency!, and! Ci =! S +! Pi ! Di = 2! QPM 35 ! Di is the frequency of thei-th signal copy. The Taylor series expansion of (!) around ! QPM gives(!) = P 1 n=0 (!! QPM ) n n! n , in which n = @ n @! n !=! QPM ; 2 is known as the group velocity dispersion parameter [1]. According to the group delay, the signal copy at ! Ci will be delayed by T (! Ci ) =L @ @! !=! C i . If higher-order dispersion parameters are negligible (i.e., j 0 for j 3), the group delay at frequency ! Ci becomes T (! Ci ) 1 L + (! Ci ! QPM ) 2 L. Therefore, the relative delay on each signal copy compared to the rst copy A DC1 (t) is T i = T (! Ci )T (! C1 ) = (! D1 ! Di ) 2 L. Thus, if phase- constant terms are ignored, the elds of the delayed copies are proportional toA DCi (t)/ A Di A P 1 A S (tT i ), assuming negligible signal distortion due to the dispersion. As shown in Figure 3.2, after passing through a dispersive medium (e.g., dispersion compensating ber, DCF) the signal copies are relatively delayed with respect to each other. These tap delays are proportional to the frequency spacing between the signal copies and can be tuned by changing the signal copies frequencies ! Ci 's (or equivalently, ! Di 's). 3.2.3 Optical Multiplexing Similar to the optical multiplexing stage, cSFG-DFG processes are used in another PPLN waveguide with the same quasi-phase matching frequency! QPM as the rst PPLN waveg- uide for optical multiplexing. As depicted in Figure 3.2 and Figure 3.5, the signal copies at ! Ci 's and their dummy pumps ! Di 's are kept and reused for phase-preserving multi- plexing. In the multiplexing stage, each delayed signal copy ! Ci mixes with its reused dummy pump ! Di through SFG and creates a signal at ! Ci +! Di = 2! QPM . Another pump laser at ! P 2 is also injected to the second PPLN waveguide for the DFG pro- cess to convert this signal to frequency ! MUX , 2! QPM ! P 2 = ! Ci +! Di ! P 2 . After the second PPLN waveguide, the eld of the i-th multiplexed copy isA MUXi (t)/ A P 2 A DDi A DCi (t), or: A MUX i (t) / A P 2 A P 1 jA D i j 2 e j i e j LCoS i A S (tT i ) (3.3) 36 In which i ,L(! Di )L(! Ci ). Because of the symmetry around ! QPM (i.e., ! QPM ! Di =! Ci ! QPM ), the Taylor series expansion of i only includes even terms as shown in (3.4). i = 1 X n=0 (! Di ! QPM ) n n! L n 1 X n=0 (! Ci ! QPM ) n n! L n (3.4) =2L 0 (! Di ! QPM ) 2 L 2 ::: Furthermore, i of a tap only depends on its parent's dummy pump laser frequency ! Di . Assuming negligible fourth and higher-order dispersion (i.e., j 0 for j 4) and ignoring constant phase terms, i (! Di ! QPM ) 2 L 2 , initial i . The total multiplexed signal is expressed by A MUX (t) = P N i=1 A MUXi (t), or: A MUX (t) / N X i=1 e j initial i jA Di j 2 e j( LCoS i ) A S (tT i ) (3.5) This is equivalent to a TDL with input A S (t), output A MUX (t), and input-output relation A MUX (t) / N X i=1 jh i je j\h i A S (tT i ) (3.6) In which: jh i j =jA D i j 2 \h i = initial i + LCoS i T i =L 2 (! Di ! D1 ) initial i =L 2 (! Di ! QPM ) 2 (3.7) 37 According to (3.7), each tap is generated by a dummy pump laser (at! Di ). Therefore, the number of taps (N) can be changed by adding/removing dummy pump lasers and the amplitude of each tap (jh i j ) can be varied independently by adjusting its dummy pump laser power (jA Di j 2 ) in the optical fan-out stage. Also, the delay of each tap (T i ) can be varied by changing the dummy pump laser frequency (! Di ). The challenge in realizing phase tuning lies in the fact that the generated signal copies need to be phase- coherent before they can be multiplexed. In our approach, the dummy pumps are kept on the same optical path along with their corresponding signal copies to preserve phase- coherence and enable phase tuning of taps. The relative phase of each replica (\h i ) can be tightly controlled by applying a phase shift using an LCoS lter ( LCoS i ) or ne detuning to the frequency of dummy lasers. A ne detuning of ! Di changes initial i by i 2L 2 (! Di ! QPM )! Di . However, the pump detuning changes the tap delays by L 2 ! Di . For system designs in which this delay oset is negligible compared to the tap-delays, the taps phases can be applied directly by detuning the dummy pumps. In either case, the phases initial i associated with the pumps located at ! Di need to be added to the desired tap-phases to initialize the system. Figure 3.4 illustrates how complex tap coecients can rotate and scale input symbols (vectors) in the complex plane and produce the TDL output by a vector addition. Figure 3.5 explains the principle of coherent addition on a constant input signal (i.e., a CW laser). Four equal-amplitude taps are used (as shown in PPLN-1 output) and depending on the phases of tap-coecients (applied by the LCoS lter) these four copies can be added constructively or destructively, resulting in either a high power peak or a low power null at ! MUX (PPLN-2 output). As an alternative to optical multiplexing, the taps can be electronically combined in a photodiode, provided that the beating terms between dierent wavelength channels fall outside the bandwidth of the photodiode. Photodiodes detect the intensity of light which is a positive quantity; therefore, if a balanced photodiode is used bipolar (negative and positive) tap-coecients can be realized. 38 The TDL can be utilized for many dierent applications by programming the tap delays, amplitudes and phases [120], [59], [123]. In the following sections we demonstrate two dierent applications: (i) pattern correlation for both amplitude and phase encoded signals [120], [123], and (ii) equalization of chromatic dispersion [120], [59]. 3.3 Experimental Setup The experimental setup for the all-optical TDL is shown in Figure 3.6. Also shown in Figure 3.6 are sample measured spectra after the rst and second PPLN waveguides for a three-tap TDL with dierent tap amplitudes. After optical wavelength multicasting (fan-out) and dispersive medium, the taps (signal copies) can be combined using either optical multiplexing or electrical multiplexing (in photodiodes). In the latter, the input signal is optical and the output is a bipolar electrical signal. 3.3.1 Complex-Coecient TDL using Optical Multiplexing As depicted in Figure 3.6, for equalization and correlation experiments 27=40 Gbit/s NRZ-BPSK and NRZ-DPSK signals, 62=80-Gbit/s NRZ-QPSK and NRZ-DQPSK sig- nals were generated using a CW laser at wavelength S 1539:3 nm and nested Mach- Zehnder modulators (MZMs). The 40-Gbit/s OOK signal was generated using an MZM symmetrically driven aroundV =2. To generate 50% RZ waveforms for 40 Gbaud signals, another MZM was cascaded as a pulse carver and was driven by a 40 GHz clock signal. Pseudo-random bit sequence (PRBS) 2 31 1 was used for the equalization experiments while a PRBS 2 7 1 pattern was chosen for the correlation results (to show a 127-bits- long waveform). For the equalization experiments, a ber-Bragg-grating-based tunable dispersion compensating module (TDCM) emulated chromatic dispersion to distort the input signal. The signal was coupled with a CW pump ( P 1 1562:1 nm, for SFG process) and four tunable CW lasers ( D14 : 1553:6 1558:4 nm for DFG processes) and 39 Dispersive Fiber Ȝ P1 BPF 2 nm 27/40 Gbaud PRBS 2 nm Ȝ S Ȝ D3 MZM 90° 40 GHz Clock Tunable Dispersion 9 nm PC LCoS Filter ǻ t IQ Mod. Ȝ D4 Ȝ D1 Ȝ D2 26dBm 24dBm 25dBm Dummy Pump Lasers Transmitter Multicasting (Fan-out) Delay and Phase Control 1,540 1,551 1,562 -60 -40 -20 0 QPM ω MUX Power (dBm) Wavelength (nm) ω P2 1,540 1,551 1,562 -60 -40 -20 0 Power (dBm) Wavelength (nm) ω D2 ω S QPM ω P1 ω C2 A A B 2 nm Ȝ P2 2 nm 18 nm 24dBm 27dBm Optical Multiplexer PPLN-2 ATT BPD DLI 1 nm 1 nm BERT Pre-Amplified Receiver Thresholding Receiver 9 nm Correlator Electrical Output Equalizer Thresholding Receiver Correlator Output 0.8 nm Equalizer Electrical Output Matched Paths BPD 9 nm Electrical Multiplexer B 1) Optical Multiplexing 2) Electrical Multiplexing (a) Optical Multicasting and Delay (b) Optical Multiplexing (c) Electrical Multiplexing PPLN-2 Figure 3.6: Experimental set-up for an optical TDL for equalization and correlation. (a) Multicasting and delay, (b) optical multiplexing, and (c) electrical multiplexing. Spectra of the rst and the second PPLN waveguide outputs are shown for a 3-tap optical TDL with various tap amplitudes. PPLN: Periodically poled lithium niobate waveguide, LCoS: liquid crystal on silicon, PC: polarization controller, BPF: bandpass lter, ATT: attenuator, DLI: delay line interferometer, BERT: bit error rate tester, BPD: balanced photodiode, MZM: Mach-Zehnder modulator. sent to the rst PPLN waveguide with a QPM wavelength of 1550:7 nm. The signal and P 1 pump powers were 80 mW, and each dummy pump power launched into the rst PPLN waveguide was 35 mW. The CW pump lasers ( D14 ) generated 40 the signal copies ( C14 ). The signal copies and corresponding pump lasers were all ltered using an amplitude- and phase-programmable lter based on LCoS technology and sent to a dispersion compensating ber (DCF) to introduce tap delays. The ber chromatic dispersion D is related to the group velocity dispersion parameter according to D2c 2 = 2 , in which c is the speed of light [1]. Therefore, a DCF of length L, induces a relative delay of t = DL between two signals with wavelength separation of . DCF lengths of 90 m and 180 m were used in equalization and correlation experiments, respectively. The DCF has D86 ps/nm/km dispersion. For 1:6 nm wavelength separation this corresponds to 12:5 ps and 25 ps delay after 90 m and 180 m DCF spools, respectively. In TDL, delays from a fraction of a symbol time to few symbol times between the taps would be desirable. For 40 Gbaud signals, the delays would be in picoseconds range and thus realizing them may not require the complexity of very large conversion-dispersion delays [68]. When ltering the signal copies and dummy pumps, the LCoS programmable lter also applied the tap phases on the dummy pumps. After the DCF, the dummy pumps and copies were amplied, and then ltered with a center- and bandwidth-tunable lter of 15-nm maximum bandwidth. The output was coupled with a CW pump laser at P 2 and sent to a second PPLN waveguide for optical multiplexing. For DFG mixing in the second PPLN waveguide, a CW pump laser P 2 1562:1 nm was used. Alternatively, the pump laser P 1 can also be split and used in both the rst and second stages. The power launched into the second PPLN waveguide was 90 mW for P 2 pump plus 200 mW for all signal copies and their re-used dummy pumps. The QPM wavelength of the second PPLN waveguide was set to 1550:7 nm as well. The rst and second PPLN waveguides were 4 cm and 5 cm long, respectively. The multiplexed signal was generated at 1539:3 nm wavelength and was ltered and sent to a pre-amplied receiver. Single- ended and balanced photodiodes with 30-GHz bandwidth were used for direct detection in the equalizer experiments. Bit error rate (BER) measurements are performed on the equalized output of the TDL. A thresholding balanced photoreceiver was used for 41 electrical thresholding of the optical correlation waveforms to distinguish the full match from partial matches. 3.3.2 Bipolar-Coecient TDL using Electrical Multiplexing A 40 Gbit/s NRZ-OOK signal ( S 1549:4 nm) is generated using an MZM driven by a 2 31 1 PRBS. An amplied spontaneous emission (ASE) noise source along with an attenuator is used to noise load the transmit signal in order to change the input optical signal to noise ratio (OSNR). The data signal is coupled with a second pump ( P 1 1553:4 nm) and four tunable continuous wave (CW) lasers ( D1 to D4 ) and is sent into a 5-cm-long PPLN waveguide with a QPM wavelength 1551:4 nm. All pumps and data signal are amplied and ltered before the PPLN waveguide to enhance wavelength conversion eciency and the optical signal-to-noise ratio (OSNR). The four pump lasers ( D1 to D4 ) allow for realization of four taps ( C1 to C4 ). For the intensity-based correlator, equal tap weights are used, while the tap weights for the three-tap equalizer are tuned for optimal equalization performance by adjusting the respective CW powers. The multicast signals are then ltered by a 9 nm lter and sent to a dispersive medium in order to induce a wavelength dependent delay. A 1 km single mode ber (SMF) is used for the correlator, where a 60 m DCF is used for the equalizer experiments with electrical multiplexing. For the correlator, the delayed signal copies are then sent to a 30-GHz bandwidth thresholding receiver in order to nd the correlation peaks. Because an equalizer requires bipolar taps weights, all positive taps are multiplexed in the positive port of a balanced photodiode and all negative taps are multiplexed on its negative port. A 36 GHz balanced photodiode (BPD) is utilized for this purpose. Positive and negative taps are rst ltered separately by 0:8 nm BPFs and are then combined together and sent to the BPD, as shown in Figure 3.6. The ber lengths are matched for the positive and negative taps prior to the BPD. An equalized electrical signal is achieved at the output of the BPD which is sent to the BER measurement system. 42 3.4 Conclusions We have demonstrated an optical tapped-delay-line (TDL) that utilizes nonlinear wave mixing and the frequency-dependence of the speed of light to achieve tunability and recongurability of all parameters of the TDL. This optical TDL uses cascaded SFG and DFG mixings in a PPLN waveguide to produce variable-amplitude signal copies (taps) and conversion-dispersion-based optical delays to realize the tap delays. Therefore, the tap-coecients and the number of taps can be varied by changing the powers and wavelengths of the pumps used for wave mixing. Optical and electrical multiplexing of the taps has been shown. If optical multiplexing is used, complex tap coecients can be realized by reusing the multicasting dummy laser pumps in the multiplexing nonlinear stage. Electrical multiplexing of the taps is also demonstrated with bi-polar tap coecients. 43 Chapter 4 Characterization of the Optical-Tapped-Delay Line In this chapter we characterize the tuning of the tap phases by using ne detuning of the pump lasers. We then characterize the performance of the nite impulse response lter and compare the results with the theoretical derivations. 4.1 Characterization of Phase Tuning using Fine Wave- length Oset 4.1.1 Introduction Tapped-delay-lines (TDLs) are a key building block for various analog and digital sig- nal processing applications, including nite impulse response (FIR) ltering, waveform generation, correlation, equalization and discrete Fourier transform [87][64]. In a TDL, the incoming signal is tapped at dierent time intervals, each tap is multiplied by an amplitude and phase coecient, and the taps are then added together. Optical imple- mentations of TDLs have been of interest for many years [76][33],[94]. Because tunable 44 lters can provide more functions than static lters, it may be of interest to develop opti- cal TDL schemes that allow for continuous tunability of the TDL parameters in order to accommodate dierent applications [64]. Recent work on optical TDL systems includes xed ber-based structures [76], cas- caded Mach{Zehnder interferometers [33][94], and opto-electronic approaches that utilize microwave techniques [15]. In general, these optical approaches tend to be either xed or tunable over a nite range for some parameters. Thus, developing a system with independent control over all four key parameters of the TDL (i.e., tap amplitudes, tap phases, number of taps, and tap delays) may be of interest [64]. Recently, we experimentally demonstrated a fully tunable complex-coecient optical TDL (FIR lter) based on conversion/dispersion delays in which all crucial parameters of the TDL could be changed by varying the properties of the tunable pump lasers injected into the system [64]. The system utilized nonlinear wavelength multicasting, conversion/dispersion tunable delays, and nonlinear multiplexing to achieve tunability and recongurability. In this technique, the tap amplitudes and delays could be inde- pendently determined by the power and wavelength of the pump lasers, respectively; however, in our previous demonstrations, a phase programmable lter (based on spa- tial light modulation) was required to set the tap phases. This could be a drawback, especially for integration purposes. In this section, we theoretically derive and experimentally characterize the tuning of tap phases, which occur because of the ne-tuning of pump lasers after de-tuned signals propagate through a dispersive element that is already part of the system. Using ne- tuning, phase shifts are induced without the need for a spatial light modulator phase lter. Our results demonstrate continuous 2 tunability of phase with a laser frequency detuning of<20 GHz, with negligible error on the wavelength-dependent tap delays. The amount of ne detuning required depends on the dispersion parameter and the dierence between the pump wavelengths [58]. 45 … 1 0 1 1 0 0 … … 1 0 1 1 0 0 … … 1 0 1 1 0 0 … … 1 0 1 1 0 0 … … 1 0 1 1 0 0 … … 1 0 1 1 0 0 … Copy 3 Time ≈ Copy 2 ≈ Copy 1 ≈ Copy 3 Time ≈ Copy 2 ≈ Copy 1 ≈ Multiplexing Nonlinear Element (PPLN #2) Dispersive Medium, β 2 (DCF) Input Signal N+1 Pumps Multicasting Output Signal Phase Filter (LCoS Filter) Nonlinear Element (PPLN #1) Delay & Phase h 1 h 2 h 3 ω C1 ω C3 ω D1 ω D3 ω P1 ω Signal Signal Copies ω C1 ω C3 ω D1 ω D3 ω P2 ω MUX Delayed and Weighted Signal Copies Delay Phase ω ω ω ω Coarse Tuning of Pump Wavelengths: ϕ i ≈ ( −2L β 2 Δ ω i ) δ ω i ∠ φ 1 ∠ φ 2 ∠ φ 3 Fine Tuning of Pump Wavelengths: Input Signal Output Signal Signal Multicasting Channel Multiplexing Negligible Delay Error Figure 4.1: The principle of operation of the complex-coecient optical tapped-delay- line. 4.1.2 Concept and Theoretical Analysis Figure 4.1 illustrates the principle of operation of the tunable optical TDL. First, cas- caded second-order (2) nonlinear processes of sum frequency generation (SFG) followed by dierence frequency generation (DFG) are exploited in a periodically poled lithium niobate (PPLN) device with the aid of multiple tunable dummy pump lasers to mul- ticast the signal to N copies at dierent frequencies. The cascaded (2) processes of SFG-DFG in a PPLN device resemble the (3) process of four-wave-mixing (FWM) in highly nonlinear ber [69][1]. The signal at frequency ! signal and a continuous wave (CW) pump at ! P 1 , symmetrically located around the quasi-phase matching (QPM) frequency ! QPM of the PPLN waveguide, mix through the SFG nonlinear process, and 46 the resulting signal then mixes with dummy pumps at ! Di through the DFG process. These cascaded mixings create signal copies at frequencies ! Ci = ! signal +! P 1 ! Di . Subsequently, these replicas travel through a chromatic dispersive element (e.g., a dis- persion compensating ber, DCF, of length L and group velocity dispersion parameter 2 ) at dierent speeds incurring a distinct time delay with respect to the rst copy T i L 2 (! Di ! D1 ). Finally, these N replicas and their dummy pumps are sent into the second PPLN device together with another CW pump at ! P 2 to be multiplexed together using the cascaded SFG-DFG processes, resulting in a multiplexed output sig- nal at frequency ! Ci =! Di +! Ci ! P 2 =! signal + (! P 1 ! P 2 ). As discussed in [64], the multiplexed signal is proportional to E MUX (t)/E P 2 E P 1 Z N i=1 (E Di E Di ) e j( i + LCoS i ) E signal (tT i ); (4.1) in which,E signal (t) is the electric eld of the input signal andE MUX (t) is the electric eld of the output of the TDL. E P 1 and E P 2 denote the electric eld amplitudes of the CW pumps at ! P 1 and ! P 2 , respectively, that impact all copies (taps) similarly. The asterisks denote the complex conjugate of the electric elds. Because the dummy pumps (E Di ) and their phase-conjugates (E Di ) are both multiplied by the input signal, the eld of each FIR lter tap is proportional to the power of the dummy pumps. The phase of the each tap is composed of an optional part ( LCoS i ) that can be set using a phase and amplitude programmable lter based on liquid-crystal-on-silicon (LCoS) technology, and another part ( i ) that is intrinsically induced by the chromatic dispersion on the path [64] i = 2 Z 1 n=0 (! Di ! QPM ) 2n (2n)! L 2n =2L 0 (! Di ! QPM ) 2 L 2 ::: (4.2) in which k = @ k =@! k !=! QPM is thek-th derivative of the wave's propagation param- eter (!) calculated at angular frequency! QPM . We note that because of the symmetry of! Di 's and! Ci 's around the QPM frequency, only the even terms remain in the Taylor 47 series expansion in (4.2). The relation between the input and output of the system can be written in the form of a complex-coecient FIR lter as E MUX (t)/ Z N i=1 jh i je j\h i E signal (tT i ) (4.3) in which h i is the complex coecient for the i-th delayed copy. Its amplitude is the power of the i-th dummy pump ! Di and its phase is related to the physical parameters of the system according to \h i = ( i + LCoS i ). In the past, a phase programmable LCoS lter was used to apply the tap phases, which can be omitted if the ! Di pumps are nely detuned in frequency. Here, we note that tap phases can be applied by ne detuning of ! Di pumps by ! Di according to (\h i ) = i 2L 2 (! Di ! QPM )! Di : (4.4) However, this ne detuning changes the tap delays by T i =T i ! Di =(! Di ! D1 ) (4.5) We studied this trade-o and determined if the pumps are reasonably far from each other and/or ! QPM , the delay error can become relatively negligible. In summary, in this scheme for optical FIR ltering, both the amplitude and phase of the taps can be varied by changing the powers of the pump lasers and ne-tuning the wavelengths of the pump lasers. The tap delays can be varied by coarse tuning of the pump wavelengths to enable baud-rate tunability. Finally, the number of taps can be scaled by injecting more dummy lasers into the devices. Because more taps occupy more bandwidth, the scaling of taps is limited to the available device bandwidths and the maximum power that can be injected into the nonlinear devices. It is well-known that a phase shift happens as a result of (!)L = L P 1 k=0 k (!! QPM ) k =k!. However, it is worth noting that in this technique, because 48 the! Ci signal and the! Di pump that are symmetrically located around! QPM are mul- tiplied in a nonlinear device, their phases add; therefore, the odd terms of this Taylor series cancel out, leaving only the even terms 0 , 2 , 4 , ::: . As calculated in (4.4), when! Di is slightly changed by! Di , a phase shift that is linearly proportional to 2 is induced because 1 and 3 terms are already eliminated in the deployed scheme. We will show that the experiments conrm that 4 has negligible impact on phase shift compared to 2 ; thus, the approximation in (4) has very high accuracy. 4.1.3 Experimental Setup Figure 4.2(a) shows the experimental setup for the phase tuning characterization. A CW input signal at wavelength signal 1540.8 nm, a pump at P 1 1559.2 nm, and a dummy pump at D1 1549.5 nm combined with another tunable pump D2 (1552.2 nm,1554.1 nm,1555.9 nm, and1557.7 nm) are separately amplied, ltered and launched into the rst 4-cm-long PPLN waveguide for multicasting. The output spec- trum of PPLN #1 is shown in Figure 4.2(b). The output is then sent into an amplitude- and phase-programmable LCoS lter which (i) passes the signal copies and dummy pumps but blocks the original signal and P 1 pump, and (ii) is used to measure and validate the amount of phase shift created by ne-tuning of wavelengths with 5 accu- racy. Subsequently, the copies and pumps pass through a spool of DCF with dispersion parameter D80 ps/nm/km and length170 m or425 m (D =2c 2 = 2 ). The two DCF lengths allow for experiments with 15 ps/nm or 34 ps/nm dispersion. Next, the signals are amplied, ltered, combined with a CW pump P 2 and sent to the second PPLN waveguide of length 5 cm. The QPM wavelengths of the two PPLN waveguides are thermally tuned to1550 nm. The P 1 pump is split and used as P 2 as well; therefore, the output multiplexed signal lands on the original signal frequency (Figure 4.2(b), PPLN #2 output spectrum). The multiplexed signal is nally ltered and sent to an optical spectrum analyzer (OSA) for power measurements. To further assess the 49 1,540 1,550 1,560 -60 -40 -20 0 Power (dB) Wavelength (nm) 1,540 1,550 1,560 -60 -40 -20 0 Power (dB) Wavelength (nm) Multicasting Stage (PPLN #1 Output) λ C2 λ Signal λ P cSFG-DFG λ C1 λ D1 λ D2 QPM Multiplexing Stage (PPLN #2 Output) λ MUX QPM (a) (b) 2 nm λ signal 9 nm 24 dBm EDFA 1 nm 2 nm λ D1 DCF ~425 m or ~170 m LCoS Filter 5-cm PPLN PC 4-cm PPLN λ D2 25 dBm λ P2 2 nm 26 dBm 2 nm 23 dBm 18 nm 29 dBm OSA or Coherent Rx 20 dBm λ P1 31 Gbaud QPSK Tx Figure 4.2: (a) Experimental setup for the tunable optical TDL using optical multicast- ing, conversion/dispersion delays, and optical multiplexing. (b) Output spectra of PPLN #1 and PPLN #2. performance of the system, the CW signal is modulated using an IQ modulator to gener- ate a quadrature-phase-shift-keyed (QPSK) signal at 31 Gbaud data rate (PRBS 2 31 -1) and detected using a coherent optical receiver. 4.1.4 Experimental Results and Discussion Because only two taps are used to study the phase tuning characteristics, the output has the form of y (t) = x (t) +e j x(tT ), which can result in constructive or destructive interference depending on the phase. Figure 4.3(a) shows the multiplexed signal for the two cases of constructive and destructive interference, creating a peak or a null with a >35 dB extinction ratio. In Figure 4.3(b), the wavelength of D2 (located 4.1 nm from QPM ) is nely detuned and 50 1540.6 1540.8 1541.0 -80 -60 -40 Power (dBm) Wavelength (nm) Peak (Constructive Interf.) Null (Destructive Interf.) (a) (b) -4 -2 0 2 4 0.0 0.5 1.0 D = 15 ps/nm, Theory D = 15 ps/nm, Experiment D = 34 ps/nm, Theory D = 34 ps/nm, Experiment Multiplexed Signal (Normalized Power) Frequency Fine Tuning (GHz) Figure 4.3: (a) Constructive or destructive interference could create a peak or null at the output, used for phase characterization. (b) Interference fringes caused by ne detuing of pump frequencies for dierent amounts of dispersion. the power is measured for dierent dispersion values. The resulting squared-cosine-shape fringes closely match with the theory derived in (4). Higher dispersion would require less ne-tuning. Figure 4.4(a) shows the theoretical and experimentally measured phases induced by ne-tuning the tap wavelengths. As predicted in (4), the slope of the phase change versus frequency ne-detuning depends on the separation between the wavelength of the pump and that of the QPM. Taps with longer time delay require larger pump-QPM wavelength separation and less ne-detuning. Figure 4.4(b) visualizes ne-tuning of the CW pump located 4.2 nm away from the QPM wavelength (i.e., middle tap in Figure 4.4(a)). In Figure 4.5, the amount of frequency detuning required for 360 phase shift is plotted versus the relative location of the tap (i.e., tap delay) for dierent dispersion values. Once again, the theory and experiments are in agreement, proving that the 51 1553.85 1554.00 1554.15 1554.30 -40 -30 -20 -10 0 Tap Phase = 180 Tap Phase = 0 Tap Phase = -180 Power (dBm) Wavelength (nm) (a) (b) -3 -2 -1 0 1 2 3 -180 -90 0 90 180 Theory, 2.3 nm Experiment, 2.3 nm Theory, 4.1 nm Experiment, 4.1 nm Theory, 7.7 nm Experiment, 7.7 nm Induced Phase (Degree) Frequency Fine Tuning (GHz) Figure 4.4: (a) Measured phase induced by frequency ne-tuning for various tap to QPM wavelength distances. (b) Fine-tuning of tap located at 4.1 nm. longer delays and larger dispersions require less detuning. For taps that are very close to the QPM wavelength, the required detuning becomes signicant because the shape of the plot has a hyperbolic asymptote on the QPM wavelength. It is worth noting that if the rst tap is chosen reasonably far from the QPM wavelength, the phase tuning is limited to <20 GHz; however, the part of the spectrum that is close to the QPM wavelength could be wasted (i.e., fewer taps can be achieved). Furthermore, for delays that are very large, a very small amount of detuning might be required, which can be done using acousto-optic modulators [80]. The eect of ne-detuning on time delay error is depicted in Figure 4.6. According to (4.5), larger dispersion values cause higher errors; therefore, the worst case (D=34 ps/nm) is considered and the delay error is plotted versus a phase induced by the ne- tuning method. For our case, in which the signals are in the C-band, the worst-case 52 0 2 4 6 8 10 -45 -30 -15 0 Power (dBm) Wavelength from QPM (nm) Ref. Tap 2.2 nm 4.1 nm 5.9 nm 7.7 nm (a) (b) 0 2 4 6 8 10 0 10 20 30 D = 15 ps/nm, Theory D = 15 ps/nm, Experiment D = 34 ps/nm, Theory D = 34 ps/nm, Experiment Frequency Offset for 360 o Phase Shift (GHz) Wavelength from QPM (nm) Figure 4.5: (a) Required frequency detuning for 2 phase shift on a tap versus tap-to- QPM wavelength distance for various DCF lengths. (b) Spectrum showing tap delay variation. -180 -90 0 90 180 -10 0 10 Delay Error Due to Fine Tuning (%) Phase Induced by Fine Tuning (Degrees) 2.2 nm 4.1 nm 7.7 nm Figure 4.6: Theoretical relative delay error versus phase applied by ne-tuning of pump wavelengths for D = 34 ps/nm disperison at dierent delays (wavelength separation). tap delay error is <10% and can be reduced by placing the taps farther from the QPM wavelength. The amount of frequency ne-detuning required for a 2 phase shift depends on the distance to the tap from the QPM wavelength (Figures 4.4(a) and 4.5(a)). If longer DCFs are used, coarser tuning will be required; however, for a given tap delay (i.e., 53 Input 31 Gbaud QPSK Output Taps: [1 1] Output Taps: [1 -1] EVM = 11.4% EVM = 12.5% Figure 4.7: Input 31-Gbaud QPSK signal constellation diagram, and the output of a 2-tap correlator with tap coecients [1 1] and [1 -1]. multiplication of DCF dispersion and wavelength separation is given), there is a trade- o between choosing longer DCFs and smaller wavelength spacing (i.e., more taps but shorter tap-delay tuning range) and shorter DCFs and longer tap-tuning range. For both cases, the ne-tuning required can be made negligible compared to the tap-wavelength spacing. Because more taps naturally appear farther from the QPM wavelength, it is intrinsic to the scheme that when more taps are added, this delay error becomes negligible, as shown in Figure 4.6. To assess the eect of delay error on the output signal quality, a 31-Gbaud QPSK signal is sent to a 2-tap TDL with one symbol time delay between the taps. As a result, the TDL works as a 2-tap QPSK correlator. Two taps are considered because they experience the largest delay error as a result of wavelength ne-tuning. Figure 4.7 depicts the input and output constellation diagrams, resulting in1% larger error vector magnitude (EVM) in the output signal when the tap phase is changed from 0 to . 4.2 Finite Impulse Response Filter Characterization 4.2.1 Introduction A key building block for many signal processing functions is a nite-impulse-response (FIR) lter, that can be used for matched ltering, equalization, pulse shaping, and 54 correlation [87]-[74]. Implementation of FIR lters requires time-delayed taps, with each tap weighted by a variable complex (amplitude and phase) coecient. For many years, there has been a keen interest in the possibility of realizing FIR lters all-optically in order to utilize the high bandwidth of optics and achieve transparent operation. Given that tunable lters are more useful than the xed lters, a crucial goal would be the continuous tunability of the optical FIR lters' characterization [101]. Utilization of the large bandwidth of photonic technologies for high-speed signal processing may require implementation of FIR lters all-optically. An optical method can potentially advance signicantly the performance of signal processing when the signal to be processed is at high speed or is a combination of many lower-speed signals [33]. Recent works that involve optical FIR lters have been based on technologies such as xed ber-based delays [76], integrated cascaded Mach-Zehnder interferometers [33], integrated ring-resonator-based lters [73][34], beating between frequency combs [101], and microwave photonics techniques [114]. Most of these approaches are generally xed or are tunable over nite or discrete ranges, and tend not to have independent control over the amplitude, phase, and delay of each tap of the FIR lter. Therefore, a laudable goal would be to demonstrate an FIR lter in which all critical parameters of the FIR lter (i.e., the FIR length, amplitudes, phases and delays) are tunable. In this section, we experimentally characterize the performance of a tunable opti- cal FIR lter with complex coecients that achieves recongurability through the use of nonlinearity-based wavelength conversions and chromatic-dispersion-based delays [57][97]. In our scheme, the n-th order susceptibility ( (n) ) in the periodically poled lithium niobate (PPLN) waveguides is exploited to realize signal multicasting and multi- plexing. Tunable optical delays are realized using the frequency-depend speed of light in a dispersion compensating ber (DCF) [97]. Phase coherent multiplexing is made possi- ble by reusing the same pump lasers that are initially used for wavelength multicasting. We experimentally assessed the tuning of tap amplitudes from 0 dB to -9 dB, tap phases 55 ࡴ ሺ ࣓ ሻ ൌ෍ ࢎ ࢏ ࢋ െ ࢐ ࣓ࢀ ࢏ ࡺ ࢏ൌ ૚ ࢟ ሺ ࢚ ሻ ൌ෍ ȁ ࢎ ࢏ ȁ ࢋ ࢐ עࢎ ࢏ ࢞ሺ࢚ െ ࢀ ࢏ ሻ ࡺ ࢏ൌ ૚ ȁ ࢎ ૚ ȁ ࢋ ࢐ עࢎ ૚ ȁࢎ ૛ ȁࢋ ࢐ עࢎ ૛ ȁࢎ ࡺ ȁࢋ ࢐ עࢎ ࡺ Variable-Weight Fan-out (Optical Wavelength Multicaster) Phase Coherent Combiner (Optical Multiplexer) × × × T i (tap delays) Frequency dependent delay (e.g., DCF) N (FIR length) Number of dummy pump lasers Ȧ Ȧ Input Output FIR Filter Response T 1 T 2 T N h 1 h 2 h 3 Ȧ C1 Ȧ C3 Ȧ D1 Ȧ D3 Ȧ P1 Ȧ signal Signal Copies (tap amplitudes) Dummy lasers’ pump powers (tap phases) (i) LCoS filter, or (ii) Fine tuning of pump laser frequencies ȁܐ ܑ ȁ עܐ ܑ ࢄ ሺ࣓ሻ ࢅሺ࣓ሻ Ȧ C1 Ȧ C3 Ȧ D1 Ȧ D3 Ȧ P2 Ȧ MUX Delayed Signal Copies Figure 4.8: Conceptual block diagram of the tunable complex-coecient optical FIR lter. (0 to 2), and the delays (37.4 ps and25 ps) by measuring the lters' frequency responses. The measurements show close agreement with theoretical lter responses. 4.2.2 Theoretical Analysis For a length-N FIR lter with N taps taken at times T i and weighted by complex- coecients h i , the relation between the input signal x(t) and the output signal y(t) is determined by y (t) = P N i=1 h i x(tT i ). Therefore, the FIR lter can be tuned and recongured by changing the number of taps (N), tap delays (T i ), and complex tap coecients (h i ). Figure 4.8 shows the conceptual block diagram of the tunable complex- coecient FIR lter. First, a nonlinear optical mixer and multiple tunable dummy pump lasers fan-out N (N = 3 in Figure 4.8) copies of the input data signal, with each signal copy located at a dierent center frequency. Subsequently, these replicas travel through a dispersive medium (e.g., DCF) at dierent speeds resulting in a dierent time delay 56 on each signal copy. Finally, these copies are multiplexed together in a phase-preserving scheme by another high-speed nonlinear mixer, creating an output signal that is ltered by the FIR lter. Each signal copy generated in the fan-out stage represents a tap in the FIR lter and thus the taps can be accurately tuned in terms of amplitude, phase and relative time delay. PPLN waveguides are used as the nonlinear optical wave-mixer. These mixing interactions are governed by conservation of energy and phase-matching conditions [69]. In the fan-out stage, cascaded (2) processes of sum frequency generation (SFG) and dierence frequency generation (DFG) create copies of an amplitude/phase encoded input signal (! signal ) [69]. In the rst nonlinear stage the signal at! signal mixes with a continuous-wave (CW) pump laser at frequency ! P 1 . The signal and the dummy pump frequencies are located at equal distance from the quasi-phase-matching frequency (! QPM ). According to the \conservation of energy rule", this generates a sum frequency term at ! signal +! P 1 which is followed by multiple (N) DFG processes with the aid of N other CW dummy pump lasers at ! Di . Consequently, copies of the signal will be generated at frequencies! Ci =! signal +! P 1 ! Di . After passing through the DCF, each signal copy (tap) is delayed by T i = 2 L(! Ci ! C1 ) = 2 L(! D1 ! Di ) relative to the rst tap ( 2 is the group velocity dispersion parameter). Similarly, cascaded SFG-DFG processes are used in another PPLN waveguide with the same QPM frequency as the rst PPLN waveguide for optical multiplexing. To maintain the relative phase of taps in the multiplexing stage, the dummy pumps from the fan-out stage are ltered together with the signal copies (taps) in a phase/amplitude programmable lter based on liquid crystal on silicon (LCoS) technology. The LCoS lter, passes the signal copies and the dummy pumps and blocks the signal and ! P 1 pump. Additionally, it applies the tap phases ( i 's) on the dummy pumps (! Di 's). Therefore, the dummy pumps are reused for the SFG mixings followed by DFG mixing using another CW pump laser at ! P 2 . Thus, all taps are multiplexed to the frequency ! MUX =! Ci +! Di ! P 2 =! signal + (! P 1 ! P 2 ) to create the FIR lter output. If same pump lasers (! P 1 = ! P 2 ) are used in both nonlinear stages, the FIR lter output is generated at the same center frequency as the 57 input signal. Governed by the \phase matching conditions" in nonlinear wave mixings, each tap contributes to the multiplexed output proportional to e j i E P 2 E Di E Di E P 1 E signal (tT i ); (4.6) in which E denotes the electrical eld amplitude and E is its complex conjugate. Neglecting the common terms between the taps (that do not depend on the indexi), the resulting output signal of the FIR lter is proportional to E MUX (t)/ N X i=1 e j i jE Di j 2 E signal (tT i ) (4.7) Therefore, the FIR length (N, number of taps) can be varied by adding/removing dummy pump lasers, FIR delaysT i can be continuously varied by tuning the dummy pumps' fre- quencies, and FIR tap amplitudes are directly controlled by the dummy pumps' powers. The FIR lter tap phases can be applied using the LCoS lter or by adding a ne oset to the dummy pump wavelengths. 4.2.3 Experimental Setup Figure 4.9 depicts the experimental setup. A vector network analyzer (VNA) sweeps the frequencies from0 to 40 GHz to modulate a1538.5 nm laser (! signal ) using a Mach- Zehnder modulator biased at the quadrature point. This input signal, a1562.5-nm CW pump laser (! P 1 ), and four CW dummy pump lasers (! D1 to ! D4 ) are separately amplied, ltered, coupled together and sent into a 4-cm PPLN waveguide. The cascaded SFG-DFG processes in the rst PPLN waveguide create copies of the signal (! C1 to! C4 ). The LCoS-based lter after the PPLN waveguide passes the dummy pumps (! Di 's) and the signal copies (! Ci 's) and cuts o the signal and the ! P 1 pump. The LCoS lter also applies the variable tap phases on the dummy pumps, as shown in Figure 4.9(b). The signal copies and the dummy pumps are sent to an L 195 m DCF to induce the 58 ω P1 2 nm PPLN-1 2 nm ω signal ω D3 MZM DCF ~195 m 9 nm PC LCoS Filter ω D4 ω D1 ω D2 26dBm 24dBm 25dBm Dummy Pump Lasers VNA Multicaster (Fan-out) Delay and Phase Control 2 nm ω P2 PPLN-2 2 nm 18 nm 24dBm 27dBm Multiplexer 1 nm Vector Network Analyzer Photodetector LCoS Phase Ȝ LCoS Amplitude Ȝ C3 Ȝ C2 Ȝ C1 Ȝ D3 Ȝ D2 Ȝ D1 0dB עܐ ૚ עܐ ૜ עܐ ૛ Ȝ signal Ȝ P1 ab Figure 4.9: (a) Experimental setup: multicaster, delay, phase control, and multiplexer. (b) A generic LCoS lter amplitude/phase prole for applying phases on the pumps. relative delays between copies. The DCF has chromatic dispersion ofD 80 ps/nm/km, resulting inDL = 15:6 ps/nm dispersion for the DCF spool. The signal copies and the pump lasers are then amplied and sent to a 5-cm PPLN waveguide, along with another CW pump laser (! P 2 ) at 1562.5 nm. The QPM wavelength of both the rst and the second PPLN waveguides are temperature tuned to1550.5 nm. Therefore, the wave mixings in the second PPLN waveguide can produce mixing products in a reciprocal fashion and generate a multiplexed output signal at the center frequency of the original input signal. Since ! P 2 =! P 1 the FIR lter's output is formed at ! signal and is ltered out, amplied, sent to a photodetector and fed back to the VNA. The VNA characterizes the amplitude and phase response of the optical FIR lter. Table 4.1 shows the reconguration capability of the FIR lter for various symbol rates. In order to congure the FIR lter for input signals with 40 Gbaud symbol rate, the tap delays of the lter need to be separated by 25 ps. Therefore, the wavelengths 59 Table 4.1: Optical FIR capability to accommodate dierent baud rates using tunable delays. DL = 15.6 ps/nm Wavelength Sepa- ration, Symbol Time, T = (DL) Digital Filter Sym- bol Rate, 1=T Analog Filter FSR, FSR = 1=T 1.6 nm 25 ps 40 Gbaud 40 GHz 2.4 nm 37.4 ps 26.7 Gbaud 26.7 GHz of adjacent dummy pumps should be 1.6 nm apart, so that after passing through 15.6 ps/nm dispersion the taps experience 25 ps relative delay. If the adjacent tap delays are equal (i.e.,T i = T ) the resulting lter will be periodic with an FSR of 1=T . To tune to a dierent input signal rate (or lter FSR), the wavelength separation is increased to 2.4 nm resulting in lters with 26.7 GHz FSR. 4.2.4 Results and Discussion Figure 4.10(a) depicts the measured spectrum after the multicasting stage for a length-3 FIR lter with37.4 ps delay (i.e., 2.4 nm wavelength spacing). In Figure 4.10(b), the output spectrum of the multiplexing stage is shown and the tap phases are set to create a null at the center frequency (destructive interference, 120 phase dierences). The frequency responses of the FIR lters are measured and shown together with normalized theoretical responses in Figure 4.10(c) and (d). The measurements are normalized with respect to one-tap operation. To demonstrate tap-coecient tuning, in Figure 4.10(c), all taps are set to have equal amplitudes and their phases are tuned using the LCoS lter. In Figure 4.10(d), amplitudes are varied by tuning laser powers in the rst stage and the phases are kept the same (3 dB attenuation results in a 0.5 factor in \jhj"). Length-4 FIR lters with FSR40 GHz are realized in Figure 4.11, where pump separations are set to 1.6 nm to induce25 ps delay between the taps. Similarly, the tuning capabilities of the length-4 FIR lters are demonstrated in Figure 4.11(c) and (d). Dummy laser powers are varied from 0 to -9 dB resulting in tap-amplitudes of 1 to 0.125. The dierences between the theoretical responses and the measurements could be the result of limitation of the 60 1540 1551 1562 -60 -40 -20 0 Power (dBm) Wavelength (nm) QPM ω MUX ω P2 0 5 10 15 20 25 30 35 40 -30 -20 -10 0 10 Amplitude (dB) |h|=[1 1 1], ∠h=[180° 0° 0°], Theory |h|=[1 1 1], ∠h=[180° 0° 0°], Experiment |h|=[1 1 1], ∠h=[0° 180° 0°], Theory |h|=[1 1 1], ∠h=[0° 180° 0°], Experiment 0 5 10 15 20 25 30 35 40 -3.14 -1.57 0.00 1.57 3.14 Phase (Radians) Frequency (GHz) | |[ ] [ ]p 0 5 10 15 20 25 30 35 40 -30 -20 -10 0 10 Amplitude (dB) |h|=[0.4 0.2 1], ∠h=[180° 180° 0°], Theory |h|=[0.4 0.2 1], ∠h=[180° 180° 0°], Experiment |h|=[1 0.16 1], ∠h=[180° 180° 0°], Theory |h|=[1 0.16 1], ∠h=[180° 180° 0°], Experiment 0 5 10 15 20 25 30 35 40 -3.14 -1.57 0.00 1.57 3.14 Phase (Radians) Frequency (GHz) | |[ ] [ ]p 1540 1551 1562 -60 -40 -20 0 ω D3 ω D2 Power (dBm) Wavelength (nm) ω D1 QPM ω P1 ω C1 ω C2 ω C3 ω signal a b c d Figure 4.10: Wave mixing spectra for (a) fan-out stage, and (b) multiplexing stage. (c), (d) Experimental and theoretical amplitude/phase response of26.7-GHz FSR length-3 FIR lters. LCoS-lter resolution (5 ) and/or polarization variations eects. The VNA frequency response measurements show close agreement with the theory. The VNA bandwidth is limited to 40 GHz, but the FSR of the lter can potentially be made wider than 40 GHz by choosing smaller delays. The reconguration time of the lter is determined by the update speeds of the LCoS technology and pump wavelength tuning. 4.3 Conclusions we used ne-tuning of pump wavelengths to apply the tap phases in a complex-coecient optical tapped-delay-line that utilized conversion/dispersion-based delays and nonlinear 61 0 5 10 15 20 25 30 35 40 -30 -20 -10 0 10 Amplitude (dB) |h|=[0.5 1 1 1],∠h=[0° 0° 0° 0°],Theory |h|=[0.5 1 1 1],∠h=[0° 0° 0° 0°],Experiment |h|=[1 0.125 0.5 1],∠h=[0° 0° 0° 0°],Theory |h|=[1 0.125 0.5 1],∠h=[0° 0° 0° 0°],Experiment 0 5 10 15 20 25 30 35 40 -3.14 -1.57 0.00 1.57 3.14 Phase (Radians) Frequency (GHz) | |[ ] [ ]p 0 5 10 15 20 25 30 35 40 -30 -20 -10 0 10 Amplitude (dB) |h|=[1 1 1 1],∠h=[0° 0° 0° 0°],Theory |h|=[1 1 1 1],∠h=[0° 0° 0° 0°],Experiment |h|=[1 1 1 1],∠h=[-135° 135° 0° 0°],Theory |h|=[1 1 1 1],∠h=[-135° 135° 0° 0°],Experiment 0 5 10 15 20 25 30 35 40 -3.14 -1.57 0.00 1.57 3.14 Phase (Radians) Frequency (GHz) | |[ ] [ ]p 1540 1551 1562 -60 -40 -20 0 Power (dBm) Wavelength (nm) ω D4 ω D1 ω P2 ω C1 ω C4 ω MUX QPM 1540 1551 1562 -60 -40 -20 0 Power (dBm) Wavelength (nm) ω D4 ω D1 ω P1 ω C1 ω C4 ω signal QPM a b c d Figure 4.11: Wave mixing spectra for (a) fan-out stage, and (b) multiplexing stage. (c), (d) Experimental and theoretical amplitude/phase response of 40-GHz FSR length-4 FIR lters. wave mixing. Full 2 phase tuning was demonstrated by detuning the frequency of laser pumps by<20 GHz, which showed close agreement with theory. Next, we experimentally characterized the performance of a continuously tunable all-optical complex-coecient nite impulse-response (FIR) lter that exploited nonlinear signal processing (multiplex- ing and multicasting) and conversion-dispersion-based optical delays. Various length (three and four) optical FIR lters with dierent tap amplitudes (from 0 to -9 dB), tap phases (from 0 to 2), and tap delays (37.4 ps and 25 ps) were realized, showing recon- guration and tuning capabilities of this FIR lter. The measured frequency responses showed close agreement with the theoretical lter responses [57][58][62]. 62 Chapter 5 Applications of the Recongurable Optical Tapped-Delay-Line 5.1 Introduction In this chapter, we demonstrate some applications of the optical TDL for equalization of chromatic dispersion, discrete Fourier transform, and correlation on amplitude and phase modulated signals. We consider various baud rates and modulation formats to show the tunability and recongurability of the system. Modulation formats such as OOK, DPSK, and DQPSK in the form of RZ and NRZ have been utilized. 5.2 Correlation and Pattern Recognition The optical TDL could be programmed to search and recognize a specic pattern on a data stream [47], [94]. A high speed pattern search to locate and identify features of interest is very desirable in dierent elds of science, especially for searching large amounts of data. A correlator can perform pattern recognition and detect the location of a pre-determined pattern in a data set. Figure 5.1 shows the concept of pattern matching 63 4 Matches “C B A A” …A C CBA A BD … …A C CBA A BD … × C* × B* × A* × A* …A C CBA A BD … time 2 Matches “C - - A” 1 Match “- - A-” Threshold Full Match Not Matched One time before Matched time One time after Pattern for Matching: “CBAA” Four T aps Signal Symbols: OOK: 0,1 ; BPSK: -1,1 ; QPSK: ; Example: A, B, C, D 2 3 2 , , , 1 π π π j j j e e e Input Data Stream Tap 3 Tap 1 Tap 2 90 o time time zero 4 Tap 1 Tap 2 Tap 3 Tap 4 Tap 4 Full Mismatch Vector Addition Time Domain Full Match Vector Addition Time Domain (a) (b) Figure 5.1: Concept of a TDL-based correlator. (a) TDL coecients are determined by the search pattern. Input data stream slides through the TDL resulting in high correlation peak when full pattern matching occurs. (b) Complex coecient taps allow for vector addition of adjacent symbols to create correlation peaks, enabling correlation on phase-shift-keyed signals. using a correlator. Generally in correlators, a data stream slides through a set of taps. These taps basically multiply adjacent data symbols by various tap coecients. The tap coecients represent the pattern which we intend to match to. After the adjacent symbols (taps) are multiplied by a complex-coecient, they are added to form the output. Figure 5.1(b) illustrates through vector addition concept, the generation of a correlation peak when patterns fully match. 5.2.1 Correlation using Optical Multiplexing The correlator in Figure 5.1(a) operates onfA, B, C, Dg symbols. The search pattern is \C B A A"; therefore, its complex conjugate is applied on the tap coecients. As the input data slides through the correlator, if all four adjacent symbols on the input 64 Time 500 ps Thresholded Waveform Time 500 ps Correlation Waveform Time 500 ps 0 50ps 0 50ps 0 50ps (a) Electrical Waveform Optical Intensity Correlation Eye Diagram Optical Intensity 40-Gbit/s RZ-OOK signal, pattern: “1 1 1 1” 40-Gbit/s RZ-BPSK signal, pattern: “ ʌ 0 ʌ 0” 80-Gbit/s RZ-QPSK signal, pattern: “ í 3 ʌ /4 3 ʌ /4 ʌ /4” 1566 1536 1551 Wavelength (nm) Multiplexing Spectrum Multicasting Spectrum Signal copies QPM Ȝ S Ȝ P1 1.6 nm QPM Ȝ MUX Ȝ P2 1566 1536 1551 (b) 500 ps Time 0 72ps 27-Gbit/s BPSK signal, pattern: “ʌʌ 0” Power Power (c) (d) 1566 1536 1551 Wavelength (nm) Signal copies QPM Ȝ S Ȝ P1 1.6 nm QPM Ȝ MUX Ȝ P2 1566 1536 1551 1566 1536 1551 Wavelength (nm) Signal copies QPM Ȝ S Ȝ P1 1.6 nm QPM Ȝ MUX Ȝ P2 1566 1536 1551 1566 1536 1551 Wavelength (nm) Signal copies QPM Ȝ S Ȝ P1 2.4 nm QPM Ȝ MUX Ȝ P2 1566 1536 1551 20-Gbit/s BPSK signal, pattern: “ ʌ 0 ʌ 0” 40-Gbit/s QPSK signal, pattern: “ ʌ /4 3 ʌ /4 íʌ /4” (e) Figure 5.2: All-optical TDL correlation results for (a) 40-Gbit/s OOK, (b) 40-Gbit/s BPSK, (c) 80-Gbit/s QPSK signals, and (d) 27-Gbit/s BPSK signal. (e) Coherent detection of 20 Gbaud BPSK and QPSK correlator output. match the search pattern, the correlator will output a full four-level signal (middle peak in Figure 5.1(a) output). However, if there is an in-exact match between the sliding data stream and the pattern (tap coecients), the correlator output will have a lower amplitude. Therefore, a thresholder can be used after the correlator to detect this 65 40G B2B AMI 40G B2B Duobinary (DB) 40G BPSK 2-Bit Corr. (π, 0): AMI 40G BPSK 2-Bit Corr. (π, π): DB 40G BPSK 4-Bit Corr. (0, π, π, 0) -Log 10 (BER) 9 8 5 4 3 2 6 7 Received power (dBm) -35 -30 -25 -20 -40 -45 40G B2B AMI 40G B2B Duobinary (DB) 40G BPSK 2-Bit Corr. (π, 0): AMI 40G BPSK 2-Bit Corr. (π, π): DB 40G BPSK 4-Bit Corr. (0, π, π, 0) 40 Gbit/s, RZ-DPSK DB AMI DB AMI Demodulated with a tunable 2-tap optical TDL Demodulated with a fixed conventional 40 GHz DLI Figure 5.3: All-optical Correlation, BER performances: 4-bit BPSK pattern correlation, and 2-bit correlation (patterns \ 0" and \") resulting in dierential demodulation of BPSK signal with the optical TDL, and comparison to conventional DLI DPSK demod- ulator performance. AMI: alternate-mark-inversion, DB: duobinary. maximum peak and simply determine \when and where" a pattern is found in the data steam and to what extent a pattern is matched. As illustrated in Figure 5.1(a), to recognize a phase/amplitude pattern of length N, a TDL with N taps located at one-symbol-time intervals is required. Moreover, the tap coecients need to be set equal to the complex conjugate of the target pattern [123]. If the TDL allows for complex tap coecients, patterns can be searched in the multi-level phase-shift-keyed signals. Figure 5.2 shows sample experimental results for correlators operating on OOK, BPSK, and QPSK signals at dierent bit rates and dierent target patterns. For each signal, the spectra of the nonlinear wave mixing for multicasting stage and multiplexing stages are shown, as well as the output eye diagram and optical output waveforms (intensity after photodiode) and electrically thresholded waveforms (electrical output of the thresholding photoreceiver). The target search pattern in the correlator is controlled by the pump wavelengths (delays) and the relative phases of each idler. In Figure 5.2(a), correlation results are presented for searching a 4-bit amplitude pattern \1 1 1 1" in 40-Gbit/s RZ-OOK signals. Figure 5.2(b) shows results on a 40-Gbit/s RZ- BPSK signal where target phase pattern is \ 0 0". For an 80-Gbit/s QPSK signal, 66 a length-three phase pattern \3=4 3=4 =4" is searched using three dummy pumps in Figure 5.2(c). For 40 Gbaud signals, the wavelength separations between dummy pumps are set to 1:6 nm which is equivalent to 25 ps delay (one symbol time) between the taps after passing through the DCF. In Figure 5.2(d), this wavelength separation is changed to 2:4 nm to accommodate 27 Gbit/s BPSK signals. For the OOK signals, the eye diagram has ve signal levels which correspond to the number of 1's in adjacent four bits. For BPSK and QPSK signals, however, do not have as many intermediate levels as OOK signals. This is due to the fact that the multiplexing is vector addition of the elds, bit-mismatches (e.g.,1) could create a vector with opposite direction as the nal desired output. For example, in 4-bit pattern search in BPSK signals, when two bits match (and the other two bits mismatch) the output level is 1 + 1 1 1 = 0, as opposed to 1+1+0+0 = 2 in OOK signals. While there is no phase information in OOK correlation, the correlation results of phase-modulated signals contain both amplitude and phase information. With direct detection correlation peaks identify the matching of phase dierences between symbols. Homodyne coherent detection can be used on the correlator output instead to better distinguish between the exact patterns on phase- encoded signals. The BPSK and QPSK correlation results at 20 Gbaud with coherent detection are shown in Figure 5.2(e). Coherent detection is performed using Agilent's N4391A Optical Modulation Analyzer. Optical elds can be recovered using coherent detection and thus exact phase pattern matching can be realized. A sample BER performance for the correlation of 4-bit pattern \0 0" in a 40- Gbit/s BPSK signal is given in Figure 5.3. A special case of the correlator for PSK signals is the 2-bit pattern search, which results in a delay-line interferometer (DLI) for dierential detection. Correlation signal at MUX can be set to the demodulated signals of alternate-mark-inversion (AMI) or duobinary (DB). In dierential demodula- tion of BPSK signals using conventional DLI, AMI and DB signals are generated at the destructive and constructive ports of the interferometer, respectively. Therefore, a 2-tap 67 500 ps/div Time (s) 0 50ps Intensity (a.u.) 8 dBm/div 2.5 nm/div Power (dBm) Ȝ S Ȝ P1 Ȝ D1 Ȝ D4 Signal copies 1.5nm QPM Ȝ C4 Ȝ C1 40 Gbit/s NRZ-OOK signal, electrical multiplexing, pattern: “1 1 1 1” 1564 1539 1551 Wavelength (nm) 500 ps/div Time (s) 0 66ps Intensity (a.u.) 8 dBm/div 2.5 nm/div Power (dBm) 2nm 30 Gbit/s NRZ-OOK signal, electrical multiplexing, pattern: “1 1 1 1” 1 x 1 x 1 1564 1539 1551 Wavelength (nm) 500 ps/div 1564 1539 1551 Wavelength (nm) 500 ps/div Time (s) 0 50ps Intensity (a.u.) 8 dBm/div 2.5 nm/div Power (dBm) 3nm 1 1 1 1 Correlator’s Output Waveform Thresholded Waveform Correlator’s Output Waveform Thresholded Waveform Correlator’s Output Waveform Thresholded Waveform 40 Gbit/s NRZ-OOK signal, electrical multiplexing, pattern: “1 x 1 x 1” (a) (b) (c) Figure 5.4: Experimental results for the tunable correlator with electrical multiplexing. Nonlinear fan-out (multicasting) spectrum, correlator output eye diagram, correlator's output waveform, and electrically thresholded output waveform for (a) 40-Gbit/s OOK pattern \1111", (b) 40-Gbit/s OOK pattern \1x1x1", and (c) 30-Gbit/s OOK pattern \1111". \x" denotes a \don't care" bit. TDL with \ 0" tap phases can demodulate BPSK to AMI, and \ " tap phases out- put a DB signal. We demodulated the 40-Gbit/s BPSK signal using the correlator. The BER results are shown in Figure 5.3. When compared to the back-to-back performance (with a commercial 40-GHz DLI as the demodulator), the correlator outputs show 1 dB power penalty. 68 5.2.2 Correlation using Electrical Multiplexing If a photodiode is used to multiplex the taps, only intensity modulated signals (OOK) can be used. Correlation results for the \1 1 1 1" sequence for a 40 Gbit/s NRZ-OOK signal are given in Figure 5.4(a). The wavelength spacing is set to 1:5 nm to induce 25 ps delay after passing through 1 km SMF with 17 ps/nm/km dispersion. The correlation output waveform obtained with a photodiode is shown in Figure 5.4(a), along with the corresponding eye diagram. The electrical thresholded waveform obtained with the thresholding receiver is also shown under the correlator pattern, identifying the occurrences of the \1 1 1 1" pattern. Correlation results for searching for a pattern with three 1 bits every other bit (pattern \1 x 1 x 1") at 40 Gbit/s are also shown in Figure 5.4(b). For further recongurability demonstration, the data rate is changed to 30 Gbit/s and is tuned to 2 nm in order to achieve 33:3 ps delays to search for \1 1 1 1" pattern (Figure 5.4(c)). 5.3 Equalization of Chromatic Dispersion Fiber chromatic dispersion (CD) distorts and broadens pulses in digital signals [1]. The TDL can be programmed to the inverse of the CD transfer function to \equalize" a distorted data stream by undoing the eect of pulse broadening [87]. Equalizers can sig- nicantly reduce the system penalties [33],[1]. Here, we demonstrate optical equalization using the optical TDL with optical and electrical multiplexing. 5.3.1 Optical TDL Equalizer with Optical Multiplexing We implemented 3- and 4-tap optical TDLs to equalize for chromatic dispersion [59]. In a TDL equalizer, the tap spacing is usually set to half the symbol time of the digital signal [38]. Figure 5.5 shows the spectra for the two nonlinear wave mixing stages (PPLN-1 and PPLN-2) of the TDL for equalization of a signal that is dispersed by 120 ps/nm 69 Ȝ C1 Ȝ C4 Signal Copies QPM Ȝ D1 Ȝ S Ȝ P1 Ȝ D4 Ȝ P2 Ȝ C1 Ȝ C4 Ȝ D4 Ȝ MUX Ȝ D1 1540.5 1550.5 1560.5 80 Gbit/s RZ-DQPSK, four taps 27 Gbit/s RZ-DPSK, three taps Ȝ C1 Ȝ C3 Ȝ D1 Ȝ S Ȝ P1 Ȝ D3 Ȝ P2 Ȝ C1 Ȝ C3 Ȝ D3 Ȝ MUX Ȝ D1 PPLN-1 output spectrum: fan-out (multicasting) PPLN-2 output spectrum: multiplexing 1540.5 1550.5 1560.5 QPM QPM 1540.5 1550.5 1560.5 1540.5 1550.5 1560.5 QPM PPLN-1 output spectrum: fan-out (multicasting) PPLN-2 output spectrum: multiplexing Wavelength (nm) Wavelength (nm) 1.6 nm 2.4 nm Figure 5.5: Experimental spectra for dierent conditions of operation for the all-optical TDL equalizer, showing tunability to dierent bit rates and modulation formats. dispersion. Figure 5.5(a) shows the spectra for four-tap operation on a 40-Gbaud signal. The wavelength separation, , between the signal copies is set to 1:6 nm, which corresponds to a 12:5 ps delay after DCF. Therefore, half-symbol-time tap-delays are achieved for the equalizer. In Figure 5.5(b), the data is switched to 27-Gbit/s DPSK. Thus, in order to achieve the half bit tap delays ( 18:8 ps), is changed to 2:4 nm. Bit error ratio (BER, i.e. the ratio of bit errors to total received bits) is measured before and after equalization for various chromatic dispersion values with direct detec- tion. Received optical power required to achieve BER value of 10 9 is measured for each modulation format at zero dispersion. For other values of dispersion, the additional optical power required to achieve the same 10 9 BER is known as power penalty and is measured in Figure 5.6(a). Corresponding eye diagrams are also depicted for the end points of some of the curves. As can be seen, 4-tap equalization results in improvements with respect to the 3-tap equalization. The 40-Gbit/s RZ-DPSK signal can tolerate 70 0 100 200 300 400 0 3 6 9 12 40 Gbit/s RZ-DPSK, dispersed 40 Gbit/s RZ-DPSK, 3-tap equalized 40 Gbit/s RZ-DPSK, 4-tap equalized 27 Gbit/s NRZ-DPSK, dispersed 27 Gbit/s NRZ-DPSK, 3-tap equalized 80 Gbit/s RZ-DQPSK, dispersed 80 Gbit/s RZ-DQPSK, 4-tap equalized Power penalty (dB) Chromatic dispersion for equalization (ps/nm) 180 ps/nm 90 ps/nm Dispersed 3-tap equalized 4-tap equalized 40 Gbit/s RZ-DPSK (a) (b) Figure 5.6: (a) Measured power penalty at 10 9 BER versus chromatic dispersion applied on the input signal for equalization, demonstrating TDL reconguration to accommodate dierent bit-rates and modulation formats. (b) Eye diagrams after direct detection in balanced photodiodes before and after equalization for 3- and 4-tap equalizers. 50 ps/nm chromatic dispersion before the power penalty exceeds 3 dB. This disper- sion tolerance can be improved to 110 ps/nm and 160 ps/nm with 3-tap and 4-tap equalization, respectively. For 80-Gbit/s RZ-DQPSK signal, the double wavelength con- version (0 ps/nm dispersion, single-tap operation) has an average penalty of 1:5 dB. Figure 5.6(b) shows the eye diagrams of dispersed and TDL equalized 40-Gbit/s RZ- DPSK signals for 90 ps/nm and 180 ps/nm dispersion. Experimental results on dispersion equalization on 80-Gbit/s RZ-DQPSK signals using four taps (with half-symbol-time spacing) are shown in Figure 11. Figure 11(a) shows the BER curves versus received optical power. From Figure 5.7(a) and Figure 5.6(a), it can be observed that at 3 dB power penalty, the dispersion tolerance can be improved from 40 ps/nm to 70 ps/nm after TDL equalization. Figure 11(b) depicts the eye diagrams of the dispersed and equalized signals. For dispersion values as high as 71 -40-35 -30-25 -20 10 8 6 4 2 0 ps/nm - dispersed 0 ps/nm - equalized 30 ps/nm - dispersed 30 ps/m - equalized 60 ps/nm - dispersed 60 ps/m - equalized 90 ps/m - equalized 120 ps/m - equalized -log 10 (Bit error rate) Received power (dBm) Dispersed 4-tap equalized 120 ps/nm 90 ps/nm 60 ps/nm 30 ps/nm 0 ps/nm 80 Gbit/s RZ-DQPSK (a) (b) Figure 5.7: (a) BER measurements on dispersed 80-Gbit/s RZ-DQPSK signals before and after equalization using the all-optical TDL. (b) Eye diagrams of dispersed signal before and after equalization for 80-Gbit/s RZ-DQPSK signal. 90 ps/nm, where the eye diagram is fully closes, BER rate of 10 9 is achieved with 7:8 dB received power penalty. The work is extended to more advance modulation formats such as 8-PSK and 16- QAM [23]. 5.3.2 Optical TDL Equalizer with Electrical Multiplexing A recongurable three-tap equalizer is demonstrated for equalization of a dispersed signal prior to detection. Two dierent equalizers are used for equalization of dispersion values from 0 to 40 ps/nm (equalizer #1), and dispersions of 50 to 90 ps/nm (equalizer #2). The multicasting spectra and the bipolar tap coecients are shown in Figure 5.8 for these two equalizers. For equalization of 0 40 ps/nm, the second and the third pump lasers are set 4 nm and 5 nm away from the rst pump to achieve delays of 20 ps and 25 ps, respectively. The delays were recongured to 15 ps and 29:5 ps by using 3 nm and 6 nm separations from the rst tap signal at C1 1563 nm. Figure 72 015 30 -120 0 120 240 Delay (ps) 015 30 -120 0 120 240 Delay (ps) Wavelength (nm) QPM Ȝ S Ȝ P2 1564 1536 1551 3 taps Power Wavelength (nm) QPM Ȝ S Ȝ P2 1564 1536 1551 3 taps Power 3 nm 3 nm 1 nm 4 nm Impulse Response Amplitude (mV) Impulse Response Amplitude (mV) Multicasting Spectrum Multicasting Spectrum Equalizer #1 for 10 to 40 ps/nm Equalizer #2 for 50 to 90 ps/nm Figure 5.8: TDL equalizer with electrical multiplexing. Multicasting spectra (top) for two equalizers with uniform and non-uniform tap-spacing, along with plots of measured tap coecients versus tap delays (bottom). Equalizers #1 and #2 are used to compen- sate 0 to 40 ps/nm and 50 to 90 ps/nm chromatic dispersion, respectively. 5.9(a) shows the BER measurement results on the dispersed back-to-back signals and on the equalized signals. The OSNR penalty for dispersed and equalized signals at BER of 10 3 are measured and shown in Figure 5.9(b) along with corresponding eye diagrams at high OSNRs. A BER of 10 9 is still achievable using the equalizer for a residual dispersion of up to 80 ps/nm. There is 60% improvement of dispersion tolerance at a 3 dB OSNR penalty. 73 025 50 75 100 0 3 6 9 12 OSNR penalty (dB) Chromatic dispersion for equalization (ps/nm) Dispersed Equalized 20 25 30 35 40 45 50 55 10 8 6 4 2 -log 10 (Bit error rate) OSNR (dB) 0 ps/nm - dispersed 0 ps/nm - equalized 20 ps/nm - dispersed 20 ps/nm - equalized 40 ps/nm - dispersed 40 ps/nm - equalized 60 ps/nm - dispersed 60 ps/nm - equalized 80 ps/nm - equalized 90 ps/nm - equalized 0 ps/nm 80 ps/nm (a) (b) Figure 5.9: (a) BER measurements of the dispersed back-to-back signal and after TDL equalization with electrical multiplexing. (b) OSNR penalty at 10 3 BER and corre- sponding eye diagrams for the equalized and dispersed signals. 5.4 Optical Discrete Fourier Transform Optical orthogonal frequency division multiplexed (OFDM) signals can be demodulated all-optically using optical discrete Fourier transform systems [22][26]. In this section, we use the optical TDL for demodulation of the OFDM by proper tuning of the tap coecients and delays. 5.4.1 All-Optical OFDM Generation and Demodulation Optical OFDM signals involve creating a wideband data channel by modulating multiple orthogonal frequency subcarriers at a lower rate, as shown in Figure 5.10. The modulated subcarriers overlap in the frequency domain [4]. An optical OFDM channel can be demodulated using parallel electronic discrete Fourier transform (DFT) or fast Fourier transform (FFT). The subcarrier modulation speed is limited to the speed at which DFT/FFT can be implemented in electronics. Optical DFT/FFT approaches can allow for the use of higher baud rates for subcarrier modulation by performing the DFT/FFT at the line rate of optics [26][48][72]. 74 Transmitter Receiver Channel + × e j2πf 0 t SC 1 × e j2πf 1 t SC 1 × e j2 πf n t SC 1 × e -j2πf 0 t SC 1 × e -j2πf 1 t SC 1 × e -j2πf n t SC 1 Spectrum of OFDM Signal N Parallel TDLs … X 0 X 1 X 2 X N-1 x N-1 . . . x 1 x 0 N input samples N-point DFT outputs ∑ − = = 1 0 2 N k k k N n j n x e X π Figure 5.10: Concept of optical orthogonal frequency modulation (OFDM) transmitter and receiver. An OFDM signal with N subcarriers separated by f can be represented as s(t) = N1 X n=0 x n (t)e j2nft ; (5.1) in which x n (t) is the n-th subcarrier signal. An N-point optical DFT can extract the n-th subcarrier signal according to x n (t) = N1 X k=0 s(t + k N f )e j2nk=N ; (5.2) which needs to be sampled at 1=f time intervals to recover the transmitted symbols. This demodulation equation follows the form of a tapped delay line in (3.6). In this section, we review two examples of optical OFDM demodulation involving a xed FFT approach and a baud-rate-tunable DFT approach based on the tunable TDL presented in chapter 3 [26][48]. 5.4.2 Adjustable Bit-Rate Optical DFT The tunable optical TDL has also been used to perform optical DFT with various num- bers of taps and bit rates [26]. Figure 5.11(a) illustrates the concept of using the tunable TDL to perform DFT for extraction of OFDM subcarriers. In order to extract the n-th 75 SC2 SC3 SC4 SC1 NL-Waveguide Multicasting Stage Multiplexing Stages NL-Waveguide NL-Waveguide NL-Waveguide NL-Waveguide NL-Waveguide NL-Waveguide NL-Waveguide NL-Waveguide OFDM Signal Multiple Wavelength Source Tunable Demultiplexing of OFDM Signals (Four 40-Gbaud QPSK Subcarriers) Concept of OTDL-Based Discrete Fourier Transform (a) (b) 1541.7 1551.7 1561.7 1541.7 1551.7 1561.7 QPM QPM λ Pump λ P’ Input Signal Output Subcarrier Multicasting Spectrum Multiplexing Spectrum Wavelength (nm) Wavelength (nm) Demodulated Output Subcarrier Eye Diagrams Signal Copies Pumps Figure 5.11: Tunable optical OFDM demodulation using optical DFT enabled by the optical tapped-delay-line: (a) concept, and (b) multicasting and multiplexing spectra and output eye diagrams of all four subcarriers in a four 40-Gbaud QPSK subcarrier OFDM signal [26]. subcarrier from an N-subcarrier OFDM signal with f separation, the tunable TDL needs to be congured to haveN taps, each separated in time by 1=(N f), with tap coecients of e j2nk=N (k2f0;:::;N 1g). In Figure 5.11(b), the multicasting and 76 multiplexing spectra for the implementation of a 4-point DFT is shown. The subcarriers are 40-Gbaud DQPSK. The eye diagrams of the extracted subcarriers are shown on the right. 5.5 Conclusions The optical TDL was used to demonstrate correlation (pattern search), discrete Fourier transform, and equalization for chromatic dispersion at the speed of the line rate (80 Gbit/s). Recongurability of the TDL is further investigated in correlation and equal- ization on optical phase- and amplitude-modulated signals, where various patterns (0=1 intensity patterns, two- and four-phase-level patterns), dierent modulation formats (OOK, BPSK, and QPSK) and dierent line rates (27=40=80 Gbit/s) are demonstrated. 77 Chapter 6 Recongurable Optical QAM Converter/Encoder In this chapter, we experimentally demonstrate a recongurable optical con- verter/encoder for quadrature amplitude modulated (QAM) signals. The system utilizes nonlinear wavelength multicasting, conversion-dispersion delays, and simultaneous non- linear multiplexing and sampling. We show baud rate tunability (31 and 20 Gbaud) and recongurable conversions from lower-order QAM signals to higher-order QAM signals (e.g., 64-QAM) [63]. 6.1 Introduction The increasing demand for higher capacity in optical networks has made it a challenge to eciently use the available bandwidth. Owing to the recent advances in the elds of high speed digital signal processing and analog to digital converters (ADCs), use of spectrally ecient quadrature amplitude modulation (QAM) formats together with optical coherent receivers has gained interest as a possible solution. In transparent optical networks, where various modulation formats and dierent baud rates are used, a laudable goal might be to encode and convert a signal from a simpler modulation format, such as binary phase shift keying (BPSK) or quadrate phase shift keying (QPSK), to a higher 78 order QAM format, such as 16-QAM or 64-QAM [112], [43]. Beside the potential for increasing the spectral eciency, conversion/encoding of QAM symbols is quite valuable for many types of coding, including encryption/decryption, and error correction [87]. To accommodate various modulation schemes, such system should probably be bit-rate and data-format transparent [64]. Reports on QAM signal generation and conversion span both electronic and all- optical approaches [43]. Previously published results on the optical techniques include: (a) electro-optic digital-to-analog conversion using parallel modulators [96], (b) multi- plexing of two 10 Gbaud QPSK signals to star 16-QAM [112], and (c) simulations on various QAM generation using dual-parallel MZM and phase modulators [128]. Most of these techniques are generally limited to certain modulation formats, and some require multiple separate input channels. Given the importance of QAM signals, a desirable goal would be to achieve an optical QAM encoder/converter that can accommodate various input/output modulation formats and operate on a single channel to increase its spectral eciency. In this section, we experimentally demonstrate a recongurable and fully tunable QAM encoder/converter that utilizes a nonlinear sampler incorporated in a coherent complex-coecient optical tunable tapped-delay-line [64] to simultaneously convert and sample 20- and 31-Gbaud BSPK/QPSK signals to 4/8/16/64-QAM [60]. 6.2 Concept Figure 6.1 depicts the conceptual block diagram of the QAM converter/encoder using an example for QPSK to 64-QAM conversion. In principle, if consecutive lower order and higher baud rate input QAM symbols, (e.g., BPSK or QPSK) are coherently combined and sampled they can generate a higher order and lower baud rate output QAM signal. If x(t) is the input signal, the output signal, y(t) is: 79 Input QPSK Output 64-QAM Higher Order Lower Baud Rate QAM) Lower Order Higher Baud Rate QAM Wavelength Multicasting (Nonlinear Element) Sampling Multiplexing (Nonlinear Element) Wavelength- Dependent Delay (Dispersion) All-Optical QAM Converter t Optical Sampling Pump 0T s 1T s 2T s + × × × × 1 0.5 0.25e j π/2 t t t S i 0.5 S i+1 0.25e j π/2 S i+2 S i+2 S i S i+1 S i+2 S i S i+1 S i+2 S i S i+1 π/4 - π/4 S i+2 S i t -3 π/4 S i+1 t 1.25 < 0° S i+2 S i S i+1 Figure 6.1: Conceptual block diagram of an optical QAM format converter using non- linear signal processing. y (t)/ 1 X i=0 (tiNT s ) N X i=1 c i x(t (i 1)T s ) (6.1) In which, (t) is a pulse function which has unit amplitude from time 0 toT s (symbol time) and is zero outside this range. The second summation represents a tapped-delay- line with N taps and complex tap coecients c i [64]. The rst summation is in fact a pulse train that samples the output of the tapped-delay-line every N symbol. In the case of QPSK to 64-QAM conversion, N is 3 and coecients (c i ) can be [1; 0:5; 0:25j]. After sampling, the available free time slots can be used for time division multiplexing. If sampling is not used, the output would be a 64-QAM signal at the baud rate of the 80 original QPSK signal, which now carries two redundant symbols for every three symbols. This symbol redundancy could be used in coded modulation formats in conjunction with Viterbi algorithm (with only 4 states) [87]. Sampling can eliminate this redundancy. We demonstrate a system that not only can encode/convert arbitrary constellation points using basic weighting, vector rotation, and addition functionalities, but can also simul- taneously sample the resulting signal. The signal is rst copied to multiple wavelengths in a nonlinear device in a process known as multicasting. The signal copies are then sent into a dispersive element in which dierent wavelengths travel at dierent speeds. The signals are then coherently multiplexed and sampled in another nonlinear device to create the output [60]. 6.3 Formulation and Experimental Setup Figure 6.2 depicts the experimental setup. The input BPSK/QPSK signal is generated by driving an IQ modulator with pseudo-random bit sequence (PRBS) 2 31 1 to modulate a continuous wave (CW) laser at wavelength S (angular frequency ! S ). The signal is then combined with four amplied CW dummy pump lasers ( D1 to D4 ) and another amplied CW pump at P and is sent into a nonlinear periodically poled lithium niobate (PPLN) waveguide. The signal S and the pump P are located symmetrically with respect to the quasi-phase matching frequency (QPM) of the waveguide; therefore, they can mix through the (2) sum frequency generation (SFG) process. The SFG signal then mixes with multiple Di pumps through dierence frequency generation process (DFG) and produces multiple replicas of the input data signal [64]. The center frequency of the generated signal copies (! Ci =! S +! P ! Di ) and their complex amplitude (A Ci (t)/ A S (t)A P A Di ) are determined by the conservation of energy and phase matching rules, respectively (the asterisk (:) denotes the complex conjugate) [69]. The output is then sent into a phase/amplitude programmable liquid crystal on silicon (LCoS) lter that (i) blocks the original data signal and the P pump, and (ii) applies phase shift of i on 81 λ D3 DCF ~425m 9 nm λ P λ D4 λ D1 λ D2 24dBm 11/14nm 27dBm 2 nm 20/31 Gbaud PRBS 2 31 -1 λ S IQ Mod. PC 25dBm λ C2 λ C1 λ D2 λ D1 λ P λ S λ C2 λ C1 λ D2 λ D1 λ P/Samp λ S φ D1 φ D2 LCoS Phase LCoS Amplitude 0 dB −50 dB 16-QAM Sampling Pump 2 nm 24dBm 1/2 or 1/4 Sampler PPLN #1 PPLN #2 λ S Sig. LO 1 nm 90º Optical Hybrid ADC 32 GHz, 80 GS/s I Q Offline Signal Processing 2 nm LCoS Filter 2 nm 25dBm MZM Δt For Sampling Only QPSK ATT PPLN-1 Output (Multicasting) LCoS Filter Shape PPLN-2 Output (Multiplexing and Sampling) Figure 6.2: Experimental setup and schematic wave-mixing spectra. PC: Polarization Controller, BPF: Bandpass Filter, ATT: Attenuator, LO: Local Oscillator. the Di pumps (Figure 6.2, schematic spectra). Keeping the original dummy pumps and their corresponding signal copies on the same path will maintain the phase coherency required for coherent addition in the nal stage. Subsequently, the signal copies and the dummy pumps are sent through a dispersion compensating ber (DCF). In the DCF, each signal copy travels at a dierent speed, resulting in a relative time delay of T =DL between the signals (D is the ber dispersion,L is the DCF length and is the wavelength separation of two signal copies). is chosen such that the adjacent signal copies are delayed by one symbol time (T s ) after the DCF. Next, the delayed signals and pumps are combined with a sampling pump ( P=Samp ) and sent into the 82 second PPLN waveguide, where similar cascaded SFG and DFG wave mixings produce a multiplexed signal at frequency! MUX =! Di +! Ci ! P=Samp =! S +(! P ! P=Samp ) with complex amplitude proportional to (A Di e j i )A Ci (t (i 1)T s )A P=Samp (t). Therefore, the total resulting multiplexed and sampled output is A MUX (t)/A P=Samp (t) N X i=1 jA Di j 2 e j i A S (t (i 1)T s ) (6.2) Equation 6.2 replicates 6.1 and is the mathematical representation of the optical QAM encoder/converter. The converter/encoder can be recongured by varying the properties of the pump lasers fed into the system: N (number of dummy pump lasers), jc i j ( Di laser power),]c i (LCoS phase on Di ),T s (spacing between Di 's). For example, 3-dB attenuation on a dummy pump power translates to a factor of 0.5 in the coecient. The sampling rate of should be set to 1=N. As shown in Figure 6.2, 20- and 31-Gbaud rates are chosen. The DCF length is L 425 m with D80 ps/nm/km dispersion. Therefore, if the adjacent dummy pumps are located = 0:95 nm apart, the induced delay is one 31-Gbaud symbol time T s = DL 32:25 ps. For 20-Gbaud signals, the pump spacing is increased to 1.46 nm. The rst and the second PPLN waveguides are 4 cm and 5 cm long, respectively, and their QPM wavelengths are thermally tuned to1549.6 nm. The signal wavelength S is1540.9 nm and the P pump is1558.3 nm. For experiments with a sampling pump, P=Samp pump is generated by driving a Mach-Zehnder modulator with a pulse train at half-clock or quarter-clock repetition rate, followed by an optical tunable delay line for synchronization. The output signal is ltered, sent into an pre-amplied receiver and coherently detected using a local oscillator at wavelength S , an optical hybrid, balanced photodiodes and 32-GHz bandwidth 80-GSample/s analog-to-digital converter (ADC). Oine signal processing is used to recover the constellation diagrams. 83 31 Gbaud BPSK to 15.1 Gbaud QPSK (Half Sampled) c i : [1, -j] EVM 11.24% 31 Gbaud QPSK to 15.1 Gbaud 16-QAM (Half Sampled) c i : [1, -0.5] EVM 7.15% 1,540 1,550 1,560 -60 -40 -20 0 Power (dBm) Wavelength (nm) 1,540 1,550 1,560 -60 -40 -20 0 Power (dBm) 1,540 1,550 1,560 -60 -40 -20 0 Power (dBm) 1,540 1,550 1,560 -60 -40 -20 0 Power (dBm) Wavelength (nm) 20 Gbaud 1/4-Sampled BPSK to 16-QAM 31 Gbaud 1/2-Sampled QPSK to 16-QAM Multicasting Spectrum Multiplexing Spectrum Multicasting Spectrum Multiplexing Spectrum λ C1 λ C2 Copies QPM λ D1 λ S λ P λ D2 λ P/Samp λ MUX Multiplexed and Sampled Input Input Output Sampling Pump CW Pump Signal Copies 20 Gbaud QPSK to 5 Gbaud 16-QAM (Quarter Sampled) c i : [1, j, 0.5, 0.5j] 20 Gbaud BPSK to 10 Gbaud 4-PAM (Half Sampled) c i : [1, 0.5] EVM 9.80% (a) (b) (c) (d) Figure 6.3: (a) Spectra of the 1st and the 2nd PLLN waveguides outputs for 31 Gbaud input signal with half rate sampling pump. (b) Output constellations. (c) Spectra for 20 Gbaud signals, and (d) output constellations. 6.4 Experimental Results and Discussion Figure 6.3(a) depicts the output spectra of the multicasting and multiplexing stages for conversion of 31-Gbaud QPSK to 15.5-Gbaud 16-QAM using a half-rate sampling pump in the second stage. D2 has 3-dB lower power than D1 , and 180 phase shift is applied on it in the LCoS lter, resulting in coecients of c i = [1; 0:5]. The constellation diagram is shown in Figure 6.3(b) together with results of another conguration where the input is BPSK and the coecients are set toc i = [1; j] to create QPSK output. The error vector magnitudes (EVM) are also noted in Figure 6.3. Figures 6.3(c,d) show results 84 1,540 1,550 1,560 -60 -40 -20 0 Power (dBm) Wavelength (nm) 1,540 1,550 1,560 -60 -40 -20 0 Power (dBm) Wavelength (nm) 31 Gbaud QPSK to 31 Gbaud 64-QAM c i : [1, 0.5, 0.25j] 31 Gbaud BPSK to 31 Gbaud Rec. 8-QAM c i : [1, 0.5] EVM 6.49% EVM 6.58% EVM 6.77% 20 Gbaud QPSK to 20 Gbaud 64-QAM c i : [1, 0.5, 0.25] 20 Gbaud BPSK to 20 Gbaud Diag. 8-QAM c i : [2 -0.5 -j2 -0.5 , 2 -0.5 j, 2 -0.5 ] EVM 9.02% 31 Gbaud QPSK to 64-QAM, 2nd PPLN 31 Gbaud QPSK to 64-QAM, 1st PPLN Input QPSK Output 64-QAM Weighted Copies (a) (b) (c) Figure 6.4: (a) Output spectra of nonlinear stages for QPSK to 64-QAM conversion. Constellation diagrams showing dierent encodings for (b) 31-Gbaud and (c) 20-Gbaud signals. on 20 Gbaud signals with quarter sampling (5 GHz repetition rate) for generation of a 16-QAM symbol from four BPSK symbols, demonstrating recongurability for dierent baud rates and encodings. The coecients determine the encoding of the generated 16- QAM. The 20-Gbaud system is recongured by turning o two lasers to create a 4-PAM signal, as shown in Figure 6.3(d). In Figure 6.4, a CW pump is used instead of the sampling pulse, resulting in gener- ation of signals with higher order QAM and same baud rate. Figure 6.4(a) depicts the spectra for generation for 31-Gbaud 64-QAM signal, by combining three QPSK sym- bols using coecients c i = [1; 0:5; 0:25]. The 64-QAM constellations for 31-Gbaud and 20-Gbaud are shown in Figures 6.4(b,c). The constellation diagrams for two sample arbitrary 8-QAM formats are also depicted showing other phase and amplitude recon- gurations. 85 10 20 30 6 5 4 3 2 EFEC Threshold -log 10 (Bit Error Rate) O SNR (dB) 31 GBd BPSK Back-to-Back 31 GBd QPSK Back-to-Back 31 GBd QPSK to 15.5 GBd 16-QAM 31 GBd BPSK to 15.5 GBd QPSK 20 GBd BPSK Back-to-Back 20 GBd QPSK Back-to-Back 20 GBd QPSK to 10 GBd 16-QAM 20 GBd BPSK to 10 GBd QPSK 10 20 30 40 6 5 4 3 2 EFEC Threshold 31 GBd BPSK Back-to-Back 31 GBd QPSK Back-to-Back 31 GBd BPSK to QPSK 31 GBd BPSK to 16-QAM 31 GBd QPSK to Diagonal 8-QAM 31 GBd QPSK to 16-QAM -log 10 (Bit Error Rate) O SNR (dB) (a) (b) Figure 6.5: BER measurements versus OSNR for experiments with (a) a sampling pump, and (b) with a CW pump. Bit error rate (BER) measurements versus optical signal-to-noise ratio (OSNR) are shown in Figure 6.5. For sampling pump experiments, the measured OSNR penalty at BER= 2 10 3 is2 dB and5 dB for conversions of 31-Gbaud BPSK to 15.5- Gbaud QPSK and 31-Gbaud QPSK to 15.5-Gbaud 16-QAM, respectively. Due to signal distortions of the transmitter for 20-Gbuad QPSK, BER results are slightly better at 31-Gbaud. In non-sampling experiments, the OSNR penalty for generation of QPSK from BPSK is1 dB compared to back-to-back measured QPSK. 16-QAM obtained from QPSK , and 16-QAM generated from BPSK, required3 dB and7 dB higher OSNR compared to a back-to-back 10 Gbaud 16-QAM, respectively (10 Gbaud 16-QAM requires19 dB OSNR for BER of 2 10 3 ). It is worth mentioning that another approach with similar technologies can also be used to coherently multiplex various lower-order phase- and amplitude-modulated signals onto higher order modulation formats [5][20][18][50][51]. 86 6.5 Conclusions We experimentally demonstrated a tunable and recongurable optical scheme for encoding and converting of QAM symbols. 20/31 Gbaud QPSK signals were encoded/converted to higher order QAMs, including 64-QAM in an all-optical tunable tapped delay line. The OSNR penalty at 2 10 3 BER is measured to be2 dB and 8 dB for conversions of 31 Gbaud BPSK to 15.5 Gbaud QPSK and 31 Gbaud QPSK to 15.5 Gbaud 16-QAM, respectively [60]. 87 Chapter 7 Tunable WDM Optical Tapped-Delay-Line for Simultaneous and Independent Data Processing In this chapter, we demonstrate an optical tapped-delay-line that is recongurable with complex tap coecients and independently and simultaneously performs data pattern recognition, equalization, and QAM format conversion on eight B/QPSK WDM signals at both 20 and 26 Gbaud, demonstrating >400 Gbit/s processing capacity [61]. 7.1 Introduction Optical signal processing techniques that maintain the phase and amplitude informa- tion of the signals hold the potential to increase the processing capacity by operating at the line rate of optical communications. The amount of data that can be processed in a bit time can be dramatically increased by encoding information bits to multi-level phase and amplitude symbols (e.g., quadrature-amplitude-modulation [QAM] formats), 88 using wavelength and polarization multiplexing, and utilizing higher symbol transmis- sion rates (baud rate). A key building block for signal processing is the tapped-delay-line (TDL), in which an input signal is tapped at various time intervals, each tap is mul- tiplied by a complex coecient, and taps are nally added to create the output [87]. Complex-coecient optical TDLs (OTDLs) have been shown to operate on the ampli- tude and phase of the data signals, to increase the processing capacity [64]. OTDLs can be congured to perform dierent functions such as nite-impulse-response ltering [33], equalization, correlation [64][55], discrete Fourier transform [48], and format conversion [63]. An OTDL equalizer based on a silica photonic integrated circuit (PIC) has been shown in [33] that can simultaneously process 16 WDM channels. However, the tap delays were not widely tunable and similar function was applied on all WDM channels. A baud-rate adjustable OTDL with tunable complex tap coecients has been shown, which exploits nonlinear wave mixing and tunable optical delays [64]. Although this OTDL is tunable, it can only operate on a single wavelength channel. In this chapter, we demonstrate a single OTDL system that can simultaneously and independently process WDM data channels. The WDM-OTDL is baud-rate adjustable and the number of WDM input channels can be easily scaled. We exploit four-wave-mixing (FWM) and three-wave-mixing in nonlinear devices such as highly-nonlinear ber (HNLF) and periodically-poled-lithium-niobate (PPLN), conversion-dispersion optical delay technique [97], and amplitude and phase pro- grammable liquid crystal on silicon (LCoS) lters to realize concurrent independent functionalities on dierent WDM channels. We show a 2-tap OTDL on four and eight WDM channels, to independently and recongurably perform equalization, 2-symbol pattern recognition and format conversion on binary phase shift keyed (BPSK) and quadrate phase shift keyed (QPSK) signals at 20- and 26-Gbaud. Format conversion from BPSK to QPSK and 4-PAM (pulse amplitude modulation), and from QPSK to 89 Independently Reconfigurable WDM Optical Tapped-Delay-Line (WDM-OTDL) (e.g., equalizer, correlator, format conversion) ω S1 ω S3 WDM Input C B A Equalization Correlation Format Conversion C’ B’ A’ Distorted Signal OOK Input C B ω C3 ω C1 WDM Processed Output C’ B’ A’ (Independent Functions on Each Channel) time 1 1 0 time Match QPSK Input A Figure 7.1: Concept of independent processing of WDM channels in a WDM optical tapped-dely-line (e.g., format conversion on channel A, equalization on channel B, and correlation on channel C. 16-QAM is shown. Finally, parallel correlation on eight 20-Gbaud QPSK WDM signals is also demonstrated with a data throughput of 416-Gbit/s [61]. 7.2 Concept of WDM Tapped-Delay-Line and Theory The concept of WDM-OTDL is illustrated in Figure 7.1. A set of WDM channels are input to the system and as the signals propagate on the same path, the WDM-OTDL can concurrently perform independent functions on each channel. In Figure 7.1, for instance, channel A is format-converted from QPSK to 16-QAM, channel B is equalized, and a correlation is performed on channel C. The fundamental building block for implementation of the WDM-OTDL is a 2-tap OTDL that operates on WDM input channels, as depicted in Figure 7.2. The principle of operation is shown in Figure 7.2(a). The WDM input channels are simultaneously wavelength-converted in a nonlinear medium, resulting in the generation of a replica for each WDM channel at a new center frequency. Because the signals and their replicas are at dierent frequencies, a relative delay is induced between each channel and its replica 90 Δt h N × h 2 × h 1 × WDM λ-Conversion (Split) Chromatic Dispersion (Tap Delays) LCoS Filter (Tap Coefficients) WDM λ-Conversion (Add) (a) The Building Block: A 2-Tap WDM-OTDL (b) Equivalent System Diagram WDM Input WDM Output WDM Input WDM Output Figure 7.2: Implementation of a 2-tap OTDL as the building block of the WDM-OTDL: (a) Block diagram, and (b) equivalent system function. after they pass through a chromatic dispersive medium. The delayed original signals and replicas are then sent into a phase and amplitude programmable lter based on LCoS technology that applies the complex tap coecients on the replicas. Finally, the delayed and weighted original signals and their replicas are sent into another wavelength converting system that copies the original signals onto the replicas for the second time. Therefore, independent 2-tap OTDLs can be implemented on each WDM channel. The equivalent system diagram is shown in Figure 7.2(b), where a distinct tap coecient can be applied on dierent WDM channels. In general, higher number of taps can potentially be implemented by cascading the 2-tap tunable building blocks. Figure 7.3 illustrates the nonlinear wave mixing for the wavelength converting stages as well as the conversion-dispersion delays. In general, N WDM input signals with electric eld amplitude E Si (t) at center frequency ! Si are considered (i2f1;:::; Ng). The WDM signals are combined with a continuous-wave (CW) pumpE P at frequency! P and are sent to a nonlinear medium to generate copies of the input signals. The pump and signal congurations need to satisfy the phase matching conditions for ecient nonlinear wave mixing [1][69]. The nonlinear medium can be a HNLF or a PPLN waveguide. In the case of HNLF, the CW pump is located close to the zero-dispersion wavelength (ZDW) of the HNLF 91 E S1 (t-T 1 ) E S3 (t-T 1 ) ω S1 ω S3 ω C1 ω C3 ω P Original Input Signals after Dispersion Phase-Conjugate Copies Delayed & Weighted (1st Taps) a 1 E S1 *(t) a 3 E S3 *(t) E S1 (t) E S2 (t) E S3 (t) ω S1 ω S3 Multiple Input Channels E S1 (t-T 2 ) E S3 (t-T 2 ) ω S1 ω S3 ω C1 ω C3 ω P 1st & 2nd Taps + a 1 E S1 *(t) +a 3 E S3 *(t) b 1 E S1 *(t-T 1 ) b 3 E S3 *(t-T 1 ) E S1 (t-T 3 ) E S3 (t-T 3 ) ω S1 ω S3 ω C1 ω C3 ω P 1st, 2 nd & 3rd Taps + a 1 E S1 *(t) c 1 E S1 *(t-T 2 )+ b 1 E S1 *(t-T 1 ) SHG+DFG or FWM SHG+DFG SHG+DFG Taps Sum Dispersive Device & LCoS Filter 1st WDM λ-Conversion (Nonlinear Device) Dispersive Device & LCoS Filter 2nd WDM λ-Conversion (Nonlinear Device) Dispersive Device & LCoS Filter 3rd WDM λ-Conversion (Nonlinear Device) Delay = Dispersion× Δ ω Figure 7.3: The principle of operation of the WDM-OTDL: (i) Taps are created by simultaneous wavelength conversion of all WDM channels in nonlinear elements. (ii) Tap delays are induced after a dispersive element, because the original signals and the wavelength converted taps are at dierent wavelength. (iii) Tap coecients are applied by an inline liquid crystal on silicon (LCoS) lter). (iv) Owing to pump reusing, weighted taps add coherently. (iv) Number of taps is the number of nonlinear wavelength con- verting stages. so that the phase matching conditions are met for ecient degenerate FWM. If a PPLN waveguide is used instead, the CW pump must be located on the quasi-phase matching (QPM) frequency of the waveguide to exploit two cascaded second order nonlinear pro- cesses of second harmonic generation (SHG) followed by dierence frequency generation (DFG). The output of cSHG-DFG is similar to the degenerate FWM. Either one results in the generation of a wavelength-converted copy for each input signal at a new center frequency! Ci = 2! P ! Si with a eld proportional toE Ci (t)/E 2 P E Si (t). The original 92 data signals E Si (t), the CW pump E P , and the phase-conjugate signal copies E Ci (t), are then sent to an LCoS lter. The LCoS lter applies a complex coecientja i je \a i on each signal copy making them proportional toa i E Ci (t). The CW pump, the signals and the weighted copies are then sent to a dispersive device (e.g., a dispersion compensat- ing ber, DCF), wherein signals at dierent frequencies propagate at dierent speeds. Therefore, in a medium of lengthL and dispersion parameterD, a relative time delay of T i =DL( Si ci ) is induced between the original data signal and its copy. It is worth mentioning that because the CW pump is not data modulated, the relative time delay on the pump is equivalent to a phase shift and can be ignored. Next, the delayed signals E Si (tT i ), the weighted and phase-conjugate copies a i E Ci (t), and the CW pump E P , mix in another PPLN waveguide and create another signal copy on the frequency of the rst signal copy, proportional to E 2 P E Si (tT i ). Therefore, the addition of the rst and the second signal copies at frequency ! Ci is E MUX;i (t)/E 2 P (E Si (tT i ) +a i E Si (t)): (7.1) This scheme can adapt to large number of WDM signals without requiring extra nonlinear elements and the delays can be varied by tuning the wavelength of the CW pump. As shown in Figure 7.3, the number of taps can be scaled by adding more non- linear stages, followed by a dispersive medium and an LCoS lter. Thus, the maximum number of taps is limited to the number of nonlinear stages used. However, in the cases that only a few taps are sucient, this scheme can dramatically increase the process- ing capacity per use of nonlinear device. For example, to independently implement a k-tap OTDL on N wavelength channels using the scheme in [64], one needs 2N nonlinear elements, while with the WDM-OTDL design, this can be reduced to k, making it a promising technique for cases requiring few taps and high number of wavelength chan- nels. Thus, by enabling parallel processing of WDM channels, this design, can require dramatically less number of elements compared to separate single channel OTDLs. 93 1 nm λ P 5 nm 19 dBm 21 dBm Phase/Amplitude Programmable Filter Δt Δt Δt Δt 10 dBm 26/20 Gbaud PRBS 2 31 -1 IQ Mod. 90° λ S7 λ S8 λ S5 λ S6 λ S3 λ S4 λ S1 λ S2 100 GHz WDM Coupler DCF ~50 m LCoS Filter 21 dBm ATT λ Ci’s Sig. LO 1 nm ~200 m HNLF 4 cm PPLN 4 cm PPLN 4-Channel Experiments 8-Channel Experiments 90º Optical Hybrid ADC 32 GHz, 80 GS/s I Q Offline Signal Processing 0.7 nm Figure 7.4: Experimental setup for two experiments: (i) 4-channel WDM-OTDL using an HNLF as the wavelength conversion medium, and (ii) 8-channel operation using a PPLN waveguide instead of the HNLF. 7.3 Experimental Setup The experimental setup is depicted in Figure 7.4. Eight CW lasers on 100-GHz frequency grid are combined in a WDM coupler, and sent to a nested Mach-Zehnder modulator that is driven by 20- and 26-Gbaud electrical data to generate BPSK and QPSK signals. The WDM channels are then amplied and decorrelated by means of a demultiplexing followed by various optical delays. A phase and amplitude programmable lter based on LCoS technology is used for demultiplexing. The lter can also distort a channel by applying a chromatic dispersion (CD) of 200 ps/nm for equalization experiments. The WDM signals and a1551/1551.6 nm CW pump are then amplied separately in erbium-doped-ber ampliers (EDFAs), ltered and coupled into either a low-dispersion- slope200 m HNLF (ZDW1560 nm) or a 4-cm PPLN waveguide. The HNLF is used 94 for 4-channel experiments at 26-Gbaud and the PPLN is used for 8-channel experiments at 20-Gbaud. The output is then sent into an LCoS lter that applies the tap coecients. All weighted signals and pumps are then travel through50 m DCF to induce the tap delays. The LCoS lter also (i) adjusts the relative time delay between the original signals and their copies, such that only one (two) symbol time delay is induced between the closer (farther) 4 WDM channels, and (ii) balances the relative power of the CW pump and the signals to account for EDFA gain proles and conversion eciencies. All signals are then amplied and sent to another 4-cm PPLN waveguide to create the second copies. For 8-channel 20-Gbaud experiments, the QPM of both PPLN waveguides are thermally tuned up from 1551 nm to1551.6 nm such that the delays are changed from38 ps (26-Gbaud) to 50 ps (20-Gbuad). Each wavelength converted signal copy is then ltered and detected coherently using a local oscillator (LO), 90-degree optical hybrid, and analog-to-digital converters to measure error-vector-magnitude (EVM) and bit-error-ratio (BER) by oine processing. 7.4 Experimental Results and Discussion Figure 7.5(a) depicts the spectra of the HNLF and PPLN output for 4-channel 26-Gbaud QPSK experiments. The 2-tap OTDL is in principle an interferometer and thus the dips of destructive interference can be can be observed at the converted signals in the PPLN output spectrum. Dierent spectral shapes are due to various functions implemented by varying the tap coecients. Examples of independent and tunable functions on the four WDM channels are shown in Figure 7.5(b). Correlation for 2-symbol pattern search and format conversion from BPSK/QPSK to 4-PAM/16-QAM are performed by applying various tap coecients, as noted in Figure 7.5(b). In Figure 7.5(c), the optical signal- to-noise ratio (OSNR) penalties at BER 2 10 3 are shown for the rst and second wavelength-conversion stages, as well as modulation format conversion. The format 95 Match 1,545 1,551 1,557 -50 -30 -10 10 Power (dBm/0.01nm) Wavelength (nm) Ch-1: QPSK to 16-QAM T aps: [1, 0.5], EVM = 8.5% EVM = 9.2% Input Output EVM = 9.5% EVM = 9.1% Input Output EVM = 11.5% EVM = 10.8% Input Output EVM = 7.8% EVM = 9.5% Input Output Ch-2: QPSK Correlator T aps: [1, -1], Ch-3: BPSK to QPSK T aps: [1, j], Ch-4: BPSK to 4-PAM T aps: [1, -0.5], 1,545 1,551 1,557 -50 -30 -10 10 Power (dBm/0.01nm) Wavelength (nm) HNLF Spectrum, 4-Ch., 26 Gbd B/QPSK (a) PPLN Spectrum, 4-Ch., 26 Gbd B/QPSK λ S1 λ S4 WDM Input Signals λ P λ C4 λ C1 Complex-Conjugate WDM Copies λ S1 λ S4 Weighted Signals QPM λ P λ C4 λ C1 Independently Processed Outputs (c) (b) 1 2 3 4 3 7 11 15 26 Gbd BPSK, 1st Conversion 26 Gbd BPSK, 2nd Conversion 26 Gbd BPSK to QPSK Conversion 26 Gbd QPSK, 1st Conversion 26 Gbd QPSK, 2nd Conversion 26 Gbd QPSK to 16-QAM Conversion OSNR Penalty (dB) Channel Figure 7.5: Four 26-Gbaud BPSK/QPSK WDM channels using an HNLF as the rst nonlinear stage and a PPLN as the second: (a) Optical spectra after the HNLF and the PPLN device, showing rst and second set of taps, respectively. (b) Input and output constellation diagrams for various modulation formats and independent functions on the channels. (c) OSNR penalty of each tap (conversion) and format conversion for BPSK to QPSK and QPSK to 16-QAM. 96 -15 -10 -5 0 5 10 15 EVM (%) Power Variations (dB) CW Pump Power All WDM Signals Power (a) (b) -24 -16 -8 0 8 16 24 9 12 15 EVM (%) Phase Variations (Degrees) CW Pump Signal 26 Gbaud QPSK to 16-QAM Conversion Figure 7.6: Sensitivity of the system to phase and power variations for QPSK to 16-QAM conversion on channel 4. converted QPSK signal for example has <7 dB OSNR penalty compared to a back-to- back BPSK measurement (i.e., <1 dB penalty compared to back-to-back QPSK). Because all signals and the CW pump are amplied in one EDFA before the second nonlinear stage, we characterized the sensitivity of the ouput to phase and power varia- tions of the WDM signals and pumps, as shown in Figure 7.6. Conversion of 26-Gbaud QPSK to 16-QAM on channel 4 is considered. The phases of all WDM signals and the CW pump are varied in the LCoS lter before the second nonlinear stage, while the powers are varied by changing the power of the two EDFAs on the WDM input signals and the CW pump. As can be seen in Figure 7.6(a), the output is twice as sensitive to the phase variations of the CW pump compared to the input signal. This is due to the fact that the second tap is proportional to the square of the CW pump eld, but proportional to the signal elds. For the same reason, the output is more sensitive to power variations in the CW pump than the signals (Figure 7.6(b)). It can be noted that increasing the CW power deteriorates the output signal more than decreasing it, we believe due to extra phase shift from self phase modulation inside the HNLF. The use of HNLF in the rst stage creates multiple parasitic mixing terms due to non-degenerate FWM between the signals and the pump which consume bandwidth. However, if cSHG-DFG in a PPLN device is used instead of degenerate FWM in the 97 1,541 1,551 1,561 -50 -30 -10 10 Power (dBm/0.05nm) Wavelength (nm) 1,541 1,551 1,561 -50 -30 -10 10 Power (dBm/0.05nm) Wavelength (nm) PPLN-1 Spectrum, 8-Ch., 26-Gbd QPSK λ S8 λ S1 WDM Input λ P λ C1 λ C8 First Taps PPLN-2 Spectrum, 8-Ch., 26-Gbd QPSK Original Signals Output (1st & 2nd Taps) (a) EVM = 9.0% EVM = 9.3% EVM = 10.0% EVM = 10.7% EVM=10.7% EVM=10.8% EVM=13.0% EVM=10.8% Ch-4, [1, -j] Ch-3, [1, -1] Ch-2, [1, j] Ch-1, [1, 1] Ch-8, [1,x,-j] Ch-7, [1,x,-1] Ch-6, [1,x,-1] Ch-5, [1,x,1] (c) 8 Correlators on 20 Gbaud QPSK WDM Channels (416 Gbit/s Processing Capacity) (b) EVM = 27.6% EVM = 34.5% Dispersed Input Equalized Output 2-Tap Equalizer for 200 ps/nm on Channel-8 Figure 7.7: Eight 20 Gbaud QPSK WDM channels using a PPLN waveguide in the rst stage: (a) Spectra after the rst and the second nonlinear stages. (b) A 2-tap equalizer for a signal that is distorted by 200 ps/nm chromatic dispersion. (c) Simultaneous 2- symbol pattern search on the eight WDM channels, resulting in a throughput of 416 Gbit/s. rst stage, then more channels can be processes. Figure 7.7(a) depicts the spectra of the two PPLN outputs for 8-channel 20-Gbaud QPSK input signals. In Figure 7.7(b), the input channel-8 is distorted by 200 ps/nm CD before the rst stage and is equalized using a 2-tap half-symbol time equalizer with proper tap coecients. The input and output constellation diagrams are shown. The system is then recongured to perform 8 parallel 2-symbol correlations on 20-Gbaud QPSK data signals, with various target patterns to achieve a throughput of 416-Gbit/s (Figure 7.7(c)). Because the eight signals span a 98 wide range of spectrum, the wavelength-dependent delay between the signals varies over a wide range and cannot be easily corrected in the LCoS lter. Therefore, we chose tap delays of two symbol time for the farther four channels. In general, if one bit delay is required, one may use a lower baud rate on farther channels, and higher baud rate on channels closer to the center [61]. 7.5 Conclusions We demonstrated a tunable optical tapped-delay-line that can simultaneously and inde- pendently operate on WDM data signals. The system utilized the wavelength dependent speed of light, together with nonlinear wavelength conversion stages. A phase-preserving scheme enabled coherent addition of the weighted taps. We recongured the system to perform simultaneous correlation (data pattern recognition), equalization and modu- lation format conversion on four and eight WDM B/QPSK channels at 26- and 20- Gbaud, respectively. Through the use of 8 WDM channels, throughput of 416-Gbit/s was achieved. 99 Chapter 8 System Design Guidelines When Utilizing Chirp-Inducing Wavelength Converters in a Fiber Transmission System Semiconductor optical ampliers (SOAs) can be used for wavelength converting of on-o- keyed (OOK) signals. These SOA based wavelength converters are known to generate a frequency-chirped output. The amount and prole (shape) of this frequency chirp depends on the scheme used for wavelength conversion and can vary for dierent designs wavelength converters. When the frequency-chirped OOK signal travels through ber, the chirp interacts with ber chromatic dispersion (CD) and nonlinearities (e.g., self phase modulation, SPM) and could cause signal degradation. In this chapter, we simulate an arbitrary chirp waveform generator to explore the ber transmission performance of the output of chirp-inducing devices. Various chirp proles are considered and their ber transmission performance is studied at the presence of small positive and negative residual dispersion for both low and high ber nonlinearities cases. We dene two parameters, namely, \average normalized chirp on leading edge" 100 and \average normalized chirp on trailing edge" and use them to classify dierent chirp proles based on their ber transmission performance and dene chirp regimes [37],[56]. 8.1 Introduction Future WDM networks will likely require wavelength converters in order to enable ecient and high-throughput routing [126]. Optical wavelength converters have been researched as to their suitability for performing this function transparently and at high speed. Several approaches have been reported, including using highly-nonlinear ber (HNLF), periodically poled lithium niobate (PPLN), semiconductor optical ampliers, and electro-absorption modulators [126]. Most of the research reported on wavelength converters deals with optimizing the output signal quality of the wavelength converter, especially in terms of extinction ratio (ER) and signal-to-noise ratio (SNR) [126],[104]. These parameters can be optimized at the output of the converter module. However, due to many dierent eects that might occur in the dierent techniques, there might be a frequency chirp induced on the output data signal [104],[95]. Frequency chirp is dened as the instantaneous frequency shift from the carrier frequency: f = 1 2 @(t) @t (8.1) In which, (t) is the instantaneous phase of the carrier removed (baseband signal). This chirp will interact with the chromatic dispersion and nonlinearities of the trans- mission ber and degrade the system performance. Such eects might be beyond the ability for simple dispersion compensators to fully correct. A key remaining question are the deleterious issues and design guidelines for optimizing the performance of the entire transmission system, which might be dierent than optimizing the performance of the wavelength converter module itself. Moreover, since each type of module will induce a dierent type of chirp for dierent operating regimes, it becomes quite valuable 101 to explore system performance for a wide variety of chirp regimes given a certain data signaling. In this chapter, we explore many dierent chirp regimes and simulate system opera- tion. First, the eect of device parameters on the output chirp prole of semiconductor optical amplier (SOA) based wavelength converters is explored using device level sim- ulations. To achieve a comprehensive analysis of the eects of frequency chirp waveform on the system performance, a variety of fundamental arbitrary frequency chirp proles are generated and simulated in both high and low ber nonlinearity regimes. Next, two new parameters are dened to quantify the average frequency chirp on the leading and trailing edges of the signal. These parameters are utilized to dierentiate and analyze the transmission of various chirp proles. The simulations show with 10 ps/nm residual dispersion, a symmetric chirp dis- tribution around the center of the pulse has higher robustness to dispersion variation by giving 2 dB lower power penalty. When nonlinearities and chirp interact in ber, for a chirp peak located on leading or trailing edge power penalty at BER of 10 9 is improved by 2 dB by the choice of optimum residual dispersion, but 5 ps/nm deviation from the optimum dispersion cancels this performance enhancement. 8.2 Frequency Chirp in Wavelength Converters SOAs and modulators can induce frequency chirping on signal. Random spontaneous emission in SOAs can induce phase and intensity changes in the laser output electric eld. In order to restore the intensity for steady-state operation, the laser intensity undergoes relaxation oscillations. These oscillations can change the imaginary part of the refractive index, n 00 that is responsible for gain of the SOA. This will also change the real part of the refractive index, n 0 (phase), through the relationship given by [42]: H = n 0 n 00 =2k 0 @n @N @g @N ! (8.2) 102 which is known as Henrys linewidth enhancement factor, H . In equation 8.2, N is the carrier density and refractive index isn =n 0 +jn 00 . This H factor is usually considered as constant. From equation 8.2, it can be observed that gain modulation ( @g @N ) will also lead to phase modulation ( @n @N ). This causes the linewidth broadening of the laser section and leads to frequency chirping in wavelength converters. For and on-o-keyed signal with optical power P (t), the frequency chirping is [42]: f = 1 2 @(t) @t = H 4 d dt lnP (t) +xP (t) (8.3) in which,x is a constant. The rst term this equation is known as \transient chirp" due to relaxation oscillations and the second term is referred to as the \adiabatic chirp" at the steady-state. This frequency chirp causes spectral broadening of the intensity-modulated signal. Although this alpha factor is a useful metric to quantify the device chirp, when a sig- nal passes through a subsystem such as an SOA-MZI wavelength converter, alpha factor denition gives a time-dependent parameter which may not be as useful for quantifying ber transmission behavior of the new chirp waveforms [83]. The following is a chirp- inducing wavelength converter that utilizes the nonlinear cross-phase-modulation inside the SOAs in a Mach-Zehnder interferometer (MZI) structure to generate wavelength converted output [67], [37]. Figure 8.1 shows a wavelength converter that utilizes cross-phase modulation (XPM) in the SOAs [67]. The high power data signal and a relatively lower power continuous- wave probe are injected into an SOA. The high power signal depletes carriers and thus can change the carrier density of the SOA. This change in carrier density causes changes the refractive index of the device. However, the carriers are recovered with a relatively slow time constant (known as carrier recovery time). The change in refractive index changes the phase of the probe, as shown in Figure 8.1(b). The phase shift on the probe caused by the high power signal is known as XPM and the amount of XPM phase-shift 103 λ Probe BPF 2 nm SOA-2 40 Gbit/s ATT 80 km SMF 2 nm PC 1 nm 1 nm Photodiode Bit Error Rate Tester λ SIG MZM 20GHz Clk TDCM Δt MZM RZ-OOKSignal SOA-1 Δ φ ATT Δt SOA-MZI Wavelength Converter 1 nm at λ Probe 17 km DCF Fiber Transmission Pre-amplified Receiver (a) (b) Figure 8.1: (a) Experimental Setup for SOA-MZI wavelength converter for RZ-OOK signals. (b) Principle of operation of the SOA-MZI wavelength converter based on dif- ferential cross phase modulation [67] is proportional to the input power of the signal. Therefore, if two SOAs are used in an MZI structure with constructive interference, the change in phase can be translated to a change in the intensity of the probe. The signal that is fed to one of the SOA's is attenuated and delayed by less than a bit-time. As illustrated in Figure 8.1, on the high power signal path (SOA-1), there is a large phase shift on the probe, while the SOA-2 path, lower phase shift occurs. When the two XPM-phase-shifted probe lasers interfere destructively at the output of the MZI, this can create a copy of the original data signal at the probe wavelength. This technique is based on the slow recovery of phase in the SOAs, and the speed of signals depend on the amount of delay between the two signal paths. Thus this can potentially work at > 100 Gbit/s speeds. On each arm of the SOA-MZI, the probe experiences time-dependent phase varia- tions, which translates to frequency chirp, according to equation 8.1. This frequency chirp is not caused by the power variations of the probe, but rather of another signal. Therefore, the alpha parameter that in equation 8.2, does not exactly apply here. Fur- thermore, the nal output signal is the coherent subtraction of the two frequency-chirped output signals of the SOAs (the MZI is set up as a destructive interferer). Because the 104 “0” and “1” Levels at MZI Destructive Port Input 1 SOA 2 SOA 1 (XPM) Level “1” Level “0” Input 2 _ + Destructive Port Output Small variations in XPM/XGM in MZI arms will not change the general shape of chirp profile. Small variations in XPM/XGM in MZI arms could significantly change the chirp profile. Level “1” Level “0” Figure 8.2: Generation of various frequency chirp proles, especially at the edges of the signal, depending on the wavelength converter design. power of the probe is almost evenly split between the two arms of the interferometer, coherent subtraction of the optical elds is equivalent to a vector addition, with vectors having almost the same amplitude but dierent phases. Figure 8.2 illustrates this con- cept. To generate output levels close to 1 (i.e., middle of the return-to-zero (RZ) pulse) the two vectors from the two arms subtract with close to phase dierence, resulting in a intensity peak. However, when the output levels get close to 0 (i.e., edges of the pulse), the two vectors subtract with 0 phase dierence. Therefore, at 0 levels, small variations in the phase or intensity of the signals can signicantly change the vector direction (i.e., phase) and when this happens in the time close to the edges it causes very large frequency chirp on the signal. Because of this, dierent system designs and physical parameters of the device can produce dierent chirp waveforms. We study a group of dierent chirp scenarios to explore the eect of chirp on transmission performance. As depicted in Figure 8.3, the goal is to build a model to generate a variety of chirp proles and explore their transmission performance, to isolate the eect of chirp from extinction ratio (ER) and signal-to-noise ratio (SNR). The study gives some guidelines for tailoring the subsystem induced chirp to an optimum ber transmission. The parameters in the subsystem, such as an XPM based SOA-MZI wavelength converter [104], could then be optimized to achieve the desired chirp prole, at the cost of degrading ER and/or SNR. 105 Chirp-Inducing Device (Wavelength Converter, Modulator, SOA, etc.) λ 2 XPM, XGM, SPM, Carrier Recovery Time, etc. λ 2 Power Chirp 1 Chirp 2 Design Guidelines Fiber Simulation and Comparison of Chirp Regimes λ 1 No Chirp Arbitrary Chirp Profile Generator Figure 8.3: Concept of arbitrary chirp waveform generator simulations to provide input for device optimization to achieve improved system performance. MATLAB • Pulse Shape (amplitude) • Chirp (phase/frequency) • Extinction ratio • Pulse width Signal Analyzer VPItransmissionMaker Transmitter • PRBS • Laser • Noise SMF DCF Various Measured Chirp Profiles and Pulse Shapes of Converted Signal Chirp Profiles Power Intensity (blue), Chirp Profile (red) Figure 8.4: Simulation technique, various chirp proles used for simulation and sample experimental chirp waveforms measurements. 8.3 Modeling and Simulation using Arbitrary Chirp Pro- le A variety of arbitrary chirp proles, shown in Figure 8.4, is generated in Matlab and is fed into VPItransmissioMaker software for ber transmission simulation. A subset of Figure 106 8.4 depicts three sample chirp and intensity proles of the wavelength converter output, experimentally measured at 40-Gbit/s for an RZ-OOK signal. We varied the delay and attenuation on one of the signal paths into the SOA-MZI and observed how the chirp waveform changes. It can be observed that although the signal intensity is almost similar in the three cases, the signal chirp waveform varies signicantly. Therefore, we chose dierent chirp proles that cover the following properties: Various amount of red shifting and blue shifting on leading and trailing edges. Dierent chirp prole shapes (symmetric and non-symmetric proles). Various location of chirp inside the pulse. For the simulations, a 40 Gbit/s RZ-OOK signal ( 1553 nm) with rst order Gaussian pulse shape and FWHM = 10 ps is generated and is driven by a 2 11 1 PRBS data. The extinction ratio is set to 30 dB. Each bit is sampled at 128 points to capture the impacts of sub-pulsewidth chirp inside the pulse. Average chirp peak is varied between50 GHz. For the ber transmission, a low nonlinearities regime (launch power of -13 dBm through one amplied and fully compensated span of 80 km SMF/DCF) and a high nonlinearities regime (launch power of3 dBm into 25 fully compensated spans, resulting in 2000 km of SMF) is simulated to study the interaction of chirp and nonlinearities. The SMF (DCF) has a rst order dispersion of 16 ps/nm/km (-90 ps/nm/km), nonlinear index of 2:6 10 20 m 2 /W (4 10 20 m 2 /W) and eective core area of 80m 2 (30m 2 ). Various residual dispersion between12 ps/nm is applied at the receiver to explore the ability of dispersion compensation to fully correct penalties induced by interaction of chirp, dispersion and nonlinearities. BER is estimated at the receiver to nd power penalties at 10 9 . 107 Power Profile P n (t) Chirp Normalized Chirp f(t) f n (t) = P n (t) × f(t) 0 1 Zero Chirp Level Zero Chirp Level Zero Power Level Figure 8.5: Concept of normalized chirp, dened as the chirp prole times the intensity prole. 8.4 Analysis of Chirp Penalties Normalized Chirp Waveform It is intuitive that a large chirp at close to zero power (edges of the pulse) is less signif- icant compared with a lower chirp at higher power (center of the pulse). The concept of \normalized chirp", depicted in Figure 8.5, takes this eect into the account. The \average normalized chirp" on leading and trailing edges are dened to help compare various chirp regimes. We rst dene the normalized power prole and normalized chirp as: Normalized power prole: P n (t) = P (t) max 0t<T bit fP (t)g (8.4) Normalized chirp prole f n (t) = f(t)P n (t) (8.5) 108 In which, P (t) is the power of the signal. P n (t) is the power prole with maximum level of 1 and f n (t) is the instantaneous normalized frequency deviation or chirp. Using this normalization, the eect of chirp at signal edges is suppressed. 8.4.1 Average Normalized Chirp Parameters We can now dene the average normalized chirp parameter on the leading (time from 0 to T bit =2) and trailing edges (time from T bit =2 to T bit ) of the signal as: f lead Ave = 1 T bit Z T bit 2 0 f n (t)dt (8.6) f trail Ave = 1 T bit Z T bit T bit 2 f n (t)dt (8.7) For the various chirp proles depicted in Figure 8.4, we calculate these two parameters and plot the result in Figure 8.6, each triangle corresponds to a chirp prole in Figure 8.4. The chirp proles that map close to the center of Figure 8.4 have lower chirp at the middle of the pulse. 8.4.2 Interaction of Chirp, Dispersion and SPM We consider three main physical properties that can vary: ber chromatic dispersion, initial frequency chirp of the pulse, and self phase modulation (SPM). Frequency chirp, chromatic dispersion and self phase modulation can induce a time- or distance-dependent phase shift on the signal and can thus interact with each other in the ber. Considering that the phase of the signal at distant z from the beginning of the ber as: ! 0 t(!)z + 2 Z t 0 f()d + o (8.8) in which, ! 0 is the optical carrier frequency, f(t) is the frequency chirp, and (!) is the propagation constant at angular frequency ! 0 . 109 -50 0 50 -50 0 50 ∆f Ave on Leading Edge, [GHz] ∆f Ave on Trailing Edge, [GHz] Power Chirp Power Chirp Power Chirp Power Chirp Power Chirp Power Chirp Power Chirp Power Chirp Norm. Chirp Norm. Chirp Norm. Chirp Norm. Chirp Norm. Chirp Norm. Chirp Norm. Chirp Norm. Chirp ∆f Ave on Trailing Edge, [GHz] Figure 8.6: Mapping of average normalized chirp on leading and trailing edges on a scatter diagram (chirp diagram). To include nonlinear eects, the nonlinear refractive index is dened as [1]: n 0 j =n j +n 2 (P=A eff ) (8.9) where n 2 is the nonlinear-index coecient, P is the optical power, and A eff is the eective mode area of the ber. For silica bers the value of n 2 is 2:6 10 20 m 2 /W. At power ranges close to 1 mW, this nonlinear coecient is relatively small, but it can cause self phase modulation when long bers are used. 110 Self phase modulation [1] is the eect where the intensity (power) of the optical signal changes the propagation constant (or refractive index) of the medium. The change in propagation constant induces a nonlinear phase shift on the signal itself: NL = P in (t)L eff (8.10) in which, P in (t) is the input power to the ber of length L, = 2n 2 =(A eff ) is the nonlinear coecient with values that depend on wavelength () and ber eective area A eff and ranges from 1 to 5 W 1 /km. L eff = [1 exp(L)]= is the eective length of the ber with attenuation of . The instantaneous frequency chirp due to SPM is thus f SPM (t) = 1 2 d NL dt = L eff 2 dP in (t) dt : (8.11) Therefore, SPM-induced frequency chirp is proportional to the derivative of the signal power. This frequency shift is positive on the leading edge of the signal and causes a blue-shifting eect and is negative on the trailing edge of the signal creating a red-shifting eect [98]. Table 8.1 summarizes these eects and illustrates how frequency chirp due to dierent phenomena map to the diagram of Figure 8.6. 8.5 Simulation Results and Discussion The power penalty at BER of 10 9 is contour-plotted in Figure 8.7. Two dierent cases are considered: (i) a transmission system with low nonlinearities, and (ii) a transmission system with high nonlinearities. The low nonlinear case is comprised of an 80-km SMF link that is fully dispersion compensated by using a DCF. The launch power is low such that the SPM is negligible. On the other hand, the high nonlinearities case is simulated by launching higher signal power (-3 dBm) into multiple compensated spans of 80-km SMF, reaching 2000 km. Slightly negative and positive residual dispersion is considered 111 Table 8.1: Interaction of chirp, ber dispersion and self phase modulation Parameter Leading Edge Trailing Edge f lead Ave f trail Ave Counteracts with: Positive Chirp (f(t)/ +t) Red shifted Blue shifted Negative Positive Anomalous dis- persion, Negative chirp Negative Chirp (f(t)/t) Blue shifted Red shifted Positive Negative Normal disper- sion, Positive chirp, SPM Anomalous Dis- persion (positive ber dispersion, e.g., SMF) Blue shifted Red shifted Positive Negative Normal disper- sion, Positive chirp, SPM Normal Dispersion (negative ber dis- persion, e.g., DCF) Red shifted Blue shifted Negative Positive Anomalous dis- persion, Negative chirp Self Phase Modula- tion (SPM) Red shifted Blue shifted Negative Positive Anomalous dis- persion, Negative chirp (8 ps/nm). As can be noted in Figure 8.7, in the low nonlinearity regime the power penalty is zero, because dispersion is fully compensated. Also, one can observe that there are symmetrical behavior around the line that crosses the second and third quadrant of the chirp diagram. One can conclude that the chirp proles that are symmetric around the center of the pulse generally incur similar power penalties. Furthermore, the inverse eect of positive and negative CD can be observed. However, for the high-nonlinearity regime, when there is a chirp peak close to the center of the pulse, then the penalties are much higher. This happens because the CD and SPM and chirp interact and distort the pulse in such a way that cannot be compensated linearly. Figure 8.8 depicts the power penalties for three dierent chirp proles that dier only in the location of the chirp peak. The average normalized chirp on each side of the pulses are shown in the gure as well (Figure 8.8(a)). In Figure 8.8(b), a regime with low nonlinearity is considered. For the high nonlinearity case, the power penalty of the reference (zero chirp) scenario is higher than 5 dB and is thus not plotted in Figure 8.8(c). One can observe that for low nonlinearities, when a peak is at the center, 112 - 8 ps/nm 0 ps/nm Low Nonlinearities 80 km SMF, Pin = - 13 dBm Power Penalty (dB) at BER = 10E-9 High Nonlinearities 2000 km SMF, Pin = - 3 dBm + 8 ps/nm (a) (b) (c) (d) (e) (f) Figure 8.7: Power penalty on the chirp diagram for (a-c) low nonlinearity ber trans- mission (80 km SMF with13 dBm input power) and (d-f) high nonlinearity ber transmission (25 80 km SMF with3 dBm input power) less degradation happens as a result of residual dispersion. But, for a positive chirp peak close to the leading edge, there is a negative power penalty (i.e., opening of eye diagram) because the CD and the chirp interact to narrow the pulse. Also for the positive dispersion the penalty increases because the CD and the chirp interact and distort the signal even more. Figure 8.9, shows the power penalties for various chirp proles. These proles are chosen to have odd and even symmetry, because according to Figure 8.7 the rest of the proles are either similar to these or their behavior can be predicted through symmetrical properties. Figures 8.8(b) and 8.9(b) show dispersion tolerance of chirp proles at low launch power and Figures 8.8(c) and 8.9(c) depict penalties when ber nonlinearities are high. From Figure 8.8, central chirp peak, CP1, has0.5dB power penalty at10 ps/nm 113 CP1: (40,20) GHz CP2: (30,30) GHz CP3: (20,40) GHz Chirp Profiles Inside a Pulse Chirp Profiles Power Low Nonlinearities 80 km SMF, Pin = - 13 dBm High Nonlinearities 2000 km SMF, Pin = - 3 dBm CRef: Zero Chirp (a) (b) (c) Figure 8.8: (a) Various chirp peak locations, (b) low nonlinearities regime: power penalty versus residual dispersion, (c) high nonlinearities regime: power penalty versus residual dispersion Chirp Profiles Power C3 C2 C1 CRef Chirp Profiles Inside a Pulse Low Nonlinearities 80 km SMF, Pin = - 13 dBm High Nonlinearities 2000 km SMF, Pin = - 3 dBm (a) (b) (c) Figure 8.9: (a) Various chirp proles, (b) low nonlinearities regime: power penalty versus residual dispersion, (c) high nonlinearities regime: power penalty versus residual dispersion dispersion, while other proles show2dB penalty. As can be seen in Figures 8.7(b), 8.8(c) and 8.8(c), when nonlinearities and chirp interact in ber, simple dispersion com- pensation does not fully correct penalties for a chirp peak at the center of the pulse. Symmetric chirp around center, C2, is more robust, but has1.5 dB penalty, while in a negative chirp, C3, power penalty is improved by2 dB with the optimum choice of 114 residual dispersion. Yet,4 ps/nm deviation from the optimum dispersion cancels this improvement. 8.6 Conclusions Same power penalty trends are observed if a chirp prole is symmetric around the center of the pulse. By comparing dierent chirp proles, we nd the optimum chirp regimes for a post-compensated ber link. It is shown that if a chirp prole has a peak on the signal edges,5 ps/nm residual dispersion on a 40 Gb/s RZ signal results in 2 dB higher power penalty compared to a chirp peak located at the center of the pulse. With higher launch power, a single chirp peak on leading or trailing edge achieves 2 dB lower minimum power penalty (at 10 9 BER) compared to the prole with a chirp peak at pulse center. The chirp of the wavelength converters based on dierential cross-phase modulation in semiconductor optical ampliers could be designed to t into a suitable chirp regime for better ber transmission. 115 Chapter 9 Conclusions There have been technological advances in the eld of optical communications that can be applied to optical signal processing. Information can be encoded on amplitude, phase, polarization and wavelength of an optical wave to increase the capacity of transmission. Nonlinear optical processes have femtosecond response times and some could preserve the amplitude, phase and polarization information of the optical signals. Optical signal processing techniques may benet not only from the high bandwidth of optical devices and signals (i.e., high baud rate), but also from these encoding dimensions to increase the processing capacity. We have provided an overview of key enabling functions for signal processing { namely multicasting, multiplexing/demultiplexing, tunable optical delays, and a tunable tapped delay line. This Ph.D. dissertation presented some applications of optical signal processing that are made possible by these basic optical functions. These applications included nite-impulse-response ltering, equalization, optical correlation, optical FFT and DFT, optical signal generation and conversion. Nonlinear photonic interactions along with photonic integration might enable further complicated signal processing applications in the future. In Chapter 1, we overviewed the basic enabling technologies that enable optical sig- nal processing from a systems point of view. Advanced in ve dierent areas that have recently impacted the eld of optical signal processing were examined. This 116 included advanced modulation formats, optical coherent detection, digital signal process- ing, advanced nonlinear materials and devices, and photonic integration. Fundamentals of optical modulation formats, optical coherent detection and optical nonlinearities were examined. Mathematical representation of second-order and third-order optical non- linearities were reviewed. Processes such as degenerate and non-degenerate FWM in third-order nonlinear media (e.g., HNLF), and SHG, SFG, and DFG in second-order nonlinear medium (e.g., PPLN device) that are commonly exploited for optical signal processing were presented. These technologies enable various functions presented in Chapter 2. In Chapter 2, prior art on the technologies and technique for optical signal multi- casting, multiplexing, demultiplexing and tunable optical delays was presented. These techniques form a set of basic functions that lay the foundation for more advanced signal processing applications, such as a tapped delay line. In Chapter 3, we demonstrated a recongurable high-speed optical tapped delay line (TDL), enabling several fundamental real-time signal processing functions such as correlation (for pattern search) and equalization. Weighted taps were created and added using optical multicasting and multiplexing schemes that utilized the nonlinear wave mixings in periodically poled lithium niobate (PPLN) waveguides. Tunable tap delays were realized using the conversiondispersion technique. In the demonstrated TDL, the amplitude and phase of the tap coecients could be varied, enabling signal processing on amplitude- and phase-encoded optical signals. In Chapter 4, we used ne-tuning of pump wavelengths to apply the tap phases in a complex-coecient optical tapped-delay-line that utilized conversion/dispersion- based delays and nonlinear wave mixing. Full 2 phase tuning was demonstrated by detuning the frequency of laser pumps by <20 GHz, which showed close agreement with theory. Next, we experimentally characterized the performance of a continuously tunable all-optical complex-coecient nite impulse-response (FIR) lter that exploited 117 nonlinear signal processing (multiplexing and multicasting) and conversion-dispersion- based optical delays. Various length (three and four) optical FIR lters with dierent tap amplitudes (from 0 to -9 dB), tap phases (from 0 to 2), and tap delays (37.4 ps and 25 ps) were realized, showing reconguration and tuning capabilities of this FIR lter. The measured frequency responses showed close agreement with the theoretical lter responses. In Chapter 5, we experimentally demonstrated the tunability of the TDL in time, amplitude, and phase. We analyzed the TDLs theory of operation and presented exper- imental results on recongurable pattern search (correlation) on ono-keyed and phase- shift-keyed signals at data rates of up to 80 Gb/s, as well as equalization for chromatic dispersion. In Chapter 6, we experimentally demonstrated a recongurable optical con- verter/encoder for quadrature-amplitude-modulated (QAM) signals. The system utilized nonlinear wavelength multicasting, conversion-dispersion delays and simultaneous non- linear multiplexing and sampling. We showed baud rate tunability (31 and 20 Gbaud) and recongurable conversions from lower order QAM signals to higher order QAM signals (e.g., 64-QAM). In Chapter 7, We demonstrated a tunable optical tapped-delay-line that can simul- taneously and independently operate on WDM data signals. The system utilized the wavelength dependent speed of light, together with nonlinear wavelength conversion stages. A phase-preserving scheme enables coherent addition of the weighted taps. We recongured the system to perform simultaneous correlation (data pattern recognition), equalization and modulation format conversion on four and eight WDM B/QPSK chan- nels at 26- and 20-Gbaud, respectively. Throughput of 416-Gbit/s was achieved. In Chapter 8, we simulated an arbitrary chirp waveform generator to explore the ber transmission performance of the output of chirp-inducing devices. Various chirp regimes were considered to nd the optimum chirp prole for a post-compensated ber link. In conclusion, if a chirp prole had a peak on the signal edges,5 ps/nm residual 118 dispersion on a 40 Gb/s RZ signal results in2 dB higher power penalty compared to a chirp peak located at the center of the pulse. With higher launch power, a single chirp peak on leading or trailing edge achieved2 dB lower minimum power penalty (at 10 9 BER) compared to the prole with a chirp peak at pulse center. The work presented in this dissertation is mainly focusing on processing of digital signal that are both phase- and amplitude-modulated. We devised techniques that can utilize separate pump lasers for wave mixing operations on these signals and yet maintain the phase coherency between the signals that were supposed to be combined. It is envisioned that this work can be extended as follows. First, maintaining the phase coherency of the signals sometimes necessitated the use of a nonlinear device to create the phase-conjugate of a signal/pump and another nonlinear element to undo the eect of the rst stage. However, one may use optical frequency combs instead of independent pump lasers. The frequency combs produce multiple narrow-linewidth laser lines that are phase coherent with respect to each other. The use of optical comb source has the advantages of (i) phase coherency, (ii) one device that functions as multiple lasers, and (iii) narrow linewidth; all of which are key to scaling the techniques presented in this dissertation. By maintaining the phase coherency, optical combs can save one or more nonlinear stages compared to using independent lasers sources. Narrow linewidth is specially important for higher-order modulation formats that require accurate phase tracking in the coherent receivers [129][18][21]. Second, we explored techniques that can manipulate amplitude and phase of optical signals. Generation of the square of a signal and its conjugate played an important role in enabling these functions. However, optical nonlinearities can also generate higher order mixing terms that result in the generation of powers of signal that are greater than two. All these features may be better utilized if the signal modulation formats are re-dened to match these physical interactions in optics. New encodings and modulations formats may allow for more advanced data processing techniques using digital optical signal processing. Some mathematical functions that may be hard to implement on the signals 119 with traditional modulation formats, could possibly be implemented if proper encodings and formats are used. Periodic nature of phase, generation of powers of signal, and phase conjugate of the signal may be some key physical properties to focus on. Third, optical phase sensitive amplication techniques utilize the fact that the signal and its phase-conjugate can simultaneously exist and be used. The real and imaginary parts of signals can thus be recovered from these signals. A possible extension of the work presented here might be in processing of the real or imaginary parts of the signal independently [113][24]. Fourth, most of the processing techniques presented in this work were implemented on one-dimensional data. A combination of the one-dimensional tapped-delay-line and the WDM tapped-delay line can be applied to designs that process two-dimensional image data and beyond [21]. Fifth, devices that can enable multiple-input-multiple-output (MIMO) signal process- ing can signicantly increase the applications of such systems. One possible candidate might be the use of multiple-QPM PPLN waveguides, in which parasitic mixing terms are much less than the FWM media and can still eciently mix multiple input signals. Considering that electronics processing capacity also grows by means of paralleliza- tion and the role of optical processing to assist electronics to perform certain functions at a very high speed is yet to be explored. 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Abstract (if available)

Abstract Technology has empowered people in all walks of life to generate, store, and communicate enormous amounts of data. Recent technological advances in high-speed backbone data networks, together with the growing trend toward bandwidth-demanding applications such as data and video sharing, cloud computing, and data collection systems, have created a need for higher capacities in signal transmission and signal processing. ❧ Optical communication systems have long benefited from the large bandwidth of optical signals (beyond tera-hertz) to transmit information. Through the use of optical signal processing techniques, this Ph.D. dissertation explores the potential of very-high-speed optics to assist electronics in processing huge amounts of data at high speeds. ❧ Optical signal processing brings together various fields of optics and signal processing -- nonlinear devices and processes, analog and digital signals, and advanced data modulation formats -- to achieve high-speed signal processing functions that can potentially operate at the line rate of fiber optic communications. Information can be encoded in amplitude, phase, wavelength, polarization, and spatial features of an optical wave to achieve high-capacity transmission. Many advances in the key enabling technologies have led to recent research in optical signal processing for digital signals that are encoded in one or more of these dimensions. Optical Kerr nonlinearities have femto-second response times that have been exploited for fast processing of optical signals. Various optical nonlinearities and chromatic dispersions have enabled key sub-system applications such as wavelength conversion, multicasting, multiplexing, demultiplexing, and tunable optical delays. ❧ In this Ph.D. dissertation, we employ these recent advances in the enabling technologies for high-speed optical signal processing to demonstrate various techniques that can process phase- and amplitude-encoded optical signals at the line rate of optics. We use nonlinear media, such as highly nonlinear fiber, periodically poled lithium niobate, and semiconductor optical amplifiers, for nonlinear mixing of optical signals. We propose and experimentally demonstrate a novel, fully tunable optical tapped-delay-line that is a key building block for signal processing functions. Applications such as finite impulse response filtering, equalization, correlation (pattern recognition), discrete Fourier transform, digital-to-analog conversion, and flexible optical signal conversion and generation are shown. The phase- and amplitude-preserving nature of the demonstrated techniques, together with their wide-tuning range, allows for processing of optical signals that carry different modulation formats with different data rates. The reconfigurability may apply to future optical networks that carry heterogeneous traffic with different modulation formats and baud rates.

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Asset Metadata

Creator Khaleghi, Salman (author)

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

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 07/21/2013

Defense Date 04/30/2013

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

Tag correlation,equalization,fiber optics,nonlinear optics,OAI-PMH Harvest,optical communications,optical signal processing,QAM,tapped-delay-line,wave mixing

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Willner, Alan E. (committee chair), Armani, Andrea M. (committee member), Chugg, Keith M. (committee member), Sawchuk, Alexander A. (Sandy) (committee member), Steier, William Henry (committee member), Touch, Joseph D. (committee member)

Creator Email khaleghi@usc.edu,sa.khaleghi@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-293503

Unique identifier UC11288405

Identifier etd-KhaleghiSa-1803.pdf (filename),usctheses-c3-293503 (legacy record id)

Legacy Identifier etd-KhaleghiSa-1803.pdf

Dmrecord 293503

Document Type Dissertation

Rights Khaleghi, Salman

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