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Microphotonics for tailored infrared emission and secure data encryption

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Microphotonics for tailored infrared emission and secure data encryption

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MICROPHOTONICS FOR TAILORED INFRARED EMISSION AND SECURE DATA ENCRYPTION

by

Romil Audhkhasi

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

May 2023

Copyright 2023 Romil Audhkhasi
ii
Dedication

To my parents, Punam Audhkhasi and G. S. Audhkhasi and my mentor, Michelle Povinelli.
Thank you all for your love, support and guidance throughout this journey.

iii
Acknowledgements

First and foremost, I would like to thank my PhD advisor, Prof. Michelle Povinelli for her constant
support and guidance throughout my time at USC. She is extremely compassionate towards her
students and takes keen interest in their professional development and overall well-being. She
always offered helpful advice and motivated me to push through hardships to achieve my goals.
Her passion for science inspires me to be a better researcher while her generosity and pleasant
attitude motivate me to become a good mentor and team leader in the future. It has been a
privilege working with her.
I would like to extend my sincere gratitude to several outstanding faculty members at
USC. I would like to acknowledge Prof. Andrea Armani for her persistent efforts in bringing about
a positive change in science and academia. As a young researcher building a career in academia,
I find her seminars and panel discussions on professional development as well as other social
media outreach an extremely valuable resource. I would also like to thank Prof. Wei Wu for
providing helpful advice on device fabrication for some of my research projects. Being a
theoretical physicist, I find his teachings extremely helpful for designing realistic photonic
devices. I would also like to acknowledge Prof. Aluizio Prata for his commitment to teaching. I
consider his class on advanced electromagnetics at USC as one of the best I have taken in my
entire career. It was also great fun interacting with him outside of class. I am also extremely
grateful to have had the opportunity to work with and learn from Profs. Jon Habif, Han Wang and
Chia Wei Hsu during my time at USC. Finally, I would like to thank Profs. Shrikanth Narayanan,
iv
Paul Daniel Dapkus and Armand Tanguay for being so warm and welcoming and helping me settle
into life at USC during my first year.
I would also like to thank both current and former group members at Povinelli lab as well
as staff members in the ECE department at USC. I would like to acknowledge Ahmed Morsy,
Aravind Krishnan, Mingkun Chen, Shao-Hua Wu and Alok Ghanekar for helping me get acquainted
with several numerical modeling methods. I would also like to thank Jiang-Bin Wu for training me
on the infrared spectrometer. I am extremely grateful to have had the opportunity to mentor Iris
Li, Cameron Davis, Marcos Girod, Sean Yamaguchi and Yujun Sun on a couple of my research
projects. It was great fun collaborating with such talented minds and I wish them all the best for
the future. I would also like to acknowledge the hard work put in by several of the staff members
in our department – Diane Demetras, Kim Reid, Susan Zarate, Cathy Huang, Benjamin Paul and
Marilyn Poplawski. Their efforts enable students and faculty members to conduct cutting-edge
research.
Last but certainly not the least, I would like to thank my brother, Kartik Audhkhasi for his
continued support and guidance throughout my career. Being a USC alumnus himself, he gave
me helpful tips on settling in at USC, navigating PhD life and in general, living in the States. His
support made this journey a lot easier.

v
Table of contents

Dedication ...................................................................................................................................... ii
Acknowledgements ....................................................................................................................... iii
List of figures ................................................................................................................................ viii
Abstract ........................................................................................................................................ xiii
PART 1: INFRARED EMISSION TAILORING ...................................................................................... 1
Chapter 1: Introduction ................................................................................................................. 1
1.1 Common photonic modes in metallic microstructures ....................................................... 2
1.1.1 Surface plasmon polariton modes in metallic gratings ................................................. 2
1.1.2 Cavity modes in MIM microstructures .......................................................................... 4
1.2 Numerical modeling of microstructures .............................................................................. 6
1.2.1 Finite Difference Time Domain method ........................................................................ 6
1.2.2 Rigorous Coupled-Wave Analysis .................................................................................. 7
1.2.3 Temporal Coupled-Mode Theory .................................................................................. 7
1.3 Thermal emission and Kirchhoff’s law ................................................................................. 8
Chapter 2: Static tuning of infrared emission .............................................................................. 10
2.1 Gold – black phosphorus nanostructured absorbers for infrared photodetection ........... 10
2.1.1 Background ................................................................................................................. 10
2.1.2 Proposed absorber design and working principle ....................................................... 12
2.1.3 Dependence of absorption enhancement on BP film thickness ................................. 13
2.1.4 Conclusion and potential impact ................................................................................ 15
2.2 Aluminum-based hybrid gratings for spectral emissivity tailoring .................................... 16
2.2.1 Background ................................................................................................................. 16
2.2.2 Defining target spectra ............................................................................................... 17
2.2.3 Designing Al grating building blocks ........................................................................... 18
2.2.4 Hybrid grating structure and results for spectral matching ........................................ 19
vi
2.2.5 Conclusion and potential impact ................................................................................ 20
2.3 Spectral emissivity prediction in hBN-based thermal emitters ......................................... 21
2.3.1 Background ................................................................................................................. 21
2.3.2 Thermal emitter design and workflow for CMT-based spectral prediction ................ 23
2.3.3 Building the CMT catalog ............................................................................................ 24
2.3.4 Results for spectral prediction .................................................................................... 25
2.3.5 Conclusion and potential impact ................................................................................ 26
Chapter 3: Dynamic tuning of infrared emission ......................................................................... 28
3.1 Graphene-based metamaterial for on-demand spectral synthesis in the infrared ........... 29
3.1.1 Background ................................................................................................................. 29
3.1.2 Metamaterial design and results for spectral tuning .................................................. 30
3.1.3 Conclusion and potential impact ................................................................................ 31
3.2 Gold – vanadium dioxide micro-gratings for thermal rectification .................................... 31
3.2.1 Background ................................................................................................................. 31
3.2.2 Two approaches to radiative thermal rectification ..................................................... 32
3.2.3 Peak extinction approach ............................................................................................ 34
3.2.4 Peak shift approach ..................................................................................................... 35
3.2.5 Conclusion and potential impact ................................................................................ 36
3.3 Vanadium-dioxide microstructures for designable, temperature-dependent thermal
emission ................................................................................................................................... 36
3.3.1 Background ................................................................................................................. 36
3.3.2 Proposed structure and working principle .................................................................. 38
3.3.3 Trends in radiated power for different structural parameters ................................... 39
3.3.4 Design of temperature-switchable spatial emission pattern ...................................... 40
3.3.5 Conclusion and potential impact ................................................................................ 40
3.4 Dynamically switchable self-focused thermal emission .................................................... 41
3.4.1 Background ................................................................................................................. 41
3.4.2 Lens design and working principle .............................................................................. 43
3.4.3 Method for direct calculation of thermal emission .................................................... 44
3.4.4 Temperature-switchable thermal focusing ................................................................. 46
3.4.5 Conclusion and potential impact ................................................................................ 48
vii
Chapter 4: Conclusion and outlook .............................................................................................. 49
PART 2: SECURE DATA ENCRYPTION ............................................................................................ 51
Chapter 5: Introduction ............................................................................................................... 51
Chapter 6: Generalized multi-channel scheme for secure image encryption .............................. 54
6.1 Encryption and decryption algorithms .............................................................................. 55
6.2 Enabling security against a brute-force attack .................................................................. 57
6.3 Enabling security against more sophisticated attacks ....................................................... 60
6.4 Table-top demonstration ................................................................................................... 64
6.5 Conclusion and potential impact ....................................................................................... 65
Chapter 7: Experimental implementation of metasurfaces for secure multi-channel image
encryption in the infrared ............................................................................................................ 67
7.1 Designing a metasurface for image encryption ................................................................. 68
7.2 Metasurface pixel design ................................................................................................... 71
7.3 Experimental implementation of image decryption .......................................................... 73
7.4 Degree of randomness of multi-channel encryption scheme ............................................ 76
7.5 Conclusion and potential impact ....................................................................................... 78
Chapter 8: Conclusion and outlook .............................................................................................. 81
References ................................................................................................................................... 83

viii
List of figures

Figure 0.1: (a) Schematic showing the dispersion relation of an SPP mode at a
metal-air interface (inset shows a block of metal). (b) Schematic showing the
dispersion relation of an SPP mode at a metal-air interface patterned with
periodicity a. The inset shows a one-dimensional metal grating. The resonant
frequencies are indicated by open, black circles.

3
Figure 0.2: Unit cell of an MIM microstructure. The blue curve in Region 1 shows
the z-component of the electric field correspnding to the TM 0 waveguide mode.

5
Figure 0.3: Schematic showing a system of N coupled resonators represented as
circles.

8
Figure 0.4: (a) Absorption enhancement structure. (b) Electric field profile for an
MDNA with d BP = 20 nm. (c) Absorption spectrum for an MDNA with d BP = 20 nm.

12
Figure 0.5: (a) Variation of λ max with L and d BP. The solid green circles indicate the
values of L needed for λ max = 4 μm. (b) Wavelength-dependent absorptivity in the
BP layer of the MDNA for few different layer thicknesses. (c) Variation of F with
d BP..

14
Figure 0.6: (a) Wavelength dependent absorptivity in the BP layer of the MDNA for
few values of the angle of incidence. (b) Spectrally averaged absorption in the BP
layer of the MDNA as a function of θ.

15
Figure 0.4: (a) Target spectrum 1. (b) Target spectrum 2. (c) Target spectrum 3.

18
Figure 0.7: (a) Schematic of an Al grating. The unit cell is indicated with a red box.
(b) Variation of peak location with slot dimensions for a = 8, 10 and 12 µm.

19
Figure 0.8: (a) Schematic showing the layout of a hybrid grating formed by
combining three Al gratings. (b) (from left to right) Comparison between target and
hybrid grating spectrum for targets 1, 2 and 3.

21
Figure 0.9: (a) Schematic of our hBN thermal emitter. (b) Workflow for CMT-based
spectral prediction.

23
Figure 0.10: (a) Unit cell of an emitter with a single hBN per unit cell (top) and the
corresponding emission spectrum (bottom). (b) Unit cell of the emitter with two
identical hBN ribbons separated by a distance d per unit cell (top) and emission
spectrum (bottom). (c) Coupling constant as a function of d.

25
ix
Figure 0.11: (a) Unit cell of an emitter with three hBN ribbons per unit cell (left)
and the corresponding emission spectrum (right). (b) Resonant frequencies of the
two modes of the system as a function of d.

26
Figure 0.12: (a) Unit cell of an emitter with three non-identical hBN ribbons per
unit cell (b) Emission spectra for different values of d 1 and d 2.

26
Figure 0.13: (a) Unit cell of proposed graphene-based metamaterial. (b) Absorption
spectra of the metamaterial or tuning resonator 1 towards (left panel) and away
(right panel) from resonator 2.

30
Figure 0.14: Schematic showing the operation of a thermal rectifier under (a)
forward and (b) reverse bias.

32
Figure 0.15: (a) Schematic of a radiative thermal rectifier under forward and
reverse bias (left and right panels, respectively). (b) In the peak extinction
approach, the emissivity of emitter 1 reduces with temperature. (c) In the peak
shift approach, an increase in temperature causes the emissive resonance of
emitter 1 to shift away from that of emitter 2. Both (b) and (c) show the rescaled
black body spectral radiance at a temperature of 300K.

33
Figure 0.16: (a) Schematic showing emitter geometries used in the peak extinction
approach. (b) An increase in temperature causes emitter 1 to switch from a metal-
dielectric grating (top panel) to a metal block (bottom panel). (c) Emission
spectrum of emitter 1 in the cold and hot states.

34
Figure 0.17: (a) Schematic showing emitter geometries used in the peak shift
approach. (b) An increase in temperature effectively reduces the dielectric slot
depth of emitter 1 (top to bottom panel). (c) Emission spectrum of emitter 1 and
2.

35
Figure 0.18: (a) Unit cell of an MIM. (b) Emissivity (left axis) as a function of
wavelength for cold and hot states of the MIM are shown by solid lines for a = 1
μm, L = 0.75 μm and d V = 0.05 μm.

38
Figure 0.19: (a) Variation of ΔP rad with L and d V. (b – d) Emission spectra for
structures with ΔP rad maximum, minimum and zero.

39
Figure 0.20: (a) Variation of ΔP rad with L for d V = 0.08 μm. (b) Layout of a switchable
emitter array. (c) Normalized radiated power of the array at 300 and 350K.

40
x
Figure 0.21: (a) Schematic of our switchable thermal lens. (b) (left panel) Side
resonator with W = 0.95 μm. (right panel) Absorption and scattering cross sections
of the side resonator. Inset shows |H|
2
for the side resonator at λ = 4 μm. (c) (left
panel) Central resonator with W = 0.54 μm. (right panel) Absorption cross sections
for the cold and hot states of the central resonator. Inset shows |H|
2
for the hot
state of the central resonator at λ = 4 μm.

44
Figure 0.22: (a) Schematic showing the dipole distribution for a calculation in which
the dipoles are placed only in the VO 2 cap. (b) Field intensities in the x-z plane at a
wavelength of 4 μm for the cold and hot states of a lens simulated with 600 dipoles.
The intensities in both states are normalized to the maximum intensity of the hot
state. (c) Focal plane intensities for the lens in both temperature states normalized
to the focal plane intensity in the hot state at x = 0. (d) Focal plane intensities in
the two temperature states normalized to their own intensity at x = 0.

47
Figure 0.23: Metasurface-based secure multi-channel communication.

52
Figure 0.24: A 9x9 pixel binary image of the letter ‘D’ is input to the encryption
algorithm that uses a key to convert it into a set of 5 seemingly random cipher
images. The decryption algorithm uses the same key to retrieve the letter ‘D’
image.

56
Figure 0.25: (a) Variation of log 2(N keys) with n. The solid red line shows the AES limit
of N keys = 2
256
for symmetric encryption. (b) Variation of log 2(n keys) with n p and n s
for n = 10.

58
Figure 0.26: (a) A 50x40 pixel binary image of the letter ‘A’. (b) Cipher images
generated by encrypting the letter ‘A’ image using a key with n = 10, n p = 5 and n s
= 126. (c) Image representing the sum of all cipher images. (d) Images generated
by attempting decryption using three incorrect keys with n = 10, n p = 5 and n s =
126.

59
Figure 0.27: (a) – (d) Variation of S mean for encrypted letter ‘A’ with n p and n s
calculated with respect to letters ‘A’ through ‘D’. S mean for each n p and n s is equal
to the mean similarity score of output images obtained by operating 1000
randomly selected keys on the cipher images.

61
Figure 0.28: Variation of mean score S mean with n calculated with respect to letters
‘A’ through ‘D’ for encrypted letter (a) ‘A’ and (b) ‘B’. Solid lines indicate average
S mean over 1000 trails with 1000 keys each, and colored bands represent the
corresponding error bounds.

63
xi
Figure 0.29: (a) A computer screen displays an image which is captured by a phone
camera. (b) Triplets of channels corresponding to n = 5 and n p = 3 are mapped to
10 colors in the RGB space to generate a lookup table. (c) A calibration image
comprising of all 10 colors displayed on the computer screen is captured and
resized to the original resolution. (d) Encryption and decryption of a 50x50 pixel
binary Trojan image using the computer screen – phone setup.

65
Figure 0.30: (a) A given plain image is converted into two random images which
are subsequently encrypted on two polarizations across four wavelength channels.
The pixel value at location (5,7) is highlighted with a green box in each of the cipher
images. (b) Schematic showing a 9x9 pixel metasurface designed to encode the
plain image in (a). A zoomed-in view of the encircled region of the metasurface
shows the pixel at location (5,7) that is designed to produce binary sequences in
accordance with the highlighted values in (a).(c) (left panel) Schematic showing a
single pixel and (right panel) model emission spectra for four-channel encryption
on a given polarization. The emissivity values at each of the channels are indicated
by yellow circles and the resulting binary sequence for every spectrum is displayed
above it.

70
Figure 0.31: (a) Schematic showing a single unit cell of a given pixel of the
metasurface: (left panel) perspective view and (right panel) side view. (b) A pixel
with a single nanorod of length L 1 per unit cell (left panel) produces a single peak
in the absorption spectrum for x-polarized incident light (right panel). (c) A pixel
with two nanorods with lengths L 1 (= 0.8 μm) and L 2 per unit cell (left panel)
produces two peaks in the absorption spectrum for x-polarized incident light (right
panel). (d) A pixel with two orthogonal sets of nanorods (left panel) produces two
peaks each for x and y-polarized incident light. Here L 1 = 0.8 μm, L 2 = 1.1 μm, L 3 =
0.9 μm and L 4 = 1 μm.

73
Figure 0.32: SEM images (left panel) and absorption spectra for four different pixel
types having: (a) L 1 = 0.8 μm, L 2 = 1.12 μm, L 3 = 0.8 μm and L 4 = 1.12 μm; (b) L 1 =
0.8 μm, L 2 = 1.12 μm, L 3 = 0.8 μm and L 4 = 1.27 μm; (c) L 1 = 0.8 μm, L 2 = 1.12 μm, L 3
= 0.9 μm and L 4 = 1.12 μm; and (d) L 1 = 0.8 μm, L 2 = 1.12 μm, L 3 = 1.12 μm and L 4 =
1.27 μm. The absorption spectra for x-polarized incident light are shown by the
blue curves and those for y-polarized light are shown by the red curves. The
absorptivity values at each of the four channels are indicated by solid yellow circles
while the threshold is displayed as the dotted green line. The binary sequence
corresponding to each spectrum is displayed above it.

75
Figure 0.33: Workflow for decrypting a binary image stored in a 50x50 pixel
metasurface. Measurement of the spectral response on two orthogonal
polarizations results in two sets of cipher images (middle panel). These are
converted to intermediate images using two keys (top right panel). The hidden
image (bottom right panel) is recovered by performing a bit-wise XOR on the two
intermediate images.
76
xii

Figure 0.34: (a) (left panel) Representing a single 8-bit pixel as 8 1-bit pixels. (right
panel) Expressing a 50x50 pixel 8-bit image as a 100x200 binary (1-bit) image. (b)
Workflow for decrypting a grayscale image stored in a 100x200 pixel metasurface.
Measurement of the spectral response on two orthogonal polarizations results in
two sets of cipher images (bottom left panel). These are converted to intermediate
images using two keys (top right panel). The hidden image (bottom right panel) is
recovered by performing a bit-wise XOR on the two intermediate images.

77
Figure 0.35: (a) (left panel) A 565x850 pixel 8-bit image of a tiger and (right panel)
its corresponding histogram. (b) (left panel) Cipher images obtained by encrypting
the tiger image using a key with n = 6, n p = 3 and n s = 10 and (right panel) their
histograms. (c) Variation of mean cipher image entropy for the tiger image with
the number of channels used for encryption.
79

xiii
Abstract

The ability to control light-matter interactions is of paramount importance for the advancement
of a wide variety of applications ranging from chemical and biological sensing to thermal
management and energy harvesting. To this end, artificially engineered materials known as
microstructures have received considerable attention from the scientific community. These
usually consist of an array of metallic or dielectric elements and can have feature sizes that are
several orders of magnitude smaller than the wavelength of light at which they are designed to
operate. Light-matter interactions in microstructures come under the purview of
microphotonics. As opposed to bulk materials that interact with light according to the laws of
geometrical optics, microstructures harness resonant interactions with light waves. This allows
such structures to achieve a richer suite of functionalities in a more compact size than their bulk
counterparts.
In this thesis, we explore the applications of microphotonics to two of the most exciting
research areas in the field of optics: infrared emission tailoring and secure data encryption. In
Part 1 of the thesis, we propose a set of microstructures capable of exhibiting customized optical
properties in the infrared wavelength range. Specifically, Chapter 2 discusses structures with
static, geometry-dependent optical properties in the infrared. On the other hand, Chapter 3
presents structures whose optical properties are dynamic i.e., can be tuned by applying an
external stimulus. In Part 2 of the thesis, we explore the utility of microstructures for secure data
encryption. Chapter 6 provides an overview of our proposed encryption scheme that allows
xiv
secure transmission of image data across multiple wavelength channels. In Chapter 7, we design
and experimentally implement a metasurface for multi-channel image encryption in the infrared.
Our results illustrate the true potential of microstructured materials in achieving
enhanced and efficient manipulation of light. This suggests intriguing possibilities for advancing
the state of the art for a broad class of applications that are currently restricted by the limited
functionality of bulk optical elements.

1
PART 1: INFRARED EMISSION TAILORING

Chapter 1: Introduction

Infrared emission is the radiation emitted by an object in the infrared (IR) part of the
electromagnetic spectrum. All warm objects emit IR radiation. In addition, the phonon vibration
energies of most molecules lie in the IR wavelength range. Moreover, the mid-wave IR (3 – 5 μm)
and long-wave IR (8 – 14 μm) wavelength bands possess high atmospheric transmission making
them ideal for remote sensing and imaging. These attributes make the infrared of great
technological significance for a wide variety of applications ranging from thermal management
to chemical and biological sensing. Consequently, there has been growing interest in developing
materials with tailored optical properties in the infrared.
Fundamentally, the interaction of light with any material is governed by Maxwell’s
equations. A consequence of this is the existence of electromagnetic (EM) modes, each
associated with fields having a specific spatial- and temporal-dependence. One way to tailor the
optical properties of a material is to alter the nature of EM modes supported by it. This can be
accomplished by patterning materials on a subwavelength scale to create microstructures. Thus,
microphotonics provides new avenues for the development of novel materials with customized
optical properties in the IR. Previous work has widely investigated microstructures for
manipulating the wavelength-, polarization- and spatial-dependence of light.
In this part of the thesis, we propose microstructures capable of manipulating optical
waves in the IR wavelength range. Specifically, Chapter 2 discusses structures exhibiting a static,
2
geometry-dependent optical response specifically for applications in chemical sensing and IR
photodetection. Chapter 3, on the other hand, discusses structures with dynamic optical
properties for thermal emission control. The remainder of this chapter discusses a few concepts
that are central to the results presented in this thesis. Section 1.1 provides an overview of some
common EM modes supported by the metal-based microstructures proposed in this work.
Section 1.2 discusses numerical and analytical modeling techniques used in this thesis to
determine the optical properties of photonic devices. Finally, Section 1.3 presents a discussion of
thermal emission and Kirchhoff’s law.

1.1 Common photonic modes in metallic microstructures
Two of the most commonly investigated metallic microstructures in literature are metal gratings
and metal-insulator-metal (MIM) cavities. This section provides an overview of surface plasmon
polariton (SPP) modes supported by metallic gratings and cavity modes supported by MIMs.
1.1.1 Surface plasmon polariton modes in metallic gratings
Surface plasmon polaritons (SPPs) are surface waves that propagate along a metal-air or metal-
dielectric interface and are associated with collective oscillations of electrons. The electric field
corresponding to these modes decays exponentially away from the interface. The dispersion
relation for SPP modes at a metal-dielectric interface is given by the following equation:

𝒌
||
=
𝝎
𝒄
&
𝝐
𝒎
𝝐
𝒅
𝝐
𝒎
+ 𝝐
𝒅

0.1

3
Here k || is the wavevector component parallel to the metal-dielectric interface, ω is the free-
space frequency and ϵ m and ϵ d are the permittivities of the metal and dielectric respectively.
Consider an EM plane wave incident normally on a metal-air interface. In order for the
wave to couple to an SPP mode at a frequency ω, k || for the SPP mode must be equal to 0. This
implies that the SPP dispersion relation must intersect the k || = 0 axis at a frequency ω. Figure
1.1(a) shows a schematic of the dispersion relation of an SPP mode at a metal-air interface (inset).
One can observe that the SPP dispersion relation does not intersect the k || = 0 axis at any
frequency. If we now pattern the metal-air interface periodically, the SPP dispersion relation for
the resultant grating is folded at the Brillouin zone edge (Fig. 1.1(b)). For a periodicity a, the SPP
dispersion relation intersects the k || axis at a frequency ω given by:

𝝎 =
𝟐𝝅𝒄
𝒂
&
𝝐
𝒎
+ 𝝐
𝒅
𝝐
𝒎
𝝐
𝒅

0.2

Figure 0.1: (a) Schematic showing the dispersion relation of an SPP mode at a metal-air interface
(inset shows a block of metal). (b) Schematic showing the dispersion relation of an SPP mode at
a metal-air interface patterned with periodicity a. The inset shows a one-dimensional metal
grating. The resonant frequencies are indicated by open, black circles.

The metallic grating is said to have an SPP resonance at the frequency ω (open, black
circles in Fig. 1.1(b)). Since the electric field associated with these modes is concentrated at the
metal-air interface, the resonance frequency is sensitive to variations in the structural
SPP band
ω
k
||
0
SPP band
ω
k
||
!/a 0
(a) (b)
4
parameters of the grating such as its periodicity, slot depth and slot width. It is important to note
that the theoretical treatment of SPP resonances in metallic microstructures assumes an
infinitely periodic structure. As a consequence, an SPP resonance cannot be exhibited by a grating
consisting of a single unit cell. The number of unit cells should be sufficiently large in order for
the structure to be considered periodic. Thus, the mode is said to be delocalized over the entire
structure. As a consequence, the spectral attributes of SPP resonances are highly dependent
upon the angle at which the plane wave is incident.
1.1.2 Cavity modes in MIM microstructures
Metal-insulator-metal microstructures consist of an insulating layer (known as a spacer)
sandwiched between an array of metallic elements at the top and a metal back-reflector at the
bottom. The existence of cavity modes in such structures can be understood by viewing each unit
cell as a combination of two waveguide regions (Fig. 1.2). In a particular wavelength range of
interest, Region 1 supports a TM 0 mode propagating in the + x direction (the blue curve in the
schematic shows an example plot of the E z field profile of this mode). On the other hand, Region
2 does not support a propagating mode. This leads to an impedance mismatch at the boundary
between regions 1 and 2, resulting in the reflection of the TM 0 mode back and forth between the
ends of Region 1. The superposition between forward and backward propagating modes leads to
the formation of a standing wave, localized below the metal stripe. We note that these modes
are in principle similar to cavity modes in Fabry Perot resonators. The only key difference is that
in an MIM structure, the standing wave is formed between the sides of the cavity as opposed to
the top and bottom as in a Fabry Perot resonator.
5
In contrast to SPP modes in metallic gratings, MIM cavity modes are localized inside the
spacer layer. As a consequence, a structure with a single or few MIM unit cells can still support
such cavity modes. The spectral attributes of MIM cavity resonances can be tuned by changing
the size of the metallic element in each unit cell, the thickness of the spacer layer or its refractive
index. The resonance wavelength of these modes is known to red-shift with an increase in the
size of the metallic element or the refractive index of the spacer or a decrease in the thickness of
the spacer. As these modes are localized within each unit cell, the spectral attributes of MIM
resonances show a very weak dependence on the angle of incidence of the exciting plane wave.
With an increase in the spacer layer thickness, the modes tend to become increasingly
delocalized. As the spacer layer thickness approaches the wavelength of operation, MIM cavity
modes start resembling delocalized, angle-dependent guided mode resonances with electric field
concentrated in the gap between consecutive metallic stripes.

Figure 0.2: Unit cell of an MIM microstructure. The blue curve in Region 1 shows the z-component
of the electric field correspnding to the TM 0 waveguide mode.

Metal
Insulator
Region 1 Region 2 Region 2
x
z
6
1.2 Numerical modeling of microstructures
A crucial step in developing microstructures for any application is the simulation of their optical
response to a given excitation source through a solution of Maxwell’s equations. This section
provides an overview of two numerical simulation methods used in this thesis: Finite Difference
Time Domain (FDTD) and Rigorous Coupled-Wave Analysis (RCWA). This is followed by a
discussion of temporal coupled-mode theory (CMT) which is used in Chapter 2 of the thesis to
predict the spectral properties of systems consisting of coupled optical resonators.
1.2.1 Finite Difference Time Domain method
The FDTD method solves Maxwell’s equations for a given structure illuminated by a source using
the method of finite differences. In this method, the simulation domain and total simulation time
are divided into finite-sized intervals. The spatial and temporal derivatives appearing in the
Maxwell’s equations are then approximated as differences over these intervals. The source is
approximated as a point or line current source and its temporal spread is given by the user-
defined wavelength range of operation. A single simulation run yields the electric and magnetic
fields as a function of space and time over the entire simulation region. These can then be
Fourier-transformed to generate the wavelength-dependent data and calculate other quantities
of interest.
The results presented in this thesis are calculated using the commercially-available solver,
Lumerical FDTD. The solver has a user-friendly Graphical User Interface (GUI) that simplifies
defining complex photonic structures and other simulation attributes. Additionally, Lumerical
7
FDTD has a built-in scripting language that enables task automation and easy processing of data
from multiple simulations.
1.2.2 Rigorous Coupled-Wave Analysis
The RCWA method solves Maxwell’s equations for a given structure by modeling it as a stack of
layers. Each layer is assumed to be periodic along the in-plane directions and homogeneous along
the direction perpendicular to the plane. For a plane wave incident on the structure with a
particular frequency, angle of incidence and polarization, the EM fields in each layer are
expressed as a superposition of diffraction orders (Floquet waves). These are then used along
with the boundary conditions at all interfaces to determine the fields in each layer. The number
of diffraction orders used dictates the accuracy of the RCWA method. Unlike FDTD that solves for
fields as a function of time, RCWA is a frequency domain method. This means that the optical
response of the structure is determined by exciting it with plane waves of different frequencies,
one at a time. As a result, the computation time for RCWA increases with the number of
frequency points used.
The results presented in section 2.3 of Chapter 2 of the thesis are obtained by using a
MATLAB implementation of RCWA from Ref. [1].
1.2.3 Temporal Coupled-Mode Theory
The CMT formalism is used to describe the optical properties of coupled-resonator systems in
terms of the attributes of their constituent resonators. Consider a system consisting of N coupled
resonators (Fig. 1.3). Each resonator is characterized by its resonant frequency ω i, absorptive
decay rate γ a,i and radiative decay rate, γ r,i (i ∈ [1,N]). The absorptive and radiative decay rates of
8
a resonator represent the contributions of intrinsic and extrinsic loss mechanisms to the overall
lifetime of the resonant mode. The coupling between resonators is expressed by the coupling
constants β i (i ∈ [1,N-1]). The mode amplitudes of the incoming and outgoing plane waves are
denoted by s + and s -, respectively.
One can formulate a set of coupled equations for this system, relating the mode
amplitudes for each resonator to those of the other resonators. By solving this set of equations,
the reflectivity of the system as a function of frequency is given as:

𝑅(𝜔)= [1+𝐷{𝑗(𝜔𝐼−Ω)+Γ}
%&
𝐷
'
]
(
0.3
Here, the matrices D and Γ depend on the decay rates of the individual resonators, while the
matrix Ω depends on their resonant frequencies and inter-resonator coupling constants. The CMT
parameters for a single resonator can be calculated from its spectral response. Section 2.3 of
Chapter 2 discusses a CMT-based model for predicting the spectral response of a metamaterial
while section 3.1 of Chapter 3 uses CMT to design a metamaterial for dynamic infrared absorption
tailoring.

Figure 0.3: Schematic showing a system of N coupled resonators represented as circles.

1.3 Thermal emission and Kirchhoff’s law
Thermal emission from any object is governed by Planck’s law which describes the wavelength-
and temperature-dependence of the spectral radiance of an ideal black body. Spectral radiance
!
1
s
-
s
+
!
2
β
1
"
a1
,"
r1
"
a2
,"
r2
!
3
β
2
"
a3
,"
r3
!
N
"
aN
,"
rN
9
refers to the power emitted by an object per unit area, solid angle and frequency. Integrating the
spectral radiance over all wavelengths and solid angles results in a linear relationship between
the power per unit area radiated by the object and the fourth power of its temperature. This
relationship, known as the Stefan-Boltzmann law, can be expressed by the following equation:

𝑃 = 𝜖𝜎𝑇
)
0.4
Here σ is the Stefan-Boltzmann constant and ϵ is the wavelength-dependent emissivity of the
object that can take values between 0 and 1. An ideal black body has unit emissivity at all
wavelengths and temperatures.
One way to modify the relationship between the power per unit area radiated by an
object and its temperature is to tune the emissivity of the object. Microstructures provide a route
to accomplishing this owing to their resonant interactions with optical waves. Moreover, it is
possible to design photonic structures with a temperature-dependent emissivity by utilizing
materials with thermally-tunable optical properties. Chapter 3 of this thesis discusses
microstructure designs for thermal emission control.
While emissivity is a crucial spectral property of any microstructure operating in the IR, it
is usually cumbersome to determine in both numerical simulations and experiments. A common
workaround for this is using the Kirchhoff’s law which states that for any object at thermal
equilibrium, its emissivity is equal to its absorptivity. The wavelength-dependent absorptivity of
a given microstructure can be straightforwardly calculated from conservation of energy as 1 –
reflection – transmission. We use this law to calculate the emissivity of the microstructures
discussed in this thesis.

10
Chapter 2: Static tuning of infrared emission

Microstructures designed for static tuning of infrared emission require a change in structural
parameters to exhibit a change in spectral properties. This chapter discusses microstructure
designs for static tuning of IR emission for applications in sensing and photodetection. Section
2.1 discusses our light-trapping microstructure design for boosting IR absorption in thin film black
phosphorus for use in photodetectors. Section 2.2 provides an overview of our work on
aluminum-based hybrid gratings for generating different predefined emission spectra in the IR.
In section 2.3, we provide an overview of our CMT-based approach for predicting the spectral
emissivity of static metamaterials based on hexagonal boron nitride.

2.1 Gold – black phosphorus nanostructured absorbers for infrared photodetection
A version of the results presented in this subsection was published in Ref. [2].
2.1.1 Background
Novel materials platforms could provide a route to room-temperature infrared detectors with
improved performance. Black phosphorus (BP) has recently been investigated for this purpose,
due to ease of integration with silicon and high mobility [3-7]. Several BP – based photodetectors
and diodes have been demonstrated with high responsivity and low switching times [5, 8-17]. In
addition, BP has an electrically tunable bandgap, providing spectral selectivity. However, for
bandgap tuning to be effective, the film thickness must be less than 50 nm, greatly reducing
11
absorption. To alleviate this concern, we introduce a nanostructured device design that uses
light-trapping techniques [18, 19] to boost absorption in thin BP films.
Light trapping strategies for photodetection rely on creating localized electromagnetic
modes with high field intensity, boosting absorption in the active layer [20-23]. Majority of the
absorption enhancement designs proposed for black phosphorus thus far [24-29] have relied on
the metallic character of 2D black phosphorus monolayers. For infrared photodetector
applications, it is desirable to exploit the properties of semiconducting black phosphorus thin
films. Due to the physically different nature of the dielectric function, the light trapping strategies
used for black phosphorus monolayers cannot directly be applied.
In this subsection, we propose a metal-insulator-metal (MIM) design for providing large
absorption enhancement in a black phosphorus thin film. We focus on the 3 – 5 µm wavelength
range, which is of particular interest for infrared imaging [30, 31] and sensing [32, 33]. In section
2.1.2, we describe our absorber design and discuss its working principle. In section 2.1.3, we
design gold – black phosphorus MIM absorbers resonating at a wavelength of 4 μm for BP layer
thicknesses ranging from 5 to 50 nm. To test the light-trapping efficiency of our absorbers, we
compute their enhancement factor and study its dependence on the BP layer thickness. By
optimizing our design, we show that the absorption enhancement exceeds the conventional 4n
2

[34] light-trapping limit for any BP layer thickness under 50 nm. We further show that the peak
absorption wavelength and amplitude is robust to angle of incidence. Section 2.1.4 presents a
summary of the results in this subsection along with a discussion of their potential impact.
12
2.1.2 Proposed absorber design and working principle
Figure 2.1(a) shows a schematic of the structure we use for absorption enhancement. It consists
of a BP layer of thickness d BP on top of a gold back reflector of thickness 50 nm. A gold grating
with thickness 0.1 μm, period a and stripe length L lies on top of the BP layer. The coordinate
axes x, y and z align with the BP crystal axes c, a and b respectively. The thickness of the back
reflector is chosen to be greater than the skin depth of gold in the infrared ( ~ 10 nm) to ensure
no transmission through the structure. We refer to this structure as the Metal-Dielectric
Nanocavity Absorber (MDNA). It has been shown that these structures support localized modes
in the dielectric layer with their resonance wavelength linearly proportional to the metal stripe
length [35].

Figure 2.1: (a) Absorption enhancement structure. (b) Electric field profile for an MDNA with d BP
= 20 nm. (c) Absorption spectrum for an MDNA with d BP = 20 nm.

We simulate an MDNA with a 20 nm thick BP layer using Lumerical FDTD solutions. We
choose a grating period of 0.6 μm and adjust the stripe length to get an absorptive resonance at
13
4 μm. The optical constants of BP are obtained from pseudopotential calculation data published
by Morita [36]. Figure 2.1(b) shows the field profile at the fundamental resonance wavelength in
a unit cell of this MDNA. It can be observed that most of the field is concentrated in the region
of the BP layer under the gold stripe. The absorption of the entire MDNA is given by 1 – reflection
from the top of the structure. The absorption in the BP layer is given by the difference in flux at
the top and bottom of the layer. We plot the wavelength dependent absorptivity of the MDNA
in Fig. 2.1(c) (black solid line). For comparison, we also show the absorptivity in the BP layer (red
solid line) and the single pass absorption in an isolated 20 nm thick BP layer (blue solid line). At a
wavelength of 4 μm, the single pass absorptivity of the isolated BP layer is 3.8 x 10
-3
. The
absorptivity of the BP layer of the MDNA is 0.6 corresponding to an enhancement of 166.
2.1.3 Dependence of absorption enhancement on BP film thickness
Next, we study the dependence of absorption enhancement on the BP layer thickness. We vary
the stripe length L from 0.1 to 0.5 μm for d BP ranging from 5 to 50 nm and simulate the
corresponding MDNAs. Figure 2.2(a) shows the variation of the resonance wavelength λ max with
L and d BP. It can be observed that for a fixed metal stripe length, the resonant wavelength reduces
with an increase in layer thickness. We use MATLAB’s linear interpolation to find the values of L
corresponding to λ max = 4 μm for each layer thickness. The resulting values are indicated by solid
green circles on the colormap, while the underlying solid white line shows an approximate
constant wavelength contour. We simulate the MDNAs corresponding to these values of L and
plot the wavelength dependent absorptivity (A BP,MDNA) in Fig. 2.2(b). It can be observed that the
absorptivity increases with the BP layer thickness and peaks at approximately 4 μm in each case.
14

Figure 2.2: (a) Variation of λ max with L and d BP. The solid green circles indicate the values of L
needed for λ max = 4 μm. (b) Wavelength-dependent absorptivity in the BP layer of the MDNA for
few different layer thicknesses. (c) Variation of F with d BP..

In order to quantify the absorption enhancement provided by our MDNA over a single
pass through a BP layer, we calculate the enhancement factor F using the following equation:

F(λ) =
A
*+,-./0
α
1
(λ)d
*+

2.1
Here α z is the absorption coefficient of black phosphorus along its b axis (z direction in Fig. 2.1(a)).
Figure 2.2(c) shows the variation of F at 4 μm with the BP layer thickness. For reference, we also
calculate the classical 4n
2
limit for BP by taking the refractive index along its b axis and neglecting
dispersion. Taking n = 2.9, this gives a value of F c = 34. It can be observed that F stays above 34
for all layer thicknesses and approaches F c as d BP increases. For a 5 nm thick BP layer, we get an
enhancement of 425 which can be further increased to 561 by reducing the grating period to 0.3
μm.
We investigate the performance of our MDNA design with d BP = 5 nm under off axis
illumination (Fig. 2.3). From Fig. 2.3(a), it can be observed that the resonance wavelength remains
close to 4 μm as the angle of incidence θ is changed from 0 to 60
o
. This is consistent with the
observation of flat dispersion in MIMs with subwavelength insulating layer thicknesses, as
reported by Todorov et al [35]. In addition, the spectrally averaged absorption over the 3 – 5 μm
15
wavelength range (AP BP, MDNA) increases with θ (Fig. 2.3(b)) due to enhanced coupling of the
incoming radiation to the region of the BP layer under the gold stripe.

Figure 2.3: (a) Wavelength dependent absorptivity in the BP layer of the MDNA for few values of the angle of
incidence. (b) Spectrally averaged absorption in the BP layer of the MDNA as a function of θ.

2.1.4 Conclusion and potential impact
In conclusion, we designed a gold-based nanostructure for achieving enhanced absorption in
subwavelength BP layers in the 3 – 5 μm wavelength range. We designed absorbers resonating
at a wavelength of 4 μm for BP layer thickness varying from 5 to 50 nm. We computed the
enhancement factor for these absorbers and compared it against the conventional 4n
2
limit. For
a 5 nm thick BP layer, we were able to achieve an enhancement of 561 at a wavelength of 4 μm.
This is significantly greater than the conventional value of 4n
2
equal to 34 for an isolated textured
BP layer.
A notable feature of our approach is that the top metallic grating in the MIM structure
can also serve as an electrical contact. The other contact is provided by the bottom metal layer,
which is in direct contact with the BP active region. This is in contrast to previous work in the
literature, done in the visible and near infrared. These designs either used a single metal top layer
[37, 38] or had a metal back reflector that was separated from the BP active layer by an insulating
region [39]. Our results suggest that by using light-trapping techniques, very thin, black-
16
phosphorus layers can be used for effective, spectrally selective photodetection in mid-IR
applications.

2.2 Aluminum-based hybrid gratings for spectral emissivity tailoring
A version of the results presented in this subsection was published in Ref. [40].
2.2.1 Background
The ability to design spectral features in different wavelength ranges is crucial for a wide range
of applications such as biosensing [41] and solar energy harvesting [42, 43]. To this end,
microstructured photonic devices have been well investigated. In the mid- to long- IR, many
designs have exploited metal-insulator-metal (MIM) resonances to achieve enhanced absorption
over a desired wavelength range. A typical MIM device is comprised of a dielectric layer
sandwiched between an array of nanoscale metal elements and a metal back reflector. While this
approach offers flexibility in spectral design, its realization requires fabrication of a three-layer
structure. For ease of fabrication, it is attractive to consider simple metal gratings for tailored
absorption. In this subsection, we propose aluminum gratings as building blocks for designing
emitters with predefined spectral response. Aluminum is highly abundant in nature and hence
inexpensive. As a result, aluminum gratings offer a cost-effective alternative for applications
requiring large area fabrication.
We propose a strategy for designing emitters with predefined emission spectra in the 7 –
15 μm wavelength range. Our emitters are formed by appropriately combining aluminum
gratings with different structural parameters on a single substrate. While such emitters can be
17
used for generating an infinite number of emission spectra, here we focus our attention on three
for concreteness. In sections 2.2.2 and 2.2.3, we define the three target spectra and describe our
approach for designing the Al grating building blocks, respectively. In section 2.2.4, we discuss
the design of our hybrid grating emitters corresponding to the three spectra and present the
results for spectral matching. Section 2.2.5 presents a summary of the results in this subsection
along with a discussion of their potential impact.
2.2.2 Defining target spectra
In general, an emissive resonance for a given system can be characterized by three spectral
attributes: peak location l 0, peak width Dl 0 and peak emissivity e max. Here e max is the system
emissivity at the wavelength l 0 while Dl 0 is the full width at half maximum (FWHM) of the
emission peak. For simplicity, we assume the resonances to have a Lorentzian lineshape. This
allows us to mathematically define emission spectra consisting of multiple resonances in terms
of their spectral attributes.
We define three target spectra with three resonances each in the 7 – 15 µm wavelength
range (Fig. 2.4). We assume the resonances to have a line width of either 0.25, 0.5 or 0.75 µm
(denoted as Dl 1, Dl 2 and Dl 3 respectively). The resonances are located at one of the seven
wavelengths spaced 1 μm apart from 8 to 14 μm. The first target spectrum (Fig. 2.4(a)) is chosen
such that a reduction in peak width is accompanied by an increase in peak amplitude. In order to
demonstrate that other trends are achievable, we create a second target spectrum (Fig. 2.4(b))
in which the narrowest peak has the lowest amplitude. Finally, the third target spectrum (Fig.
18
2.4(c)) shows the possibility of moving the peaks closer together in wavelength, while changing
their relative amplitudes.

Figure 2.4: (a) Target spectrum 1. (b) Target spectrum 2. (c) Target spectrum 3.

2.2.3 Designing Al grating building blocks
The first step in designing hybrid emitters is to select the appropriate Al gratings for generating
each of the nine resonances in the three target spectra. For this purpose, we consider a reference
library of gratings relating their spectral properties to their structural attributes. Each Al grating
is characterized by three structural parameters: period a, slot depth d and slot width w (Fig.
2.5(a)) and supports surface plasmon polariton (SPP) resonances in the infrared. We begin with
8 gratings having the same slot dimensions and vary the period from 7 to 14 µm in steps of 1 µm
so as to generate resonances in the 7 – 15 µm wavelength range. For each of these gratings, we
vary d and w from 0.5 to 2.5 µm in steps of 0.5 µm. We simulate these gratings using Lumerical
FDTD solutions and record the reflection spectrum. The gratings considered here are thicker than
the skin depth of aluminum in the infrared and hence opaque to the incoming radiation.
Therefore, the absorptivity and hence emissivity is given by 1- reflectivity.
Figure 2.5(b) shows the variation of peak location l 0 with slot dimensions for three grating
periods. It can be observed that for d, w << a, the emission peak is located at a wavelength
19
approximately equal to the grating period. This is expected from the SPP dispersion relation at a
metal-air interface [44]. However, for slot dimensions comparable to the grating period, the peak
shows a red shift. These variations in l 0 are accompanied with changes in Dl 0 and e max. The peak
emissivity in particular can be increased to 1 by suitably tuning the grating parameters so as to
achieve the critical coupling condition.

Figure 2.5: (a) Schematic of an Al grating. The unit cell is indicated with a red box. (b) Variation of
peak location with slot dimensions for a = 8, 10 and 12 µm.

We use interpolation to determine these spectral attributes on a three-dimensional grid
with a Î [7, 14] µm, d Î [0.5, 2.5] µm, w Î [0.5, 2.5] µm and a grid point spacing of 0.1 µm along
all dimensions. We then develop a search algorithm based on minimization of errors in peak
location and width to identify gratings from the library corresponding to peaks in our target
spectra. We simulate these gratings to test the correctness of our search algorithm.
2.2.4 Hybrid grating structure and results for spectral matching
We use the gratings identified above to design hybrid structures for generating each of the target
spectra presented in Fig. 2.4. Consider a substrate of area A patterned with three gratings with
area fractions a 1, a 2 and a 3 (Fig. 2.6(a)). These area fractions are chosen depending on the
relative amplitudes of emission peaks required in the resultant spectrum. We further assume
20
that emission from these hybrid structures is recorded in the far-field such that the emissivities
of individual gratings simply add. The total emissivity e eff of the hybrid grating is then given by:

e
𝒆𝒇𝒇
= Ea
𝒊
e
𝒊
𝟑
𝒊6𝟏

2.2
Here e I is the emissivity of the ith grating. We assume that the lateral extent of each grating is
larger than its period, so that the emissivity e I is given by calculations for the periodic case
presented above. For each target spectrum, the area fractions are determined by equating the
total emissivity defined in Eq. 2.2 to the target emissivity multiplied by a scaling constant at three
different wavelengths corresponding to the peak locations. This gives us a system of three linearly
independent equations which can be solved for a i and the scaling constant under the constraint
that the area fractions add up to 1.
Figure 2.6(b) presents a comparison between the three target spectra and the
corresponding hybrid grating spectra. It can be observed that the target and actual spectra match
well in each case. However, the grating emissivities are higher than the targets at wavelengths
away from the peak locations. This discrepancy arises due to our assumption of Lorentzian line
shapes for the emission peaks, which in general does not hold for SPP resonances. Despite this,
the above approach can be used to design hybrid structures with a variety of spectral responses.
2.2.5 Conclusion and potential impact
In conclusion, we have designed infrared emitters with predefined spectral response using
aluminum gratings as building blocks. Using FDTD simulations and interpolation, we created a
reference library of gratings relating their structural parameters to attributes of their infrared
spectra. We developed a search algorithm based on minimization of errors to select gratings from
21
the library to generate emission resonances with desired spectral characteristics. Finally, we
discussed an approach for designing hybrid structures from these gratings to generate a few
predefined target spectra. This approach can be extended to design structures with complex
spectral responses. Instead of using bulk aluminum gratings, one can also achieve the same
spectral response with surface gratings having thicknesses greater than the skin depth of
aluminum in the infrared (~ 10 nm). This offers the possibility of fabricating these hybrid
structures on polymers, making them useful for applications benefiting from flexible substrates.

Figure 2.6: (a) Schematic showing the layout of a hybrid grating formed by combining three Al
gratings. (b) (from left to right) Comparison between target and hybrid grating spectrum for
targets 1, 2 and 3.

2.3 Spectral emissivity prediction in hBN-based thermal emitters
A version of the results presented in this subsection was published in Ref. [45].
2.3.1 Background
The ability to tailor spectral emissivity in the infrared is useful for a wide variety of applications
including thermal management [46-49], energy harvesting [50, 51] and sensing .[52-54] To this
end, microstructured emitters utilizing resonant photonic modes have been investigated [40, 55,
56]. Localized photonic modes, such as those supported by metal-insulator-metal (MIM)
structures, have been used to synthesize emissive spectra [57, 58]. By combining localized
22
resonators with different sizes, one can generate spectral peaks at multiple, desired wavelengths
of interest [59]. More recent work has demonstrated the use of coupled, many-resonator
systems to significantly increase the complexity of the synthesized spectrum [60]. The
computational technique was based on machine learning and relied on training data generated
from multi-resonator simulations [61].
Recently, an alternative approach to thermal emitter design based on temporal coupled-
mode theory (CMT) has been proposed [62, 63]. In this approach, a catalog is first built based on
simulations of single resonators and a model of their coupling. The catalog is then used in
conjunction with a semi-analytical model to calculate the electromagnetic quantities of interest.
A major advantage of this approach is that once the catalog is constructed, the method can be
used to maximize various objective functions with very little additional, computational cost [63].
Previous work has demonstrated the use of this method to design self-focusing thermal emitters
and thermal holograms [62, 63]. Here, we demonstrate that the method can be adapted for
prediction of thermal emission spectra.
In particular, we use our CMT approach to predict the emission spectra of hexagonal
boron nitride (hBN) thermal emitters. Periodic emitters based on 2D materials such as hBN have
been shown to exhibit high quality factor (Q factor) resonances in the mid-infrared [64]. Emitters
with several uncoupled hBN ribbons per unit cell have been used to generate a rich, multi-
resonant spectral response. Moreover, recent work has demonstrated that inter-resonator
coupling serves as an additional degree of freedom to generate non-trivial spectral features [65].
By accounting for inter-resonator coupling in addition to isolated resonator attributes, our model
is able to accurately predict the spectral response of complex thermal emitters.
23
In section 2.3.2, we describe our thermal emitter design and discuss the workflow for
CMT-based spectral prediction. Section 2.3.3 presents an overview of the process of constructing
the CMT catalog for our system. We use this catalog to predict the spectral response of two
specific hBN thermal emitter structures in section 2.3.4. Section 2.3.5 presents a summary of the
results in this subsection along with a discussion of their potential impact.
2.3.2 Thermal emitter design and workflow for CMT-based spectral prediction
Our thermal emitter structure consists of a periodic array of hBN ribbons placed on a 1.4 μm thick
MgF 2 layer and a semi-infinite Ag substrate [64] (left panel of Fig. 2.7(a)). In general, each unit
cell of the structure consists of multiple hBN ribbons with different lengths (right panel of Fig.
2.7(a)).

Figure 2.7: (a) Schematic of our hBN thermal emitter. (b) Workflow for CMT-based spectral
prediction.

24
Figure 2.7(b) describes the workflow for CMT-based spectral prediction. The first step is
building a catalog of CMT parameters for the system. This involves running electromagnetic
simulations of emitters with one and two hBN ribbons per unit cells and using the resulting
spectral responses to determine the individual resonator parameters and inter-resonator
coupling constants (left panel of Fig. 2.7(b)). The resulting CMT catalog can then be used in
conjunction with a semi-analytical model to predict the spectral response of more complex
thermal emitters consisting of multiple hBN ribbons per unit cell (right panel of Fig. 2.7(b)).
2.3.3 Building the CMT catalog
We first begin by simulating an emitter with a single hBN ribbon per unit cell (Fig. 2.8(a)). The
length of the ribbon L is 20 nm and the unit cell length, a is 0.2 μm. Figure 2.8(a) shows the
emission spectrum of the structure calculated using RCWA. To isolate the resonant contribution,
we subtract a constant value of background emission and plot the adjusted spectrum (dashed
green curve). The single-resonator CMT model fits well with the simulation data and is used to
calculate the decay rates. Next, we run simulations of two identical hBN ribbons of length 20 nm
separated by a distance d (Fig. 2.8(b)). The fitted two-resonator spectrum is used in conjunction
with the single-resonator decay rates to obtain the coupling constant β as a function of d (Fig.
2.8(c)). As expected, the magnitude of Re(β) reduces with d, indicating weak coupling at large
separations. The imaginary part of β is two orders of magnitude smaller than Re(β) and its
variation with d can be neglected.
25
2.3.4 Results for spectral prediction
We use the single- and double-resonator CMT parameters obtained above to calculate the
emission spectrum of an emitter with three identical resonators (Fig. 2.9(a)). The resonators are
of length 20 nm each and are separated by a distance d. The spectra predicted by CMT for d = 1
and 5 nm (top and bottom panels of Fig. 2.9(a)) are in good agreement with simulation results.
Figure 2.9(b) shows the resonant frequencies of the two modes of the system as a function of d.
The frequencies for mode 2 are only displayed up to d = 10 nm as beyond this the resonant peak
merges with that for mode 1. It can be observed that the CMT-predicted resonant frequencies
match well with the simulation results for d ≥ 5 nm.

Figure 2.8: (a) Unit cell of an emitter with a single hBN per unit cell (top) and the corresponding
emission spectrum (bottom). (b) Unit cell of the emitter with two identical hBN ribbons separated
by a distance d per unit cell (top) and emission spectrum (bottom). (c) Coupling constant as a
function of d.

We adopt a similar approach as above to predict the emission spectra of an emitter
comprised of three non-identical resonators per unit cell (Fig. 2.10(a)). The ribbons have lengths
L 1 = 20 nm, L 2 = 30 nm and L 3 = 40 nm. Figure 2.10(b) shows the simulated and CMT-predicted
emission spectra for different values of the inter-resonator separations d 1 and d 2. For all cases,
the spectra predicted by CMT match well with simulations.
Figure 2 raw
(b) (a) (c)
L
hBN
Ag
MgF
2
a
1.4 μm
L
d
d = 5 nm
Ag
MgF
2
a
1.4 μm
L
hBN
26

Figure 2.9: (a) Unit cell of an emitter with three hBN ribbons per unit cell (left) and the
corresponding emission spectrum (right). (b) Resonant frequencies of the two modes of the
system as a function of d.

2.3.5 Conclusion and potential impact
We proposed a CMT-based model for predicting the emission spectra of complex thermal
emitters. We considered emitters consisting of a periodic array of hBN ribbons on top of an MgF 2
layer and a semi-infinite Ag back reflector. We began by building a catalog of CMT parameters by
simulating thermal emitters with single and double hBN ribbons per unit cell. This was
subsequently used to predict emission spectra of structures consisting of three hBN ribbons per
unit cell. We showed that our model can accurately predict the emission response of such
emitters for inter-ribbon separations greater than 5 nm.

Figure 2.10: (a) Unit cell of an emitter with three non-identical hBN ribbons per unit cell (b)
Emission spectra for different values of d 1 and d 2.

Figure 3 raw
(a) (b)
L
hBN
Ag
MgF
2
a
1.4 μm
L
d
L
d
Mode 1
Mode 2
Mode 1
Mode 2
Figure 4 raw
(a) (b)
d
1
= d
2
= 20 nm
d
1
= 20 nm, d
2
= 5 nm
d
1
= d
2
= 5 nm
d
1
= 5 nm, d
2
= 20 nm
d
2
L
1
hBN
Ag
MgF
2
a
1.4 μm
L
2
d
1
L
3
27
Our results suggest a number of interesting directions for future work. While we have
focused on hBN ribbon emitter, we expect our approach to be applicable to a broad class of
metallic and dielectric microstructures supporting photonic resonances. Moreover, our approach
is suited for a variety of spectral optimization tasks. The most significant computational cost
comes from building the catalog. Once built, the same catalog can be reused to optimize a given
objective function at minimal additional cost. For example, one could maximize or minimize
emissivity at single or multiple wavelengths of interest, or even determine the collection of
emitters that gives a “best fit” to a specified emissive spectrum. We thus expect that the orders-
of-magnitude reduction in computation time offered by the CMT model can potentially allow
optimization within a previously inaccessible design space.

28
Chapter 3: Dynamic tuning of infrared emission

In recent years, there has been growing interest in achieving dynamic control of infrared emission
for several applications such as sensing, energy harvesting and thermal management. To this end,
microstructures with electrically- or thermally-tunable spectral properties have been
investigated. Such devices rely on materials whose optical properties can be tuned by applying
an external stimulus. For electrical tunability, photonic devices based on graphene, ITO and III-V
semiconductors have been studied. Microstructures for thermal control of infrared emission
have most commonly incorporated vanadium dioxide (VO 2) or gallium antimony telluride (GST)
to achieve a temperature-dependent change in infrared emission.
In this chapter, we discuss our work on both electrical and thermal control of infrared
emission. Section 3.1 presents our work on a graphene-based metamaterial capable of achieving
a voltage-tunable absorptivity in the mid-infrared. The structure relies on the ability of graphene
to exhibit a change in Fermi energy with applied voltage which in turn results in a change in its
optical properties. Sections 3.2 through 3.4 discuss three different photonic devices for
temperature-dependent spectral and spatial control of infrared emission. These devices rely on
the ability of VO 2 to act as an insulator below a transition temperature of 340K and a metal above
it. This phase transition of VO 2 is accompanied by a dramatic change in its optical properties. The
work proposed in this chapter provides avenues for the development of a wide array of
applications ranging from dynamically-reconfigurable sensing to energy harvesting.
29
3.1 Graphene-based metamaterial for on-demand spectral synthesis in the infrared
A version of the results presented in this subsection was published in Ref. [66].
3.1.1 Background
Recent work has focused on designing tunable metamaterials that can be used to reshape the
spectral response on demand. Graphene has emerged as a promising material for this purpose
[67-70], due to its electrically-tunable optical properties [71-76]. Previous studies have
investigated metamaterials incorporating graphene to achieve tunable absorption in the infrared
[77-93]. One promising approach is to incorporate graphene within a metal-insulator-metal
(MIM) absorber [35, 94]. Previous work has shown that a resonant mode of the MIM can be
tuned by applying a voltage to the graphene [95-103]. However, this work focused on either
single or multiple, uncoupled resonances.
Meanwhile, recent work has explored the use of coupled resonator modes to produce a
complex, adaptive spectral response [60, 65]. In a previous paper [65], we showed that tuning
the coupling between two MIM resonators can change the spectral response from a single peak
to a double peak. However, the proposed tuning scheme required the fabrication of multiple
devices with varying structural parameters to achieve different spectra. It is of great interest to
find a method for achieving in situ tuning within a single device, for which the spectral response
can be tuned with an applied voltage. Here, we propose a design for in situ tuning of the infrared
absorption spectrum from single- to double-peaked and vice versa, using coupled graphene MIM
resonators.
30
Section 3.1.2 describes our metamaterial design along with results for spectral tuning and
section 3.1.3 presents a summary of the results in this subsection and a discussion of their
potential impact.
3.1.2 Metamaterial design and results for spectral tuning
We consider a periodic metamaterial in which every unit cell consists of two coupled gold crosses
placed on top of an Al 2O 3 layer and a gold back reflector (Fig. 3.1(a)). We assume that the
graphene sheets under the two crosses can be tuned independently. We keep the Fermi energy
of the right cross, E f2 fixed at 0.026eV and tune the Fermi energy of the left cross (E f1) to tune its
resonance frequency. Through FDTD simulations, we show that the spectral response of the
metamaterial changes from single-peaked to double-peaked as the resonance wavelength of
resonator 1 is tuned towards that of resonator 2 (Fig. 3.1(b)). On the other hand, the absorption
changes from double- to single-peaked as resonator 1 is tuned away from resonator 2.

Figure 3.1: (a) Unit cell of proposed graphene-based metamaterial. (b) Absorption spectra of the
metamaterial or tuning resonator 1 towards (left panel) and away (right panel) from resonator
2.

31
3.1.3 Conclusion and potential impact
In this subsection, we proposed an electrically tunable metamaterial absorber for spectral
tailoring in the infrared. Our results suggest the possibility of achieving tunable multi-band
absorption using metamaterials composed of multiple coupled resonators. This ability to
dynamically modulate spectral absorptivity can potentially benefit several applications such as
infrared imaging and thermal management.

3.2 Gold – vanadium dioxide micro-gratings for thermal rectification
A version of the results presented in this subsection was published in Ref. [104].
3.2.1 Background
While electronic devices form the foundation of modern computing systems, their operation is
limited in high temperature environments . As a result, there has been considerable interest in
the development of thermal analogs of electronic devices, which would operate by controlling
heat flow rather than electron transport. Thermal rectifiers form one such class of devices that
create an asymmetry in heat flow between two bodies maintained at different temperatures.
Figure 3.2 presents a schematic describing the operation of a thermal rectifier. In the considered
example, the thermal rectifier allows for a larger heat flow in the forward direction (left terminal
at higher temperature) than the reverse direction (right terminal at a higher temperature). In
general, thermal rectifiers can be designed to control conductive or radiative heat flow. In this
subsection, we limit our discussion to radiative heat transfer.
32
A key figure of merit for thermal rectifiers is the rectification ratio, R which measures the
degree of asymmetry between forward and reverse heat flow. In recent years, several radiative
thermal rectifier designs based on vanadium dioxide have been proposed. Designs for near-field
devices, where the gap is small compared to the thermal wavelength, have yielded high
rectification ratios. However, experimental implementation is likely to require tight tolerances
on alignment and fabrication. Far-field devices can relax these constraints, provided strategies
can be found to achieve high rectification ratios. Previous work has achieved R > 11 for far-field
devices based on Fabry-Perot modes. In this subsection, we explore an alternative strategy to
far-field thermal rectification based on surface plasmon modes.

Figure 3.2: Schematic showing the operation of a thermal rectifier under (a) forward and (b)
reverse bias.

In section 3.2.2, we describe two approaches to achieving radiative thermal rectification.
Sections 3.2.3 and 3.2.4 present our thermal rectifier designs for both these approaches along
with a discussion of their working principle. Section 3.1.5 presents a summary of the results in
this subsection along with a discussion of their potential impact.
3.2.2 Two approaches to radiative thermal rectification
Here, we propose two approaches to achieving thermal rectification: peak extinction and peak
shift. A radiative thermal rectifier consists of two emitters separated by a gap (Fig. 3.3(a)). Note
33
that we define forward bias as the case in which emitter 1 is at a lower temperature compared
to emitter 2. In the peak extinction approach, emitter 1 is assumed to have a temperature-
dependent emission spectrum consisting of an emission peak at a predesigned wavelength.
Emitter 2, on the other hand, is a blackbody (emissivity is 1 at all temperatures and wavelengths).
In this case, an increase in the temperature of emitter 1 beyond a certain threshold causes its
emission peak to switch off (Fig. 3.3(b)). This causes the heat flow in the reverse direction to be
smaller than that in the forward direction.
In the peak shift approach, emitter 1 has a temperature-dependent emission spectrum
consisting of an emission peak. On the other hand, emitter 2 has a temperature-independent
emission peak. When the temperature of emitter 1 is below a threshold, its emission peak
overlaps with that of emitter 2 resulting in a large heat flow. When the temperature is above a
threshold, the emission peak of emitter 1 shifts (Fig. 3.3(c)), causing the heat flow to reduce.

Figure 3.3: (a) Schematic of a radiative thermal rectifier under forward and reverse bias (left and
right panels, respectively). (b) In the peak extinction approach, the emissivity of emitter 1 reduces
with temperature. (c) In the peak shift approach, an increase in temperature causes the emissive
resonance of emitter 1 to shift away from that of emitter 2. Both (b) and (c) show the rescaled
black body spectral radiance at a temperature of 300K.

34
3.2.3 Peak extinction approach
In this study, we consider the operation of our emitters at 300 and 350K (referred to as cold and
hot states, respectively). In the peak extinction approach (Fig. 3.4), we consider emitter 1 to be a
gold grating with VO 2-filled slots. For T 1 = 300K, VO 2 is in the insulating state and behaves as a
dielectric. Consequently, emitter 1 acts as a metal grating with dielectric-filled slots and exhibits
a surface plasmon resonance close to 10 μm. For T 1 = 350K, VO 2 is in the metallic state and
behaves similar to gold. This causes emitter 1 to act as a metal block, having zero emissivity. This
difference in emissivities creates an asymmetry in heat flow between the forward and reverse
directions. For this configuration, we achieve a rectification ratio of 4.9.
It is important to note that even though VO 2 is metallic in the high temperature state, its
loss is much smaller than that of gold. Consequently, emitter 1 in the high temperature state has
lower emissivity than a block of gold. This suggests that tuning the optical constants of VO 2 can
improve the rectification ratio. Several studies have demonstrated the effect of doping and
changes in annealing parameters on the electrical and optical properties of VO 2 thin films. For
the current design, the rectification ratio can be increased from 4.9 to 20.7 by scaling the metallic
state loss by 10x and insulating state loss by 5x.

Figure 3.4: (a) Schematic showing emitter geometries used in the peak extinction approach. (b)
An increase in temperature causes emitter 1 to switch from a metal-dielectric grating (top panel)
to a metal block (bottom panel). (c) Emission spectrum of emitter 1 in the cold and hot states.

Thermal rectifier figure 3
(a) (b)
VO 2
Au
Black body
P
f
P
r
Emitter 2
Emitter 1
unit cell
VO
2
Au
VO
2
VO
2
VO
2
VO
2
VO2
Au
VO2 VO2 VO2 VO2
(c)
35
3.2.4 Peak shift approach
In the peak shift approach (Fig. 3.5), we consider emitter 1 to be a gold grating with slots partly
filled with VO 2 and Si. Emitter 2 is considered to be a gold grating with Si-filled slots. For T 1 =
300K, VO 2 is in the insulating state and behaves as a dielectric. Consequently, emitter 1 acts as a
metal grating with dielectric-filled slots and exhibits a surface plasmon resonance close to 15 μm.
This overlaps with the surface plasmon resonance of emitter 2 resulting in a large heat flow. For
T 1 = 350K, VO 2 is in the metallic state and behaves similar to gold. This causes the depth of
dielectric slots of emitter 1 to reduce, shifting the surface plasmon resonance down to 12 μm. As
this no longer overlaps with the emissive resonance of emitter 2, the heat flow reduces
significantly. For this configuration, we achieve a rectification ratio of 1.3.
In the peak shift approach, an increase in the insulating state VO 2 loss enhances the peak
emissivity of emitter 1 in the cold state. On the other hand, increasing the metallic state loss
reduces the overlap between the emission peak of emitter 1 in the hot state and that of emitter
2. For this approach, scaling both the metallic and insulating state losses by 10x increases the
rectification ratio from 1.3 to 8.4.

Figure 3.5: (a) Schematic showing emitter geometries used in the peak shift approach. (b) An
increase in temperature effectively reduces the dielectric slot depth of emitter 1 (top to bottom
panel). (c) Emission spectrum of emitter 1 and 2.

Thermal rectifier figure 4
(a) (b) (c)
Si
Au
VO 2
Au
Si
P
f
P
r
Emitter 2
unit cell
Emitter 1
unit cell
VO 2
Au
VO 2 VO 2 VO 2 VO 2
Si Si Si Si Si
VO 2
Au
VO 2 VO 2 VO 2 VO 2
Si Si Si Si Si
36
3.2.5 Conclusion and potential impact
We proposed gold micro-grating structures with VO 2-filled slots to achieve enhanced, far-field
thermal rectification. We exploited the ability of these gratings to exhibit tunable, surface
plasmon resonances and investigated two approaches to thermal rectification: peak extinction
and peak shift. For both approaches, we observed that scaling the extinction coefficient of VO 2
resulted in higher rectification ratios. These observations suggest that materials research focused
on manipulation of the optical properties of VO 2 could yield more efficient thermal rectifier
devices, as the general strategy of tuning the optical loss could potentially yield higher
rectification ratios for a variety of device geometries. Moreover, we have shown that by
appropriately considering mechanisms for coupling evanescently-decaying surface modes to the
far field, such modes can play a critical role in far-field rectifier design.

3.3 Vanadium-dioxide microstructures for designable, temperature-dependent thermal emission
A version of the results presented in this subsection was published in Ref. [105].
3.3.1 Background
The ability to control thermal radiation is crucial for the development of novel emitters not
governed by Planck’s law [106, 107]. In particular, thermal sources capable of achieving spectrally
as well as spatially-selective emission could be useful for a wide variety of applications such as
energy harvesting [50, 51], biochemical sensing [52-54] and thermal management [46-49]. To
this end, metamaterials have been widely investigated. These are engineered materials that
37
consist of an array of metallic or dielectric elements, each of which can be individually designed
so as to generate a predefined spectral and spatial emission profile [59].
One commonly studied class of metasurfaces is based on the metal-insulator-metal (MIM)
configuration [35, 94, 108, 109]. The structures are comprised of a dielectric layer sandwiched
between an array of nanoscale metal elements and a metal back reflector. In previous work,
MIMs have been used to design narrowband as well as broadband perfect absorbers [57, 59, 110,
111], isotropic thermal emitters [112-114] and spatially-varying emission patterns and images
[58, 115].
Temperature-dependent thermal emissivity has many important applications, arising
from the non-T
4
behavior of the thermally radiated power [116]. These include thermal
regulation [117, 118], thermal runaway [119], and thermal rectification [104]. Previous work has
incorporated vanadium dioxide (VO 2) into MIM metasurfaces [120-131] to yield a strongly
temperature-dependent emissivity. Vanadium dioxide (VO 2) is a solid-state phase change-
material with an insulator-to-metal transition at ~340 K, which is accompanied by a strong
change in optical properties [132]. Previous work in the literature has demonstrated VO 2 MIM
structures for which the thermal emissivity either increases [125] or decreases [121] with
temperature across the phase transition, depending on the vertical layer structure used.
Here, we propose a VO 2 MIM emitter for which either trend can be achieved in the same
vertical layer structure, allowing the possibility of spatial variation across the device surface.
Section 3.3.2 presents our proposed design along with a discussion of its working principle. In
section 3.3.3 we present trends in the power radiated by our device for different structural
parameters. We use these to design a thermally-switchable spatial emission pattern in section
38
3.3.4. Section 3.3.5 presents a summary of the results in this subsection along with a discussion
of their potential impact.
3.3.2 Proposed structure and working principle
Figure 3.6(a) shows a unit cell of our metal-insulator-metal (MIM) thermal emitter. It consists of
a two-layer stack of Si and VO 2 with a total thickness of 0.1 μm sandwiched between a 0.1 μm
thick gold stripe grating at the top and a 0.1 μm thick back reflector at the bottom. The grating
has a period a and stripe length L. We label the thickness of the VO 2 layer as d V. We calculate the
emission spectrum of the structure at 300 and 350K (referred to as the ‘cold’ and ‘hot’ states)
using the FDTD method (Fig. 3.6(b)). One can observe that the structure exhibits a fundamental
emission resonance at 7.5 μm in the cold state which shifts to 10 μm in the hot state. This shift
can be attributed to the change in the effective index of the waveguide mode propagating in the
cavity formed under the gold stripe. When VO 2 switches from its insulating to metallic state, it
effectively narrows the width of the dielectric layer, increasing the mode index.

Figure 3.6: (a) Unit cell of an MIM. (b) Emissivity (left axis) as a function of wavelength for cold
and hot states of the MIM are shown by solid lines for a = 1 μm, L = 0.75 μm and d V = 0.05 μm.

Figure 3.6(b) also shows the black body irradiances in the cold and hot states (dotted lines).
The thermal radiated power of an emitter at a given temperature in a certain wavelength range
is equal to the overlap integral between the black body irradiance and the emissivity. Therefore,
39
by tuning the emissivity difference between two temperature states, one can tune the difference
in thermal radiated powers.
3.3.3 Trends in radiated power for different structural parameters
We define ΔP rad = P rad,hot – P rad,cold as the difference in cold and hot state radiated powers and
study its dependence on the MIM geometry. In Fig. 3.7(a), we present the dependence of ΔP rad
with L and d V. The grating period is fixed at 1 μm and the radiated powers are calculated over a
wavelength range of 8 – 14 μm. One can observe that by suitably tuning the design parameters
of the MIM, the difference in radiated power can be made positive, negative or zero. Overlaid
symbols indicate values of L and d V for which ΔP radI is maximum (white circle), minimum (black
triangle) and zero (grey square). In order to exclude structures for which both P rad,hot and P rad,cold
are small, we only consider the region of our parameter space above the dashed black line. The
emission spectra for these structures are presented in Figs. 3.7(b) through (d). For the structure
with ΔP rad maximum, the hot state emits more than the cold state (Fig. 3.7(b)) while for ΔP rad
minimum, the cold state emits more than the hot state (Fig. 3.7(c)). For the structure
corresponding to Fig. 3.7(d), the difference in emissivities exactly balances out the difference in
black body irradiances between the cold and hot states, resulting in ΔP rad equal to zero.

Figure 3.7: (a) Variation of ΔP rad with L and d V. (b – d) Emission spectra for structures with ΔP rad
maximum, minimum and zero.

40
3.3.4 Design of temperature-switchable spatial emission pattern
We use our emitters to design metasurfaces with thermally invertible spatial emission patterns.
We present the variation of ΔP rad with L at d V = 0.08 μm in Fig. 3.8(a). We identify three values of
L for which ΔP rad is maximum, minimum and zero (labelled as L +, L - and L 0 respectively). Figure
3.8(b) shows a square grid comprised of 5 pixels along the horizontal and vertical directions. Each
of these pixels is marked with a ‘+’, ‘0’ or ‘-‘ to form a sample pattern. These correspond to
gratings with metal stripe lengths of L +, L - and L 0 respectively. The power radiated by the square
grid in the cold and hot state is shown on the left and right side of Fig. 3.8(c) respectively. In the
cold state, the ‘+’ pixels are relatively dark while the ‘-‘ pixels are bright. This pattern is flipped in
the hot state: the ‘+’ pixels are bright and the ‘-‘ pixels are dark. The ‘0’ pixels radiate equally in
the two states. Therefore, an increase in temperature caused the spatial emission pattern of the
square grid to be inverted.

Figure 3.8: (a) Variation of ΔP rad with L for d V = 0.08 μm. (b) Layout of a switchable emitter array.
(c) Normalized radiated power of the array at 300 and 350K.

3.3.5 Conclusion and potential impact
We have proposed a VO 2-based thermal emitter for which the difference in radiated power
between two temperature states can be tuned via structural design. The emitter geometry is
based on incorporating VO 2 in a gold-dielectric-gold waveguide. When the VO 2 transitions from
41
insulator to metal state, it effectively narrows the width of the dielectric layer, changing the
waveguide effective index. We exploited this effect to design an MIM emitter with a
temperature-dependent emissivity. We showed that by suitably tuning the length of the MIM
cavity, the difference in emissivities between the cold and hot states can be tuned, and
consequently the difference in radiated powers, can be made positive, negative, or zero. This
property can potentially be exploited to design metasurfaces with thermally-invertible spatial
emission patterns, using lithographic techniques to pattern the top metallic layer. We anticipate
that this capability could benefit diverse applications including generation of thermally-emissive
images [133], remote temperature monitoring, and thermoelectric power generation.

3.4 Dynamically switchable self-focused thermal emission
A version of the results presented in this subsection is currently under review [134].
3.4.1 Background
Several applications such as thermal management and sensing require precise control over the
spectral selectivity and directionality of thermal emission. Historically, thermal emission had
been considered incoherent. In 2002, Greffet et al showed that coherent wave effects can be
exploited in periodically-patterned SiC films to achieve directional thermal emission in the long-
wave infrared (IR) [135]. Since then, several microphotonic devices have been proposed and
investigated for generating tailored spectral [40, 59, 136] or directional [137-141] emission
profiles in the infrared.
42
In recent years, there has been growing interest in achieving more exotic functionalities
such as the generation of focused thermal emission. It is important to note that devices capable
of generating focused thermal emission are fundamentally different from conventional
metalenses. A conventional lens uses an array of scatterers to impart a phase profile to an
incident monochromatic plane wave to focus it at a desired location in space [142]. On the other
hand, a thermal lens is designed to focus emission from multiple, incoherent thermal sources
that reside within it.
Recent work from Chalabi et al showed that an array of SiC beams on a SiC film can be
used for achieving self-focused thermal emission [143]. The working principle of this device was
based on the existence of surface phonon polariton modes in SiC in the long-wave IR.
Consequently, the wavelength range of operation of the lens was limited to a narrow spectral
band. More recently, Zhou et al numerically demonstrated self-focused thermal emission in a
freely-suspended array of coupled, dielectric nanorods [62]. The nanorods were considered to
be dispersionless with only the central nanorod having a non-zero material loss. The sizes of the
nanorods and the spacing between them could be adjusted to tune the operating wavelength of
the lens.
In this work, we adopt the modeling approach used by Zhou et al to design a practically
realizable lens with temperature-dependent, self-focused thermal emission. The lens relies upon
the phase change properties of vanadium dioxide (VO 2) .Through direct calculation of thermal
emission, we show that our lens focuses intensely above the phase transition of VO 2 while
emitting a relative focal plane intensity that is 330 times lower below it.
43
Section 3.4.2 presents our lens design along with a discussion of its working principle.
Section 3.4.3 discusses the method used for direct calculation of thermal emission while section
3.4.4 presents an illustration of the temperature-dependent focusing effect. Section 3.4.5
presents a summary of the results in this subsection along with a discussion of their potential
impact.
3.4.2 Lens design and working principle
Figure 3.9(a) shows a schematic of our switchable thermal lens. It consists of 25 silicon nanorods
on a 0.1 μm thick Al 2O 3 layer. The central nanorod has a VO 2 cap on the top. For simplicity, we
only consider the behavior of our structure at 300 and 350K, hereby referred to as the cold and
hot states, respectively. The lens is optimized to focus at a wavelength of 4 μm in the hot state.
We consider the lens to be infinite along the y direction and as having a width of 80 μm along the
x direction.
The side resonators of our lens are chosen to be 0.7 μm tall Si nanorods with width W
(left panel of Fig. 3.9(b)). The right panel of Fig. 3.9(b) shows the absorption and scattering cross
sections for a nanorod with W = 0.95 μm. One can observe that the scattering cross section is
orders of magnitude larger than the absorption cross section, implying that the resonators are
effectively lossless. The squared magnitude of the magnetic field on resonance, |H|
2
, shown in
the inset resembles that of a magnetic dipole Mie resonance. Such resonances in freely
suspended dielectric nanorods have been shown to exhibit isotropic far-field radiation profiles
[62]. In our thermal lens, we mount the resonators on a 0.1 μm thick free-standing Al 2O 3
membrane to ensure nearly isotropic emission. Thin Al 2O 3 layers on back-etched Si wafers have
44
previously been used as optically transparent membranes for the fabrication of metasurfaces in
the infrared [144].
We incorporate a 0.15 μm thick VO 2 cap on the top of the central resonator (left panel of
Fig. 3.9(c)) in order to make it lossier than the side resonators. The right panel of Fig. 3.9(c) shows
the absorption cross sections of the central resonator for W = 0.54 μm in the cold and hot states.
One can observe that the absorption cross section has a peak at 4 μm in the hot state which blue
shifts and reduces in height in the cold state. This change can be understood by looking at the
squared magnitude of the magnetic field in the hot state shown in the inset. The field is mostly
concentrated at the interface between Si and VO 2 and has sufficient overlap with the VO 2 cap. As
a result of this field overlap, the resonance wavelength and absorption cross section are sensitive
to changes in the optical properties of VO 2. As VO 2 in the hot state is lossier and has higher
refractive index than the cold state, an increase in temperature causes a significant change in the
absorption cross section. This change results in the lens having a temperature-dependent
focusing behavior. We calculate the widths and center-to-center separations of the nanorods
from a gradient descent optimization based on temporal coupled-mode theory (CMT) [62].
3.4.3 Method for direct calculation of thermal emission
To emulate thermal emission, we run multiple Finite Difference Time Domain (FDTD) simulations
each with a single, randomly oriented magnetic dipole placed at a random location inside the
lens. The dipole location in each of the simulations is chosen so as to have an overall unform
distribution of dipoles in the lens. The number of dipoles in different parts of the lens is directly
proportional to their respective areas. The far-field intensities obtained from each of these
simulations are multiplied by a weighting factor and added together. Similar approaches have
45
been used for calculating thermal emission in mixed-material systems [145, 146]. The weighting
factor for a dipole in the ith simulation located in a material A is given as:

𝑤
8
= 𝐼𝑚(𝜖
9
)
ℏ𝜔
:
expM
ℏ𝜔
𝑘
;
𝑇
O−1

3.1
Here Im(ϵ A) denotes the imaginary part of the permittivity of material A, ω is the operating
frequency, T is the temperature, ℏ is the modified Planck’s constant and k B is the Boltzmann
constant. Due to the symmetry of the lens structure, the resultant field intensity must be
symmetrical about the y-z plane passing through its center. To ensure this, we also

Figure 3.9: (a) Schematic of our switchable thermal lens. (b) (left panel) Side resonator with W =
0.95 μm. (right panel) Absorption and scattering cross sections of the side resonator. Inset shows
|H|
2
for the side resonator at λ = 4 μm. (c) (left panel) Central resonator with W = 0.54 μm. (right
panel) Absorption cross sections for the cold and hot states of the central resonator. Inset shows
|H|
2
for the hot state of the central resonator at λ = 4 μm.

Figure 1: Schematic and lens
components
Central
resonator Al
2
O
3
Si
VO
2
Side resonators
0.7 μm
W
0.15 μm
0.7 μm
W
(a)
(b)
(c)
x
z
46
We verify through separate calculations that the contribution to the overall field from
dipoles placed in the VO 2 cap is much greater than from those placed elsewhere inside the lens.
Therefore, in order to get results that are statistically significant, one must have a large number
of dipoles in the VO 2 cap. We note that the VO 2 cap occupies only about 0.4% of the total lens
area. Therefore, a calculation with N dipoles in the VO 2 cap will require a total of 250N dipoles
distributed uniformly across the structure. Such a calculation would incur an unnecessary
computational cost as most of these dipoles will not contribute to the overall emission from the
lens. To avoid this computational expense, we choose to perform all our calculations with dipoles
placed only in the VO 2 cap.
3.4.4 Temperature-switchable thermal focusing
Figure 3.10(a) shows a schematic of the lens in which all dipoles are placed only in the VO 2 cap.
We vary the number of dipoles till the obtained spatial field intensity profiles have converged.
Figure 3.10(b) presents the resulting field intensities in the x-z plane at a wavelength of 4 μm for
a calculation with 600 dipoles. The field intensities in both temperature states are normalized to
the maximum intensity of the hot state. The x and z coordinates are normalized to the operating
wavelength λ 0 = 4 μm and the dashed black line marks the designed focal length of 20λ 0. One can
observe a clear focal spot in the hot state at z ≈ 24λ 0. On the other hand, the cold state has nearly
zero field intensity across the entire x-z plane.
Figure 3.10(c) shows the field intensity of the lens in the cold and hot states at the
designed focal length of 20λ 0. The field intensities in both temperature states are normalized to
the maximum focal plane intensity in the hot state. The peak centered at x = 0 in the field intensity
of the hot state represents the focal spot. The full width at half maximum (FWHM) of this peak is
47
9.2 μm, which is approximately 11% of the total width of the lens along the x direction (80 μm).
Additionally, one can notice a sideband on either side of the central peak. The peak intensities of
these sidebands are approximately 20% of the peak focal spot intensity.
In order to investigate the emission from the lens in the cold state, we plot the field
intensities at the focal plane in the two temperature states normalized to their own maximum in
Fig. 3.10(d). One can observe a central peak in the field intensity of the cold state flanked by two
sidebands on either side. The peak intensities of these sidebands are more than 60% of the
central peak intensity. In an actual measurement of the focal plane intensity in the cold state,
one may not be able to distinguish the focal spot from the background due to its poor intensity
contrast with respect to the sidebands. On the other hand, the focal spot will be clearly visible in
the hot state.

Figure 3.10: (a) Schematic showing the dipole distribution for a calculation in which the dipoles
are placed only in the VO 2 cap. (b) Field intensities in the x-z plane at a wavelength of 4 μm for
the cold and hot states of a lens simulated with 600 dipoles. The intensities in both states are
normalized to the maximum intensity of the hot state. (c) Focal plane intensities for the lens in
both temperature states normalized to the focal plane intensity in the hot state at x = 0. (d) Focal
plane intensities in the two temperature states normalized to their own intensity at x = 0.

Figure 3: Result for N = 600
Al
2
O
3
Si
VO
2
S
1
S
2
S
3
(a)
(b)
(c)
(d)
Cold Hot
x
z
48
3.4.5 Conclusion and potential impact
We proposed a microphotonic lens for achieving temperature-switchable self-focused thermal
emission. By utilizing the coupling between isotropic Mie scatterers and the phase change
properties of VO 2, we were able to design a lens to selectively emit focused radiation at a
wavelength of 4 μm in the hot state. We validated the performance of our design by directly
calculating thermal emission from the lens in both temperature states. For this purpose, we ran
multiple, single-dipole FDTD simulations of the structure and added the results together
incoherently with the appropriate scaling factors. Our calculations showed that not only does the
lens have nearly zero intensity in the cold state relative to the hot state, it also has a smeared out
focal spot in the cold state due to a large background emission.
Our switchable thermal lens could potentially benefit several applications. The ability to
emit thermal radiation above a certain temperature at a desired wavelength could be useful for
the construction of next-generation thermophotovoltaics. Microphotonic devices capable of
emitting focused thermal radiation above a certain temperature could be used in conjunction
with IR detectors for temperature monitoring and efficient contact-free sensing. One could also
envision an on-chip infrared communication system in which such thermal lenses are utilized to
establish a directional, free-space power flow between two predefined points. Given the wide
range of applications, our switchable microphotonic lenses could pave the way for next-
generation thermal sensing and infrared communication systems.

49
Chapter 4: Conclusion and outlook

In this part of the thesis, we discussed microstructures capable of achieving static as well as
dynamic control of infrared emission. Chapter 2 investigated light-trapping structures for black
phosphorus-based photodetectors (section 2.1) and aluminum hybrid gratings for chemical
sensing (section 2.2). Additionally, Section 2.3 provided a demonstration of spectral prediction
in static hBN-based emitters using our semi-analytical model based on temporal coupled-mode
theory. Chapter 3 provided an overview of dynamically-tunable microstructures for IR emission
control. Specifically, section 3.1 discussed an electrically-tunable IR absorber based on graphene.
On the other hand, sections 3.2 through 3.4 provided an overview of thermally-tunable photonic
devices based on vanadium dioxide for spectral and spatial control of thermal emission.
While the structures proposed in this part of the thesis were optimized for specialized
applications, the underlying design strategies are fundamental and hence applicable to other
domains of science and technology. For instance, the ability to design structures with strong field
enhancement as in the case of MIMs can be leveraged to design nonlinear photonic devices. On
the other hand, one may utilize the relaxed thickness constraint offered by metallic gratings to
fabricate narrowband IR absorbers on flexible polymer substrates. These may potentially be
useful in wearable biosensors. The microstructure designs presented in Chapter 3 provide new
avenues for controlling thermal emission beyond Stefan-Boltzmann law. This provides the
intriguing possibility of creating thermal analogs to electrical devices. Section 3.2 discussed one
such photonic device that serves as the thermal analog of an electrical diode. One may similarly
50
exploit the optical tunability offered by phase change materials to design thermal logic gates, and
potentially, computers that perform calculations using heat instead of electricity. Such devices
could have widespread implications for thermal management and energy harvesting.
With the rapidly growing number of applications adopting photonics-based solutions for
enhanced functionality, the demand for fast and efficient photonic design tools is at an all-time
high. In section 2.3 of Chapter 2, we attempted to address this demand by proposing a semi-
analytical model for spectral prediction and microstructure optimization. Contrary to
conventional machine-learning based techniques, our model relies on understanding the physical
interactions between different elements of the device. We believe that such physics-informed
modeling approaches can significantly reduce computational costs while at the same time result
in devices with higher efficiencies.
51
PART 2: SECURE DATA ENCRYPTION

Chapter 5: Introduction

In recent years, metamaterials have benefited several applications ranging from sensing [52-54]
to energy harvesting [50, 51] and thermal management [46-49] owing to their ability to
manipulate optical waves in the spatial and spectral domain. Over the past few years, there has
been growing interest in using metamaterials for storing information. The majority of the
proposed metamaterials encode image-based information in the form of holograms on
predefined spectral and polarization channels [147-162]. However, the encoded images are
easily recovered by using the correct illumination, undermining the security of data storage. In
contrast, one may design metamaterials for encrypting images [163-165]. In this case, the original
image is first converted to a set of random images that are subsequently stored on separate
wavelength and polarization channels using the metasurface. Since the random images can only
be transformed back to the original image via a series of mathematical operations described in a
key, encryption provides enhanced security over typical image encoding.
The ability of metamaterials to achieve simultaneous spatial, spectral and polarization
control of optical waves [166, 167] makes them uniquely suitable to be used as physical tags
containing image information encrypted over multiple channels. Such physical tags containing
encrypted data could have several applications, for example, in anti-counterfeiting. Meanwhile,
rapid advancements in multispectral imaging capabilities provide a method to record spatially-
and spectrally-resolved information. We thus envision secure tagging and anti-counterfeiting
52
applications utilizing metamaterials and multispectral imagers for encrypted, multi-channel data
storage and retrieval.
Recent developments in the field of electrically-reconfigurable metasurfaces [168] also
provide intriguing opportunities for secure multi-channel communication using metamaterials
and hyperspectral imagers. The basic idea is illustrated in Fig. 5.1. A metasurfaces is triggered by
an external voltage source to display a set of random images on separate channels when
illuminated by a broadband light source. The intended recipient records these images using a
hyperspectral imager and uses the decryption key to retrieve the hidden image. The metasurface
can in principle be reconfigured by the control signal to encrypt any desired image.

Figure 5.1: Metasurface-based secure multi-channel communication.

In chapter 6, we describe a generalized encryption and decryption algorithm suited to the
transmission of image data on multiple wavelength channels. The algorithms depend upon
possession of a key, which is chosen from a space of all possible keys (key space). Unlike
traditional image encryption schemes, which transform the image into a single cipher image [169-
177] (1-to-1 transformation), our scheme performs a 1-to-n transformation to distribute the
Figure 1: system schematic
Broadband
light source
Metasurface
Multispectral
imager
Cipher
images
Control signal
Output
image
Decryption
key
53
image across multiple channels. The images measured on each channel serve as cipher images,
from which the intended recipient can recover the original image by using the decryption key.
We evaluate the robustness of our scheme against two different kinds of attacks of varying
complexity and show that security is guaranteed provided the number of channels used is more
than a small threshold value. Finally, we perform a table-top experiment to illustrate the utility
of our encryption scheme.
In chapter 7, we present an experimental implementation of metasurfaces for secure,
multi-channel image encryption in the mid-IR. Our metasurfaces consist of an array of pixels,
each designed to produce a wavelength- and polarization-dependent IR absorptivity. We design
a basis set of pixels for encrypting images of arbitrary resolution on a given number of wavelength
and polarization channels. We then fabricate these pixels and experimentally measure their
spectral response using Fourier Transform infrared spectroscopy. We use the measured data to
emulate encryption and decryption of binary and 8-bit grayscale images. Finally, we evaluate the
security of our encryption scheme by performing statistical analyses on the image data stored on
different channels.
Chapter 8 provides a summary of the results in chapters 6 and 7 and discusses their
potential impacts to the fields of IR communication and anti-counterfeiting.

54
Chapter 6: Generalized multi-channel scheme for secure image encryption

The ability of metamaterials to manipulate optical waves in both the spatial and spectral domains
has provided new opportunities for image encryption. Combined with the recent advances in
hyperspectral imaging, this suggests exciting new possibilities for the development of secure
communication systems. While traditional image encryption approaches perform a 1-to-1
transformation on a plain image to form a cipher image [169-177], here we propose a 1-to-n
transformation scheme. Plain image data is dispersed across n seemingly random cipher images,
each transmitted on a separate spectral channel. We show that the size of our key space
increases as a double exponential with the number of channels used, ensuring security against
both brute-force attacks and more sophisticated attacks based on statistical sampling. Moreover,
our multichannel scheme can be cascaded with a traditional 1-to-1 transformation scheme,
effectively squaring the size of the key space. Our results suggest exciting new possibilities for
secure transmission in multi-wavelength imaging channels.
Section 6.1 provides a discussion of the encryption and decryption algorithms. In sections
6.2 and 6.3, we evaluate the robustness of our encryption scheme against two different kinds of
attacks while in section 6.4, we illustrate its utility with the help of a table-top experiment.
Section 6.5 presents a summary of the results in this chapter.
A version of the results presented in this chapter was published in Ref. [178].
55
6.1 Encryption and decryption algorithms
We begin by defining general terms relevant to our encryption scheme. The image being
encrypted is referred to as a plain image. For simplicity, we assume our plain images to be binary,
i.e., each pixel has a value of 0 or 1. Figure 6.1 shows an example plain image, a 9x9 letter ‘D’.
Here, the black pixels have a value of 0 and the white pixels have a value of 1. The plain image is
transformed into a set of cipher images using an encryption algorithm, a mathematical procedure
that depends on the choice of a key. Intuitively, the goal of encryption is to “hide” the information
present in the plain image. Figure 6.1 shows the cipher images C 1 through C 5 generated using a
specific choice of the key. None of the images obviously resembles a ‘D.’ An output image is
generated by applying a decryption algorithm to the cipher images. If the same key is used for
decryption as encryption, the output image is the same as the plain image. In general, the number
of possible keys (size of the key space) should be large enough that an attacker is unlikely to guess
the correct key at random.
Our key space is implicitly defined by a set of mathematical decryption functions, where
each function is written as a sum of products (SOP) of cipher images. Decryption is performed by
operating the SOP function on the cipher images. For images C 1 through C n, the output image is
a sum of n s terms, where each term is a product of n p non-repeating cipher images. For instance,
consider the SOP function shown in the green box in Fig. 6.1, {C 1C 4C 5 + C 1C 3C 4 + C 2C 3C 5 + C 2C 3C 4 +
C 2C 4C 5}. All operations are performed in a pixel-wise fashion. In this case, n = 5, n p = 3, and n s = 5.
The corresponding key is a sequence of integers that represents the SOP function. The integer
before the colon indicates the number of cipher images (here, n = 5), and the integers following
the colon represent the product terms. At a given pixel location, a product term contributes a
56
value of 1 to the output image if and only if all the cipher images in the product term have a 1 at
that pixel location. For example, the product term C 1C 4C 5 at the pixel location (4,7) indicated by
the green box in Fig. 6.1 produces the white pixel indicated in the output image.

Figure 6.1: A 9x9 pixel binary image of the letter ‘D’ is input to the encryption algorithm that uses
a key to convert it into a set of 5 seemingly random cipher images. The decryption algorithm uses
the same key to retrieve the letter ‘D’ image.

The first step of the encryption algorithm can be understood as the converse of
decryption (blue box in Fig. 6.1). For ease of reference, we call the five product terms in the
example ‘key triplets’. For n = 5, one can have at most 10 triplets of non-repeating integers
(excluding permutations). The remaining five triplets that do not appear in the key are referred
to as ‘non-key triplets’. Each white pixel (value 1) of the plain image is randomly assigned to a
key triplet, and a 1 is stored at the same location in its constituent cipher images. For example,
Plain image
5 : (1,4,5) (1,3,4) (2,3,5) (2,3,4) (2,4,5)
n
s
= 5
n
p
= 3 n = 5
Key
Convert key to mathematical function
C
1
C
4
C
5
+ C
1
C
3
C
4
+ C
2
C
3
C
5
+ C
2
C
3
C
4
+ C
2
C
4
C
5
Key
Mathematical
function
Multiply cipher images according to the function
5 : (1,4,5) (1,3,4) (2,3,5) (2,3,4) (2,4,5)
Choose one key triplet
randomly:
Choose one non-key
triplet randomly:
(i,j)th pixel
145 134 235 234 245
Store a 1 in the
(i,j)th pixel of
C
1
, C
4
and C
5
Store a 1 in the
(i,j)th pixel of
C
1
, C
2
and C
5
Encryption algorithm
345 135 123 124 125
Cipher images
C
1
C
2
C
3
C
4
C
5
Decryption algorithm
57
the white pixel highlighted by the green box in the letter ‘D’ image is assigned to the triplet
(1,4,5), so that cipher images C 1, C 4 and C 5 each have a 1 at their (4,7) pixel locations. This
approach uniformly divides the ‘1’ pixels of a plain image among its cipher images, visually
disguising the information in the plain image.
The second step of the encryption algorithm introduces “red herring” pixels in each cipher
image. This is accomplished by assigning each black pixel (value 0) of the plain image to a
randomly-chosen non-key triplet and storing a 1 at the same location in its constituent cipher
images. For example, C 1, C 2 and C 5 each have a 1 at their (6,6) pixel locations. The triplet (1,2,5)
does not appear in the key, and the plain image has a 0 at this location (highlighted by the red
box). The red herring pixels prevent an attacker from deducing the non-zero pixels of the plain
image simply by noting the locations of any non-zero pixels in the cipher images. Moreover, since
all pixels of the plain image are mapped to either a key triplet or a non-key triplet, a simple sum
of all cipher images yields a uniform image, devoid of information. This point is illustrated with
an example in the next section.
We note that repeated applications of the encryption algorithm to the same plain image
can yield a different set of cipher images, even when the key is held fixed. This is due to the
element of randomness in the algorithm that occurs when assigning pixels to key and non-key
product terms.

6.2 Enabling security against a brute-force attack
For the encryption algorithm to be resistant to a brute-force attack, the key space should be large
enough that an attacker cannot manually test all the possible keys. Given the number of cipher
58
images, we can determine the total number of possible keys, N keys by combinatorics. Figure 6.2(a)
shows a plot of log 2(N keys) versus n. For reference, the maximum key space size of 2
256
for practical
AES symmetric encryption is shown by the solid red line. It can be observed that the total number
of keys increases double-exponentially with n and becomes nearly equal to the AES limit for n =
10. This indicates that encrypting a plain image into more than 10 cipher images would render a
brute force attack infeasible.

Figure 6.2: (a) Variation of log 2(N keys) with n. The solid red line shows the AES limit of N keys = 2
256

for symmetric encryption. (b) Variation of log 2(n keys) with n p and n s for n = 10.

We denote the number of keys for fixed n, n p and n s as n keys. Figure 6.2(b) shows the variation of
log 2(n keys) with n p and n s for n = 10. Here n s ranges from 1 to C(10,n p) and n p ranges from 1 to 10.
It can be observed that n keys is maximum for 𝑛
<
= ⌊10/2⌋ = 5 and 𝑛
=
= ⌊𝐶(10,5)/2⌋= 126,
where ⌊𝑥⌋ denotes the greatest integer less than or equal to x. In general, one should choose
𝑛
<
= ⌊𝑛/2⌋ and 𝑛
=
= \𝐶(𝑛,𝑛
<
)/2], which maximizes the size of the key space (see Fig. 6.3 for
a numerical example with n = 10).
To illustrate the security of the optimized system against brute-force attacks, consider a
50x40 pixel binary image of the letter ‘A’ (Fig. 6.3(a)) that has been encrypted using a key with n
= 10, n p = 5 and n s = 126. The resulting cipher images are displayed in Fig. 6.3(b). As can be seen,
Figure 3: optimal parameters
a b
log
2
(N
keys
) = 256
log
2
(n
keys
(n
p
,n
s
))
59
simple visual inspection of the cipher images does not reveal any meaningful information about
the plain image. Moreover, a sum of all cipher images results in a uniform intensity image with
all pixel values equal to 5 (Fig. 6.3(c)).

Figure 6.3: (a) A 50x40 pixel binary image of the letter ‘A’. (b) Cipher images generated by
encrypting the letter ‘A’ image using a key with n = 10, n p = 5 and n s = 126. (c) Image representing
the sum of all cipher images. (d) Images generated by attempting decryption using three incorrect
keys with n = 10, n p = 5 and n s = 126.

We assume that the attacker has access to the cipher images and the system parameters
that were used for encryption (n, n p, and n s). We further assume that the attacker has knowledge
of the encryption and decryption algorithms but does not have access to the encryption key. So,
he resorts to randomly trying out a small number of keys with n = 10, n p = 5 and n s = 126 and
visually inspecting the output images to guess the encrypted plain image. Figure 6.3(d) shows the
output images for three such keys, none of them being the original key used for encryption. Here
again, it is difficult to gather any information about the plain image by simply looking at the
output images. Therefore, one would expect that an attacker relying solely on visual inspection
would have a very low probability of recovering a plain image encrypted using our scheme.
Figure 4: encryption example
a b
c d
60
6.3 Enabling security against more sophisticated attacks
Next, we evaluate the security of our encryption scheme in a scenario where an attack more
sophisticated than simple visual inspection is used to recover a plain image. In the example of
Figure 6.3, none of the incorrect keys tried yielded an output image that obviously resembled the
plain image (Fig. 6.3(d)). However, one might ask whether there is more subtle information
contained in the output images obtained from incorrect keys. A more sophisticated attacker
might therefore go beyond visual inspection to calculate a similarity score with a known set of
possible plain images.
We consider the problem of transmitting messages written using a four-letter alphabet.
The alphabet comprises of 50x40 pixel binary images of the letters ‘A’, ’B’, ’C’ and ‘D’. Let’s
assume that the letter ‘A’ needs to be transmitted and has been encrypted using a key with n =
10, n p = 5 and n s = 126. An attacker intercepts the transmission channel and gains access to the
cipher images. We assume that the attacker is familiar with the encryption and decryption
algorithms but does not have access to the key that was used. Since there are ten cipher images,
he guesses that n = 10.
As discussed previously, the size of the key space for n = 10 is large enough to make it
infeasible for the attacker to try out all possible keys. To get around this problem, the attacker
constructs a randomly-selected sample set of 1000 keys for each n p and n s. He uses these keys to
generate 1000 output images and computes their mean similarity score, S mean with respect to the
four letters. The similarity score S for an image M’ with respect to an image M is given by:

𝑆 = _
𝑐𝑜𝑣(𝑀,𝑀′)
𝑐𝑜𝑣(𝑀,𝑀)
_

6.1
61
Here cov(M’,M) refers to the covariance of M’ and M. We normalize M’ by its maximum value to
ensure that none of its pixels take a value greater than 1. As a result, the similarity score takes a
value between 0 (totally dissimilar images) and 1 (M’ = M).
The score S mean with respect to the letters ‘A’ through ‘D’ is displayed as a function of n p
and n s in Figs. 6.4(a) through (d). We note that in a practical situation, the attacker would stop
traversing the key space as soon as he hits the right key. We assume that this does not happen
in this situation as the probability of finding the right key is very low (~1/10
74
).

Figure 6.4: (a) – (d) Variation of S mean for encrypted letter ‘A’ with n p and n s calculated with respect
to letters ‘A’ through ‘D’. S mean for each n p and n s is equal to the mean similarity score of output
images obtained by operating 1000 randomly selected keys on the cipher images.

From Fig. 6.4, one can observe that for n p ≤ 5, the mean scores with respect to letter ‘A’
are in general higher than those for all the other letters. In particular, S mean for letter ‘A’ takes its
maximum value close to n p = 5 and n s = 126, which are the parameters used for encryption.
Therefore, the attacker will be able to guess the encryption parameters and the encrypted letter
by simply looking at the mean score colormaps for the four letters.
S
mean
a b
c d
S
mean
S
mean
S
mean
62
In addition, it can be observed that the mean scores for all keys with n p > 5 are equal to
zero. Since the letter ‘A’ image was encrypted using a key with n p = 5 and n s = 126, each of its ‘1’
pixels is stored in one of the 126 groups of five channels. This implies that only five of the ten
cipher images can store a ‘1’ at any given pixel location. Multiplying more than five cipher images
would result in a complete cancelation of pixel values and generate an image with all pixels equal
to 0. This happens when evaluating the decryption function for keys with n p > 5. Decryption using
such keys results in all-zero images that have a similarity score of 0 with respect to all the four
letters.
In order to make it difficult for the attacker to identify the encrypted letter, we must
decrease the difference in S mean calculated with respect to the four letters. One way to accomplish
this is to increase n. Figure 6.5(a) presents the variation of S mean with n for letter ‘A’ encrypted
using 𝑛
<
= ⌊𝑛/2⌋ and 𝑛
=
= \𝐶(𝑛,𝑛
<
)/2]. Since S mean tends to be higher close to the encryption
parameters, we only present its value at 𝑛
<
= ⌊𝑛/2⌋ and 𝑛
=
= \𝐶(𝑛,𝑛
<
)/2] for each n. The solid
lines represent the average S mean computed over 1000 trials with 1000 samples each, while the
colored bands represent the corresponding error bounds.
One can notice that for small values of n, the scores with respect to ‘A’ are significantly
larger than those with respect to the other letters. As n increases, S mean with respect to ‘A’
reduces while it remains nearly constant for the other letters. For n ≥ 14, the error bounds on
S mean for ‘A’ start to overlap with those for ‘C’ and ‘D’. This implies that encrypting ‘A’ into 14 or
more cipher images will make it difficult for the attacker to identify it on the basis of similarity
scores. One may note that the value of n needed to ensure security in this case is higher than
that required to prevent a brute-force attack (n = 10). In general, the number of cipher images
63
(n) required to defend against a sophisticated attacker who uses a randomly-selected key set is
larger than for a brute-force attacker. However, provided n is chosen large enough, the system
will remain secure.

Figure 6.5: Variation of mean score S mean with n calculated with respect to letters ‘A’ through ‘D’
for encrypted letter (a) ‘A’ and (b) ‘B’. Solid lines indicate average S mean over 1000 trails with 1000
keys each, and colored bands represent the corresponding error bounds.

Even though the analysis presented thus far is for encrypted letter ‘A’, the conclusion
remains the same for all letters in the alphabet. To validate this, we present the variation of S mean
with n for encrypted letter ‘B’ in Fig. 6.5(b). Here again, the scores with respect to letter ‘B’ are
higher for small values of n and reduce as n increases. One can also note that the scores with
respect to letters ‘C’ and ‘D’ in Fig. 6.5(b) are close to those with respect to letter ‘B’ due to the
similarity in the shapes of these three letters. For n ≥ 13, the error bounds on S mean for ‘B’ start
to overlap with those for the other letters. Therefore, from Figs. 6.5(a) and (b), one can conclude
that choosing an n ≥ 14 makes it difficult for the attacker to identify messages written using a
combination of ‘A’ and ‘B’. A similar calculation can be done for the letters ‘C’ and ‘D’ to
determine a lower bound on n for the entire system. Similar conclusions are obtained for the
case in which an attacker decides to use maximum scores instead of mean scores. In this
Figure 6: Mean scores as a function of n
a b
64
situation, the error bands on scores are much broader and the lower bounds on n for secure
encryption of letters ‘A’ and ‘B’ are 12 and 11, respectively.

6.4 Table-top demonstration
To illustrate the utility of our encryption scheme, we conduct a table-top demonstration using a
color display and a color camera (Fig. 6.6(a)). While a true n-channel encryption scheme (as
described above) requires independent control over transmission and detection at n distinct
wavelengths, we can emulate the full behavior using a simple RGB system (Fig. 6.6(b)) with
calibration (Fig. 6.6(c)). A plain image is first XORed with a 50x50 one-time pad (labeled as
‘standard encryption’ in the figure). Using the key, the white and black pixels are randomly
assigned to the key triplet and non-key triplet colors, respectively (Fig. 6.6(d)) to produce the
display image. We capture the display image on the camera and use the color lookup table to
recover the output image, as shown. The output image shows high fidelity with respect to the
original plain image with a similarity score of 0.98. This simple demonstration shows the
robustness of our encryption system to noise.
The demonstration of Fig. 6.6 illustrates how our multi-spectral scheme can be used to
add an “extra dimension” of security to image encryption. In the example above, we cascaded
standard and multi-spectral encryption schemes. To successfully decrypt the resultant image, the
receiver must correctly guess both the standard key K 1 and the multi-spectral key K 2. Suppose
the standard scheme uses a 256-bit key chosen from a key space size of 2
256
. For a multi-spectral
scheme with n > 10, the cascaded key space is larger than (2
256
)
2
. The multi-spectral scheme we
describe thus effectively squares the key space size. We conclude that our approach can provide
65
an extra dimension for secure encryption, one which can leverage emerging technologies for
multi-wavelength transmission and imaging.

Figure 6.6: (a) A computer screen displays an image which is captured by a phone camera. (b)
Triplets of channels corresponding to n = 5 and n p = 3 are mapped to 10 colors in the RGB space
to generate a lookup table. (c) A calibration image comprising of all 10 colors displayed on the
computer screen is captured and resized to the original resolution. (d) Encryption and decryption
of a 50x50 pixel binary Trojan image using the computer screen – phone setup.

6.5 Conclusion and potential impact
In summary, we proposed an encryption scheme based on pixel multiplexing for transmission of
images across multiple wavelength channels. Our encryption algorithm divides the pixels of a
given plain image into multiple, seemingly random cipher images. Decryption by the intended
recipient is performed by using a key to convert the cipher images into meaningful information.
We considered a generalized key space based on mathematical decryption functions, each
a c
Calibration image
Captured and resized
calibration image
d
Plain image
Captured and resized
display image
Cipher images
Standard
encryption
Display image
Assign to one of the key triplet colors
Assign to one of the non-key triplet colors
Key Color lookup table
Output image
Standard
decryption
Key
b n = 5 and n
p
= 3
Number of colors = 10 Color lookup table
(1,2,3)
(1,2,4)
(1,2,5)
(1,3,4)
(1,3,5)
(1,4,5)
(2,3,4)
(2,3,5)
(2,4,5)
(3,4,5)
66
written as a sum of products of cipher images. Using combinatorics, we showed that encryption
of a given plain image into more than 10 channels ensures security against a brute-force attack.
We also considered a more sophisticated attack; one in which an attacker uses mean similarity
scores of randomly chosen samples of the key space to extract information about the plain image.
For a 50x40 pixel image, we showed that encryption remains secure as long as more than 14
channels are used.
While this work uses RGB display and imaging to emulate a 5-channel scheme, we find
that increasing the number of channels leads to increased noise levels and decryption errors.
True implementation of n-channel encryption and decryption will require independent control
of transmission and detection on n separate wavelength channels. To this end, the continued
development of tunable metasurfaces, paired with multi- and hyper-spectral imagers, will
illustrate the true potential of the proposed encryption method.

67
Chapter 7: Experimental implementation of metasurfaces for secure multi-channel image
encryption in the infrared

The ability to tailor light-matter interactions using artificially engineered materials has opened
up new avenues for secure data storage and communication. In this chapter, we propose and
experimentally investigate metasurfaces for secure, multi-channel image encryption in the
infrared (IR). Our metasurfaces consist of an array of pixels, each designed to produce a
wavelength- and polarization-dependent IR absorptivity. We design a basis set of pixels for
encrypting images of arbitrary resolution on a given number of wavelength and polarization
channels. We then fabricate these pixels and experimentally measure their spectral response
using Fourier Transform infrared spectroscopy. We use the measured data to emulate encryption
and decryption of binary and 8-bit grayscale images. Finally, we evaluate the security of our
encryption scheme by performing statistical analyses on the image data stored on different
channels. Our results suggest intriguing possibilities for the development of encrypted tagging
technologies in the infrared and thus have implications for secure object identification and anti-
counterfeiting.
Sections 7.1 and 7.2 describe our approach for designing image encrypting metasurfaces
and our specific pixel design, respectively. In section 7.3, we present our results for encryption
and decryption of binary and 8-bit grayscale images. In section 7.4, we quantify the security
provided by our encryption scheme by performing statistical analyses on the generated cipher
images. Section 7.5 presents a summary of the results in this chapter along with a discussion of
their potential impact.
68
A version of the results presented in this subsection is currently under review [179].

7.1 Designing a metasurface for image encryption
The first step in designing the metasurface is to encrypt a given image into a set of random images
that can subsequently be encoded on separate wavelength and polarization channels. The image
that needs to be encrypted is known as the plain image, and the random images generated as a
result of encryption are known as cipher images. Suppose, for example, we wish to encrypt a 9x9
pixel image of the letter ‘D’ (left panel of Fig. 7.1(a)) into four wavelength channels across two
polarizations. For simplicity, we consider binary images i.e., each pixel takes a value of either 0
(black pixels) or 1 (white pixels). We first divide the plain image into two intermediate images
such that performing a pixel-wise XOR operation on the intermediate images gives back the plain
image. The two sets of cipher images produced by encrypting the intermediate images can then
be encoded on two orthogonal polarizations P 1 and P 2.
Encryption of intermediate images is performed using our multi-channel scheme [178]
and requires two keys. Each key is characterized by three parameters: n, n p and n s, which
collectively describe the manner in which a given image is converted to cipher images. We note
that n denotes the number of cipher images generated, which corresponds to the number of
wavelength channels used. Since the intermediate images need to be encrypted on four
wavelength channels, we choose n = 4. Figure 7.1(a) displays the two sets of cipher images
obtained by encrypting the intermediate images using keys with n = 4, n p = 2 and n s = 3. One can
observe that the cipher images look completely random and do not reveal any meaningful
69
information about the plain image. Here n p = 2 indicates that for every pixel location of a given
intermediate image, exactly two of its four cipher images have a value 1.
We wish to design a metasurface that stores the two sets of cipher images in its
wavelength- and polarization-dependent emission profile. The metasurface is an array of pixels,
where each pixel is designed to store values of the corresponding pixel location in the cipher
images. For instance, consider the encircled pixel on the metasurface of Fig. 7.1(b). Emissivity
measurements on the pixel for two polarizations (P 1 and P 2) on each of the four spectral channels
produce two sets of binary sequences, as shown in the right panel of Fig. 7.1(b). These sequences
correspond to the values of the pixel at the corresponding location in the cipher images (green
box in Fig. 7.1(a)).
We design pixels consisting of optical resonators supporting localized photonic modes
(left panel of Fig. 7.1(c)). Such a configuration enables the pixels to have strong, polarization-
dependent emission at certain predefined wavelengths. In accordance with n = 4 and n p = 2, we
design the pixels to emit strongly at two of four predefined wavelength channels (λ 1 through λ 4)
on each polarization. The right panel of Fig. 7.1(c) shows the six possible emission spectra. The
number of spectra is equal to the number of ways of choosing two out of four channels. By
applying a threshold (red dotted line), the emissivity values at each of the four channels (solid
yellow circles) can be converted to a binary sequence. The binary sequence corresponding to
each spectrum is displayed above it. Since each pixel of the metasurface is designed to produce
one of the six shown spectra on each polarization, there are 36 possible pixel types. In general,
each pixel may contain a periodic array of unit cells.
70

Figure 7.1: (a) A given plain image is converted into two random images which are subsequently
encrypted on two polarizations across four wavelength channels. The pixel value at location (5,7)
is highlighted with a green box in each of the cipher images. (b) Schematic showing a 9x9 pixel
metasurface designed to encode the plain image in (a). A zoomed-in view of the encircled region
of the metasurface shows the pixel at location (5,7) that is designed to produce binary sequences
in accordance with the highlighted values in (a).(c) (left panel) Schematic showing a single pixel
and (right panel) model emission spectra for four-channel encryption on a given polarization. The
emissivity values at each of the channels are indicated by yellow circles and the resulting binary
sequence for every spectrum is displayed above it.

71
In the next section, we describe the specific design of our metasurface pixels that allows
them to have a wavelength- and polarization-dependent spectral response.

7.2 Metasurface pixel design
We design the metasurface pixels using a two-dimensionally periodic array of optical resonators
capable of producing a wavelength- and polarization-dependent spectral response in the 3 – 5
μm wavelength range. Each unit cell comprises of two sets of orthogonal gold nanorods on an
Al 2O 3 spacer and a gold back reflector (Fig. 7.2(a)). Each nanorod along with the underlying spacer
and back reflector serves as a metal-insulator-metal (MIM) cavity supporting a lateral Fabry-Perot
mode for a particular polarization of incident light [35]. The resonance wavelength of each of the
four cavities can be tuned independently by adjusting the corresponding nanorod length. The
nanorods have a thickness of 50 nm and lengths L 1 through L 4. We choose a unit cell of size 2x2
μm
2
, a spacer layer thickness of 220 nm and a back reflector thickness of 50 nm.
Figures 7.2(b) through (d) illustrate the process through which a unit cell of our
metasurface pixel is constructed. A pixel having a single nanorod with length L 1 oriented along
the x-direction per unit cell produces a single absorption peak for x-polarized incident light (Fig.
7.2(b)). The spectral location of this peak can be red-shifted by increasing L 1. The absorption
spectrum of the pixel is calculated using Lumerical FDTD.
Figure 7.2(c) shows the effect of adding a second nanorod with length L 2 oriented along
the x-direction to the unit cell. The right panel of Fig. 7.2(c) shows the absorption spectrum of
the pixel with L 1 fixed at 0.8 μm and L 2 varied from 0.8 to 1.1 μm for x-polarized incident light.
One can observe that the absorption spectrum now has 2 peaks, each contributed by one of the
72
two nanorods. The two peaks can be moved independently of each other by adjusting L 1 and L 2.
A pixel with two nanorods oriented along the same direction produces absorption resonances
only for incident light polarized along the axis of the nanorods. In order to get a spectral response
for the orthogonal polarization, we introduce another set of two nanorods with their axes aligned
along the y-direction. Figure 7.2(d) shows the absorption spectrum for a pixel with L 1 = 0.8 μm,
L 2 = 1.1 μm, L 3 = 0.9 μm and L 4 = 1 μm. It can be observed that the pixel produces two distinct
absorption spectra for the two polarizations of incident light.
In the context of the afore-mentioned encryption scheme, one can adjust the nanorod
lengths to obtain 36 distinct pixel types. Each of these pixels will generate absorption resonances
at two of the four spectral channels on each polarization. We note that in order to design a
metasurface for encrypting images on two polarizations using keys with n = 4 and n p = 2, one only
needs to know the 36 pixel types and their spectral response. The 36 pixels thus form a basis set
using which all metasurfaces for encrypting images using the n = 4 and n p = 2 scheme on
predefined wavelength and polarization channels can be designed. We choose our spectral
channels to be located at wavelengths 3.16, 3.66, 4.16 and 4.7 μm. The nanorod lengths L 1
through L 4 are optimized to produce resonances at two of the four wavelength channels on each
polarization.

73

Figure 7.2: (a) Schematic showing a single unit cell of a given pixel of the metasurface: (left panel)
perspective view and (right panel) side view. (b) A pixel with a single nanorod of length L 1 per
unit cell (left panel) produces a single peak in the absorption spectrum for x-polarized incident
light (right panel). (c) A pixel with two nanorods with lengths L 1 (= 0.8 μm) and L 2 per unit cell
(left panel) produces two peaks in the absorption spectrum for x-polarized incident light (right
panel). (d) A pixel with two orthogonal sets of nanorods (left panel) produces two peaks each for
x and y-polarized incident light. Here L 1 = 0.8 μm, L 2 = 1.1 μm, L 3 = 0.9 μm and L 4 = 1 μm.

7.3 Experimental implementation of image decryption
We fabricate the complete set of 36 pixel types required for the (n = 4, n p = 2) encryption scheme.
The pixels are fabricated on a Si wafer. First, the Si wafer is cleaned with Nano-Strip (VWR) for 30
minutes at 60°C. After cleaning the substrate, the metallic bottom layer is deposited with
74
electron beam evaporation (Kurt J. Lesker) by successively depositing 10 nm of Ti, 50 nm of Au,
and then 3 nm of Ti. Then, 220 nm of Al 2O 3 is deposited with electron beam evaporation
(Angstrom Engineering). To pattern each pixel array, a bilayer poly(methyl methacrylate) (PMMA,
Kayaku Advanced Materials) electron resist stack is spin-coated on the Si wafer. The bottom layer
of the stack is PMMA 495K A6, which is spun at 3500 RPM for 60 seconds and then baked at
180°C for 4 minutes. The top layer is PMMA 950K A2, which is spun at 3500 RPM for 60 seconds
and then baked at 180°C for 5 minutes. The resist stack is patterned with an electron beam
pattern generator (Raith) at 100 kV with a 10 nA beam. We expose pixel arrays consisting of 200
× 200 unit cells. The gold nanorods are deposited with electron beam evaporation by first
depositing 3 nm of Ti and then 50 nm of Au. The metallic film is lifted off with an acetone bath at
room temperature for 1 hour. The thickness of each layer is verified with an atomic force
microscope. Finally, reflectance spectra for each pixel in both polarization states are measured
with a Fourier transform infrared spectrometer (Bruker Vertex 70). The incident light’s
polarization is controlled with a linear polarizer (Bruker).
Figure 7.3 shows the SEM images and measured absorption spectra (solid curves) for four
different pixels. One can observe that the measured spectra are in good agreement with those
determined from simulations (dotted curves). The binary sequences for each of the pixels for
both polarizations are displayed above the corresponding absorption spectra.
We consider image decryption using two metasurfaces: one encoding a binary image and
the other, an 8-bit grayscale image. Figure 7.4 describes the process of decrypting a 50x50 pixel
binary image of the Trojan logo. Each pixel of the corresponding metasurface is chosen from the
36 pixel types described in the previous section. For decryption, we use the measured spectral
75
response of each pixel for a given polarization of incident light to retrieve its four-channel binary
sequence. Repeating this process for all pixels of the metasurface for both polarizations gives two
sets of cipher images (middle panel of Fig. 7.4). Two keys with n = 4, n p = 2 and n s = 3 are used to
convert the two sets of cipher images to their respective intermediate images. The hidden image
is retrieved by performing a bit-wise XOR operation between the intermediate images.

Figure 7.3: SEM images (left panel) and absorption spectra for four different pixel types having:
(a) L 1 = 0.8 μm, L 2 = 1.12 μm, L 3 = 0.8 μm and L 4 = 1.12 μm; (b) L 1 = 0.8 μm, L 2 = 1.12 μm, L 3 = 0.8
μm and L 4 = 1.27 μm; (c) L 1 = 0.8 μm, L 2 = 1.12 μm, L 3 = 0.9 μm and L 4 = 1.12 μm; and (d) L 1 = 0.8
μm, L 2 = 1.12 μm, L 3 = 1.12 μm and L 4 = 1.27 μm. The absorption spectra for x-polarized incident
light are shown by the blue curves and those for y-polarized light are shown by the red curves.
The absorptivity values at each of the four channels are indicated by solid yellow circles while the
threshold is displayed as the dotted green line. The binary sequence corresponding to each
spectrum is displayed above it.

Next, we consider the decryption of a 50x50 pixel 8-bit grayscale image of the Trojan logo.
For such an image, the pixel values range from 0 to 255. Each 8-bit pixel of the original plain
image can be expressed as 8 1-bit pixels (left panel of Fig. 7.5(a)). The original 50x50 pixel
grayscale image can thus be converted to an equivalent 100x200 pixel binary image (right panel
of Fig. 7.5(a)). The metasurface required to encrypt this image using the n = 4 and n p = 2 scheme
is a 100x200 rectangular array of pixels, each belonging to one of the 36 possible types. We use
76
the measured spectral response of the pixels to obtain two sets of cipher images (bottom left
panel of Fig. 7.5(b)). These are then converted to intermediate images using two keys with n = 4,
n p = 2 and n s = 3. The intermediate images are XORed, and the resulting image is converted back
to the 8-bit representation to retrieve the hidden image.

Figure 7.4: Workflow for decrypting a binary image stored in a 50x50 pixel metasurface.
Measurement of the spectral response on two orthogonal polarizations results in two sets of
cipher images (middle panel). These are converted to intermediate images using two keys (top
right panel). The hidden image (bottom right panel) is recovered by performing a bit-wise XOR
on the two intermediate images.

In the next section, we evaluate the level of security provided by our encryption scheme
by performing statistical analyses.

7.4 Degree of randomness of multi-channel encryption scheme
We first evaluate the degree of randomness of the cipher images generated by our encryption
scheme by performing a histogram analysis. Figure 7.6(a) shows a 565x850 pixel grayscale image
of a tiger (left panel) and its histogram (right panel). One can observe that majority of the pixels
77
have values between 0 and 64 owing to the dark background of the image. We encrypt this image
on 6 channels using a key with n = 6, n p = 3 and n s = 10. The left panel of Fig. 7.6(b) shows the
generated cipher images in their 8-bit representation while the right panel presents the
corresponding histograms. The histograms for all cipher images are flat, indicating that each
image has a uniform distribution of pixel values from 0 to 255. This analysis qualitatively
demonstrates that the cipher images generated by our encryption scheme are highly random.

Figure 7.5: (a) (left panel) Representing a single 8-bit pixel as 8 1-bit pixels. (right panel)
Expressing a 50x50 pixel 8-bit image as a 100x200 binary (1-bit) image. (b) Workflow for
decrypting a grayscale image stored in a 100x200 pixel metasurface. Measurement of the
spectral response on two orthogonal polarizations results in two sets of cipher images (bottom
left panel). These are converted to intermediate images using two keys (top right panel). The
hidden image (bottom right panel) is recovered by performing a bit-wise XOR on the two
intermediate images.

78
To quantify the randomness of cipher images generated by our encryption scheme, we
calculate their mean entropy as a function of the number of channels n, used for encryption (Fig.
7.6(c)). For each value of n, we use an encryption key with 𝑛
<
= ⌊𝑛/2⌋ and 𝑛
=
= \𝐶(𝑛,𝑛
<
)/2],
where C(n,n p) is the number of ways of choosing n p channels out of n and ⌊𝑥⌋ is the greatest
integer less than or equal to x. The mean entropy for a given value of n is the sum of entropies of
all the cipher images divided by n. One can observe that the entropies for even values of n are
higher than those for odd values. This can be understood by considering the cipher images in
their 1-bit (binary) representation. For even n, equal number of cipher images store a ‘0’ and a
‘1’ at each pixel location while for odd n, the number of cipher images storing a ‘1’ is greater than
those storing a ‘0’. As the number of channels increases, the mean entropy converges to a value
of 8 corresponding to a perfectly random 8-bit image. This calculation quantitatively validates
the randomness of our encryption scheme and shows that the degree of randomness can be
enhanced by increasing the number of channels.

7.5 Conclusion and potential impact
We proposed and experimentally implemented metasurfaces for multi-channel image encryption
in the infrared. In our encryption approach, an image is first converted into a set of cipher images
that are subsequently encoded on separate wavelength- and polarization-channels. We
considered metasurfaces consisting of an array of pixels, each having a predefined wavelength-
and polarization-dependent IR absorptivity. Next, we designed and experimentally-characterized
a set of 36 pixels, sufficient to construct metasurfaces for encrypting images of arbitrary
resolution on 4 wavelength and 2 polarization channels in the mid-IR. We used the measured
79
spectral response of the pixels to emulate encryption and decryption of both binary and 8-bit
grayscale images. Finally, we validated the security provided by our encryption scheme by
performing statistical analyses on the generated cipher images.

Figure 7.6: (a) (left panel) A 565x850 pixel 8-bit image of a tiger and (right panel) its corresponding
histogram. (b) (left panel) Cipher images obtained by encrypting the tiger image using a key with
n = 6, n p = 3 and n s = 10 and (right panel) their histograms. (c) Variation of mean cipher image
entropy for the tiger image with the number of channels used for encryption.

In the current work, we restricted our discussion to four spectral channels owing to the
broad resonance lineshapes of gold-alumina MIMs. Future implementations of our multi-channel
encryption scheme may utilize high quality factor microstructures to allow for a larger number
of wavelength channels to be used. We anticipate that our proposed metasurfaces and multi-
channel encryption scheme will pave the way for next-generation IR cryptographic systems.
These in turn will have far-reaching implications for secure object tagging, identification and anti-
counterfeiting applications. Moreover, rapid advances in the development of electrically-
80
reconfigurable metasurfaces [168] will provide opportunities for on-demand data encryption and
secure, multi-channel communication in the infrared.

81
Chapter 8: Conclusion and outlook

In this part of the thesis, we utilized the ability of metamaterials to manipulate optical waves in
the spatial and spectral domain for secure encryption of image data. In Chapter 6, we proposed
a multi-channel encryption scheme suited for secure transmission of images using
metamaterials. Our encryption algorithm divides the pixels of a given plain image into multiple,
seemingly random cipher images. Decryption by the intended recipient is performed by using a
key to convert the cipher images into meaningful information. We defined a generalized key
space and evaluated the security of our scheme against attacks of varying complexity. In Chapter
7, we provided an experimental implementation of multi-channel image encryption in the IR
using metasurfaces. We designed, fabricated and experimentally characterized a basis set of
microstructured pixels and used their spectral response to emulate encryption and decryption of
both binary and grayscale images.
Our results demonstrate the utility of microstructures in storing a large amount of data
distributed across multiple channels within a small form factor. The proposed metamaterials can
thus serve as compact physical tags containing encrypted, spectrally-multiplexed image
information. Such physical tags can have widespread implications in anti-counterfeiting and
object tagging and identification. Additionally, rapid advances in the development of electrically-
reconfigurable metamaterials along with ongoing progress in the field of hyperspectral imaging
provide intriguing possibilities for realizing secure communication systems. The IR wavelength
range is particularly suited for such applications as working within the two atmospheric
82
transmission bands (3 – 5 μm and 8 – 15 μm) allows for remote image collection and processing
with broad spectral bandwidth. We anticipate that our proposed multi-channel encryption
scheme and metasurfaces will pave the way for next-generation IR communication and
cryptographic systems.

83
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Abstract (if available)

Abstract The ability to control light-matter interactions is of paramount importance for the advancement of a wide variety of applications ranging from chemical and biological sensing to thermal management and energy harvesting. To this end, artificially engineered microstructures have received considerable attention from the scientific community. Unlike bulk materials that interact with light according to the laws of geometrical optics, microstructures harness resonant interactions with light waves. This allows such structures to achieve a richer suite of functionalities in a more compact size than their bulk counterparts. Light-matter interactions in microstructures come under the purview of microphotonics. In this thesis, I discuss the applications of microphotonics to two of the most exciting research areas in the field of optics: infrared emission tailoring and secure data encryption. The first part of the thesis presents photonic devices with customizable optical properties in the infrared for applications in chemical sensing, photodetection and thermal emission control. The second part explores the utility of microstructures in secure data storage with a discussion of a data-multiplexing based encryption scheme followed by its experimental implementation. The results presented in this thesis illustrate the potential of microstructures in efficiently manipulating optical waves, thereby providing intriguing opportunities for advancing the state-of-the-art for a broad class of applications.

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Asset Metadata

Creator Audhkhasi, Romil (author)

Core Title Microphotonics for tailored infrared emission and secure data encryption

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Degree Conferral Date 2023-05

Publication Date 02/28/2023

Defense Date 02/14/2023

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

Tag anti-counterfeiting,Cryptography,energy harvesting,infrared,nanotechnology,OAI-PMH Harvest,photonics,thermal radiation

Format theses (aat)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Povinelli, Michelle Lynn (committee chair), Armani, Andrea Martin (committee member), Wu, Wei (committee member)

Creator Email 18romil94@gmail.com,raudhkha@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC112764293

Unique identifier UC112764293

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Legacy Identifier etd-AudhkhasiR-11490

Document Type Thesis

Format theses (aat)

Rights Audhkhasi, Romil

Internet Media Type application/pdf

Type texts

Source 20230313-usctheses-batch-1009 (batch), University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

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