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Optimized nanophotonic designs for thermal emission control
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Optimized nanophotonic designs for thermal emission control
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Content
OPTIMIZED NANOPHOTONIC DESIGNS FOR THERMAL EMISSION CONTROL
by
Bo K. Shrewsbury
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(PHYSICS)
December 2024
Copyright 2024 Bo K. Shrewsbury
ii
Acknowledgements
First, I thank my wife and family. Through every challenge and moment of doubt, their unwavering
love and support made this possible.
I am also deeply grateful to my advisor, Dr. Michell Povinelli, whose commitment to her
students’ wellbeing and success fosters and environment where we can all thrive, even as our goals
evolve.
I extend my gratitude to our collaborators at Northrop Grumman for their valuable
contributions to our work.
Finally, I thank my lab mates and co-researchers: Romil Audhkhasi, Raymond Yu, Alok
Ghanekar, Silvia Guadagnini, Max Lien, Tien Wang, Mashnoon Sakib, and Ahmed Morsy. The
guidance, support, and camaraderie shared within our group were vital to my growth as a
researcher.
iii
Table of Contents
Acknowledgements ....................................................................................................................... ii
List of Tables...................................................................................................................................v
List of Figures............................................................................................................................... vi
Abstract........................................................................................................................................ vii
Chapter 1:
Introduction.................................................................................................................................1
1.1 Introduction........................................................................................................................1
1.2 Static thermal emission control..........................................................................................2
1.3 Static thermal emission control at high temperatures........................................................4
1.4 Electrically tunable thermal emission control....................................................................5
1.5 Temperature tunable thermal emission control..................................................................6
1.6 Methods..............................................................................................................................9
Chapter 2:
Design and optimization of high emissivity coating for high-temperature
environments................................................................................................................................12
2.1 Introduction......................................................................................................................12
2.2 Results and discussion .....................................................................................................13
2.3 Conclusion .......................................................................................................................23
Chapter 3:
Symmetry breaking of dark-mode metamaterials for voltage-switchable infrared
absorption .....................................................................................................................................25
3.1 Introduction......................................................................................................................25
3.2 Results and Discussion ....................................................................................................26
3.3 Conclusion .......................................................................................................................32
Chapter 4:
Multilayer planar structure for optimized passive thermal homeostasis ............................33
4.1 Introduction......................................................................................................................33
4.2 Optimization of planar homeostasis devices....................................................................35
4.3 Discussion of performance metrics..................................................................................39
4.4 Discussion........................................................................................................................42
4.5 Conclusion .......................................................................................................................44
4.6 Supplementary .................................................................................................................45
Chapter 5:
iv
Optimization of stacked Fabry-Perot cavities for VO2-based broadband adaptive
thermal radiators.........................................................................................................................49
5.1 Introduction......................................................................................................................49
5.2 Approach..........................................................................................................................51
5.3 Single cavity optimization ...............................................................................................54
5.4 Stacked cavity optimization.............................................................................................57
5.5 Contribution of the individual cavities in stack to total absorption.................................60
5.6 Materials comparison for stacked cavity coating performance .......................................66
5.7 Conclusion .......................................................................................................................69
Chapter 6:
Conclusion and future work
6.1 Static thermal emission control........................................................................................70
6.2 Electrically tunable thermal emission control..................................................................70
6.3 Temperature-tunable thermal emission control................................................................71
References.....................................................................................................................................73
v
List of Tables
Chapter 2:
Table 2.1 Optimized Layer Thicknesses for Periodic Multi-cavity Coatings...........................17
Table 2.2 600nm-MgO-Restricted Optimized Layer Thicknesses............................................19
Chapter 4:
Table 4.1 List of devices found in literature .............................................................................35
Chapter 5:
Table 5.1 Optimized geometry of multi-cavity periodic coatings............................................57
vi
List of Figures
Chapter 1:
Figure 1.1 Diagram of stack represented in TMM......................................................................9
Figure 1.2 Depiction of the 2D Yee cell....................................................................................10
Chapter 2:
Figure 2.1 Schematics of single- and multi-cavity devices ......................................................13
Figure 2.2 Optical constants of MgO, SRO, and STO..............................................................15
Figure 2.3 Performance of the single-cavity coating................................................................16
Figure 2.4 Performance of the optimized multi-cavity coatings...............................................18
Figure 2.5 Performance of the optimized multi-cavity coatings with thickness limits ............21
Figure 2.6 Performance comparison of the periodic and aperiodic 3 cavity coatings..............22
Chapter 3:
Figure 3.1 Schematic and absorption spectrum of a single MIM unit cell...............................26
Figure 3.2 Schematic and absorption spectrum of a coupled MIM unit cell............................28
Figure 3.3 Carrier concentration of GaAs as a function of applied voltage .............................29
Figure 3.4 Refractive index of GaAs as a function of applied voltage.....................................29
Figure 3.5 Tunable on/off switching of a narrowband absorption peak ...................................30
Figure 3.6 Geometric tuning of the coupled MIM structure.....................................................31
Chapter 4:
Figure 4.1 Comparison of device structures and tunable emissivities......................................36
Figure 4.2 Schematic and absorption spectrum of single-cavity device...................................37
Figure 4.3 Schematic and absorption spectrum of double-cavity device .................................39
Figure 4.4 Temperature regulation performance comparison...................................................41
Figure 4.5 Temperature regulation comparison for varying environments...............................43
Figure 4.6 Refractive index of Si, ZnSe, and VO2....................................................................46
Figure 4.7 Angle-dependence of the three devices...................................................................47
Figure 4.8 Absorption in each layer of the ZnSe devices.........................................................48
Chapter 5:
Figure 5.1 Operational modes of an adaptive thermal radiator ................................................52
Figure 5.2 Effects of a constant (n, k) spacer on the performance of an ATR..........................55
Figure 5.3 Schematics and absorption spectra of multi-cavity coatings...................................58
Figure 5.4 Absorption in each layer of the multi-cavity coatings in the hot state ....................61
Figure 5.5 Absorption in each layer of the multi-cavity coatings in the cold state...................64
Figure 5.6 Comprehensive study of the performance of real materials as spacer layers..........67
vii
Abstract
In this dissertation, we use computer simulations and optimization methodsto study how to control
infrared thermal emission in small-scale nanophotonic devices.
Our first goal is to design a broadband, high emissivity coating for extreme temperature
environments. Previous research has focused on larger-scale systems, while we use
microstructured designs. We analyze the static thermal emission control of a layered Fabry-Perot
cavity coating designed for high broadband emissivity in high temperature environments. We find
that an optimized, non-uniform multi-cavity coating achieves the best performance with minimal
material growth needed.
Our next goal is designing a tunable, narrowband emission peak that can be turned on and off,
with nearly 100% modulation. We study and optimize a coupled metal-insulator-metal (MIM)
structure using the III-V semiconductor, GaAs, as the insulating layer. The coupled design creates
a dark mode that cannot interact with a normally-incident plane wave due to symmetry restrictions.
By electrically tuning one of the coupled resonators, we can break symmetry and enable coupling
to the dark mode. This results in an on/off switchable narrowband resonance with nearly 0 to 1
absorption modulation.
Our final goal is to design of a temperature-tunable, broadband emitter for use as an adaptive
thermal radiator (ATR). We focus on planar, multi-cavity Fabry-Perot designs using the phase
change material, VO2. We find that the tunable emission of the ATR can be improved by optimizing
spacer layer thickness, selecting optimal spacer materials, and cascading Fabry-Perot cavities.
Chapter 1
Introduction
1.1 Introduction
Thermal radiation is a fundamental process by which all objects with nonzero temperature
emit light. Most of the objects we use and interact with are near room temperature, which
corresponds to emission primarily in the infrared spectrum. Emissivity is a measure of an object's
efficiency in emitting energy as radiation. Emissivity can vary between 0 and 1, with 1
corresponding to the blackbody. Rough black surfaces, like asphalt, tend to have a high emissivity.
Smooth, polished metals tend to have a low emissivity. Broadly, each material has its own spectral
emissivity. Spectral emissivity also varies from 0 to 1 but is dependent on wavelength. For
example, an object may have high spectral emissivity in one region of the infrared spectrum and
low emissivity in another region. One example of this is the unique absorption/emission lines used
to identify elements and molecules. Real materials have a dispersive, complex refractive index,
which makes selecting the best material for a desired effect a nontrivial problem. Many times, the
optimal material for a certain objective does not exist in nature. Furthermore, some applications
require a tunable emissive feature, meaning an emissive feature that can be changed by adjusting
an input.
A field of research has grown to study how a device can be designed to radiate with a certain
emissivity at a specified location in the infrared spectrum [1-7]. This field is called thermal
emission control. Control over the thermal emission spectrum is useful for various applications.
2
Some of these applications include selective thermal emitters for thermophotovoltaics [7, 8],
thermal camouflage [9], and radiative cooling [10].
In order to meet these areas of interest, there has been extensive research in the field of
nanophotonics to control the thermal emission by using nanostructures. These nanostructures may
be thin layers, gratings, periodic arrays, or more complex geometries. Any of these nanophotonic
structures can be modeled numerically to calculate the reflection (R) and transmission (T) spectra
when illuminated by a plane wave source. Absorption (A) can then be taken as 𝐴𝐴 = 1 − 𝑅𝑅 − 𝑇𝑇.
Kirchhoff’s Law of thermal radiation states that at thermal equilibrium, the spectral absorption of
an object is equal to its spectral emission. By assuming thermal equilibrium and applying
Kirchhoff’s Law, one can equate the absorption and emissivity spectra. Therefore, we can
effectively calculate the spectral emissivity of a nanophotonic device through numerical methods.
Using the right geometry and materials for the nanostructures is crucial to achieve the desired
emissive features. There are a wide range of geometries used in nanophotonic designs, including
cavities [11-16], photonic crystals [7, 17, 18], gratings [19-21], and metamaterials [22, 23].
Additionally, there are different types of thermal emission control.
1.2 Static thermal emission control
The first type of thermal emission control in which we are interested is static. Designs for
static thermal emission control do not require a tunable material. A static emissive feature’s
amplitude and spectral position remain constant and do not depend on an external input. The static
emissive feature can be either narrowband [7], meaning in a narrow wavelength range, or
broadband [24], meaning over a large wavelength range. A narrowband feature typically would
look like a sharp peak or dip in the spectral emissivity. The spectral location, amplitude, and width
of the peak are all possible figures of merit for the design objective [25]. Additionally, one may
3
also care about the direction of the emission. The directional, or angular, control of thermal
emission is another common figure of merit for certain designs. Many strategies have been studied
towards the directional control of thermal emission [26].
A broadband feature would typically be a high or low amplitude spectral emissivity over a
large wavelength range. Ideally, this would look like a flat line at 0 (low) or 1 (high) if one were
to plot spectral emissivity as a function of wavelength. Sometimes one may even want low
emissivity in one region and high emissivity in another. In these cases, it is useful to define the
total emissivity [13]. Total emissivity is defined as the wavelength-integrated irradiance of a
graybody at temperature T normalized to that of a blackbody, IBB, at the same temperature:
𝜺𝜺𝒕𝒕𝒕𝒕𝒕𝒕,𝑻𝑻 = ∫𝒅𝒅𝒅𝒅⋅𝑰𝑰𝑩𝑩𝑩𝑩(𝝀𝝀,𝑻𝑻)⋅𝜺𝜺(𝝀𝝀,𝑻𝑻)
∫𝒅𝒅𝒅𝒅⋅𝑰𝑰𝑩𝑩𝑩𝑩(𝝀𝝀,𝑻𝑻) (1.1)
Equation 1.1 can be used to calculate the total emissivity over a specific wavelength range,
defined by the integration limits. For the case of desired high and low emissivity, one would want
a total emissivity of 1 or 0, respectively. For the case of the high emissivity in one range and low
in another, one would integrate over those regions separately.
There has been extensive research towards statically controlling the spectral and angular
properties of emission. An early demonstration of spectral control of thermal emission utilizing a
metamaterial design was done by Sai, et al. in 2001 [1]. They showed that a metasurface consisting
of an array of reverse-pyramid cavities can produce a peak in thermal emission. A letter in 2002
by Greffet, et al. [2] showed angular control of thermal emission by patterning a microstructured
grating onto a polar material, SiC.
The review article by Inoue, et al. from 2014 [27] provides a comprehensive overview of the
research conducted up to that time. One of the most notable papers by Liu, et al. [7] combined
4
metamaterial cross designs to demonstrate a dual-band emitter. They showed that combining up to
16 of these individual cross designs into a unit cell can result in a more broadband response.
More recently, the work has been focused on combining spectral and directional control of
thermal emission. For example, the work by Qu, et al. in 2020 [28] combined an emitter with a 1D
photonic crystal stack to achieve a directional and narrowband thermal emitter. Not long after, a
directional and broadband thermal emitter was studied by Xu, et al. [29] in 2021. Their design
utlilized a gradient stack to achieve high emissivity with directional control. Even more recently,
Yu, et al. [30] investigated asymmetric directional thermal emission control in 2023, which they
achieved by introducing periodic perturbations into a metagrating design.
1.3 Static thermal emission control at high temperatures
The bulk of the work done in the field of static thermal emission control is at room
temperature, and it is much less studied at higher temperatures. Achieving thermal emission control
at high temperatures requires the use of materials that can withstand those conditions and,
importantly, not deform or melt. In 2003, Sai, et al. [3] used a 2D tungsten grating to achieve
spectral control of thermal emission and thermal stability. They report that after heating the grating
to 1400K, the tungsten grating’s reflectance spectrum remained unchanged. Another work by
Arpin, et al. [31] in 2013 demonstrated thermal emission control at high temperatures (1400°C)
using tungsten photonic crystals. They showed that the tungsten PCs had high thermal stability by
heating them up to 1400°C and reexamining them under a microscope. Their design achieved a
high spectral emissivity that coincided with the blackbody’s peak wavelength at 1400°C.
Although tungsten gratings and photonic crystals can withstand the high temperature
environments and produce narrowband peaks, these designs require lithography for fabrication. A
simpler, planar design utilizing alternating layers of immiscible oxides was used by McSherry, et
5
al. [32] in 2022. They showed that the interfaces of the alternating oxides in the stack remained
sharply contrasted after annealing to 1100°C. Similarly, Gong, et al. [24] used a bilayer of B4C on
AlN, both of which have a melting point above 2000°C, to achieve a broadband (1.1-1.65µm)
absorption near 95%. While this work is impressive, the broadband wavelength range is somewhat
limited and does not fully capture the blackbody spectrum.
In this work, we study planar, Fabry-Perot designs of coatings using high-T materials for high
broadband (500nm-8µm) emissivity. We find that a periodic, multi-cavity Fabry-Perot design
consisting of the absorptive oxide, SRO, and the transparent oxide, MgO, can achieve a total
emissivity integrated over the wavelength range of 500nm-8µm up to 0.968. However, this design
requires substantial material growth that exceeds the capabilities of PLD. Alternatively, we studied
an aperiodic, multi-cavity Fabry-Perot design consisting of the same materials that achieves a
comparable total emissivity of 0.94 while requiring significantly less material growth.
1.4 Electrically tunable thermal emission control
Designs for tunable emission control must use at least one material with tunable optical
properties. Electrically tunable devices are typically based on materials such as graphene [33-35],
ITO [36-38], or III-V semiconductors [39]. The optical properties of each of these materials
changes when electrically tuned by an applied voltage. The changes in their refractive indices can
lead to dramatic shifts in an emissive feature’s amplitude or spectral position. Controlling the
amplitude of an emissive feature can have many applications in optical modulators, sensing, and
infrared communications. This control of the amplitude of a narrowband absorption/emission peak
is defined as absorption, or emission, modulation. A tunable peak that can effectively be switched
on and off would have a modulation of 100%.
6
One of the most popular material choices for the purpose of emission/absorption amplitude
switching is graphene. In 2015, Brar, et al. [35] studied demonstrated that their design utilizing
graphene nanoresonators could successfully modulate emission by ~2.5% at a specific wavelength.
In 2018, Kim, et al. [33] used graphene ribbons in combination with metallic antennas to enhance
coupling and achieved nearly 72% absorption modulation.
Other materials that have been studied for emissive amplitude include Indium Tin Oxide
(ITO), which is a transparent conducting oxide, and GaAs, which is a III-V material. Park, et al.
[38] investigated a metal-insulator-metal (MIM) design in 2015 consisting of Au, ITO, and HfO2.
They found that this design achieves a modulation of ~15%. One of the most notable works in this
field by Inoue, et al. [39] in 2014, used GaAs as the electrically tunable material and showed an
electrically switchable, narrowband thermal emission peak with an amplitude modulation of
~50%.
While all of these previous works represent important advances in the field of switchable,
narrowband thermal emission, they do not achieve full on/off switching. In this work, we endeavor
to design a device capable of near-100% emission modulation. We design a coupled-resonator
metal-insulator-metal (MIM) system that produces an on/off switchable narrowband absorption
peak with an absorption modulation of 97%.
During the preparation of our work on switchable emission, a study by Nagpal, et al. (2023)
[40] was published independently addresses similar objectives. While their study achieves
comparable results in switchable, narrowband thermal emission using graphene, our study
provides unique insights into the use of III-V materials, offering tunable switching capabilities
within a mature material system.
1.5 Temperature tunable thermal emission control
7
Another type of tunability depends on the temperature of the device. The temperature tunable
materials used in these designs are called phase change materials (PCMs) and can come in two
types: volatile or non-volatile. Volatile PCMs transition between their phases whenever its internal
temperature crosses its critical temperature. A common volatile PCM is vanadium dioxide (VO2)
with a critical temperature, Tc, of 68°C (341K) [41]. Non-volatile PCMs, on the other hand, will
remain in their current phase until they undergo a specific heat input signal. One of the most
common non-volatile PCMs is Germanium-Antimony-Tellurium (GST), which will transition into
its crystalline phase when brought above 160°C but requires a quick annealing process above
640°C to return to its amorphous phase [42, 43].
For the purposes of this work, we focus on the volatile PCM, VO2, which can passively switch
between its phases in response to temperature changes. Our goal was to design an adaptive thermal
radiator (ATR) coating that can passively regulate its temperature [11, 13-16, 22, 23, 44, 45]. When
the coating gets hot, the VO2 crosses into its metallic phase and the coating enters its
absorptive/emissive mode. When the coating gets cold, the VO2 returns to its insulating state and
the coating enters its reflective mode. Towards this end, we implemented VO2 into planar, FabryPerot designs to achieve a passively tunable, broadband total emissivity. For these designs, the
figure of merit is the tunable emissivity, which is the difference between the total emissivity,
defined by Equation 1.3, of the hot and cold states:
𝜟𝜟𝜟𝜟 = 𝜺𝜺𝒕𝒕𝒕𝒕𝒕𝒕,𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉 𝑻𝑻 − 𝜺𝜺𝒕𝒕𝒕𝒕𝒕𝒕,𝒍𝒍𝒍𝒍𝒍𝒍 𝑻𝑻 (1.3)
Many designs have been studied to achieve a high tunable emissivity in an adaptive thermal
radiator using VO2. One such design was the array of VO2-coated Si microspheres embedded in
polyethylene, which was studied by Chen, et al. [44] in 2019. The tunable emissivity for this
design, which was calculated using numerical methods, was found to be ~0.59. Another example
8
is the metamaterial design by Sun, et al. [23] in 2018, which uses an array of Al2O3-on-VO2
squares. They measured the tunable emissivity of the metamaterial to be ~0.48.
Moving away from the complexities of lithography and patterning, many planar designs based
on the absorption enhancement of a Fabry-Perot cavity have also been studied. A notable example
is the publication by Kim, et al. [12] in 2019, in which they design an adaptive thermal radiator
consisting of a stack of Au, BaF2, and VO2, from bottom to top. This stack was deposited upsidedown on a Si substrate and optically characterized using an FTIR. They determined that this device
achieved a tunable emissivity, Δε, of ~0.52. We note that having the Si substrate on top of the ATR
greatly reduces the performance, especially in the cold state. Another planar, Fabry-Perot adaptive
thermal radiator that used a 200µm thick silicon layer as the spacer was experimentally realized
by Ahmed Morsy, et al. in 2020 [13] and they measured a tunable emissivity of ~22%.
In our work, we set out to design a planar, Fabry-Perot ATR with the highest possible tunable
emissivity. To begin, we hypothesized that replacing the spacer layer with a more transparent
material, such as ZnSe or BaF2, would greatly enhance the tunable emissivity. This hypothesis was
confirmed by our numerical calculations. Furthermore, we hypothesized that adding a second
Fabry-Perot cavity designed to absorb at a different wavelength than the first would increase the
tunable emissivity by widening the broadband effect. This resulted in a 20% increase in tunable
emissivity when compared to that of the single-cavity ZnSe coating. However, the maximum
tunable emissivity we could reach was still only 0.69. In an effort to further push the tunable
emissivity to its upper bound, we investigated the properties of a theoretical optimal spacer
material and determined that it should have a low real and imaginary part of its refractive index.
We then studied the benefits and limitations of continuing to add more Fabry-Perot cavities.
Ultimately, we found that adding up to three cavities can significantly increase the tunable
9
emissivity up to 0.79, but going beyond three cavities leads to negligible increases in tunable
emissivity.
1.6 Methods
In this work, we aim to tailor the thermal emission of our nanophotonic designs by making
use of electromagnetic numerical methods, such as the Transfer Matrix Method (TMM) and Finite
Difference Time Domain (FDTD), coupled with optimization techniques. Both of these numerical
methods require the complex, dispersive refractive index data for all materials used over the entire
simulated wavelength range. This data is typically acquired from literature or, for increased
accuracy, can be obtained through ellipsometry measurements and fitting.
We use the TMM to calculate the reflection and transmission spectra for a one-dimensional
stack. In the TMM, each layer is represented as a matrix, Mi, and can be multiplied together to get
the overall transfer matrix, M. Then, one can calculate the amplitude and phase of the reflected
and transmitted waves by solving Equation 1.4, where I is the incident plane wave, R is the
reflected wave, and T is the transmitted wave [46, 47]. From the calculated reflection and
transmission, one can calculate the absorption using the equation 𝐴𝐴 = 1 − 𝑅𝑅 − 𝑇𝑇, and absorption
is equal to emission for steady-state temperatures according to Kirchhoff’s Law.
Figure 1.1. Diagram of stack represented in TMM. I is the incident plane wave, R is the reflected wave, and T is
the transmitted wave. Reprinted from ISU TMM Photonic Crystal Simulation Package Quick Start Guide (10) by
author Ming Li, 2005, Iowa State University Research Foundation. Copyright 2005-2009 by Iowa State
University Research Foundation.
10
� 𝑰𝑰
𝑹𝑹� = 𝑴𝑴 �
𝑻𝑻
𝟎𝟎
� (1.4)
When dealing with geometries that vary in two or three dimensions, it is more convenient to
use the FDTD method [48-50]. The two- or three-dimensional space is discretized into a Yee cell,
in which each field component is solved at a different point within the cell. Maxwell’s equations
are solved at each spatial grid cell and updated with time. Similarly to the TMM, one can place
power monitors on either side of the simulation region to calculate the intensity of the reflected
and transmitted waves proportional to that of the incident plane wave. Once again, the equation
𝐴𝐴 = 1 − 𝑅𝑅 − 𝑇𝑇 can be used to calculate the absorption spectra from the reflection and
transmission. Alternatively, one can calculate absorption for a specific volume of the simulation
region by using Equation 1.5, where E is the calculated electric field, ω is the frequency, and ε is
the permittivity of the material in the selected volume.
𝑃𝑃𝑎𝑎𝑎𝑎𝑎𝑎 = −0.5ω|𝐸𝐸|2𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝜀𝜀) (1.5)
Figure 1.2. Depiction of the 2-dimensional Yee cell, where E is the electric field and H is the magnetic field.
Reprinted from Electromagnetic simulation using the FDTD method (50) by author D. M. Sullivan, 2000, IEEE.
Copyright 2000 by IEEE.
11
The geometry of a nanophotonic structure can be optimized by using these numerical methods
in tandem with optimization methods. The geometric parameters of the nanophotonic device are
the optimization variables and the objective function includes either a TMM or FDTD calculation.
When evaluating the objective function, the final value may come directly from the numerical
calculation, or it may require additional processing. This method of optimizing the geometry of a
nanophotonic design can yield results that may not have been immediately obvious to a human
designer attempting to accomplish the same goals.
In this dissertation, all optimization problems are solved using either the simplex method or
the interior point method. The simplex method [51] is implemented by use of the Matlab function
fminsearch in Chapter 4, with all other optimizations in this work using the interior point algorithm
[52, 53] via the fmincon Matlab function. The simplex method is an iterative method for solving
optimization problems without the use of derivatives. Instead, it creates a simplex, which is a shape
with one more vertex than the number of dimensions. It evaluates the solution at each vertex of
the simplex and then reshapes the simplex towards a minimum by either reflecting, expanding, or
contracting. Once the vertex with the best solution found so far is within the simplex, it shrinks
towards that point.
On the other hand, the interior point algorithm is an iterative method that leverages derivatives
for solving optimization problems with equality and inequality constraints. It does so by
incorporating those constraints into a barrier function, which is then added to the objective
function. The barrier function penalizes solutions that approach the boundaries of the feasible
region, which is the set of points that satisfy all constraints. The penalty is gradually decreased as
the optimization progresses, allowing the algorithm to approach an optimal solution that may lie
on the boundary of the feasible region.
12
Chapter 2
Design and optimization of high emissivity coating for hightemperature environments
2.1 Introduction
The field of photonics has grown to include many novel devices that are designed to operate in
standard environmental conditions. Recently, there has been increasing interest in the development
of photonic devices that can operate in extreme environments, such as extremely high temperatures
exceeding 1000°C. This interest has largely been driven by the need for such devices in the field
of thermophotovoltaics (TPVs). Within the scope of TPVs, researchers are primarily focused on
selective emitters that are designed to achieve a high total emissivity in a narrow wavelength range
while withstanding high temperatures [32, 54-56].
Other fields, such as energy harvesting and radiative cooling focus on achieving a high
spectral emissivity across a broadband range of wavelengths. Many approaches towards this end
are being pursued, including ceramics [57, 58], composites [59], photonic microstructures [60],
and bilayers of dielectrics [24]. Although some of these solutions achieve a total emissivity greater
than 0.9, they only consider a small portion of the overall blackbody spectrum.
Total emissivity is defined as the wavelength-integrated irradiance of a graybody at
temperature T normalized to that of a blackbody at the same temperature:
𝜺𝜺𝒕𝒕𝒕𝒕𝒕𝒕,𝑻𝑻 = ∫𝒅𝒅𝒅𝒅⋅𝑰𝑰𝑩𝑩𝑩𝑩(𝝀𝝀,𝑻𝑻)⋅𝜺𝜺(𝝀𝝀,𝑻𝑻)
∫𝒅𝒅𝒅𝒅⋅𝑰𝑰𝑩𝑩𝑩𝑩(𝝀𝝀,𝑻𝑻) (2.1)
13
Therefore, one must integrate over the full wavelength range of the blackbody at the chosen
temperature. Otherwise, the designed device may have low spectral emissivity values beyond the
wavelength integration bound while the blackbody still has a significant, nonzero spectral
emissivity. Here, we design a broadband thermal emitter that operates across the wavelength range
of 500nm – 8 µm at 1500°C.
2.2 Body
Our goal is to design a coating with high total emissivity at temperatures up to 1500°C. The
blackbody spectrum at this temperature ranges from approximately 500nm to 8µm, with a peak at
1.6µm. Towards this end, we wish to design a device with a Fabry-Perot enhanced absorption
resonance [11-16, 61, 62]. Absorption and emissivity are equal in steady state at a given
temperature T according to Kirchoff’s Law. Therefore, a material with high absorption in this
wavelength range is necessary to achieve high emissivity values. Additionally, we require a
Figure 2.1. (a) Schematic of a single-cavity device made up of a transparent dielectric (MgO), a lossy oxide
(SRO), and a substrate layer (STO). The transparent layer acts as an anti-reflection coating and the lossy oxide
acts as the absorber. (b) Schematic of a multiple-cavity device made up of the same materials. This multi-cavity
device has N cavities, consisting of a single MgO and SRO layer each.
14
material with low loss in the near- to mid- infrared. Our chosen absorptive and transparent layers
are SrRuO3 (SRO) and MgO, respectively, since they are known to be compatible with each other
[63, 64] and our substrate material, STO, for growth via pulsed laser deposition (PLD).
We first consider a simple bilayer cavity structure with MgO on top to act as an anti-reflection
layer, SRO as our absorber, and STO as the substrate. The schematic for this bilayer structure is
shown in Figure 2.1(a). Next, we investigate the effects of adding additional identical cavities
composed of MgO and SRO to the stack. The schematic for the multi-cavity device is shown in
Figure 2.1(b), where the number of identical cavities is denoted as N.
To accurately model this system, we performed ellipsometry measurements on all three of our
materials. We note that these measurements were taken at room temperature, and the results may
change when done at high temperatures. The optical constants, n and k, were fitted in the
ellipsometry software. However, the ellipsometer used is limited to a minimum wavelength of 1.5
µm, so we used Lumerical’s material fitting software to fit the optical constants and extrapolate
out to 500nm. The fitted optical constants, n and k, are plotted in Figure 2.2. The optical constants
for MgO are plotted in Figure 2.2(a), where one may note that the k value has a low value of ~10-
1 across the entire wavelength range of interest. SRO, the absorptive material, has a much higher
k value of ~10, as shown in Figure 2.2(b). The optical constants for our substrate, STO, are plotted
in Figure 2.2(c) and we note that it also has a low k value and is not absorptive in this range.
We used the optical constants obtained from the ellipsometry fit in our Transfer Matrix
Method (TMM) [46] calculations for the single-cavity coating shown in Figure 2.3(a). We began
by calculating the total emissivity for a sweep of both MgO and SRO thickness, while holding the
STO substrate constant at 500µm thick. The design space is shown in Figure 2.3(b), where the
MgO thickness sweep is along the y-axis and the SRO thickness sweep is along the x-axis. The
15
optimal stack with the largest total emissivity occurs at an MgO thickness of 10µm and SRO
thickness of 150nm with a total emissivity of 0.958.
We calculated the reflection, transmission, and absorption spectra for a normally-incident
plane wave interacting with the single-cavity device shown in Figure 2.3(a). To get a snapshot of
what the absorption looks like, we selected a few sample spectra with varying MgO thickness, d,
(0.5, 1.5, and 2.5µm) and a constant SRO thickness of 30nm. These absorption spectra are plotted
in Figure 2.3(c), where the green, blue, and red curves correspond to MgO thicknesses of 0.5, 1.5,
and 2.5µm. We note that as the MgO thickness increases, the absorption peak shifts up in
Figure 2.2. Optical constants, n and k, obtained through ellipsometry measurements and fitting for (a) MgO, (b)
SRO, and (c) STO.
16
wavelength. Additionally, as MgO thickness is increased and the resonant wavelength increases,
we begin to see additional resonant peaks appear in the lower wavelengths. These features are
characteristic of a Fabry-Perot resonant cavity. We also included the normalized blackbody
radiation curve at 1500°C plotted as the black line Figure 2.3(c). Although the fundamental
Figure 2.3. (a) Schematic of the single-cavity coating with varying MgO thickness, d. (b) Emissivity design
space for the single-cavity device with varying MgO thickness on the y-axis and varying SRO thickness on the
x-axis. The z-axis (colorbar) is the integrated emissivity over the spectral range of 500nm-10µm. The optimum
has an MgO thickness of 600nm and an SRO thickness of 30nm. (c) The calculated blackbody spectrum at
1500°C and the calculated absorption spectra for the single-cavity device with varying MgO thickness, d and
fixed SRO thickness of 30nm. As d increases, the primary peak shifts up in wavelength, which is a characteristic
of the fundamental mode for a Fabry-Perot resonator.
17
absorption peak with the 0.5µm-thick MgO layer coincides more closely with the blackbody peak
wavelength, the absorption magnitude across the spectrum is lower than the stacks with thicker
MgO.
To improve upon our design, we start by introducing additional cavities of MgO and SRO into
the stack, where each MgO and SRO layer has the same respective thickness. We used the Transfer
Matrix Method to calculate the absorption, reflection, and transmission spectra for stacks with 1,
2, 3, 5, and 10 cavities. We optimized the MgO and SRO layer thicknesses by performing a sweep
of both from 0–10µm and 0–150nm, respectively. The optimal thicknesses for the MgO and SRO
layers found from the sweep are reported in Table 1.1. The absorption, reflection, and transmission
spectra for these optimized stacks are plotted in Figure 4 (a), (b), and (c), respectively. As the
number of cavities increases, the magnitude of absorption increases very slightly due to the
increased total material thickness. Since the MgO has a nonzero part of its refractive index, the
maximum emissivity trends towards the maximum thickness of MgO, which is our upper limit of
10 µm in this case. There is little difference between the spectra for the optimized stacks above 3
cavities.
Table 2.1. Optimized Layer Thicknesses for Periodic Multi-cavity Coatings
Number of Cavities ε MgO Layers (µm) SRO Layers (nm)
1 0.958 10 150
2 0.961 10 5
3 0.961 10 0
5 0.961 10 0
10 0.961 10 0
18
Inspecting the absorption and reflection spectra, one may notice that Fabry-Perot fringes are
present for only the 1 and 2-cavity cases. They are no longer present in the 3+ cavity cases since
the SRO layer thickness goes to zero, eliminating those cavity effects. The fringes have similar
frequency in the 1 and 2-cavity cases due to the similarity of their MgO thicknesses. The slight
offset we see between the peaks of the red and blue curves is attributed to the difference in their
respective SRO layer thicknesses.
Figure 2.4. (a) Comparison of the absorption spectra for optimized multi-cavity devices with 1, 2, 3, 5, and 10
identical cavities. (b) Comparison of the reflection spectra. (c) Comparison of the transmission spectra. (d) Total,
normal emissivity plotted with increasing number of identical, optimized cavities.
19
The 3, 5, and 10 cavity devices have nearly identical optimized emissivity, absorption,
reflection, and transmission values with identical optimized layer thicknesses; therefore, we only
have the 3-cavity case plotted in Figure 2.4 (a, b, & c). Furthermore, this trend indicates that with
a large enough MgO layer, SRO is unnecessary. However, thicker layers would be challenging for
fabrication via PLD. To remedy this, we could instead consider a case where we restrict the MgO
thickness to a maximum of 600nm.
We reoptimized the periodic multi-cavity coatings with the restriction of keeping MgO layers
less than 600nm thick. We also added a case with 20 cavities. The restricted optimized layer
thicknesses for the 1, 2, 3, 5, 10, and 20 cavity cases are shown along with their respective
emissivities in Table 1.2. When we apply this thickness restriction of 600nm on the MgO layers,
we find that including SRO is more necessary since SRO thickness is nonzero for all the restricted
cases. The 1, 2, 3, and 5 cavity cases all optimized towards the maximum allowed MgO thickness,
600nm, which is similar to the previous optimization. On the other hand, the 10 and 20-cavity
cases resulted in local maxima with optimal MgO thicknesses that are not on the edge of the sweep
space. In fact, the 20-cavity, MgO-restricted case resulted in a emissivity (0.968) greater than the
10-cavity, MgO-unrestricted case (0.961) with significantly less grown MgO as well. The MgOrestricted case only requires 6.1 µm of MgO and SRO growth, while the MgO-unrestricted case
requires a total 100 µm of MgO growth to achieve that lesser emissivity. Therefore, it is actually
beneficial to limit the MgO layer thickness and allow for more cavities.
Table 2.2. 600nm-MgO-Restricted Optimized Layer Thicknesses
Number of Cavities ε MgO Layers (nm) SRO Layers (nm)
1 0.642 600 30
2 0.801 600 20
20
Figure 2.5(a) shows the absorption spectra for the optimized, MgO-restricted multiple cavity
coatings. Since the thickness of the MgO layers are much smaller than the previous, unrestricted
cases, the Fabry-Perot fringes are much wider, and the fundamental maxima are within our
wavelength range of interest. The spectral location of the fundamental Fabry-Perot peak depends
on both the MgO and SRO thicknesses. This is why the fundamental peaks for the 1, 2, 3, and 5-
cavity coatings, with about double the thickness of MgO per cavity, appear at larger wavelengths
than the 10 and 20-cavity coatings. Physically, it would make sense that to maximize emissivity
one would want the fundamental peak to coincide with the location of the blackbody peak.
However, there is a tradeoff between peak location and amplitude that must be considered. Taking
the 1-cavity case as an example, the optimal total emissivity is 0.642 when the fundamental
absorption peak is located at 4.03 µm and the blackbody peak is at 1.6 µm. The off-optimal
geometries, although possibly producing a Fabry-Perot peak closer to the spectral location of the
blackbody peak, have lower total emissivity.
The transmission through the multi-cavity stacks is plotted in Figure 2.5(c). With a single thin
MgO and SRO cavity, there is substantial transmission through the stack. By increasing the number
of cavities, we reduce the transmission and boost the absorption, or emissivity, considerably.
Therefore, we maintain that the 20-cavity periodic coating is our best design yet with an emissivity
3 0.862 600 15
5 0.913 600 10
10 0.952 340 10
20 0.968 300 5
21
of 0.968 and only 6.1 µm of material growth required. The total thickness of the optimized stack,
excluding the STO substrate layer, is plotted in blue alongside the optimized total, normal
emissivity in red in Figure 2.5(d). As expected, additional cavities require more material to be
grown. The coatings with up to 5 cavities follow a mostly linear trend as their optimal MgO
thickness hits the upper limit of our allowed design space. The 10 and 20-cavity coatings, however,
Figure 2.5. (a) Comparison of the absorption spectra for optimized multi-cavity devices with 1, 2, 3, 5, 10, and
20 identical cavities with MgO layer thickness restricted to less than 600nm. (b) Comparison of the reflection
spectra. (c) Comparison of the transmission spectra. (d) Total, normal emissivity plotted with increasing number
of identical, optimized cavities.
22
do not follow the same trend. The optimal MgO thickness for these two cases occurs at around
300nm, which is not on the boundary of the allowed thicknesses. The reason for this is the same
as described above when we discussed the shift in fundamental Fabry-Perot peak location seen in
Figure 2.5(a). Although the 10 and 20-cavity coating achieve high total normal emissivities of
0.952 and 0.968, they still require over 3 µm of material growth, which is still out of the realm of
feasibility for PLD.
Therefore, we investigate an alternative approach towards increasing the total emissivity
value. Instead of adding cavities with identical optimized thicknesses of MgO and SRO, we
optimize each layer individually. For reference, we have provided the absorption spectrum and
schematic of the previous 3-cavity stack in Figure 2.5(a). We note that the MgO and SRO layers
in this schematic are of equal respective thicknesses. The absorption spectrum has a peak above
4µm and a large di p at ~2µm. This large dip is undesirable being so close to the peak wavelength
for blackbody radiation at 1500°C. The integrated total emissivity for this stack is 0.86 with a total
material thickness of 1.845µm, not including the substrate.
Figure 2.6. (a) Absorption spectra of the optimized 3-cavity device with the restriction that each cavity must
have equal layer thicknesses. The inset is a schematic of the device’s geometry. (b) Absorption spectra of the
optimized 3-cavity device where each layer is individually optimized. The inset is a schematic of the device’s
geometry.
23
The stack with individually optimized layers is presented schematically as an inset within its
calculated absorption spectrum in Figure 2.5(b). Allowing the layer thicknesses to optimize
individually enables each cavity to have its own resonant wavelength, which results in additional
absorption peaks. The magnitude of absorption is greater than 0.9 for most of the region from 0.5–
4µm. Although there is still a dip present in this key region of the absorption spectrum, it is not as
large as the one seen in Figure 2.5(a). The integrated total emissivity is calculated to be 0.94 with
only 1.416µm of total material, excluding the substrate. This total emissivity value is nearly as
high as the predicted emissivity value for the 10-cavity stack which required 3.5µm of total
material, excluding the substrate. Thus, the individually optimized 3-cavity stack is able to match
the performance of the pair-optimized 10-cavity stack with less than a third of the required
material.
2.3 Conclusion
In this work, we optimized a planar design of alternating transparent and metallic oxides to
maximize total emissivity across the spectrum of 500 nm – 8 µm. The designs achieving the highest
total emissivity values are the ones whose Fabry-Perot resonances coincide more closely with the
peak blackbody radiation at 1500°C. The 20-cavity coating has the highest calculated total
emissivity of 0.968 has the highest emissivity value. However, these designs require tens of
microns of material growth. If we restrict the MgO thickness to 600nm, we showed that a 3-cavity
coating can achieve a calculated total emissivity of 0.86 with significantly reduced material
growth. However, this method reduces the total emissivity more than desired. Therefore, we
proposed a 3-cavity design with optimized, aperiodic layer thicknesses which achieved a nearly
equivalent calculated total emissivity value of 0.94 while only requiring 1.416 µm of material
24
growth. This optimized, aperiodic design cuts the need for material growth while maintaining a
high total emissivity.
25
Chapter 3
Symmetry breaking of dark-mode metamaterials for voltageswitchable infrared absorption*
*
This chapter has been previously published in Optics Letters, Vol. 48, Issue 9, pp. 2441-2444 (2023)
3.1 Introduction
There has been considerable interest in controlling emission and absorption in the infrared (IR)
wavelength range with artificially engineered materials such as photonic crystals and
metamaterials [4-7, 25, 65-67]. Having control over the IR absorptivity is desirable for applications
in sensing [68-70], thermal management [71-73] and energy harvesting [74, 75]. Recent work has
advanced the study of voltage-tunable metamaterials, including devices based on graphene [33-
35], ITO [36-38], and III-V semiconductors [39]. These devices rely on refractive index tuning to
either shift or split the absorption resonance, changing the absorption wavelength. In this work,
we propose an alternative mechanism for absorption control. Our approach uses an applied voltage
to break spatial symmetry, creating a spectral absorption feature.
We consider absorbers consisting of coupled, metal-insulator-metal (MIM) resonators.
Isolated MIM resonators are known to support two kinds of modes: bright and dark [76]. Bright
modes can couple to a normally-incident plane wave, giving rise to an absorption peak in the
spectrum. On the other hand, dark modes are symmetry-forbidden and hence, cannot couple to a
normally-incident plane wave. We study a system consisting of two coupled, identical bright
resonators that supports a bright and a dark supermode. By breaking the symmetry of this system,
one can cause the dark supermode to couple to a normally-incident plane wave, potentially
26
producing an absorption peak in the spectrum. While symmetry breaking has previously been used
to create high quality factor modes in coupled resonance systems [77, 78], these studies involved
static, rather than tunable, structures.
Below, we propose an implementation of symmetry-breaking induced radiative coupling in a
tunable, III-V semiconductor device. The III-V material forms the insulator layer of the MIM
resonator and contains a p-i-n junction to allow the tuning of refractive index with applied voltage.
By optimizing our device geometry, we design switchable resonances in the long-wave IR (LWIR)
with an amplitude modulation of approximately 97% and quality factor (Q) close to 100. Our
results suggest new possibilities for shaping IR absorption that could benefit applications such as
sensing and photonics-assisted encrypted communication [79].
3.2 Results and Discussion
We calculate the absorption spectrum of the structure in Figure 3.1(a) using Lumerical FDTD. The
optical constants of gold and intrinsic GaAs are taken from the built-in material library while those
of the heavily doped layers are calculated using the Drude semiconductor approximation,
discussed later in the paper. We use periodic boundary conditions along the x direction and PML
along the y direction. The structure is illuminated with a normally-incident plane wave source
polarized along the x direction. Reflection (R) as a function of wavelength is calculated using a
power flux monitor. Since the gold substrate acts as a back reflector, transmission through the
structure is zero. Therefore, absorption is given as 1-R.
Figure 1(b) shows the absorption spectrum for the structure having dimensions indicated in
Figure 1(a). The absorption peak at 9.2 μm corresponds to the bright mode of the individual MIM
resonators of the array. The Hz field profile on resonance for a single unit cell is shown in the inset
of Figure 1(b) and matches well with that expected from literature [80]. From symmetry Figure 3.1. (a) Schematic of one unit cell of the periodic device, containing a single MIM resonator with a gold back
reflector. (b) Absorption spectrum for the single MIM resonator with the Hz field profile at resonant absorption in
the inset.
27
arguments, an Hz profile that is even with respect to the mirror plane shown (green dashed line)
has the correct symmetry to couple to a normally incident plane wave with E-field in the x direction
[76].
Next, we consider a periodic array of two coupled, identical MIM resonators (unit cell shown
in Figure 3.2(a)). The corresponding absorption spectrum is shown in Figure 3.2(b). A system
consisting of two identical bright resonators supports a bright and a dark supermode with respect
to the midplane between the resonators (green dashed line). For the considered structure, the bright
supermode contributes an absorption peak at about 9.32 μm (black curve). The dark supermode
does not couple to a normally-incident plane wave and hence does not show up in the plane-wave
spectrum. To determine the spectral location of the dark supermode resonance, we excite the
structure using a cloud of randomly oriented dipoles and record the field intensity using a cluster
of time monitors. The red curve in Figure 3.2(b) shows the normalized sum of the Fourier
transforms of field intensities recorded by all the time monitors. The dark supermode resonance is
located at a wavelength of 6.8µm.
The Hz field profiles corresponding to the bright and dark supermodes are shown in the inset
of Figure 3.2(b). One can observe that Hz for the bright supermode is even with respect to the
mirror plane denoted by the green dashed line. Hence, the bright supermode can couple to the
plane wave, producing an absorption peak in the spectrum. On the other hand, Hz for the dark
supermode is odd and hence does not couple to the plane wave. The dark mode is thus said to be
symmetry-forbidden.
One way to break the symmetry of the structure in Figure 3.2(a) is to make the resonators in
each unit cell non-identical. This can potentially cause the dark supermode to couple to a normallyincident plane wave, producing an absorption peak in the spectrum. Below, we explore the effect
28
of electrically tuning the refractive index (RI) of the spacer layer of one of the resonators in each
unit cell on the spectral properties of the structure.
The RI of GaAs can be tuned by changing its carrier concentration (CC) via an applied voltage.
We use Lumerical CHARGE to numerically investigate the effect of applied voltage on the n-type
CC in the intrinsic GaAs spacer layer. We simulate a single MIM strip with a 100 nm gold cap, 11
nm n++ GaAs, 970 nm intrinsic GaAs, 46 nm p++ GaAs, and a semi-infinite gold substrate having
the same length as the strip. We use steady-state boundary conditions and set the gold cap as the
top contact with a voltage of 0V and the gold substrate as the bottom contact with voltage varying
from -0.5 to 2V. The heavily doped n++ and p++ layers are defined using a constant doping region
and set to a CC of 5x1018cm-3
.
Figure 3.3(a) shows the spatial-dependence of the n-type CC in the GaAs layers with an
applied voltage of 0 and 1.65V (top and bottom panels, respectively). In the case of zero applied
voltage, the n++ layer has the largest n-type CC, as expected. With an applied voltage of 1.65V,
the intrinsic GaAs layer has a CC value of 5.55x1018cm-3 at y = 513.5nm. We refer to this as the
midpoint CC. We use this value for RI calculations instead of the spatial average over all the GaAs
Figure 3.2. (a) Two-resonator coupled MIM system with the same layer thicknesses as the single resonator. (b)
Absorption spectrum for the two-resonator coupled MIM excited by incident plane wave (black curve) and dipole
cloud (red curve). The Hz field profile insets correspond to the peaks closest to them – one from plane wave
excitation and one from dipole cloud excitation.
29
as averaging will include regions close to the heavily doped interface, which may skew the data.
Figure 3.3(b) shows the variation of midpoint CC with applied voltage. The midpoint CC of GaAs
increases from about 2x106
cm-3 at 0V to 1x1019cm-3 at 1.5V, after which it appears to plateau.
We use the CC values to calculate the optical constants of GaAs as a function of applied
voltage. For this purpose, we use the semiconductor Drude approximation described in ref. [81].
The calculated real and imaginary parts of the RI for a few of the values of the applied voltages
are plotted in Figure 3.4(a) & (b), respectively. The model predicts that at a wavelength of 6.8 μm,
the real part of RI, n, can be reduced from 3.3 to 2.7 by increasing the applied voltage from 0 to
1.65V.
Figure 3.3. (a) n-type CC map of the strip’s GaAs stack at 0 and 1.65V. (b) Midpoint n-type CC within the intrinsic
GaAs layer as a function of applied voltage.
Figure 3.4. The (a) real and (b) imaginary parts of the RI as a function of wavelength for several applied voltages,
calculated using the semiconductor Drude correction.
30
Next, we optimize the coupled resonator structure shown in Figure 3.5(a) to produce a
switchable resonance with a high Q and large amplitude modulation with applied voltage. The
structure is characterized by the parameters L, p, D, dn, d, and dp. We set L to 1.35µm to produce
resonances in the 8 - 9 µm wavelength range. The other parameters are optimized using the fmincon
function in MATLAB interfaced with Lumerical FDTD to minimize an objective function. We
choose our objective function as the negative product of Q and resonance amplitude modulation.
Here, amplitude modulation is defined as the difference in the absorptivity value on resonance for
an applied voltage of 0V and 1.65V.
Figure 3.5(c) presents the absorption spectrum for the optimized structure; optimized
parameters are given in the caption. With zero applied voltage, the structure does not produce an
absorption peak in the spectrum (black curve). When a voltage of 1.65V is applied, the structure
produces an absorption peak at 8.2 μm with an amplitude modulation of ~97% and a Q-factor of
90 (red curve). This demonstrates that breaking the symmetry of the structure indeed causes the
Figure 3.5. Device structure where: L is the length of the strips, p is the periodicity, D is the separation between
strips, and dn, d, dp, are the thicknesses of the n++, intrinsic, and p++ GaAs layers, respectively. For all figures
p=3.54µm, L=1.35µm, dn=11nm, d=970nm, and dp=46nm. (b) Hz field profile of the two-strip coupled device at
dark mode resonance (λ=8.2µm) with the left strip tuned with a voltage of 1.65V. (c) Absorption spectra when both
strips have no applied voltage (black line) and when the left strip has an applied voltage of 1.65V [1.5V] (red line
[bl li ])
31
dark supermode to couple to a normally-incident plane wave. The resulting absorption peak can
be switched on and off by changing the applied voltage.
Figure 3.5(c) also shows the effect of using a smaller applied voltage. When the device is
switched from 0V to 1.5V, the spectral absorption peak appears at higher wavelength than for
1.65V. Although the amplitude modulation is lower, Q is nearly double (165). Therefore, by
appropriately choosing the on-state voltage, one can control the position and width of the
absorption peak.
In Figure 3.6, we explore the effect of tuning the structural parameters of the optimized device.
Figure 3.6(a) shows the absorption spectra for a few values of the inter-strip separation D at an
applied voltage of 1.65V. Increasing the value of D from 25 to 250 nm causes the peak to blueshift by about 70 nm. This shift is accompanied by a slight reduction in Q and a change in the
amplitude modulation. This analysis indicates that our device retains its functionality as a
switchable absorber even in the presence of fabrication variations.
Lastly, we show that the absorption feature can be tuned by adjusting the strip length. Figure
3.6(b) presents the absorption spectra for different values of strip length L with fixed inter-strip
separation 50nm and applied voltage 1.65V. The resonance red shifts with increasing L. From
Figure 3.6. The (a) Absorption spectra at 1.65V of devices with different strip separation (D). (b) Absorption spectra
of our two-strip coupled device with varying strip length, L.
32
previous work, we expect the wavelength of the individual resonators to increase with strip length;
we observe that the shift in the broken symmetry coupled mode is in the same direction as the shift
in the individual resonator wavelength. We note that for a given unit cell length, p, the values of L
and D must be chosen such that p – (2L + D) > D. This ensures that there is no coupling between
MIM cavities located in adjacent unit cells and the overall structure is not symmetric with an
applied voltage.
3.3 Conclusion
In conclusion, we proposed and numerically investigated a device capable of producing electrically
switchable narrowband resonances in the infrared. The absorber was modeled as a system
consisting of two coupled, identical bright resonators. Each resonator was designed as an array of
Au-GaAs strips on an Au substrate in an MIM configuration. Applying a voltage to one of the
resonators caused the RI of its spacer GaAs layer to change, breaking the symmetry of the system.
This resulted in the previously-dark supermode to couple to an incoming plane wave, producing
an absorption resonance in the spectrum. We investigated the effect of tuning the voltage as well
as the structural parameters of our device on its spectral response. These analyses validated the
robustness of the device’s switching functionality to fabrication imperfections while revealing an
additional mode of operation as a tunable absorber. Our results pave the way for next-generation
electrically reconfigurable absorbers fabricated using semiconductor growth [82] or transfer
methods. We expect the results could benefit several applications such as sensing, thermal
management, and image encryption.
33
Chaspter 4
Multilayer planar structure for optimized passive thermal
homeostasis*
*
This chapter has been previously published in Optics Materials Express Vol. 12, Issue 4, pp. 1442-1449 (2022)
4.1 Introduction
Thermal regulation has been a wide area of interest for many applications. Active thermal
regulation approaches based on electrical or mechanical tuning have been widely studied [83] but
require power. More recently, passive thermal regulation, or “thermal homeostasis,” utilizing the
phase-change properties of materials has been growing in interest [84]. Solid-state phase change
materials, such as Vanadium Dioxide (VO2), change their crystalline structure at the critical
temperature, thereby changing their optical properties [41]. Changes in the VO2 absorptivity at the
phase transition can result in large changes in emittance.
Previous work has incorporated VO2 in the design of passive, thermal homeostasis devices
based on planar [13, 15, 16, 45, 85-87], flexible planar [88], microsphere [89], and metamaterial
[23, 44, 90] geometries. A common figure of merit is the tunable emittance Δε. The tunable
emittance is defined as the difference in total emittance between the high- and low-temperature
states of VO2, where the total emittance is defined as the wavelength-integrated radiated power
divided by the blackbody reference value. Values from the literature are given in Table 1. The best
experimental device to date is a planar design consisting of a VO2 layer on top, HfO2 middle layer,
and Ag back reflector. This layer structure forms a Fabry-Perot cavity and has a Δε of 0.55 [16].
34
For a new design to be a promising candidate for experimental fabrication and testing, the
value of Δε obtained in a numerical simulation should be at least as large as previous experimental
values. The highest simulated value of Δε to date is 0.8, based on an array of microstructured Si
cones coated in a layer of VO2 [90]. However, this requires a special structure that is difficult to
fabricate and may be impractical for widescale implementation. Another design, based on
microspheres coated with VO2 [44] has a simulated value of 0.59. However, the simulated value
of Δεin an ideal numerical simulation tends to overpredict the experimental value [13]. This design
is thus unlikely to offer improved experimental performance relative to the state of the art.
Here, we propose and optimize a multilayer planar design to maximize the simulated value of
Δε. For comparison, we first consider a simpler Fabry-Perot device based on a stack of VO2, ZnSe
(an infrared transmissive material), and gold. We optimize the device dimensions for this stack to
obtain a calculated Δε of 0.574 in simulation. Using the same materials, we then optimize a
multilayered stack to obtain a calculated Δε of 0.69 in simulation. For the multilayer stack, we find
that the addition of a second Fabry-Perot cavity increases the number of absorption peaks in the
spectrum and reduces the depth of the absorption dip in the metallic state.
We further analyze how the figure of merit Δε relates to temperature-regulation performance.
We define the environment in terms of the power levels absorbed by the device in a hot and cold
state, assuming the device makes a complete phase transition between the two states. We quantify
the temperature-regulation performance by the magnitude of temperature fluctuations experienced
by the device within the environment; smaller fluctuations correspond to better regulation. Under
these assumptions, we find that for a particular environment, higher Δε correspondsto better device
performance. We then compare our device to a constant emissivity material over a range of
environments. We find that the reduction in temperature fluctuations relative to a constant
35
emissivity material is largest when the device is “well matched” to the environment. That is, the
absorbed power in the hot state is just large enough for the device to transition to the metallic state,
while the absorbed power in the cold state is just small enough for the device to transition to the
insulator state. To this end, the high-Δε planar designs studied here will allow optimal performance
in environments with widely varying heat input levels, without the need for micropatterning.
Table 4.1. List of devices found in literature
Δε Reference Type Materials Exp or
Sim
0.69 This Work Planar VO2/ZnSe/VO2/ZnSe/Au Sim
0.574 This Work Planar VO2/ZnSe/Au Sim
0.8 [90] Microstructured
Cones
VO2/Si Sim
0.594 [44] Microspheres VO2/Si/Polyethylene/Al Sim
0.55 [16] Planar VO2/HfO2/Ag Exp
0.52 [45] Planar Si/VO2/BaF2/Au Exp
0.49 [87] Planar VO2/SiO2/Au Exp
0.48 [23] Metamaterial
Squares
VO2/SiO2/Al/Al2O3/Si Exp
0.46 [86] Planar VO2/Si/Al Exp
0.41 [15] Planar VO2/Spacer/Al Exp
0.39 [89] Flexible Planar a-Si:H/SiO2/VO2 on Al Exp
0.25 [22] Metamaterial
Disks
VO2/HfO2/Al Exp
0.22
(0.29)
[13] Planar VO2/Si/Au Exp (Sim)
0.18 [88] Planar VO2/Cu/VO2/Si Exp
4.2 Optimization of planar homeostasis devices
Figure 4.1(a) shows three planar device structures studied in this work. Device 1 is the planar
homeostasis device studied in Ref. [13]. It consists of 62nm of VO2 coated on a 200µm silicon
layer. The device has a 100nm gold back reflector. Figure 4.1(b) shows the normal-incidence total
36
emittance in the metallic and insulating states of VO2, calculated as in Reference [13]. Here, the
total emittance is defined as the thermal radiated power at 330K divided by the blackbody radiated
power at 330K. The optical constants of VO2 were taken from [13], which obtained values through
ellipsometry performed on an ALD-fabricated thin film for the metallic and insulating states. The
optical constants for Si and gold were taken from [91] (see Supplemental Figure 4.6). The
difference in total emittance between the two states is approximately 0.3.
We next investigate the effect of tuning the thickness of the dielectric spacer layer. For this
purpose, we use ZnSe as the spacer material, which has good transparency in the infrared. Figure
2(a) shows a planar structure with a ZnSe intermediate layer, which we refer to as a single-layer
device. We used the built-in Matlab function fminsearch and the Transfer Matrix Method (TMM)
to determine the optimal layer thicknesses for the VO2 and ZnSe, while keeping the gold layer
constant at 100nm. The optimal result was 68nm and 650nm for the VO2 and ZnSe layers,
Figure 4.1. (a) Device structures; (b) Total emittance in metallic and insulating states for devices shown in (a)
37
respectively. The largest difference in total emittance comes from a εmet of 0.631 and εins of 0.057,
leading to a total emittance tunability (Δε) of 0.574.
Comparing the optimal ZnSe single-layer device (Device 2) to our previous Si design (Device
1) in Figure 1, we see that it has a higher total emittance in the metallic state and a lower total
emittance in the insulating state. This increases the total emittance tunability Δε to 0.574, nearly
double that of the Si design. The absorption spectrum for the optimal single-layer ZnSe device can
be seen in Figure 2(b). The metallic absorption is higher than the insulator state absorption over
the 2–30µm range. The peaks seen in the insulating state from 12–25µm can be attributed to the
wavelength-dependent absorptivity of VO2, as observed in [13]. The prominent dip observed at
4µm is due to the Fabry-Perot effect in the cavity formed by the metal-insulator-metal layer
structure.
Physically, a key difference between Device 1 and Device 2 is the thickness of the middle
layer, which acts as a spacer layer in the Fabry-Perot cavity. In our previous work [13], we kept
the silicon layer fixed as 200µm, simply for fabrication convenience. The Fabry-Perot fringes were
Figure 4.2. (a) Single-layer ZnSe device schematic; (b) Absorption spectrum for optimized device with ZnSe
thickness of 650.7 nm
38
spaced very closely, giving rise to a highly oscillatory spectrum. To calculate the total emittance,
this function must be integrated against the broad, blackbody spectrum at 330K. Integrating a
strongly oscillating function over a broad wavelength range necessarily yields a low total emittance
in the metallic state. Reducing the thickness of the spacer layer increases the distance between
Fabry-Perot peaks and dips in wavelength space. Because the materials making up the cavity are
all dispersive, the metallic-state absorption spectrum, shown in Figure 2(b), is modified with
respect to a simple, non-dispersive cavity. However, one can clearly observe a Fabry-Perot dip at
~4µm and a Fabry-Perot peak just below 10µm. The absorption value in the metallic state is > 0.5
across the ~5–17µm range. Integration of this more slowly oscillating curve against the blackbody
spectrum at 330K yields a higher value of total emittance in the metallic state than for our previous
device (Device 1). We note that a qualitatively similar absorption spectrum can be obtained using
an optimized Si spacer layer, though the calculated Δε was lower (< 0.5). Moreover, the overall
physics is very similar to the VO2 / HfO2 / Ag device of Ref. [16], as the absorption spectrum is
qualitatively similar.
To further improve performance, we consider the multilayer device shown in Figure 3(a). To
determine the optimal layer thicknesses, we used the same optimization process described
previously. The initial layer thicknesses were set to 17nm, 750nm, 55nm, and 715nm, from top to
bottom of the stack. The result of the optimization is shown in Figure 3(a). The optimal layer
thicknesses were found to be 3.5nm, 672nm, 145nm, and 365nm, from top to bottom. The
maximized Δε corresponding to these thicknesses was calculated to be 0.69, with εmet = 0.772 and
εins = 0.082.
This increase in Δε from the single-layer device can be better understood looking at the
absorption spectrum in Figure 3(b). Comparing this spectrum to the one in 2(c), the absorption in
39
the metallic state is increased significantly. This is particularly true near 4µm, where the
pronounced Fabry-Perot dip of the single-layer structure has been smoothed. The additional cavity
in the multilayer structure also gives rise to an additional absorption peak between 5 and 10μm.
Although the absorption in the insulating state also increases somewhat, there is an overall
improvement in the difference between the two. We have further verified that the performance at
off-normal angles represents an improvement over both the single layer Si device and the singlelayer ZnSe device (see Supplemental Figure 4.8).
4.3 Discussion of performance metrics
We next examine how an increase in Δε improves the performance of a thermal homeostasis
device. Such devices are designed to passively regulate temperature in a fluctuating environment.
We assume that the environment we are discussing oscillates between a “hot” and a “cold” state.
In Figure 4(a), we assume that the fluctuating environment produces an absorbed power (Pabs) of
680W/m2 in the hot state, and 55W/m2 in the cold state, with a time period of 1 hour. We calculated
Figure 4.3. (a) Multilayer ZnSe device; (b) Absorption spectrum for insulating and metallic states of vanadium
dioxide
40
the resulting temperature fluctuations in the device using the time-dependent heat equation,
following the method of Ref. [13].
Figure 4(b) illustrates the performance of the VO2/ZnSe multilayer device, the VO2/Si singlelayer device, and a constant emissivity material with ε = 0.35. The multilayer device yields the
best performance, reducing the temperature fluctuations to ~25K. This value is significantly
smaller than the temperature fluctuations of the Si single-layer device and the constant emissivity
device, which are ~140K and ~200K, respectively.
To compare the performance of the multilayer device to an ideal device, we define a
generalized performance space. Consider a thermal homeostasis device in an environment that
toggles between a hot state and a cold state. We assume that each state persists long enough for the
temperature to reach steady state. The device takes on steady-state emissivity values εhot and εcold,
which lie between 0 and 1. In steady state, the absorbed and radiated powers are equal (Pabs = Prad),
and we can use Stefan-Boltzman Law to calculate the temperature in each state.
Figure 4(c) plots the temperature difference as a function of εhot and εcold. We assume that εhot
> εcold, which restricts our attention to the portion of Figure 4(c) above the dashed line. The white
region at εcold < 0.08 is excluded from the graph, since the steady-state temperature in the cold state
is too high for the device to undergo a complete phase transition. Looking at the colormap in Figure
4(c), we see that the difference in temperature decreases greatly as we increase εhot and decreases
as we decrease εcold. The best-performing devices have the large difference in emissivity between
the hot and cold states.
For each of the devices shown in Figure 4(b), we can determine the corresponding values of
εhot and εcold. The two emissive states of the VO2 devices can be approximated as two constant
emissivity states with a switch at the critical temperature, Tc = 330K. The three devices are shown
41
by colored dots in 4(c). The temperature difference for the VO2/ZnSe multilayer device is nearly
optimal, while the Tdiff of the Si single-layer device and the constant emissivity material are much
larger.
Depending on the environment in which a device is operated, the values of absorbed power
will change. Figure 4 was plotted for a particular choice of absorbed power in the hot and cold
states, shown in Figure 4(a). To understand how our multilayer device performs in various
environments, we calculated the temperature fluctuations that result from different choices of
absorbed power levels.
Figure 5(a) plots the temperature difference ratio as a function of the absorbed power in the
hot and cold states. The temperature difference ratio is defined as the temperature difference for
the multilayer device divided by the temperature difference for a constant-emissivity value
material with ε = 0.35. Values less than one indicate that the multilayer device reduces temperature
Figure 4.4. (a) Absorbed power as a function of time; (b) Temperature of ZnSe Multilayer Device (solid red), Si
Single-Layer Device (dashed blue), and a 0.35 Constant Emissivity Device (dotted green); (c) Colormap of
temperature difference as a function of hot and cold state emissivities. Values listed next to each device
correspond to their respective cold and hot state emissivities.
42
fluctuations better than a constant-emissivity reference. Smaller values indicate improved
performance.
Figure 5(a) shows that the multilayer device outperforms the constant emissivity device over
the entire range of potential heat states simulated. Even at the device’s worst performance (high
Pabs,high and low Pabs,low, or top, left corner of colormap), the temperature difference ratio is 0.71,
corresponding to a 29% reduction in temperature fluctuations relative to a constant emissivity
device. For low Pabs,high and high Pabs,low (bottom right corner of colormap), the performance of the
multilayer device improves greatly. At about 657 and 55 W/m2
, the multilayer device’s temperature
fluctuations are about 90% smaller than that of the constant emissivity device. The white regions
in Figure 5(a) indicate parameter values outside the range of our quantitative model.
4.4 Discussion
To gain insight into the trends in Figure 5(a), we can consider the hysteresis curve for our
multilayer film, plotted in Figure 5(b). The curve is plotted using the model from Reference [92].
Within this model, the hot and cold states of the device are approximated as constant emissivity
curves, with emissivity values calculated from the electromagnetic simulations (Figure 3). Here,
the values correspond to 0.690 and 0.085, respectively. The constant emissivity curve
corresponding to our ε = 0.35 material is also shown for comparison. The red line indicates the
multilayer device response as it is heated, and the blue line as it is cooled.
From Figure 5(b), we observe that the absorbed power values yielding the best performance
in Figure 5(a), 657 and 55 W/m2
, correspond to values just above and below the hysteresis loop.
For these values, temperature fluctuations are most strongly reduced relative to a constantemissivity reference device. We conclude that a device operates optimally when the heat states of
its environment line up closely to the upper and lower radiative power limits of its hysteresis loop.
43
This leads us to believe that the best PCM-based temperature regulation device for a specific
environment will be tailored specifically for that environment’s heating cycle.
For hot and cold state absorbed powers that fall inside the hysteresis loop (grey region in
Figure 5(b); white regions in Figure 5(a)), the device will not make a complete phase transition.
From the literature [93-95], we expect minor loops to form within the major hysteresis loop [85].
While outside the range of our mathematical model, it is interesting to speculate what may occur
in this region. If the device behavior along the minor loop is qualitatively similar to that of the
major loop, it may also perform better than a constant emissivity reference.
In the analysis above, we have analyzed the performance of various devices assuming given
values of absorbed power. This allows a straightforward comparison between devices with
different cold and hot state emissivities, as well as the illustration of certain general trends. In real
applications, the absorbed power may depend both on the presence of nearby heat sources and
absorption of sunlight. In the latter case, the change in optical properties across the phase transition
Figure 4.5. (a) Ratio of temperature difference between the Multilayer ZnSe device and a 0.35 constant
emissivity device as a function of Pabs,high and Pabs,low; (b) Modeled hysteresis loop of Multilayer ZnSe device.
The blue and red curves correspond to the device’s cooling and heating cycles, respectively. The dashed black
lines mark constant emissivity curves denoted by their labels. The greyed-out area was excluded from the
prediction in (a).
44
will also change the solar absorption of the device. The absorbed power in the “cold” and “hot”
states will thus depend both on the incident solar flux and the state of the device (insulator or
metallic). For the devices presented in this paper, we have found that the solar absorption increases
somewhat across the transition. For use in a dynamically fluctuating solar environment, solar
absorption should ideally decrease across the transition, in order to damp temperature fluctuations
in the device. Future work could incorporate a more complex, multi-band objective function to
achieve this goal.
4.5 Conclusion
In this paper we improved the design of planar, thermal homeostasis devices based on VO2. We
found that replacing the Si device layer with a thinner ZnSe layer strongly increased the total
emissive tunability found in numerical calculations. This quantity, Δε, increased from a calculated
value of 0.3 for our previously published Si device to 0.574 for a ZnSe device. Physically, the
improvement results from reducing the thickness of the Fabry-Perot cavity formed by metallic
VO2 and the gold back reflector, which increases the wavelength spacing between peaks and
valleys of the absorption spectrum. Rather than exhibiting a strongly oscillating spectrum as in
Ref. [13], the absorption spectrum now oscillates more slowly, with values > 0.5 over wavelengths
from approximately 5–17µm. When the absorption spectrum is integrated against the broad
blackbody spectrum at 330K, the more slowly varying spectrum results in a higher value of total
emittance in the metallic state.
Adding a second pair of VO2 and ZnSe layers to form a multilayer device further improves
Δε to a predicted value of 0.69. In the metallic state, the introduction of a second Fabry-Perot
cavity in the stack both introduces an additional absorption peak and reduces the depth of the
lowest absorption dip, resulting in a higher total emittance.
45
We further investigated how the difference in emissivities across the transition affects device
performance. The intuitive notion that a larger switch between εhot and εcold results in better
performance was found to be correct: larger Δε corresponds to smaller temperature fluctuations in
the device. We also found that a device performs optimally when the environment is “matched” to
its hysteresis loop. That is, when the absorbed power levels in the hot / cold states are just large /
small enough for the device to experience a complete phase transition in each cycle, the reduction
in temperature fluctuations relative to a constant-emissivity device is strongest. For larger
fluctuations in the environment, and more widely separated values of absorbed power, the device
will still damp temperature fluctuations, but less strongly than when the environment is matched
to the hysteresis loop. For environmental fluctuations that are too small to result in a complete
phase transition, direct experimental measurements should shed further insight on behavior in this
region and are a fruitful area for future study. We note that one route to experimental fabrication
is provided by ALD growth methods. Both VO2 and ZnSe [96, 97] are compatible with ALD
growth methods, allowing precise control over layer thickness.
4.6 Supplementary
In Figure 4.6, we replot the optical constants for silicon, ZnSe, and VO2 for the convenience of the
reader. The data for silicon and ZnSe are taken from Ref. [91]. The data for VO2 is taken from Ref.
[13] and represents an experimental measurement on ALD-grown films.
46
In Figure 4.7, we plot the total emittance in the metallic state, insulating state, and difference
between the two for all three devices. Figure 4.7(a,b) correspond to the total emittance with TE
and TM incident light, respectively, for the 200μm silicon single-layer device. Figure 4.7(c,d)
correspond to the TE and TM cases, respectively, for the ZnSe single-layer device. Finally, Figure
4.7(e,f) correspond to TE and TM, respectively, for the ZnSe multilayer device.
In Figure 4.8, we plot the absorption in the individual layers of the (a,b) single-layer ZnSe
device and (c,d) multilayer ZnSe device for the insulating and metallic states, respectively. The
absorption primarily happens within the VO2 layer(s) of the structures, with little to no absorption
in the ZnSe layer(s).
Fig. 4.6. Real part of refractive index, n, as a function of wavelength for (a) Si, (c) ZnSe, and (e) VO2.
Imaginary part of refractive index, k, as a function of wavelength for (b) Si, (d) ZnSe, and (f) VO2.
a
b
c
d
e
f
47
d
ee f
c
Fig. 4.7. Total Emittance as a function of incident angle for (a) & (b) the Single Layer (200μm) Si Device; (c)
& (d) the Single Layer ZnSe Device; (e) & (f) the Multilayer ZnSe Device with TE and TM polarization,
respectively.
a b
48
c dd
Fig. 4.8. Absorption in each layer for (a, b) the single-layer ZnSe device, and (c, d) the multilayer ZnSe device
for the insulating and metallic states, respectively.
a b
49
Chapter 5
Optimization of stacked Fabry-Perot cavities for VO2-based
broadband adaptive thermal radiators*
*
This chapter has been accepted for publication in Optics Express and is awaiting publication
5.1 Introduction
Thermal regulation technologies are necessary for satellites to manage the heat from direct sunlight
and on-board electronics [83, 98]. The miniaturization of satellite technology has led to increasing
interest in passive thermal regulation technologies, such as adaptive thermal radiators (ATRs).
Previous studies have demonstrated the thermochromic phase change material (PCM) vanadium
dioxide (VO2) [11-16, 22, 23, 44]. VO2 is an attractive choice since it is a volatile PCM that rapidly
and reversibly changes its electrical and optical properties when transitioning between phases
across its critical temperature, T*. Below 340 K, the insulating state of pure VO2 behaves as a
dielectric. Above 340 K, the material behaves as a metal [41]. Researchers have taken advantage
of this phase-change property to design ATRs with high emission in a hot state and low emission
in a cold state.
Some geometries of an ATR coatings include planar [11-16], metasurfaces [22, 23] and
microsphere [44] designs. We focus on planar, Fabry-Perot designs, which eliminate the need for
complex lithography and patterning and have comparable figures of merit to more complex
metasurface designs [62]. The geometry of single-cavity Fabry-Perot ATRs can be designed to
make the absorption peak coincide with the wavelength of peak blackbody irradiance at a given
temperature. However, a single cavity alone is limited in its ability to control the entire thermal
50
spectrum. Drawing inspiration from the multi-junction solar cell, different layers absorb specific
regions of the spectrum while transmitting the rest to the layers below. This work considers multicavity ATR designs that achieve the same effect in the hot state (to increase thermal emissivity)
while becoming primarily transparent in the cold state (to decrease the thermal emissivity). In
previous work, we have optimized a dual-cavity Fabry-Perot design with low loss ZnSe spacer
layers [62]. Adding the second cavity introduced an additional absorption resonance and improved
performance by approximately 20%. More recently, a theoretical three-cavity Fabry-Perot design
has been studied by Bowei et al. [61] which was predicted to achieve a Δε of 0.78. These works
suggest that by designing each cavity to absorb at a different resonant wavelength, while
transmitting at non-resonant wavelengths, one can achieve an efficient broadband response.
In this work, we comprehensively explore the parametric space of multi-cavity ATR design.
Our goal is to identify the maximum variable thermal emissivity that can be obtained by optimizing
the complete stack, thereby maximizing broadband absorption in the hot state and minimizing it
in the cold state. In this context, several key questions remain in the design of optimized, multicavity ATR coatings. First, several theoretical and experimental studies have used a wide variety
of spacer materials, each with a unique, dispersive refractive index across the wavelength range of
interest (2-30 µm). This makes direct comparisons between studies difficult, obscuring the
question of optimal material choice. Moreover, the ultimate performance limits are not yet known
for multi-cavity ATRs. One crucial design question is whether the tunable emissivity increases
indefinitely as cavities are added to the stack.
We performed a numerical optimization study to provide insight into the optimal design of
multi-cavity ATRs. We first investigated the effects of spacer material within a single-cavity
coating. To highlight the relevant trends, we considered a hypothetical spacer with wavelength-
51
independent optical constants. For optimal performance, we find that a spacer material should
minimize both the real part and imaginary part of the refractive index n. Since BaF2 satisfies these
conditions, we investigated the effects of stacking Fabry-Perot cavities using BaF2 spacer layers.
From Kirchoff’s law, the steady-state emissivity is equal to the absorptivity. Our results point to a
fundamental trade-off in the design of the multi-cavity ATR, which must maximize emissivity
(absorptivity) in the hot state, while minimizing it in the cold state. We find that while adding
additional cavities creates additional resonant peaks in the hot state, increasing broadband
absorptivity, it also increases the residual absorptivity in the cold state. This trade-off limits the
improvement that can be obtained by increasing the number of cavities.
We then performed a systematic study of optimized, multi-cavity structures across a wide class
of spacer layer materials, including BaF2, ZnSe, HfO2, ZnS, and Si. For any of the materials
studied, we find that there is negligible performance benefit in using more than three cavities.
Overall, we find that BaF2-based ATRs have the best performance metrics. To exceed the
performance of a single-cavity BaF2 device using ZnSe or ZnS, one must use at least two
cavities. For HfO2 and Si, it is not possible to exceed the performance of the single-cavity BaF2
coating, no matter how many cavities are used. These results should prove useful in helping to
guide future materials growth efforts for adaptive thermal radiators.
5.2 Approach
We consider an adaptive thermal radiator consisting of a top VO2 layer, a dielectric spacer material,
and a metallic back reflector to prevent transmission. An ATR has two operating states, cold and
hot, which are shown schematically in Figures 5.1(a) and (b).
Figure 5.1(a) illustrates the reflective (i.e. low emissivity) mode in the cold state when T < T*,
where T* is VO2 phase change temperature. In this operating mode, VO2 is in its insulating state.
52
The real part of its refractive index is similar to a dielectric (n ~ 2–3), and the imaginary part of its
refractive index is relatively low (k ~ 0 – 1), across the spectrum of 2–30 µm. Due to the gold back
reflector, there will be no transmission through the coating. Ideally, all incident light is reflected
back to the environment, as indicated schematically by the blue line in Figure 5.1(c), and the
absorptivity is zero. In practice, losses in the VO2 layer, as well as any residual loss in the spacer
and substrate, may give rise to small absorptive features.
Figure 5.1(b) illustrates the absorptive (i.e. high emissivity) mode in the hot state when T >
T*. In this operating mode, VO2 is in its metallic state. It has a real part of its refractive index
similar to a metal (n ~ 6) and a high imaginary part (k ~ 4–5) across the spectrum of 2–30 µm. The
Figure 5.1. Schematics detailing operational modes of an adaptive thermal radiator. (a) Single-cavity schematic of
the cold state reflective mode when T < T* and VO2 is in its insulating state. (b) Single-cavity schematic of the hot
state absorptive mode when T > T* and VO2 is in its metallic state. (c) Simplified absorption spectra for a singlecavity ATR with resonant enhancement in the hot state and little to no absorption in the cold state. (d) Multi-cavity
schematic of the cold state reflective mode. (e) Multi-cavity schematic of the hot state absorptive mode where each
cavity is designed to have resonant absorption at a different wavelength. (f) Simplified absorption spectra where the
dashed red lines indicate the absorption peaks for each cavity if they were single-cavity coatings and the solid red
line shows the broadband response achieved by superposing those Fabry-Perot cavities.
53
metallic VO2 and gold back reflector act as mirrors, forming a Fabry-Perot cavity with an
absorption resonance. Incident light at the resonance wavelength gets trapped in the cavity, reflects
multiple times, and produces an enhanced resonant absorption. Figure 5.1(c) illustrates the
resonant absorption peak schematically.
The performance of the ATR depends on the difference between the hot and cold absorption
spectra (red and blue lines) depicted in Figure 5.1(c). To further increase the difference, it may be
desirable to create more than one hot state absorption peak. Towards this end, one could stack
additional VO2 and spacer layers onto the coating, as shown in Figure 5.1(d), to create multiple
Fabry-Perot cavities with multiple resonant wavelengths. This idea is illustrated by the dashed red
lines in Figure 5.1(e), where each single-cavity coating is responsible for a single dashed red peak.
Ideally, when the VO2/spacer pairs are stacked on top of each other, they would combine to yield
a broadband response [61], such as the solid red line in Figure 5.1(e).
The absorption spectrum of an ATR is related to its emissivity spectrum by Kirchoff’s Law,
which states that absorptivity and emissivity are equal in steady state. To get the total emittance
εtot,T at a given temperature T, one must integrate the coating’s graybody irradiance and normalize
it by a blackbody’s irradiance at the same temperature, as shown in Equation 1 [13].
𝜺𝜺𝒕𝒕𝒕𝒕𝒕𝒕,𝑻𝑻 = ∫𝒅𝒅𝒅𝒅⋅𝑰𝑰𝑩𝑩𝑩𝑩(𝝀𝝀,𝑻𝑻)⋅𝜺𝜺(𝝀𝝀,𝑻𝑻)
∫𝒅𝒅𝒅𝒅⋅𝑰𝑰𝑩𝑩𝑩𝑩(𝝀𝝀,𝑻𝑻) , (5.1)
Here, εtot,T is the total emissivity at temperature T, ε(λ,T) is the spectral emissivity at
temperature T, and IBB(λ,T) is the blackbody radiance. In our numerical results below, the
wavelength integral was taken from 2 to 30 µm and the hot and cold states were taken to be 300
and 350 K, respectively.
The figure of merit for these coatings is the tunable emittance Δε, which is the difference
between the total emittances of the hot and cold states [99].
54
𝚫𝚫𝚫𝚫 = 𝜺𝜺𝒕𝒕𝒕𝒕𝒕𝒕,𝒉𝒉𝒉𝒉𝒉𝒉 − 𝜺𝜺𝒕𝒕𝒕𝒕𝒕𝒕,𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄, (5.2)
The ideal ATR would have an εhot and εcold of 1 and 0, respectively.
5.3 Single cavity optimization
We first investigate the effects of the optical properties of the spacer layer on the performance of
the ATR. Previous work has demonstratedinfrared transparent spacer materials,, such as BaF2 [12,
61] and ZnSe [62]. However, recent studies have demonstrated less transparent materials like HfO2
[16] or Si [13]. To test what optical properties the optimal spacer would have, we used the Transfer
Matrix Method (TMM) to simulate a single-cavity stack of VO2/spacer/Au, represented by the
schematic in Figure 5.2(a). The spacer layer has a constant n and k that sweeps over 1 to 3 and 10-
5 to 1, respectively. For each combination of n and k, we numerically optimize the layer thicknesses
of the VO2 and spacer layers to maximize the tunable emittance. For this optimization, we used
the Matlab function fmincon, in which we used the interior point algorithm to optimize the layer
thicknesses as we swept over n and k. The objective function used is written here as Equation 5.3,
where t is layer thickness and T is temperature. The tunable emissivity, Δε, is evaluated at each
step by running separate TMM simulations at Thot and Tcold, and using the calculated absorption
spectra to calculate εtot,hot and εtot,cold.
max
𝑡𝑡𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠,𝑡𝑡𝑉𝑉𝑉𝑉2
Δ𝜀𝜀�𝑡𝑡𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠,𝑡𝑡𝑉𝑉𝑉𝑉2,𝑇𝑇ℎ𝑜𝑜𝑜𝑜, 𝑇𝑇𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐� (5.3)
The optimized tunable emittance, Δε, for each combination of constant n and k is plotted as a
colormap in Figure 5.2(b). As shown in the figure, the optimum lies in the bottom left corner of
this colormap, corresponding to low n and low k. As n increases along the y-axis, Δε decreases
rather smoothly. Conversely, as k increases along the x-axis, Δε stays relatively constant until it
reaches a value >10-2 where it begins to drop rapidly.
55
These behaviors can be better understood by looking at the individual total emittances of the
Figure 5.2. Effect that a constant n and k spacer has on the performance of an ATR. For each combination of n and k,
an optimization is performed to achieve maximum tunable emittance. (a) Schematic of the single-cavity coating that
we are optimizing. The spacer material has constant n and k. (b) Optimized VO2 thickness for each combination of n
and k. (c) Optimized spacer thickness for each combination of n and k. (d) Total emittance in the hot state when VO2
is in its metallic state. (e) Total emittance in the cold state when VO2 is in its insulating state. (f) Optimized tunable
emittance for each combination of n and k. The optimum lies in the bottom left corner, corresponding to low n and
low k
56
cold and hot states. The values of εcold are shown in Figure 5.2(c). To minimize εcold, k should be
chosen to be less than 10-2
. A low-loss spacer is optimal in the cold state because any absorption
in the spacer layer tends to increase the total emittance εcold. The ideal dielectric spacer has n that
matches the dielectric constant n of the insulating VO2 (approximately n = 3) to minimize
interfacial reflections. The optimized values of εhot are plotted in Figure 5.2(d). In this state, the
optimal k value is below 10-1 and the optimal n value is about 1. In the hot state, a large refractive
index mismatch is desirable to increase the reflections at the VO2/spacer boundary. VO2’s n in its
metallic state ranges from 2 – 8 across the wavelengths of 2 – 30 µm [13], so a spacer material
with n near 1 would have the largest difference in refractive index within our range of test values.
The optimized layer thicknesses of the VO2 and spacer layers are shown as a function of the
n and k in Figures 5.2(e) and 2(f). Figure 5.2(e) shows that the real part of the refractive index
plays a large role in determining the optimal spacer thickness. We expect this behavior for the
spacer layer’s optimal thickness because of the Fabry-Perot equation for resonant cavities, shown
as Equation 2, which has an inverse relationship between tspacer and n.
𝒕𝒕𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 = 𝒎𝒎𝒎𝒎
𝟒𝟒𝒏𝒏 � , (5.4)
There is little variation in much of Figure 5.2(f) and the optimal thickness of VO2 is ~60 nm
for the majority of combinations of n and k. The optimal thickness of the VO2 layer must balance
the desired absorption in the hot state with the undesirable, residual absorption in the cold state.
Additionally, a very thick VO2 layer will also increase the magnitude of reflection off the interface
of air and VO2.
We note that there is a region in the top right of the colormap that has a much thicker optimal
VO2 thickness and much thinner optimal spacer thickness. This region occurs only for spacer
materials with very high k values as shown in in Figures 5.2(b), (c), and (d). The overall
57
performance of these coatings is much worse (ε < 0.5) than with a low n and low k spacer. With k
increasing to a large value, the cold state’s total emittance would increase significantly. Therefore,
the optimization minimizes the thickness of spacer material present in the design. It also increases
the thickness of the VO2 layer to boost absorption in the metallic state. However, the overall
performance is poor in this region of high-k spacers (Figure 5.2(b)), in comparison to the optimal
region.
We conclude that the optimal spacer layer for a VO2/spacer/Au single-cavity stack should
have a low n near 1 and a k below 10-2 to optimize tunable emittance. In our wavelength range of
interest (2-30 µm), BaF2 is a good candidate material with relatively constant n of 1.5 and k below
10-3 up to 15 µm.
5.4 Stacked cavity optimization
Table 5.1 Optimized geometry of multi-cavity periodic coatings
Layer
Thicknesses
1-Cavity
Coating (nm)
2-Cavity
Coating (nm)
3-Cavity
Coating (nm)
4-Cavity
Coating (nm)
Gold Reflector 200 200 200 200
Cavity 1 Spacer 1150 829 575 615
Cavity 1 VO2 60 82 99 91
Cavity 2 Spacer - 1126 730 586
Cavity 2 VO2 - 16 31 23
Cavity 3 Spacer - - 1060 452
Cavity 3 VO2 - - 6 16
Cavity 4 Spacer - - - 1039
Cavity 4 VO2 - - - 3
We next investigate the effects of additional Fabry-Perot cavities on the performance of our ATR’s.
We used TMM to simulate four structures: a single-cavity, 2-cavity, 3-cavity, and 4-cavity coating,
where each cavity consists of VO2, BaF2, and Au. These stacked cavities are represented by the
schematics in Figure 5.3(a-d), and the constituent layer thicknesses are numerically optimized to
maximize tunable emittance. The Matlab function fmincon with the interior point algorithm was
58
used here, with Equation 5.5 as the objective function, where T is temperature, t is layer thickness,
i goes from 1 to N, and N is number of cavities. The tunable emissivity, Δε, is evaluated at each
Figure 5.3. Schematics of the (a) single-, (b) double-, (c) triple-, and (d) quadruple-cavity coatings using a low n
and k candidate spacer material, BaF2 and their accompanying optimized total, normal emissivity spectra in the hot
(red) and cold (blue) states. Further shown in figures (b)-(d) is the difference in total normal emissivity for each
state, with respect to the case with one fewer cavity.
59
step by running separate TMM simulations at Thot and Tcold, and using the calculated absorption
spectra to calculate εtot,hot and εtot,cold.
max
𝑡𝑡𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠,𝑖𝑖,𝑡𝑡𝑉𝑉𝑉𝑉2,𝑖𝑖
Δ𝜀𝜀�𝑡𝑡𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠,𝑖𝑖,𝑡𝑡𝑉𝑉𝑉𝑉2,𝑖𝑖, 𝑇𝑇ℎ𝑜𝑜𝑜𝑜,𝑇𝑇𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐� (5.5)
The resulting optimized layer thicknesses for each of these coatings are listed in Table 1. The
refractive index data for VO2 comes from ellipsometry performed in Morsy et al., 2022 [13]. The
BaF2 and Au refractive index data are taken from Querry [100] and Palik [91], respectively.
First, we look at the single-cavity coating in Figure 5.3(a). Its accompanying emissivity
spectra is shown below its schematic where the red line is the hot state, and the blue is the cold. In
the cold state, VO2 is in its insulating state, in which its imaginary part of the refractive index
ranges from nearly 0 to 2. The features we see in the cold state match closely to features also seen
in the imaginary part of VO2’s insulating refractive index. In the hot state, VO2 is in its metallic
state. The metallic VO2, BaF2, and Au form a Fabry-Perot cavity which results in an enhanced
emissivity peak at 10 µm. The peak has an unusual shape due to the dispersion in VO2’s refractive
index near 10 µm. The integrated values of the hot and cold emissivities are 0.07 and 0.76,
respectively, for a tunable emittance, Δε, of 0.69.
The schematic of the 2-cavity coating and its emissivity spectra are shown in Figure 5.3(b).
The goal of including additional cavities is to increase the tunable emittance, Δε, which would
require that the increase in the hot state is greater than that of the cold state. The cold state’s
emissivity spectrum has increased from the single-cavity case, and we attribute this to the increased
overall thickness of insulating VO2 in the stack. In the hot state, there are now two enhanced
emissivity peaks at 6.6 µm and 11.7 µm which leads to a large increase in emissivity in the range
of 2-30 µm. The grey shaded region indicates the difference between the double- and single-cavity
coatings’ emissivity spectra, which can be interpreted as the effect of adding an additional cavity.
60
Looking closely at the grey shaded region, there is clearly greater enhancement in the hot state
than the increase in the cold state. This is confirmed by the integrated emissivity values, which are
0.105 in the cold state and 0.886 in the hot state (Δε = 0.781). Thus, including an additional
VO2/BaF2 layer pair in the stack increased the tunable emittance by 0.09.
Increasing to 3 cavities results in similar trends. In Figure 5.3(c), the cold state increases due
to the greater thickness of VO2, with an εtot,cold = 0.12. In the hot state, a third peak is present in the
lower wavelengths, which increases integrated emissivity to 0.912. The tunable emittance for the
3-cavity coating is 0.792, which is greater than the 2-cavity coating by 0.011. The grey region
shows the difference between the 2 and 3-cavity coatings, which is reduced from the improvement
going from single to 2-cavity coatings.
Adding yet another cavity to the coating in Figure 5.3(d) produces a negligible change in
tunable, thermal emissivity.. The integrated emissivity for the hot and cold states are 0.92 and
0.124, respectively, with a tunable emittance, Δε, of 0.796. Comparing this to the tunable emittance
of the 3-cavity coating, there is only an increase of 0.004.
5.5 Contribution of individual cavities in stack to total absorption
To better understand how each cavity affects the emissivity spectrum, we calculate the absorption
and transmission for each cavity. The absorption in each layer is calculated by using Equations
5.6-5.8, where R is the overall reflection from the top surface of the structure, T is the overall
transmission through the whole structure, Ai is the absorption in layer i, obtained from the
difference in downward flux between the top and bottom interfaces of the layer, Ti is the
transmission through layer i, obtained from the downward flux at the bottom interface of the layer,
and n is the number of layers. These spectra are shown for all four coatings’ hot state in Figure 4.
For the schematics in Figure 4(a, (d), (g), and (j), we combined the VO2 and BaF2 layers into
61
cavities, where the primary absorber in each cavity is the VO2 layer and the BaF2 layer is largely
Figure 5.4. Schematics of the (a) single-, (d) double-, (g) triple, and (j) quadruple-cavity coatings with their
respective plots of (b), (e), (h), (k) absorption and (c), (f), (i), (l) transmission through each cavity in the hot state.
62
unabsorbing.
𝐴𝐴1 = 1 − 𝑅𝑅 − 𝑇𝑇1, (5.6)
𝐴𝐴𝑖𝑖 = 𝑇𝑇𝑖𝑖−1 − 𝑇𝑇𝑖𝑖, (5.7)
𝐴𝐴𝑛𝑛 = 𝑇𝑇𝑛𝑛−1 − 𝑇𝑇, (5.8)
The absorption in Cavity 1 for the single-cavity coating is plotted in Figure 5.4(b) where, as
expected, the absorption in the cavity is equal to the total absorption of the stack. Similarly, there
is effectively zero transmission through Cavity 1 into the gold layer, as shown in Figure 5.4(c).
In Figure 5.4(e), we see how each cavity affects the total absorption of the 2-cavity stack. The
total absorption for the 2-cavity coating is plotted as the grey shaded region, and it has two peaks
at 6.6 µm and 11.7 µm. The absorption in the top cavity, Cavity 2, has a peak at 9.7 µm, and the
absorption in the bottom cavity, Cavity 1, has a peak at 5.5 µm. The transmission through each
cavity of the 2-cavity coating is plotted in Figure 5.4(f). Similarly to the single-cavity coating, we
see little to no transmission through the bottom cavity, Cavity 1, into the gold layer. Also, the shape
of the transmission through Cavity 2 closely matches the shape of the absorption of Cavity 1. There
is minimal absorption and no transmission through the gold layer; thus, any light not absorbed by
Cavity 2 is absorbed by Cavity 1.
Figure 5.4(g) depicts the 3-cavity coating with Cavity 3 on top and Cavity 1 on the bottom.
Looking at the absorption in each cavity plotted in Figure 5.4(h), the absorption spectra for Cavities
1 and 2 have similar shapes to what we saw for the 2-cavity coating in Figure 5.4(e). Cavity 1 has
a peak at 8.8 µm, Cavity 2 has a peak at 4.4 µm, and Cavity 3 has a small peak at 4.1 µm. The total
absorption spectrum has peaks 12.4 µm, 7.8 µm, and a smaller peak at 4.7 µm. The absorption in
Cavity 3 is much lower in magnitude than Cavities 1 and 2 since it has a much thinner layer of
VO2, which is the primary absorbing material. The locations of the peaks in the total absorption
63
spectrum are a result of the summative combination of the three cavities’ individual absorption
spectra.
The transmission through each cavity for the 3-cavity coating is plotted in Figure 5.4(i). The
transmission through Cavity 1 is nearly zero since the gold layer has nearly perfect reflection.
Compared to the 2-cavity case, the transmission through Cavity 2 matches closely with the shape
of the absorption in Cavity 1. The transmission through Cavity 3 is much greater than through
Cavity 2 since the absorptive layer (VO2) in Cavity 3 is only 6nm thick.
The 4-cavity coating is presented schematically in Figure 5.4(j). The absorption spectra for
each cavity are plotted in Figure 5.4(k) along with the total absorption of the stack shaded grey.
Cavities 1 and 2 have peaks at 8.8 µm and 3.8 µm, respectively. Cavity 3 plays a more prominent
role than in the 3-cavity coating, with an absorption peak at 5.3 µm and a larger absorption value
trending towards 2 µm and below. Cavity 4 only has 3 nm of VO2, so it has a much lower
magnitude of absorption when compared to the other cavities. It does not have any distinct
absorption peaks, but it does contribute towards enhancing the total absorption in the longer
wavelengths.
Figure 5.4(l) shows the transmission through each cavity for the 4-cavity coating. There is
nearly zero transmission through Cavity 1 into the gold layer. There is increasingly more
transmission through each cavity as we go from the bottom to the top. The shape of the
transmission through Cavity 2 matches closely to the absorption of Cavity 1, as we saw in the
previous coatings. Most of the light that was not reflected transmits through Cavity 4 due to the
very thin 3 nm layer of VO2.
Next, we examine the absorption in and transmission through each cavity for all four coatings
in the cold state. The single-cavity coating is shown schematically in Figure 5.5(a), and we see in
64
Figure 5.5(b) that the absorption of Cavity 1 matches closely with the total absorption of the
Figure 5.5. Schematics of the (a) single-, (d) double-, (g) triple, and (j) quadruple-cavity coatings with their
respective plots of (b), (e), (h), (k) absorption and (c), (f), (i), (l) transmission through each cavity in the cold state.
65
coating. This is expected since the only layer outside of Cavity 1 is the gold layer, which does not
absorb as much as the VO2. The transmission through Cavity 1 is shown in Figure 5.5(c), which is
nearly zero across the spectrum.
The absorption for the 2-cavity coating is plotted in Figure 5.5(e). It shows that the increased
absorption in the cold state is a combined effect of the two cavities. The absorption spectra for
both cavities have similar shapes and magnitudes. Cavity 1, with 82 nm of VO2, has a slightly
greater magnitude of absorption than Cavity 2, which has only 16 nm of VO2. The transmission
through each cavity, shown in Figure 5.5(f), shows that very little transmission gets through Cavity
1 and the shape of the transmission through Cavity 2 matches closely to the shape of the absorption
in Cavity 1.
The 3-cavity coating’s schematic is shown in Figure 5.5(g). Its accompanying absorption
spectra are plotted in Figure 5.5(h). Again, the absorption in each cavity has a similar shape and
magnitude to each other and they combine to form the total absorption, plotted as the grey shaded
region. Cavity 3 has the lowest magnitude of absorption since it has the thinnest layer of VO2. The
transmission through the three cavities is plotted in Figure 5.5(i). The magnitude of the
transmission decreases as we go from the top cavity (Cavity 3) to the bottom cavity (Cavity 1).
Finally, the 4-cavity coating is shown schematically in Figure 5.5(j) with its absorption spectra
plotted in Figure 5.5(k). The absorption spectra for Cavities 1, 2, and 3 overlap for much of the
region from 2-30 µm with similar shapes and magnitudes. Cavity 4 has a lower magnitude of
absorption across the spectrum due to it only having a 3 nm layer of VO2. The transmission through
each cavity is plotted in Figure 5.5(l), in which we see that the magnitude of the transmission
decreases as we go from the top cavity to the bottom cavity.
66
From our investigation, we conclude that the 4-cavity coating does not provide additional
enhancement of the tunable, thermal emissivity. Therefore, the optimal coating is the 3-cavity
coating which achieved a tunable emittance of 0.792. Notably, its hot state emissivity is greater
than 90%, which is very important for radiating away heat when a satellite is in direct sunlight.
Additionally, it has a low cold state emissivity of only 12%.
5.6 Materials comparison for stacked cavity coating performance
The calculations above considered BaF2 as a spacer material. We examined if our conclusions
about the benefits of multiple, stacked cavities apply more generally. We optimized single-,
double-, triple-, and quadruple-cavity ATR coatings with a variety of spacer materials in the same
manner as the BaF2 coatings. The materials we used as the spacer layers are BaF2, ZnSe, HfO2,
ZnS, and Si. We used the same methods as with the BaF2 coatings to optimize the layer thicknesses.
The resulting hot and cold emissivities are plotted in Figure 5.6(a), where the x-axis is the cold
state emissivity, and the y-axis is the hot state emissivity. The best coating should have a low cold
emissivity and a high hot emissivity, which would correspond to the upper right corner of the plot.
Conversely, the worst performing coatings are in the lower right corner, which corresponds to high
cold state emissivity and low hot state emissivity. It is important to note the scales of the x- and yaxes: The hot emissivity scale goes from 0.5 to 1, and the cold emissivity scale goes from 0.05 to
0.18. Thus, there is less variation in the cold state than there is in the hot state. This is also
demonstrated in Figure 5.6(b) in which the cold state lines are all clustered very closely and the
hot state lines have a wider spread.
Clearly, the BaF2 coatings outperform those with other spacer materials in terms of
maximizing the hot state emissivity. It is followed by the coatings using ZnSe, ZnS, Si, and HfO2,
67
which all have consecutively lower tunable, thermal emissivity in the hot state. As we showed in
the study performed in Figure 5.2, the optimal spacer material should have low real and imaginary
part of its refractive index. ZnSe, ZnS, and Si have mostly low k values across the wavelength
range of 2-30 µm, but they all have n values greater than 2. HfO2 has n values below and above 2
with significant dispersion throughout the 2-30 µm range and has large k values above 10 µm, and
it leads to the worst performance.
The jump in performance from the single- to double- cavity coatings is present in all our
material systems. Some have larger increases, such as the hot state increasing from 0.55 to 0.73
for the coating with the Si spacer, and some have less significant increases, such as the hot state
increasing from 0.68 to 0.74 for the coating with the HfO2 spacer. We should note that there is an
increase in each coating’s cold state emissivity as well; however, this increase is much smaller than
that of the hot state since the scales of the x- and y- axes are different.
a b
Cavities Materials
One
Two
Three
BaF2
HfO2
ZnSe
ZnS
Four Si
Figure 5.6. Comparison of performance with varying number of Fabry-Perot cavities and different spacer materials.
(a) Scatter plot of the optimized hot (y-axis) and cold (x-axis) total normal emissivity values for coatings with one
(circle), two (triangle), three (square), and four (diamond) cavities. (b) Plot of total emittance in the hot (red box)
and cold (blue box) states as a function of number of Fabry-Perot cavities.
68
The enhancement of the tunable, thermal emissivity decreases from two to three cavities for
some of our material candidates. For example, the 3-cavity HfO2 coating is roughly in the same
position as the 2-cavity coating. Looking at Figure 5.6(b), it is apparent that the 3-cavity Si coating
has no improvement in the hot state when compared to its 2-cavity coating. However, some
coatings, such as the ZnSe and ZnS 3-cavity coatings, have a noticeable increase in their hot state
emissivity. For all spacer materials, the increase from 2- to 3-cavities is smaller than the increase
from 1 to 2.
For all the 4-cavity coatings, we see no significant improvement and, in some cases, a decrease
in performance. The BaF2 coating has a very small increase in both its hot and cold states, which
leads to a negligible increase in its tunable emittance. The ZnSe, ZnS, and HfO2 coatings have a
small increase in their cold states but stay relatively constant in the hot states, which leads to an
overall decrease in tunable emittance. We note that for the 4-cavity simulations, we imposed a
lower bound of 5 nm on layer thickness. The worst 4-cavity coating is Si which has an increase in
the cold state and a decrease in the hot state, leading to a significant decrease in the tunable
emittance.
Although each material system has different emissivity values in their hot and cold states, the
overall trend we see when increasing the number of cavities remains the same. We expect a large
increase in tunable emittance when going from one to two cavities. We see another, smaller
increase in tunable emittance when going from two to three cavities. Finally, going up to four
cavities either negligibly or negatively affects the tunable emittance value.
In addition to the tradeoffs we have already covered with material choices, the ease of fabrication
is also an important consideration. A single-cavity consisting of VO2/BaF2/Au has been
experimentally realized by H. Kim, et al. in [12]. Additionally, it has been shown that VO2 can be
69
deposited via atomic layer deposition (ALD) for precise thickness control [101, 102]. However, it
may prove inconvenient to deposit multiple cavities of alternating VO2 and certain materials. Thus,
more work is needed and is ongoing to determine the optimal material from the perspective of
material growth. For example, R. Yu, et al. is currently investigating the deposition of VO2 on ZnS
[103].
5.7 Conclusion
This work investigated two opportunities to improve in the field of adaptive thermal radiators for
satellite thermal regulation. First, we studied the effects of the spacer material on the ATR’s
performance. To maximize the tunable emittance, it is necessary to choose a spacer material with
low n and k throughout the 2–30 µm region. Second, we investigated the effects of introducing
additional Fabry-Perot cavities into the stack, to absorb a different portion of the thermal spectrum
in each cavity. Here, we tested five spacer materials: BaF2, ZnSe, HfO2, ZnS, and Si. We found
that adding a second Fabry-Perot cavity broadened the spectral coverage, significantly improving
the tunable emittance for all spacer materials. Adding a third cavity, however, improved
performance for only some of the spacer materials, with less loss. Adding a fourth cavity did not
yield noticeable improvements in tunable emittance. This was due to a fundamental trade-off: any
increase in total emittance for the hot state (due to better spectral coverage) was offset by an equal
or greater increase in cold state emittance (due to residual absorption). Ultimately, the three-cavity
case represents an attractive trade-off between maximizing performance and minimizing the total
number of layer deposition steps. This work intends to inform future efforts toward realizing
optimal adaptive thermal radiators for satellite thermal control.
70
Chapter 6
Conclusion and future work
6.1 Static thermal emission control
In this work, we investigated the design and optimization of periodic and aperiodic multi-cavity
Fabry-Perot coatings using high-temperature stable oxides for broadband, high emissivity at high
temperatures. We found that an optimized, periodic design can achieve up to 0.96 total emissivity
integrated over 500nm-8µm. However, this design requires tens of microns of material growth,
which is infeasible for pulsed laser deposition (PLD). The optimized, aperiodic design, on the other
hand, achieved a comparable total emissivity of 0.94 with only ~1.4µm of material growth.
One limitation of this work was the inability to measure the materials’ refractive indices at
high temperatures. In order to do so, one would require a specialized high temperature stage that
is compatible with an ellipsometer. If one were to measure a sample of MgO and SRO at high
temperatures with an ellipsometer and fit the refractive indices of the materials, this would further
improve the reliability of our simulation results.
Furthermore, we expect to see the experimental realization of a bilayer structure consisting of
an STO substrate, an absorptive SRO layer, and a transparent MgO layer. The reflection and
transmission of this bilayer structure could be measured via FTIR and compared to simulation
results. A direct emissivity measurement of the bilayer coating would be the best way to quantify
its performance at high temperatures.
6.2 Electrically tunable thermal emission control
71
In Chapter 3, we studied the effects of electrically tuning one MIM resonator per unit cell in a
coupled resonator system. Putting two identical MIM resonators very close together gives rise to
a bright and dark coupled supermode. A normally incident plane wave can couple to the bright
supermode, but it cannot couple to the dark supermode due to the symmetry of the coupled MIM
system. By using GaAs as the insulating layer, electrically tuning one resonator changes the
refractive index of the GaAs layer and breaks the mirror symmetry. Upon breaking that symmetry,
the dark mode couples to the normally incident plane wave, and a narrowband absorption/emission
peak with a quality factor of 90 is created. Varying the applied voltage from 0V to 1.65V, the on/off
switching of that narrowband resonance leads to an absorption amplitude modulation of 97%.
Some experimental work has already been conducted in the effort to study the GaAs-based
MIM resonators. Hyun Uk Chae, et al. showed in [82] that an MIM resonator with a III-V material,
InAs in this case, can be fabricated. They further showed in [104] that a GaAs-based MIM
resonator can be electrically tuned to achieve a spectral shift of the resonant peak. The next steps
include fabrication of the coupled MIM design and characterization of its optical and electrical
properties.
Alternatively, this line of work is also being continued through a separate study of the
electrical tuning of graphene. This similar study of the tunable, on/off switchable electrical control
of a narrowband absorption resonance has been carried out by Silvia Guadagnini, et al., and is
currently in review. The use of graphene allows for more dynamic control of the resonance,
including amplitude and spectral location control.
6.3 Temperature-tunable thermal emission control
Chapters 4 and 5 covered our extensive study of the multi-cavity Fabry-Perot coatings using the
phase change material, VO2, for passive thermal regulation. We found that the optical properties
72
of the spacer material play a large role in the overall tunable emissivity of the coating. Specifically,
an optimal spacer material should have low real and imaginary parts of its refractive index. A low
real part, n, leads to a large index mismatch in the metallic, or hot, state which increases the number
of reflections at the VO2-spacer boundary. A low imaginary part, k, is necessary to eliminate any
extra absorption occurring in the insulating, or cold, state. The best materials to fit this description
are BaF2 and ZnSe. Furthermore, we found that stacking additional cavities and designing each
one to absorb at different peak wavelengths leads to significant improvements in tunable
emissivity. However, those improvements do not extend past three cavities. Adding a fourth cavity
led to only negligible improvements in the tunable emissivity.
Although we have extensively explored the design space of the VO2-based Fabry-Perot
adaptive thermal regulators, experimental realization of these optimized results has not yet been
achieved. As a first step, Raymond Yu, et al. has studied the deposition of VO2 on ZnS via PLD
for the same applications in [103]. Additional work will be necessary to experimentally
demonstrate the high tunable emissivity of the optimal coating. Such work includes developing
material growth methods, characterization of those materials, growing a multi-cavity coating,
optical characterization, and direct emission measurements.
73
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Abstract (if available)
Abstract
In this dissertation, we use computer simulations and optimization methods to study how to control infrared thermal emission in small-scale nanophotonic devices.
Our first goal is to design a broadband, high emissivity coating for extreme temperature environments. Previous research has focused on larger-scale systems, while we use microstructured designs. We analyze the static thermal emission control of a layered Fabry-Perot cavity coating designed for high broadband emissivity in high temperature environments. We find that an optimized, non-uniform multi-cavity coating achieves the best performance with minimal material growth needed.
Our next goal is designing a tunable, narrowband emission peak that can be turned on and off, with nearly 100% modulation. We study and optimize a coupled metal-insulator-metal (MIM) structure using the III-V semiconductor, GaAs, as the insulating layer. The coupled design creates a dark mode that cannot interact with a normally-incident plane wave due to symmetry restrictions. By electrically tuning one of the coupled resonators, we can break symmetry and enable coupling to the dark mode. This results in an on/off switchable narrowband resonance with nearly 0 to 1 absorption modulation.
Our final goal is to design of a temperature-tunable, broadband emitter for use as an adaptive thermal radiator (ATR). We focus on planar, multi-cavity Fabry-Perot designs using the phase change material, VO2. We find that the tunable emission of the ATR can be improved by optimizing spacer layer thickness, selecting optimal spacer materials, and cascading Fabry-Perot cavities.
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Optimized nanophotonic designs for thermal emission control
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2024-12
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absorption
electro-optics
emissivity
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thermal homeostasis
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