Metamaterial Super Absorber for Light

Metamaterial Super Absorber for Light-

Matter Interaction: from Broadband to

Extreme Field Confinement

by

Dengxin Ji

February, 2018

A Dissertation Submitted to the

Faculty of the Graduate School of

the University at Buffalo, State University of New York

in Partial Fulfillment of the Requirement for the

Degree of

Doctor of Philosophy

Department of Electrical Engineering

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This dissertation is approved and recommended for acceptance as a

dissertation in partial fulfillment of the requirements for the degree of

Doctor of Philosophy in Electrical Engineering.

Data

Accepted Date

Committee Members:

Dr. Qiaoqiang Gan (Dissertation Director) Date

Dr. Edward Furlani Date

Dr. Pao-Lo Liu Date

Dr. Hao Zeng Date

ii

Acknowledgements

First and foremost, I would like to express my sincere gratitude to my advisor Prof.

Qiaoqiang Gan for his support, encouragement, and inspiration in the last six years of my

Ph.D. study. All the achievements presented in this doctoral dissertation would not have

been possible without the support and contribution from him. His scientific vision, critical

thinking, and creativity are remarkable. Under his guidance, I feel that I matured

significantly, especially in setting short-term and long-term research targets, and

conceiving and establishing research plans. I feel truly lucky to be Prof. Gan’s student and

have benefited in every possible way that a student can benefit under his extreme support

and guidance. In addition to his role as my advisor, I have also enjoyed his friendship over

the years.

I am also grateful to Prof. Edward Furlani, Prof. Pao-Lo Liu, and Prof. Hao Zeng as

my committee members for their help to complete this dissertation.

I would like to thank Prof. Haifeng Hu (from Northeastern University, China), for his

advices and collaboration in my Ph.D. study. The presented hyperbolic metamaterial super

absorber is a beautiful cutting-edge project that requires strong theoretical physics and

nanophotonic background. I cannot image I can accomplish this much if not with his

expertise and advices throughout these years. I will thank Prof. Alexander N. Cartwright,

Prof. Zongfu Yu (from University of Wisconsin-Madison), and Prof. Suhua Jiang (from

Fundan University), for their expertise and valued advice.

iii

Working in the Nano-optics & Biophotonics lab has been a great experience for me in

my Ph.D. studies. I appreciate the assistance from my group mates, Dr. Xie Zeng, Dr.

Haomin Song, Mr. Nan Zhang, Mrs. Youhai Liu, Mr. Lyu Zhou, Mr. Matthew Singer, Mr.

Chenyu Li, Mr. Qingyang Liu, Mr. Chu Wang, Dr. Zhejun Liu, and Ms. Yanbo Guo. I also

appreciate my friends in University at Buffalo, including Jingbo Sun, Borui Chen, Alec

Cheney, Yuan Yuan, Feng Zhang, Yunchen Yang, Chang Liu, etc.

I want to thank Nana Lin for your support.

Finally, I want to thank my parents, Yongqiang Ji and Yuqin Wang, for all the love

they gave me. It is because of your endless support, love, and caring that I can turn my

dream into reality. I want to dedicate this dissertation to my parents.

iv

TABLE OF CONTENTS

Acknowledgements iii

List of Tables viii

List of Figures ix

Abstract xvi

1 Introduction 1

1.1 Background and Motivation 1

1.2 Metamaterial Super Absorber 2

1.2.1 Development of Metamaterial Super Absorber 2

1.2.2 Broadband MDM Super Absorber 4

1.2.3 Biosensing based on Metamaterial Super Absorber 6

1.3 Organization of This Thesis 7

1.4 References 10

2 Broadband Absorption Engineering of Hyperbolic Metamaterial (HMM) Patterns

14

2.1 Introduction 14

2.2 Light Trapping in Lossless and Lossy HMM Waveguide Tapers 15

2.2.1 Effective Medium Theory Model 16

2.2.2 Numerical Validation Using Real Optical Constants 24

2.2.3 Period Dependence 27

v

2.3 Multi-layered HMM Waveguide Taper Array for Broadband Absorption

Engineering 30

2.3.1 Experimental Realization of Multi-layered HMM Waveguide Taper Array

for Broadband Absorption 30

2.3.2 Multi-unit Pattern Array Based on Less Metal/Dielectric Films 36

2.3.3 Scattering Property of HMM Waveguide Taper Array 39

2.4 Summary 40

2.5 References 42

3 Surface Enhanced Infrared Absorption Spectroscopy Using Nanogap MDM Super

Absorber 48

3.1 Introduction 48

3.2 Interaction between adjacent patterns in planar MDM structures 50

3.2.1 Theoretical analysis of planar MDM structure 51

3.2.2 Spectral tunability in Terahertz (THz) domain 55

3.3 Efficient light trapping in corrugated MDM structure with ALD-defined gaps 56

3.3.1 Theoretical analysis of corrugated MDM structure 56

3.3.2 Experimental realization of corrugated MDM structure 58

3.4 Spectral tunability with fixed lateral dimensions 60

3.5 Summary 62

vi

64 3.6 References

4 Surface enhanced infrared absorption spectroscopy using nanogap MDM super

absorber 68

4.1 Surface enhanced sensing around ultra-small gaps 68

4.2 SEIRA for PMMA 69

4.2.1 Experimental results for PMMA molecules sensing 69

4.2.2 Enhancement factor calculation for PMMA coatings 71

4.2.3 Comparison of sensing area 74

4.3 SEIRA for ODT 75

4.3.1 Experimental results for ODT monolayer sensing 75

4.3.2 Enhancement factor calculation for ODT monolayer 76

4.4 Increasing the area occupied by nanogaps 81

4.5 Summary 82

4.6 References 83

5. Conclusions 86

Publications 88

VITA 91

vii

I I

Table 2.1 Conditions for existence of TM0, TM1 and TM2 modes in the HMM waveguide.

1/2

2 1 2/ 12

z x

k wV

List of Tables

Consider that , the corresponding thickness of the HMM core layer

to support |f> and |b> modes can therefore be determined.

viii

List of Figures Fig. 1.1 Schematic illustrations of a) atoms in a natural material; b) artificially designed

“atoms” in a metamaterial. Figure reproduced from ref. [9].

Fig. 1.2 Simulated (red) and measured (blued) absorbance curve. The dashed gray

absorbance curve is a Gaussian weighted average of the metamaterials absorber. Inset:

schematic illustration of metamaterial super absorber proposed by Landy et al. Figure

reproduced from Ref. [10].

Fig. 1.3 Schematic diagrams of broadband metamaterial super absorber with a) parallel

distributed multi resonators (reproduced from ref. [23]), b) concentric square ring

resonators (reproduced from ref. [24]), and c) stacked multiple resonators (reproduced

from ref. [25]).

Fig. 1.4 Raman signal comparison of BPE molecules on the universal substrate (pink

curves), reference nanoparticles on glass (green curves) and two commercial products of

rSERS (blue curves) and QSERS (red curves) excited by five laser lines. Reproduced form

ref. [15].

Fig. 2.1 Propagation constants of TM0, TM1 and TM2 modes, β, as a function of the HMM

waveguide width. The two branches for each mode are separated by a degeneracy point,

represented by empty circles.

Fig. 2.2 Normalized power flows of TM0, TM1 and TM2 modes, Pnorm, as a function of the

HMM waveguide width.

Fig. 2.3 |E|-field distribution of TM0, TM1 and TM2 modes in HMM waveguide tapers. In

the length of 3λ along the z-direction, the tapered width increases from 0.1λ to 0.22λ in the

ix

upper panel, from 0.3λ to 0.42λ in the middle panel, and from 0.55λ to 0.62λ in the lower

panel, respectively.

Fig. 2.4 The width-dependence of (a) the real part of the propagation constant, βr, (b) the

attenuation coefficient, βi.

Fig. 2.5 The effective modal area of the fundamental mode (TM0) in the lossy HMM

waveguide taper.

Fig. 2.6 The |E|-filed distribution in the HMM waveguide taper for the TM0 mode.

Fig. 2.7 a) The local modal amplitudes of | f+>, | f->, |b+> and |b-> modes along the z-

direction. b) The |E| -filed distribution for the | f+> mode (the upper half panel) and | b+>

mode (the lower half panel), respectively.

Fig. 2.8 Conceptual illustration of HMM waveguide taper arrays constructed by alternating

metal-dielectric films.

Fig. 2.9 The width-dependent dispersion curve for the propagation constants of λ=3.5 μm

(i.e. the real part, βr, and the imaginary part, βi).

Fig. 2.10 |E|-field distributions in the (a) lossless and (b) lossy HMM waveguide tapers for

the TM0 modes, respectively.

Fig. 2.11 (a) 1D absorption cross-section of a single 8-pair HMM waveguide taper unit. (b)

Absorption spectra of three periodic patterns with the period of (A) 2.26 μm, (B) 1.35 μm

and (C) 1.14 μm.

Fig. 2.12 Modeled E-field distributions in (a) structure C and (b) structure A at the

wavelength of 5.15 μm.

Fig. 2.13 Modeled |E|-field distributions in the 8-paired HMM waveguide taper (i.e. sample

3).

x

Fig. 2.14 a) 54˚-tilted SEM images of 3 samples of super absorptive meta-films with 1, 4,

and 8 pairs of Ag/SiO2 stacks. b) and c) show measured and modeled absorption spectra of

these 3 samples, respectively.

Fig. 2.15 a) 54˚-tilted SEM images of samples 4. b) and c) show measured and modeled

absorption spectra of sample 2 and 4, respectively.


absorption spectra of sample 5.



Fig. 2.18 Surface roughness of multi-layered films with a) 1-pair, b) 4-pair, c) 8-pair

Ag/SiO2 layers. The root mean square roughness data for these films are 2.9 nm in a), 3.6

nm in b) and 3.9 nm in c), respectively.

Fig. 2.19 a) 54˚-tilted SEM images of super absorptive meta-films with multiple patterns

in a single period. The scale bar is 500 nm. Images (b-c) show measured and modeled

absorption spectra of these 2 samples, respectively. For comparison, the measured and

modeled absorption spectra of sample 3 with 8-pair Ag/SiO2 layers are plotted by solid red

curves. (d) and (e) are modeled |E|-field distributions in the (d) 1D two-pattern structure

and (d) 2D four-pattern HMM waveguide taper structure. The cross-sectional mode

distribution shown in (e) is modeled along the x or y axis with corresponding x- or y-

polarized incident light.

Fig. 2.20 Comparison between the zero-order reflection spectra (see dots) and total

reflection spectra (see solid curves) for all 8 samples.

xi

Fig. 3.1 Conceptual illustration of metamaterial structure with 1D periodic distributed

patterns on the top surface.

Fig. 3.2 Preliminary modeling of the absorption spectra of patterned MDM super absorber

structures.

Fig. 3.3 Localized-field enhancement distribution (i.e., |E/E0|2) within the a) 10-nm-wide,

b) 5-nm-wide and c) 2-nm-wide gaps.

Fig. 3.4 Effective circuit model for MDM super absorber structure.

Fig. 3.5 a) Schematic illustration of the model. b) Absorption curves for gap sizes from 15

nm to 65 nm in the THz regime. Period was fixed at 26.2 µm (need other geometric

parameters and materials). Note that reducing the gap by 50 nm induces an asymptotic red

shift in the resonance from 259 µm (g= 65 nm) to 300 µm (g= 15 nm), while maintaining

absorption greater than 90%. Therefore, the gap-induced tunability discussed in the main

text is also observed in the THz regime. Maps of electric field enhancement (|E|/|E0|)2 are

shown in figs. c) – h) for gap sizes decreasing from 65 nm to 15 nm in a step of 10 nm, at

resonant wavelengths of 259 µm, 262 µm, 267 µm, 274 µm, 283 µm and 300 µm,

respectively (corresponding to the resonance peaks in the curves shown in a). The peak

field enhancement in fig. g was over 1.38×107 near the corners of the structure. The scale

of the color bar was chosen for clarity across all of figs. c) – h).

Fig. 3.7 Schematic illustration of the MDM metamaterial structure with corrugated ground

plate.

Fig. 3.8 Modeled absorption peak of a designed structure with the geometric parameters of

(P= 600 nm, D= 300 nm, tm = 40 nm, td= 60 nm, g= 5 nm, tb=100 nm).

Fig. 3.9 Effective circuit model for MDM structure with corrugated ground plate.

xii

Fig. 3.10 a) Modeling of the absorption spectra of structure in 3.7. b) Modeled electric field

enhancement distribution around the ultra-small gap. The peak value of the scale bar is set

to 4000 to show the localized field more clearly. The actual peak value is 1.55×104.

Fig. 3.11 a)-c) Manufacturing procedure to fabricate corrugated MDM super absorbers

with ultra-narrow gaps.

Fig. 3.12 a) Top-view and b) cross-sectional SEM images of a fabricated structure with the

parameter of P= 600 nm, D= 300 nm, tm = 40 nm, td= 60 nm, g= 5 nm, and tb= 100 nm. c)

Measured absorption spectrum of the fabricated structure (blue solid curve) and the

modeled absorption curve (red dotted curve) by considering real parameters extracted from

the SEM image.

Fig. 3.13 a) Top-view and b) cross-sectional SEM images of a structure with the parameter

of P= 500 nm, D= 250 nm, tm = 30 nm, td= 60 nm, g= 5 nm, and tb= 150 nm. c) Measured

absorption spectrum of the fabricated structure (blue solid curve) and the modeled

absorption curve (red dotted curve) by considering real parameters extracted from the SEM

image.

Fig. 3.14 a) SEM image of the first layer grating with P=300 nm and D=150 nm. b) Cross-

sectional SEM image of a fabricated structure (tm = 40 nm, td= 40 nm, and tb=200 nm) with

the gap size of ~5 nm. c) Absorption spectra of three samples with different gap sizes of

~3 nm (blue curve), ~5 nm (black curve) and ~7 nm (red curve), respectively. Insets:

Schematic illustration of the MDM metamaterial structures with different gaps.

Fig. 4.1 Conceptual illustration of SEIRA sensing using nanogaps.

xiii

Fig. 4.2 Experimental reflection spectra of nanogap-assisted MDM super absorber with

(red curve) and without (blue curve) PMMA coating, and PMMA film directly spin-coated

on bare Ag film (orange curve).

Fig. 4.3 Reflection differences for both the nanogap-assisted MDM super absorber sample

(red curve), and bare Ag film (blue curve). R and R0 are the reflection of bare Ag film/

MDM super absorber with and without PMMA, respectively.

Fig. 4.4 |EX|2 and |EZ|2 distributions around the 5 nm gap.

Fig. 4.5 a) and b) are |EX|2 distribution along x and z directions, respectively. Blue dotted

lines indicate the 1/e2 intensity position.

Fig. 4.6 a) and b) are |EZ|2 distribution along x and z directions, respectively. Blue dotted

lines indicate the 1/e2 intensity position.

Fig. 4.7 a) b) |EX|2 and |EZ|2 distributions around the grating structure.

Fig. 4.8 a) and b) are |EX|2 distribution along x and z directions, respectively. c) and d) are

|EZ|2 distribution along x and z directions, respectively. Blue dotted lines indicate the 1/e2

intensity position.

Fig. 4.9 a) Experimental reflection spectra of nanogap-assisted MDM super absorber with

(red curve) and without (blue curve) ODT coating, and ODT film directly spin coated on

bare Ag film (orange curve). b) Reflection differences of nanogap-assisted MDM super

absorber sample.

Fig. 4.10 a) Schematic illustration of ODT molecules bond on metal surface around

nanogap. b). Absorption spectrum of ODT molecules on bare silver film measured with

PM-IRRAS.

xiv

Fig. 4.11 |EZ|2 distribution across the nanogap indicating the effective sensing width for

the ODT sample.

Fig. 4.12 Simulated absorption spectra for the structure with the parameters of (P= 500

nm, D= 250 nm, tm = 40 nm, td= 40 nm, g= 5 nm, and tb= 150 nm) (black curve) and (P=

230 nm, D= 115 nm, tm = 40 nm, td= 40 nm, g= 3 nm, and tb= 150 nm) (red curve).

xv

Abstract

Metamaterial is a new class of artificially structured media exhibiting exotic properties

that do not exist in conventional materials. In recent decades, the investigation of light-

matter interactions with metamaterials have become an intense area of research in the field

of photonics. The engineered response of metamaterials can be designed to exhibit strong

coupling with the electric and/or magnetic component of an incident electromagnetic wave

by tailoring the shape, size, lattice constant, interatomic interaction of the “atoms”.

Light absorption, which is one of the most fundamental light-matter interaction, is an

essential phenomenon in a variety of the optical application, such as photovoltaics and

thermal management. Therefore, a particular branch – the metamaterial super absorber –

has garnered interest due to the fact that it can achieve angle- and polarization- insensitive

and near unity absorptivity of electromagnetic waves.

This thesis is largely focused on the development of plasmonic metamaterial super

absorber for light-matter interaction from two aspects: 1. Increasing the absorption band

for broadband application, e.g. on-chip thermal management, radiative cooling, and

thermal photovoltaics; 2. Maximize the electric field generated by the magnetic resonance,

for extremely sensitive sensing applications.

In chapter 2, I will discuss a novel platform – hyperbolic metamaterial (HMM) – for

broadband plasmonic metamaterial super absorber. By properly designing the geometric

parameters of the structures, the on-chip broadband super absorber structure based on

xvi

HMM waveguide taper array with strong and tunable absorption profile from NIR to mid-

infrared (MIR) spectral region can be realized.

In chapter 3, the plasmonic metamaterial super absorber will be combined with

nanometric gaps to maximize the localized field by squeezing EM waves into sub-5nm-

gaps. Optical field can be concentrated into deep-subwavelength volumes and realize

significant localized-field enhancement (so called “hot spot”) using metallic nanostructures.

In chapter 4, the structures investigated in chapter 3 is used to design a novel surface

enhanced sensing platform. Such a novel metamaterial super absorber substrate represents

a record for surface enhanced infrared absorption spectroscopy.

xvii

Chapter 1

Introduction

1.1 Background and Motivation

Metamaterials is a new class of artificially structured media exhibiting exotic properties

that do not exist in conventional materials. In recent decades, the investigation of light-

matter interactions with metamaterials have become an intense area of research in the field

of photonics [1-8]. The core concept of metamaterials is using artificially designed and

a b

Fig. 1.1 Schematic illustrations of a) atoms in a natural material; b) artificially designed “atoms” in a metamaterial. Figure reproduced from ref. [9].

fabricated structural units to mimic the “atoms” and “molecules” (as shown in Fig. 1.1) in

conventional continuum materials [9]. Since the objects’ size and spacing are much smaller

than the target wavelength, we can conceptually consider the otherwise inhomogeneous

medium as a homogeneous material from the electromagnetic point of view [1]. The

engineered response of metamaterials can be designed to exhibit strong coupling with the

electric and/or magnetic component of an incident electromagnetic wave by tailoring the

shape, size, lattice constant, interatomic interaction of the “atoms”. This leads to their

unique properties such as negative refractive index [1], anomalous reflection/refraction [3],

1

super-resolution imaging [11] over a broad range of wavelengths, from microwave all the

way down to visible regime or even ultra-violet region [12].

Light absorption, which is one of the most fundamental light-matter interaction, is an

essential phenomenon in a variety of the optical application, such as photovoltaics and

thermal management. Therefore, a particular branch – the metamaterial super absorber –

has garnered interest due to the fact that it can achieve angle- and polarization- insensitive

and near unity absorptivity of electromagnetic waves [7].

In this chapter, I will first summarize the development for conventional metamaterial

super absorbers, including narrowband metamaterial super absorbers for different

wavelength regimes and the broadband metamaterial super absorbers. Then the

organization of this dissertation will be outlined.

1.2 Metameterial Super Absorber

This super absorption ability is essentially a property of impedance matching to the free

space, i.e. 𝑍 = √𝜇(𝜔)/휀(𝜔) = 𝑍0, where 𝑍0 is the free space impedance, 𝜇(𝜔) and 휀(𝜔)

are the effective magnetic permeability and electric permittivity of the material,

respectively [7]. Metamaterial super absorbers have wide range of applications across the

radio frequency (RF) and optical regimes, including photon harvesting [13, 14], surface

enhanced biosensing [15, 16], photocatalysis [17], and thermal energy management [18,

19].

1.2.1 Development of Metamaterial Super Absorber

2

1.0

0.8

QJ u

0.6 C

"' .0 0 "' 0.4 .0 <:

0.2

0.0 8 9 10 11 12

Frequency (GHz)

The first metamaterial super absorber was proposed by Landy et al. [10], constructed

by two patterned metallic layers and a dielectric spacer, and demonstrated a simulated

absorptivity of ~99% at 11.48 GHz, as shown

in Fig. 1.2. The top metal layer consists of an

array of electric ring resonators (ERR), which

provide the electric response by coupling

strongly to incident electric field at resonance

frequency. The second metal layer consists of Fig. 1.2 Simulated (red) and measured

(blued) absorbance curve. The dashed gray an array of cut wires from the top layer,

absorbance curve is a Gaussian weighted

average of the metamaterials absorber. separated by a dielectric spacer, see inset of Inset: schematic illustration of metamaterial

super absorber proposed by Landy et al. Fig. 1.2. Magnetic resonance is achieved due Figure reproduced from Ref. [10].

to antiparallel currents in the cut wire and the center wire of the ERR. The magnetic field

of the incident light may couple to these antiparallel currents resulting in a magnetic

moment, thus yielding a Lorentz like magnetic response. The advantage of the combined

design allows for tuning of the electric and magnetic responses separately, i.e. adjustment

of the geometry of the ERR permits tuning the frequency position and strength of a Lorentz

resonance, while altering the spacing of the two metallic structures, and their geometry,

allows the magnetic response to be modified.

However, the fabrication of this metamaterial super absorbers is complicated due to the

multi-step lithography process, and the alignment of ERRs and cut wires. Therefore, the

experimental absorptivity only reaches 70% at 1.3 THz due to fabrication error. In an

improved metamaterial super absorber design, the bottom cut-wire layer was replaced by

a continuous metal ground plate, which is thicker than the penetration depth of incident

3

light [20]. The ground plate also eliminates any transmission (i.e. T = 0) at the resonant

wavelength. Moreover, unlike the cut-wire layer, the continuous metal ground plate is

polarization independent. Thus, the metamaterial super absorber with a continuous metal

ground plate become the most commonly used structure in the researches. Simultaneously,

the top ERR was also simplified to cross-shaped electric resonator [20], and eventually

metal strip for polarization dependent application and metal nano-disk/square for

polarization independent applications. Based on the simplified design, a polarization

independent super absorber was experimentally demonstrated at near-infrared (NIR)

regime [21]. The absorbance is ~99% at normal incidence and remains very high over a

wide incident angle range of ±80°[21].

1.2.2 Broadband MDM Super Absorber

Due to the resonant nature of conventional metamaterial super absorbers, the

absorption bandwidths are typically narrow. However, in many applications, such as solar

energy harvesting and selective thermal emitters, broadband absorption is required. In

order to broaden the absorption bands, Gu et al. used lumped resistance elements embedded

in metamaterial super absorber to lower the Q-factor [22], but this method is difficult to

extend to shorter wavelength regime. A more universal solution is to utilize multiple

resonators in each unit-cell, exploiting the fact that structures with different geometric sizes

resonate at different wavelengths. In this case, multiple resonances will be achieved in the

absorbance spectrum. When these resonances are close enough to each other, they will

merge together and form a broadband absorbance [23], as shown in Fig. 1.3a. One design

employ nested elements, e.g. concentric square rings and achieve multiband absorption

4

b

_: ;.... b C

I J

p I I

a

C

-L, -

I

[24], as shown in Fig. 1.3b. Nevertheless, these bands are not close enough to form a

broader absorption band due

to the limitation of element

sizes in the nested

configuration. Another

method to combine

resonators in one unit-cell is

to stack multiple ERR layers Fig. 1.3 Schematic diagrams of broadband metamaterial

super absorber with a) parallel distributed multi resonators and share the same ground (reproduced from ref. [23]), b) concentric square ring

resonators (reproduced from ref. [24]), and c) stacked plane (see Fig. 1.3c). Such multiple resonators (reproduced from ref. [25]).

structures demonstrated

greatly broadened absorption bands in terahertz (THz) [25] regime. However, due to the

fabrication difficulties caused by lithography and alignment between stacked layers, this

design is not particle to scale down for the application in the infrared and/or visible range.

The aforementioned structures highly rely on top-down lithography technique, which

imposes a significant fabrication cost barrier for large-scale practical applications. As we

discussed in the previous section, the spectral position of the absorption resonance is

mainly determined by geometric parameters of the top metallic patterns. Since this

mechanism does not depend on periodical or any other special arrangement of top patterns,

random nanoparticles are utilized to realize spectrally tunable and broadband metamaterial

super absorber in visible and NIR regime [26]. Though this method is simple, low-cost and

large-area, it is difficult to realize in longer wavelength due to the limited nanoparticle size

based on direct deposition and post thermal treatment. In this dissertation, I will propose a

5

novel structure to realize broadband metamaterial super absorber with high spectral

tunablity.

1.2.3 Biosensing Based on Metamaterial Super Absorber

Surface-enhanced Raman spectroscopy (SERS) refers to a vibrational spectroscopy

technique for characterization of low concentration analytes bound to or near patterned

metallic surfaces [15]. It has been widely used as a highly surface-sensitive and label-free

analytical technique for chemical and biological sensing applications down to single

molecule level. The extremely high sensitivity originates from the significantly enhanced

Raman scattering when molecules are adsorbed on metallic nanostructures [27]. It is

generally believed that the huge enhancement of Raman scattering arises from the

enhancement in the near field intensity as a result of the excitation of surface plasmons.

The metamaterial super absorbers provide a perfect platform for SERS applications, due to

the increased field enhancement in comparison to conventional SERS substrates (i.e.

nanoparticles on glass substrates). Chu et al. reported a SERS enhancement factor of 106

based on a gold nano-disk metamaterial super absorber at pump wavelength of 725 nm.

However, this SERS substrate can only work for individual excitation wavelength, limited

the application to identify anonymous trace molecules or mixed samples. To overcome this

limitation, Nan et al. proposed a universal substrate based on ultra-broadband metamaterial

super absorber for low-cost and high performance SERS sensing. Due to broadband light

trapping and localized field enhancement, this structure can work for almost “all” available

laser lines from 450 to 1100 nm. This predicted feature is validated by SERS experiment

6

a b C cl e 4

X 104 X 103 12

X 103 2 X 103 S X 104

,__ ::i

514nm 2 532 nm 633nm 671 nm 785nm

~ '-'

£ 8 Metasurface

"' 2 4 = 4> Reference .... xs .5 = 4 rSERS ~ xs E ~ 0 QSERS ~ 0 xs

1300 0 0 0

900 1700 900 1300 1700 900 1300 1700 900 1300 1700 900 1300 1700

Raman shift (cm·1)

using five different excitation laser lines, obtaining a high enhancement factor of 5.3 ×107

and very good uniformity over large areas, as shown in Fig. 1.4 [15].

Fig. 1.4 Raman signal comparison of BPE molecules on the universal substrate (pink curves),

reference nanoparticles on glass (green curves) and two commercial products of rSERS (blue

curves) and QSERS (red curves) excited by five laser lines. Reproduced form ref. [15].

Surface enhanced infrared absorption spectroscopy (SEIRA), the complementary

sensing technique to SERS, can identify molecular composition by analyzing “fingerprints”

of signature functional groups directly [28]. It also benefits from metamaterial super

absorber due to enhanced electromagnetic interaction with chemical vibrational bonds in

the MIR regime. However, since the vibrational absorption signal of SEIRA is proportional

to |E/E0|2 in contrast to |E/E0|

4 for SERS, the enhancement factor for SEIRA is usually

orders of magnitude lower than SERS [29]. This weakness significantly restricts the

application of SEIRA in ultrasensitive applications. In this dissertation, a metamaterial

super absorber with extremely high SERIA enhancement will be proposed.

1.3 Organization of This Thesis

In this thesis, I will focus on the development of plasmonic metamaterial super absorber

for light-matter interaction from two aspects: 1. Increasing the absorption band for

7

broadband application, e.g. on-chip thermal management, radiative cooling, and thermal

photovoltaics; 2. Maximize the electric field generated by the magnetic resonance, for

extremely sensitive sensing applications.

In chapter 2, I will discuss a novel platform – hyperbolic metamaterial (HMM) – for

broadband plasmonic metamaterial super absorber. In this dissertation, we theoretically

clarified the origin of broadband super absorption property. To demonstrate the feasibility,

we experimentally realize the on-chip broadband super absorber structure based on HMM

waveguide taper array with strong and tunable absorption profile from NIR to mid-infrared

(MIR) spectral region.

In chapter 3, I will combine the plasmonic metamaterial super absorber with

nanometric gaps to maximize the localized field by squeezing EM waves into sub-5nm-

gaps. Optical field can be concentrated into deep-subwavelength volumes and realize

significant localized-field enhancement (so called “hot spot”) using metallic nanostructures.

It is generally believed that smaller gaps between metallic nanopatterns will result in

stronger localized field due to optically driven free electrons coupled across the gap.

However, it is challenging to squeeze light into extreme dimensions with high efficiencies

mainly due to the conventional optical diffraction limit.

In chapter 4, I will experimentally demonstrate a metamaterial super absorber structure

with sub-5-nanometer gaps fabricated using atomic layer deposition processes that can trap

light efficiently within these extreme volumes. Light trapping efficiencies up to 81% at

MIR wavelengths. Importantly, the strong localized field supported in these nanogap super

absorbing metamaterial patterns can significantly enhance light-matter interaction at the

nanoscale, which will enable the development of novel on-chip energy

8

harvesting/conversion, and surface enhanced spectroscopy techniques for bio/chemical

sensing. By coating these structures with chemical/biological molecules, we successfully

demonstrated that the fingerprints of molecules in the MIR absorption spectroscopy is

enhanced significantly with the enhancement factor up to 106~107, representing a record

for surface enhanced infrared absorption spectroscopy.

9

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terahertz metamaterial devices, Nature 2006, 444, 597-600.

[3] D. Schurig, J. Mock, B. Justice, S. A. Cummer, J. B. Pendry, A. Starr,D. Smith,

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[7] C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S.

Krishna, D. R. Smith,W. J. Padilla, Terahertz compressive imaging with metamaterial

spatial light modulators, Nature Photonics 2014, 8, 605-609.

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dimensional subwavelength structures, Journal of Materials Chemistry C 2017, 5, 4361-

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[9] V. M. Shalaev, Metamaterials: A new paradigm of physics and engineering, 2008,

10

[10] N. I. Landy, S. Sajuyigbe, J. Mock, D. Smith,W. Padilla, Perfect metamaterial

absorber, Physical review letters 2008, 100, 207402.

[11] X. Zhang,Z. Liu, Superlenses to overcome the diffraction limit, Nature materials 2008,

7, 435-441.

[12] T. Xu, A. Agrawal, M. Abashin, K. J. Chau,H. J. Lezec, All-angle negative refraction

and active flat lensing of ultraviolet light, Nature 2013, 497, 470-474.

[13] A. Vora, J. Gwamuri, N. Pala, A. Kulkarni, J. M. Pearce,D. O. Guney, Exchanging

Ohmic losses in metamaterial absorbers with useful optical absorption for photovoltaics,

Sci Rep 2014, 4, 4901.

[14] W. Li,J. Valentine, Metamaterial perfect absorber based hot electron photodetection,

Nano letters 2014, 14, 3510-3514.

[15] N. Zhang, K. Liu, Z. Liu, H. Song, X. Zeng, D. Ji, A. Cheney, S. Jiang,Q. Gan,

Ultrabroadband Metasurface for Efficient Light Trapping and Localization: A Universal

Surface-Enhanced Raman Spectroscopy Substrate for “All” Excitation Wavelengths,

Advanced Materials Interfaces 2015, 2, 1500142.

[16] D. Ji, A. Cheney, N. Zhang, H. Song, J. Gao, X. Zeng, H. Hu, S. Jiang, Z. Yu,Q. Gan,

Efficient Mid-Infrared Light Confinement within Sub-5-nm Gaps for Extreme Field

Enhancement, Advanced Optical Materials 2017, 5, 1700223.

[17] Y. Tian, F. P. Garcia de Arquer, C. T. Dinh, G. Favraud, M. Bonifazi, J. Li, M. Liu,

X. Zhang, X. Zheng, M. G. Kibria, S. Hoogland, D. Sinton, E. H. Sargent,A. Fratalocchi,

Enhanced Solar-to-Hydrogen Generation with Broadband Epsilon-Near-Zero

Nanostructured Photocatalysts, Adv Mater 2017, 29,

11

[18] I. Puscasu,W. L. Schaich, Narrow-band, tunable infrared emission from arrays of

microstrip patches, Applied Physics Letters 2008, 92, 233102.

[19] X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst,W. J. Padilla, Taming the

blackbody with infrared metamaterials as selective thermal emitters, Phys Rev Lett 2011,

107, 045901.

[20] X. Liu, T. Starr, A. F. Starr,W. J. Padilla, Infrared spatial and frequency selective

metamaterial with near-unity absorbance, Phys Rev Lett 2010, 104, 207403.

[21] N. Liu, M. Mesch, T. Weiss, M. Hentschel,H. Giessen, Infrared perfect absorber and

its application as plasmonic sensor, Nano Lett 2010, 10, 2342-2348.

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metamaterial absorber, Journal of Applied Physics 2010, 108, 064913.

[23] Y. Cui, J. Xu, K. Hung Fung, Y. Jin, A. Kumar, S. He,N. X. Fang, A thin film

broadband absorber based on multi-sized nanoantennas, Applied Physics Letters 2011, 99,

253101.

[24] Y. Ma, Q. Chen, J. Grant, S. C. Saha, A. Khalid,D. R. Cumming, A terahertz

polarization insensitive dual band metamaterial absorber, Optics letters 2011, 36, 945-947.

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broadband terahertz metamaterial absorber, Optics letters 2011, 36, 3476-3478.

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free metasurface with spectrally tunable super absorption, Nanoscale 2014, 6, 5599-5605.

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12

[28] R. Aroca, Surface-enhanced vibrational spectroscopy, John Wiley & Sons, 2006.

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spectroscopy, Annu Rev Anal Chem (Palo Alto Calif) 2008, 1, 601-626.

13

Chapter 2

Broadband Absorption Engineering of

Hyperbolic Metamaterial (HMM) Patterns

2.1 Introduction

As we discussed in Section 1.2.2, it is difficult to realize ultra-broadband metamaterial

super absorbers with high spectrum tenability. However, such components are important

in real applications, for example efficient optical absorbers are highly desired on the

microscale where they can play a significant role in preventing crosstalk between optical

interconnects on integrated photonic chips. In the thermal spectral region, waste heat is a

major energy loss (including thermal radiation loss) in both industrial sectors and our daily

life [1]. Particularly, as the density of integrated circuits in portable

electronic/optoelectronic devices increases, on-chip thermal management becomes a

critical research topic. To recover thermal radiation energy from objects with varying

temperature, an efficient ultra-broadband absorber is an indispensable component. In

classic microwave electromagnetic (EM) approaches, EM wave absorbers have long been

explored and widely utilized for important military applications, such as improving radar

performance and providing concealment against others’ radar systems [2]. In general,

however, EM wave absorbers have been limited by their large, bulky dimensions. Recently,

the trapped “rainbow” storage of light was proposed using metamaterials [3] and plasmonic

graded surface gratings [4, 5], generating considerable interest for on-chip manipulation of

light. In principle, the incident energy will be absorbed if a broadband “rainbow” is trapped

in a practical lossy structure. Therefore, the “rainbow” trapping effect will result in a

14

promising platform for an on-chip broadband absorber. However, due to the challenges in

achieving broadband metamaterial and/or high quality and high efficiency surface

plasmonic structures, limited experimental successes have been reported [6-9]. To

overcome these limitations faced by metamaterial super absorber and rainbow trapping

structures, in this study, we report a patterned hyperbolic meta-film with engineered and

freely tunable absorption band from near-IR to mid-IR spectral regions based on

multilayered metal/dielectric films. Compared with recently reported compact

plasmonic/meta-absorber based on crossed trapezoid grating arrays [10] and ultra-sharp

convex metal grooves [11], the proposed hyperbolic metafilm pattern is superior on its

ultra-wide spectral tunability from optical (i.e. visible to near-IR) to thermal (i.e. mid- and

far-IR) spectral regions, and can be easily integrated with other on-chip

electronic/optoelectronic devices. The ability to efficiently produce broadband, highly

confined and localized optical fields on a chip is expected to create new regimes of

optical/thermal physics, which holds promise for impacting a broad range of energy

technologies ranging from photovoltaics, to thin-film thermal absorbers/emitters, to

optical-chemical energy harvesting.

2.2 Light Trapping in Lossless and Lossy HMM Waveguide Tapers

HMM refers to an artificial medium with subwavelength features whose iso-frequency

surface is a hyperboloid [12-16]. This type of metamaterial (also called indefinite medium

[12]) has a diagonal form of the permittivity tensor (i.e. ε=diag(εx, εy, εz)) whose diagonal

elements have different signs (e.g. εx =εy <0, εz >0), leading to the hyperbolic iso-frequency

surface, i.e. ω2/c 2=kx2/εz +ky

2/εz +kz2/εx [12, 13], corresponding to highly anisotropic

15

optical properties (i.e. dielectric in one direction and metallic in other directions). This

unique feature is promising for a variety of applications, including three-dimensional

indefinite cavities [17], spontaneous emission enhancement [15], active nanoplasmonic

devices [18, 19], etc. Recently, an interesting concept was proposed to realize an on-chip

ultra-broadband and tunable super absorber in near-IR, mid-IR to microwave domain [20-

22] using patterned HMM waveguide taper arrays constructed by multilayered

metal/dielectric thin films. The physical mechanism of this intriguing ultra-broadband

absorption was attributed to slow light modes confined in HMM waveguide tapers, leading

to the enhanced light-matter interaction and therefore, strong/perfect absorption of the light.

2.2.1 Effective Medium Theory Model

To explain the fundamental mechanism, we analyze the waveguide modes supported

in an air/HMM/air planar waveguide by solving the eigenequation analytically based on

the effective medium theory. Considering an HMM waveguide in the inset of Fig. 2.1 with

a dielectric cladding layer (ε1 =1) and an anisotropic core layer (e.g. ε2x =-25+0.25i,

ε2z=5+0.05i), the propagation constant β of the transverse-magnetic (TM) modes can be

obtained by solving Eq. (2.1),

2 12

1 2

tan( / 2)z w

, for even modes (2.1a)

2 12

1 2

cot( / 2)z w

, for odd modes (2.1b)

16

12 X

3 8 y•

~ -C1

4 \._TMO ··.TM ·•. 1

cladding core

cladding

···· .. ~M2

E 0.5 0

Q_c 0.0

-0.5

z

™o ™1 fTM / 2

,•·

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 w/'A

where 2 2 1/2

1 1( )k , 2 2 1/2

2 2 2 2( / )z z xk . kω=ω/c is the vacuum wave

vector, w is the width of the core layer, and μ is the permeability (μ=1 for nonmagnetic

materials). Here we first analyze the lossless case by neglecting the imaginary part of the

permittivity of the HMM core layer, i.e. ε2x =-25, ε2z=5. Using Eq. (2.1), the geometric

dispersion curves of TM0, TM1 and

TM2 modes are plotted in Fig. 2.1.

One can see that an HMM core layer

with a given width can support two

different propagation constants for Fig. 2.1 Propagation constants of TM0, TM1 and

TM2 modes, β, as a function of the HMM waveguide each TM mode. As the core layer

width. The two branches for each mode are separated

by a degeneracy point, represented by empty circles. width increases, a degeneracy point

can be obtained as indicated by empty circles. To distinguish the optical properties of these

two modes with different propagation constants, we calculate the normalized power flow

in Fig. 2.2, i.e.

where Sz is the z-component of the

Poynting vector. For modes with

smaller propagation constants

/norm z zP S dx S dx

below degeneracy points in Fig. 2.1

(see solid lines), the power flow is Fig. 2.2 Normalized power flows of TM0, TM1 and

TM2 modes, Pnorm, as a function of the HMM parallel to the propagation direction waveguide width.

(which is defined as |f> mode), i.e. P>0 as plotted by solid lines in Fig. 2.2; while for modes

with larger propagation constants above degeneracy points shown in Fig. 2.1 (see dotted

lines), the power flow is anti-parallel to the propagating direction (which is defined as |b>

17

mode), i.e. P<0 as plotted by dotted lines in Fig. 2.2. One can see that these two modes are

getting close to each other and be degenerate finally as the width of the core layer increases,

which is similar to the TM0 mode behavior in IMI waveguide (when |εcore|<εcladding) [23].

Interestingly, at the degeneracy point (see empty circles), Pnorm is 0 indicating that these

TM modes will be trapped in the proposed HMM waveguide structure. To validate this

prediction, we then model the electric-field (|E|-field) distribution guided in a tapered

HMM waveguide using finite element method (FEM). In the numerical simulation shown

in Fig. 2.3, the guided TM0, TM1 and

TM2 modes are directly launched

into the waveguide taper from the

narrow end. For instance, the core

layer width of the narrow end is 0.1λ

in the upper panel of Fig. 2.3,

corresponding to two propagation

constants of 1.077kω and 9.180kω

for the TM0 mode in Fig. 2.1. Since

the smaller β (i.e. 1.077kω) is very Fig. 2.3 |E|-field distribution of TM0, TM1 and TM2 modes

in HMM waveguide tapers. In the length of 3λ along the z-close to the vacuum wave vector, kω, direction, the tapered width increases from 0.1λ to 0.22λ in

the upper panel, from 0.3λ to 0.42λ in the middle panel, and it should be easy to launch the |f>

from 0.55λ to 0.62λ in the lower panel, respectively.

mode practically using a free-space

beam. As the |f> mode is guided along the waveguide taper with an increasing width, it

will be trapped at the degeneracy point finally (i.e. w=0.173λ, indicated by white arrows in

Fig. 2.3), agreeing very well with the FEM modeling. Similarly, |f> modes for TM1 and

18

I I I I

TM2 modes cannot propagate beyond their corresponding degeneracy points at w=0.380λ

and 0.591λ, as show in the middle and lower panels of Fig. 2.3, respectively. Due to the

power flow of the modes decreases to 0, the incident energy is trapped at these degeneracy

points. In addition, the tangent line at the degeneracy point is parallel to the vertical

direction, indicating that the group velocity is zero [24] and therefore revealing an

encouraging promise to realize rainbow trapping in these HMM waveguide tapers.

In previously reported simulation results exploring the feasibility of realizing rainbow

trapping in INI, IMI and MIM waveguide tapers [23, 25-27], a rainbow trapping condition

parameter for having the degeneracy point, σε=|εcore/εcladding|, has been analyzed and

compared. According to ref. [27], this condition for the relatively practical MDM

waveguide taper structure is still challenging (e.g. for TM1: 1< σε <1.3510), which requires

a very large permittivity of the dielectric core layer (e.g. GaP) so that the rainbow trapping

can be realized in a very limited spectral range for TM1 modes. It will be demonstrated that

the proposed HMM waveguide structure is not limited by these severe theoretical

constraints required by INI, IMI and MIM waveguide tapers. Here we first define three

parameters, 1/2

2 1 2/ 1z x

wV

, U=wγ2/2, and 2 2 1/x z , to simplify the

characteristic Eq. (2.1) as follows:

2 2 / tanU V U U

2 2 / cotU V U U

, for even modes (2.2a)

, for odd modes (2.2b)

In this equation, V and σ are constants for a given waveguide structure. U is related to the

propagation constant of the waveguide mode. The solution to this equation can be obtained

19

I I

by graphically determining the intersection points between curves of W=tanU or W=-cotU

(i.e. the term on the left-hand side of Eq. (2.2)) and 2 2 /W U V U (i.e. the term on the

right-hand side of Eq. (2.2)) in the (U, W) space. Based on this graphical analysis,

conditions for supporting |f> and |b> branches of TM0, TM1 and TM2 modes are listed in

Table 1. Particularly, the TM1 and TM2 |f> modes exist in the ranges of π/2≤V≤V1 and

π≤V≤V2, respectively, corresponding to ranges from cutoff points for TM1 and TM2 modes

(indicated by arrows in Fig. 2.1) to their degeneracy points. In order to realize the rainbow

trapping for a given wavelength, degeneracy points have to be realized, which can be met

by tuning the core layer width (w) of the HMM waveguide. Consequently, as the incident

TM0 mode propagates along the HMM waveguide taper from the narrow end to the broad

end, the |f> and |b> modes will get close to each other and degenerate finally. Noticeably,

during this process, only the hyperbolic condition (i.e. ε2x<0, ε2z>0) of the core layer is

needed. Any reported metamaterials with hyperbolic iso-frequency surfaces (e.g. [12, 14,

15]) can be used to enable the degeneracy condition, and therefore representing a

significant promise to realize the rainbow trapping practically.

TM0 TM1 TM2

|f> 0<V≤V0 π/2≤V≤V1 π≤V≤V2

|b> 0<V≤V0 0<V≤V1 0<V≤V2

Table 2.1 Conditions for existence of TM0, TM1 and TM2 modes in the HMM waveguide.

Consider that 1/2

2 1 2/ 12

z x

k wV

, the corresponding thickness of the HMM core layer

to support |f> and |b> modes can therefore be determined.

20

In the discussion presented above, the loss of the HMM material was neglected. This

ideal but impractical assumption was usually employed to approximately predict optical

behaviors of plasmonic structures and metamaterials. For example, the metal loss was

neglected in previous theoretical designs of trapped rainbow of THz waves in metamaterial

[28] and plasmonic surface grating structures [3], which resulted in a debate on the

feasibility of the proposed “stop” light effect [29]. In recent years, many simulation results

have shown that adiabatic metallic metamaterials or plasmonic structures do not permit the

complete “stopping” of light waves even under the assumption of lossless materials due to

the fundamental nonadiabaticity near the degeneracy point [27]. More specifically, the

adiabaticity condition for the graded core width variation [30], dw/dz<<wkω∆n/π where ∆n

is the effective index difference between eigenmodes (i.e. |f> and |b>), cannot be met at the

degeneracy point since ∆n=0. However, this criterion was still omitted occasionally in

recent theoretical designs [20]. It should be noted that a complete stop of light is also not

achievable in the lossless HMM waveguide tapers although the group velocity at the

degeneracy point is 0 in principle. The incident |f> mode will convert to |b> mode and

escape from the “trapped” position. In the next paragraph, we will consider the loss of

HMM materials to explore this mode conversion process and evaluate the rainbow trapping

performance further.

21

4 -- If> ···· · · ··· lb>

26==========:___:........___.___~ a 00,-------.---------.---~==-,

%. 1 -p/k for lb>

~ 1 ff1 • · · ··•·

1

···~ ·· · ········· ··· ·· 0)

E 10-2

1 ff3 t=;;...._ _ _.__ _ ___._ __ _,__ _ ___J

-S, 0. 3...,.....----.-------.------,.---,

~ 0.2 If> < ... . ..... lb> ro 0.1 .... '---.-.-,.-~-

"'C •..•.•..•..

~ 0&12 0.14 0.16 0.18 0.20

wtA

To reveal the difference by considering the absorption (i.e. ε2x =-25+0.25i, ε2z=5+0.05i

in our modeling), we plot the real

and imaginary parts of the

propagation constants, βr and βi, as

shown in Fig. 2.4a and 2.4b,

respectively. One can see from Fig.

2.4a that the absorption breaks the

degeneracy point connecting |f> and

|b> modes in the lossless case. The Fig. 2.4 The width-dependence of (a) the real part of

the propagation constant, βr, (b) the attenuation geometric dispersion curve for TM0

coefficient, βi.

modes will extend to the right side of

the lossless degeneracy point with significantly larger loss as shown in Fig. 2.4b. The TM0

mode behaves as an evanescent wave in this “cutoff” region, due to the large attenuation

coefficient, which is defined as βi/kω. On the other hand, the propagation loss for the |b>

mode is much larger than that of the |f> mode, revealing a key difference before and after

a

b

the mode conversion. To further

evaluate the field confinement, the

effective modal area is defined by

2 2| | / max | |A dx E E , as plotted in

Fig. 2.5 The effective modal area of the fundamental Fig. 2.5. Generally, the |b> mode

mode (TM0) in the lossy HMM waveguide taper. indicated by the dotted line has a

smaller modal area than the |f> mode indicated by the solid line. The model areas of these

two eigenmodes match approximately near the degeneracy point as the mode conversion

22

0.5

~ 0 X

-0.5

-- --- ~~ ·- ---- .-. ! 2

1

0

occurs. To reveal the behavior of the mode propagation in the tapered lossy HMM

waveguide, we perform the FEM simulation in Fig. 2.6. One can see that the incident |f>

mode cannot propagate beyond the

degeneracy point position indicated

by the vertical dotted line. An

Fig. 2.6 The |E|-filed distribution in the HMM

obvious oscillation field distribution waveguide taper for the TM0 mode.

is observed due to the interference between the incident |f> mode and the reflected |b>

mode.

To provide a quantitative understanding on this mode conversion and light trapping

mechanism, the mode expansion method is employed to calculate the amplitude of the local

guide modes in the tapered waveguide. The total field can be expressed as the linear

combination of all the possible modes supported by the waveguide structure in Eq. (2.3).

, , , , ,

,

( ) ( )x total x f f x f b b x b x

f b

E a E a a E a a E a E

(2.3a)

, , , , ,

,

( ) ( )y total y f f y f b b y b y

f b

H a H a a H a a H a H

(2.3b)

Here the signs “+” and “-” denote the forward- and backward- propagation directions; ρ

represents the high order modes or the radiation modes. In the lossy waveguide, we use the

unconjugated general form of orthogonality condition [30, 31], [Hy,σ|Ex,σ']=δσσ'[Hy,σ|Ex,σ], to

obtain the amplitudes of |f+>, |f->, |b+> and |b-> TM0 modes in the tapered waveguide, as

shown in Fig. 2.7a. One can see that the incident |f+> mode converts to the |b+> mode near

the degeneracy point, while the amplitudes of the other two modes, |f-> and |b->, are

negligible in this structure. Consider that the power flow of the |b+> mode is antiparallel

23

a 1.0 _ lf+> It

+I If-> ..... 0 0 .5 ·········· lb+> ..... •······

0 ········-J~~.?: ...... •····· -----·····

0 0 ···················································-······ ....... . . 0 1 2 3

b o.s

~ 0 X

-0.5

z/11,

a +> :::::::;::::::::;::::::::; ........ : ........ : ........ .-......... :.. . I b . -

Gb+ +>

2

1

0

to the propagation direction (the power flow directions for these two eigenmodes are

indicated by arrows in Fig. 2.7a), the incident energy therefore escapes from the trapped

position through the mode conversion process. To distinguish the mode areas of these two

eigenmodes, the |E|-field for

af+|f+> and ab+|b+> are plotted

in Fig. 2.7b. When the TM0 |f>

mode is launched from the

narrow end of the structure, the

mode width of the |E|-field

distribution is indicated by

white dots, showing that the Fig. 2.7 a) The local modal amplitudes of | f+>, | f->, |b+>

and |b-> modes along the z-direction. b) The |E| -filed guided modal area shrinks distribution for the | f+> mode (the upper half panel) and |

b+> mode (the lower half panel), respectively. towards the degeneracy point

(see the upper half panel). After the mode conversion from |f> to |b> near the degeneracy

point, the |b> mode is squeezed into the HMM waveguide taper further due the much larger

propagation loss (see the lower half panel in Fig. 2.7b). Due to this decreasing modal area

from the |f+> mode to the |b+> mode with a significantly enhanced propagation loss, the

tapered HMM waveguide is therefore promising to develop applications for super

absorbers [10, 32] based on the intriguing rainbow trapping effect. In the next section, we

consider real metal-dielectric materials to design the HMM waveguide taper and validate

the rainbow trapping effect predicted using effective medium theory.

2.2.2 Numerical Validation Using Real Optical Constants

24

As explained in Section 2.2.1, the rainbow trapping condition can be fulfilled as long as

the HMM can be realized. To validate this prediction, we investigate a HMM pattern array

consisting of alternating layers of silver (Ag) and silicon dioxide (SiO2) films surrounded

by air (i.e. ε1 =1), as shown in Fig. 2.8. According to the effective medium theory [33],

when the film thickness of each layer is much smaller than the wavelength, its permittivity

tensor can be approximately described as:

ε2x=ε2y=fεAg+(1-f)εSiO2, 1/ε2z=f/εAg+(1-f)/εSiO2, where f

is the thickness filling ratio of the metal layer. In a

HMM waveguide array, its waveguide modes in

adjacent units will interact with each other due to the

overlap of their evanescent fields. Therefore, the EM

field in this periodic structure can be described by

the Bloch mode, i.e. F(x+P)=F(x)exp(-ikx0P) [34].

Here, P is the period of the structure; kx0 represents

the momentum along the x-direction of the Bloch

mode. Under the normal incident condition, the Bloch mode with kx0=0 can be excited. Its

propagation constant β can be calculated by Eq. (2.4):

Fig. 2.8 Conceptual illustration of

HMM waveguide taper arrays

constructed by alternating metal-

dielectric films.

2

2 1 2 1 1 2 2 1

2 1 2 1 1 2 2 1

exp( ) exp[ ( )] exp( ) exp[ ( )]

exp( ) exp[ ( )] exp( ) exp[ ( )]

z

z

i w P w i i w P w

i w P w i i w P w

(2.4)

25

25

3 ::!: 15 § iij Cl)

-- If> lossless -- lb> lossless

o If> real metal ~ lb> real metal • a::

3 .:,:

5 8 9 ~ 0 0

101!:"~~~~~~-:-=-~-!~_rt:._=_~_~:._'§._'=-_~_~_~J3_~~.::_..::.__:_::~~=~~-;;9~:e~7e(::,";J~

~~~~~e~~e~~~~e~~~

~ 10-1

Cl (II

E - 10·3

0.5

·13/k~ for lb>

oO 0 0 0 0

0 00

0 0 0 0 o O 0 0 o o o O O

!3./k for If> I <»

0.6 0.7 W(µm)

0.8

Here, 2 2 1/2

1 1( )k , 2 2 1/2

2 2 2 2( / )z z xk , 𝑘𝜔 = 𝜔⁄𝑐 is the vacuum wave

vector, and w is the width of the HMM layer. The dispersion curves of Bloch modes

supported in a periodic HMM waveguide arrays can be plotted by solving this

eigenequation as shown in Fig. 2.9.

In this modeling, dispersive optical

constants of Ag are considered and

the filling factor, f, is 0.538. We set

the period of the HMM pattern to

P=1.17 μm and the incident

wavelength to λ=3.5 μm. The width Fig. 2.9 The width-dependent dispersion curve for the

propagation constants of λ=3.5 μm (i.e. the real part, of the HMM waveguide taper βr, and the imaginary part, βi).

increases from 500 nm to 950 nm,

with the vertical dimension of 2 μm. In this case, the anisotropic permittivity tensor

elements are ε2x = -240.05+40.391i, ε2z = 4.64+0.0042i. Under the lossless assumption,

attained by neglecting the imaginary parts of ε2x and ε2z (see the red curve), one can see that

a degeneracy point is achieved, connecting the two branches of |f> and |b> modes, as

indicated by the arrow in Fig. 2.9. According to our previously reported theoretical analysis

[34], the group velocity is 0 in principle at this degeneracy point, which, however, cannot

be reached due to the mode conversion mechanism. Consequently, obvious interference

patterns can be observed in the electric field distribution confined in the lossless HMM

waveguide taper, because of the interference between the |f> and |b> modes, as shown in

Fig. 2.10a. When the real loss of Ag is considered in the modeling (e.g. ε2x=-

240.05+40.391i, ε2z=4.64+0.0042i), the waveguide mode is mainly attenuated in the x

26

0

0.8

1.6 -E = 0 N

0.8

1.6

-0.5 0 0.5 X (µm)

Max

Min

direction due to the large imaginary part of ε2x (see Fig. 2.10b). One can see from Fig. 2.10b

that the intensity of the guided mode inside the HMM

taper is significantly lower than that in the lossless

case, shown in Fig. 2.10a. An obvious difference is

that the degeneracy point cannot be realized, as

shown by the blue and green dotted lines in Fig. 2.2.

As the ideal degeneracy point is approached, the

absolute value of the imaginary part of the

propagation constant, βi, increases significantly for

the |f> mode (see the blue line) and remains large

when the mode is converted to the |b> mode (see the

green line). Therefore, the mode intensity is

attenuated strongly as the degeneracy point position

Fig. 2.10 |E|-field distributions in

the (a) lossless and (b) lossy HMM

waveguide tapers for the TM0

modes, respectively.

is approached, with the simultaneous mode

conversion in the lossy HMM waveguide. One can see that the interference pattern shown

in Fig. 2.10b is suppressed as compared with the lossless situation shown in Fig. 2.10a,

indicating the weak intensity of the |b> mode converted from the |f> mode. Based on the

understanding of the mode conversion and loss properties of the HMM waveguide taper

array, an unambiguous mechanism of the predicted broadband absorption is therefore

clarified.

2.2.3 Period Dependence

27

3.0--------- 1.0..---,....,,..,..,....,...-----,

2.5 a 0.8 b

§ 2·0 .2 0.6 .::; 1.5 o. J 1.0 -······ ~ 0.4

0.5 ~ 0.2 0.0J:=::::: ____ ____::::====J 0.0-'-------------1

2 4 6 8 2 4 6 8 Wavelength (µm) Wavelength (µm)

For most periodic grating structures, their optical properties are usually sensitive to the

periodicity of patterns. In previously reported theoretical design, the period of the array

was generally selected based on the bottom width of the HMM waveguide taper [20-22].

It has not been revealed that how the period selection will affect the absorption properties

of the patterned HMM films. To demonstrate the absorption engineering tunability, here

Fig. 2.11 (a) 1D absorption cross-section of a single 8-pair HMM waveguide taper unit. (b)

Absorption spectra of three periodic patterns with the period of (A) 2.26 μm, (B) 1.35 μm and

(C) 1.14 μm.

we model the one-dimensional (1D) absorption cross-section, σabs, for a single unit of the

HMM waveguide taper, which is defined as the power absorbed by the HMM waveguide

taper (in the unit of Watt) divided by the incident power density (in the unit of Watt/μm in

two-dimensional modeling) [35, 36]. As an example, an 8-pair HMM waveguide taper unit

with the top and bottom widths of 550 nm and 1.14 μm, respectively, was analyzed in Fig.

2.11a. One can see that when the 1D absorption cross-section is larger than the physical

dimension of the bottom width (i.e. 1.14 μm, see the dotted line in Fig. 2.11a), the strong

absorption can be obtained within the wavelength range from 2.9 ~ 5 μm (see the shaded

region in Fig. 2), corresponding to two wavelength edges of the absorption band that can

be obtained by this pattern array. To validate this prediction, we model the absorption

spectra of the HMM waveguide taper array by tuning the period of the patterns. As shwon

in Fig. 2.11b, when the period decreases from 2.26 μm (structure A) to 1.35 μm (structure

28

-

0.6

0.2

§_ -0.2 ;::. o.6

0.2

-0.2 --2

, , , , a Max

~ ~ ~ ~

' = ='- '= =' - - --· b

, ____ , , ____ , , ____ , Min

-1 0 2 X (µm)

B) and 1.14 μm (structure C), the central position of the absorption band did not change

with the period, indicating that the absorption property of the proposed HMM waveguide

taper array is mainly determined by the top and bottom width of the HMM waveguide taper

rather than the period. The period selection will only affect the profile and intensity of the

absorption spectrum. One can see that in the short wavelength side, the absorption of

structure A (P=2.26 μm) is generally lower than those for structures C (P=1.14 μm) and B

(P=1.35 μm) since the absorption cross-section (i.e. 0.06 – 1.16 μm as shown in Fig. 2.11a)

is much smaller than the period of structure A. In addition, the absorption of structure C in

the long wavelength side is obviously stronger than the other two samples due to the mode

interaction between two ajacent pattern units in the subwavelength scale. According to the

modeling results shown in Fig. 2.11b, the absorption for structure A and C at the

wavelength of 5.15 μm are 93% and 45%, respectively. To reveal the difference between

these two structures, we plot the normalized E-field distribution at this wavelength, as

shown in Fig. 2.12a for structure C and Fig. 2.12b for structure A, respectively. One can

Fig. 2.12 Modeled E-field distributions in (a) structure C and (b) structure A at the

wavelength of 5.15 μm.

see that the localized field in structure A is obviously enhanced in the air gap between

adjacent HMM waveguide taper due to the mode interaction (see the white squares in Fig.

29

0.7

0.35 A=3.4µm

0 0.7

0.35 A=3.8µm

E 0 2: 0.7 N

0.35 A=4.2µm

0 0.7

0.35 A=4.6µm

-0.3 0 0.3 0.6

X(µm)

2.12b). This mode interaction within subwavlength scale resulted in the enhanced

absorption at longer wavelengths.

The mode distribution is modeled in an 8-pair HMM waveguide taper as an example

to interpret the broadband absorption observed in

Fig. 2.11. As shown in Fig. 2.13, four different

wavelengths (i.e. 3.4 μm, 3.8 μm, 4.2 μm and 4.6

μm) are trapped at four different positions along

the vertical direction of the structure, agreeing

well with the theoretical prediction shown in Fig.

2.9. In the next section, we discuss the fabrication

and characterization to realize the spectrally

tunable on-chip broadband super absorptive

hyperbolic metafilm from near IR to mid IR Fig. 2.13 Modeled |E|-field

distributions in the 8-paired HMM

waveguide taper (i.e. sample 3). spectral regions.

2.3 Multi-layered HMM Waveguide Taper Array for Broadband Absorption

Engineering

2.3.1 Experimental Realization of Multi-layered HMM Waveguide Taper Array for

Broadband Absorption

The alternating multi-layered Ag-SiO2 films were deposited in a multi-target electron-

beam evaporation system. The thickness of each Ag/SiO2 layer was controlled at 30 nm ±

5 nm. To improve the surface roughness of these alternating layers, 2-nm-thick Ge layers

30

a ~.d _ lJ 1J ! l[ ~- '. ~ --: ~- .-; ~ ~ jk_; ,-; -

1-- - 2 3 1z·r,~-b o.8

- 1-pair c 1.0 - 4-pair

C: - 8-pair 0.8 o 0.6

0.6 .; Q. ~ 0.4 0.4 VI

~ 0.2 0.2

o_o 0.0 2 4 6 8 2 4

I. ,:J_ ,__ 1-

- 1-pair - 4-pair - 8-pair

6 Wavelength (µm) Wavelength (µm)

8

were inserted between Ag and SiO2 layers to enhance the wettability between these two

materials [37-39]. In this experiment, we first deposited one-pair Ag/SiO2 layer on top of

a 150-nm-thick Al film and fabricated a one-dimensional (1D) patterned meta-absorber

using focused ion beam (FIB) lithography, as shown in Fig. 2.14a (sample 1). The period

and width of the top Ag pattern are 950 nm and 720 nm, respectively. Due to the optically

Fig. 2.14 a) 54˚-tilted SEM images of 3 samples of super absorptive meta-films with 1, 4, and

8 pairs of Ag/SiO2 stacks. b) and c) show measured and modeled absorption spectra of these 3

samples, respectively.

opaque ground plane (i.e. the 150-nm-thick Al film), the optical absorption of the structure

can be characterized by 1-R where R is the reflection intensity. With x-polarized incident

illumination, an absorption peak exceeding 75% was observed experimentally at the

wavelength of 3.5 μm, as shown by the solid black curve in Fig. 2.14b, agreeing well with

the numerical modeling result shown by the solid black curve in Fig. 2.14c. To demonstrate

the broadened absorption band based on the proposed HMM waveguide taper, we

deposited a 4-pair Ag/SiO2 layer on top of the 150-nm-thick Al film and patterned the

waveguide taper, as shown in Fig. 2.14a (sample 2). The alternating multi-layered

metal/dielectric films were deposited in a multi-target electron-beam evaporation system

(BOC Edwards Auto 500 system). All patterned hyperbolic metafilm structures were

31

fabricated using a focus ion beam milling system (Zeiss CrossBeam® Workstation system).

To obtain reasonably good fabrication quality, the milling current was set to 120 pA. The

fabrication area of each sample was 50 μm X 50 μm. The period of the HMM pattern is

1.17 μm and the width of the waveguide taper increases from 500 nm on the top end to 950

nm on the bottom end. As shown by the solid red curve in Fig. 2.14b, the measured full

width at half maximum (FWHM) of the absorption band was broadened from 2.5 to 4.7

μm, agreeing reasonably well with the modeling result shown in Fig. 2.14c, and covering

the narrow band absorption resonance obtained by the 1-pair Ag/SiO2 film structure

completely. To further broaden the absorption band, we then deposited 8-pair multi-layers

and patterned the waveguide taper array with the period, top width and bottom width of

(1.35 μm, 480 nm, 1.14 μm) as shown in Fig. 2.14a (sample 3). According to the

measurement and modeling results shown by solid blue curves in Figs. 2.14b and 2.14c,

the FWHM of the absorption band can be extended to 2 to 6.53 μm and 2.70 to 5.52 μm,

respectively.

The reflection/absorption spectra of patterned hyperbolic metafilms were characterized

using a microscopic Fourier transform infrared spectroscopy (Bruker, VETEX 70 +

Hyperion 1000). The wavelength range of this system is 450 nm ~ 28.5 μm. The

observation area for each sample was set to 50 μm X 50 μm. Two linear polarizers in the

visible-IR (i.e. Thorlabs, LPNIR100, 650 nm to 2 μm) and mid-far IR (i.e. Thorlabs,

WP25H-K, 2 μm to 30 μm) were used to control the polarization state of the incident light

in the characterization, respectively. It should be noted that the numerical aperture of the

15X objective lens is 0.4, which can only collect the scatter light within an angle of 23.6˚.

It is very difficult to characterize the absorption of small area structures accurately if the

32

b o.8 5 0.6 :.::; e- 0.4 0

~ 0.2 c

o.o----------2

b o.8 5 0.6 :.::; e- 0.4 0

~ 0.2 c

4 6 8 Wavelength (µm)

5

0.0+---~-~--..----' 0.9 1.2 1.5 1.8

Wavelength (µm)

C 1.0

0.8

0.6

0.4

0.2

C 0.8

0.6

0.4

0.2


0.0+---~-~--..----' 0.9 1.2 1.5 1.8

Wavelength (µm)

scatter light is beyond this collection angle. Fortunately, according to the modeling analysis,

the zero-order reflection spectra from all 8 samples are identical to their total reflection

spectra, indicating that higher order reflection/scattering signal is negligible. Therefore, the

measured absorption spectra reported in this article are reliable compared with their

corresponding numerical modeling results.

Importantly, this broad absorption band is tunable by changing the geometric

parameters. For instance, for the 4-pair HMM waveguide taper array, when the period, top



width and bottom width were tuned to 1.57 μm, 850 nm, 1.35 μm, respectively (see sample

4 in Fig. 2.15a), the FWHM of the absorption band was tuned to 3.80-6.03 μm and 4.05-

6.00 μm, indicated by the solid black curve in Figs. 2.15b (measured result) and 2.15c


absorption spectra of sample 5.

(modeled result). As shown in Fig. 2.16b (measured result) and Fig. 2.16c (modeled result),

we also tuned the absorption band to 0.90-2.00 μm by adjusting the period, top width and

bottom width to 300 nm, 110 nm, 270 nm based on the 8-pair multi-layers (see sample 5

33

https://0.90-2.00

https://3.80-6.03

! 1 >-

10 0

1 X(µm)

b 0.0

g 0.6 .. e: 0.4 0

2 0.2 c(

0.0-1----~--~------1 2 4 6 8

Wavelength (1,1m)

! 1 >-

10 0

1 X(µm)

C 1.0

0.8

0.6

0.4

0.2

o.oL--__ ....::::::::==d

!1 >-

0

2 4 6 8 Wavelength (1,1m)

•• ~~. ~ • 4 • • • • . ........ ~...-• •• ... I . .,, ~ - ~ .,,. .. • i ~' · • -~ .. •~· • I •. .. . t .• > . . :

10

1 X(µm)

in Fig. 2.16a). Furthermore, by extending the 1D tapered structure into the two-dimensional

(2D) pyramidal pattern array (see sample 6 in Fig. 2.17a, in which the period, top width

and bottom width are 1.17 μm, 500 nm, 950 nm, respectively), a polarization insensitive

absorption band can be realized for normal incident light, as shown by the black dotted

(i.e., y-polarization) and blue solid curves (i.e., x-polarization) in Fig. 2.17a (measured re



sult) and the black curve in Fig. 2.17b (modeled result).

However, a noticeable difference can be observed between experiment and modeling

results as the layer number increases, mainly due to the imperfect quality of the multi-

layered films, surface roughness and fabrication errors of the patterns. According to the

atomic force microscopic characterization shown in Fig. 2.18 (characterized by an AIST-

Fig. 2.18 Surface roughness of multi-layered films with a) 1-pair, b) 4-pair, c) 8-pair Ag/SiO2

layers. The root mean square roughness data for these films are 2.9 nm in a), 3.6 nm in b) and

3.9 nm in c), respectively.

NT SmartSPM™ 1000 system), the top surface roughness increases with more alternating

layers, which is one mechanism resulting in the difference between theoretical modeling

and experimental observation shown in Fig. 2.14. Meanwhile due to the fabrication error

34

-

of FIB milling process, the designed waveguide taper structure cannot be reproduced

perfectly, leading to the mismatch between modeling and measured results. The most

significant mismatch is that the width of the top Ag strip is slightly smaller than the

designed value. For instance, as shown in Fig. 2.14 (sample 2), the bottom width and

designed top width are 950 nm and 530 nm, respectively. However, the observed top width

is approximately 500nm as shown in the SEM image. In addition, the cross-sectional

profile of sample 5 is in a curved shape, which is different from ideal waveguide taper.

Consequently, in the modeling shown in Fig. 2.14, all geometric parameters of modeling

were adjusted based on the cross-sectional SEM images. Scattering and reflection from

these defects lead to the reduced coupling efficiency of the incident light into the HMM

waveguide tapers. According to a recent experimental report, tapered/pyramidal patterns

with fixed side-wall angle of 75˚ were manufactured using electron-beam lithography and

lift-off processes, which was not desired for the original design of those reported indefinite

cavities based on HMM waveguide patterns [17]. On the other hand, this intrinsic

tapered/pyramidal structure should provide a better surface roughness on side walls to

improve the quality of the pattern, which is still under optimization. Nevertheless, the

systematic experiment and modeling results presented in this section demonstrate the

feasibility and spectral tunability of the proposed super absorptive hyperbolic metafilms.

It should be emphasized that the ultra-broadband absorption tunability is a remarkable

feature of the proposed patterned hyperbolic metafilm compared with previously reported

compact plasmonic/meta-absorbers and structured plasmonic black metal surfaces [10, 11]

which were only realized in visible to near-IR spectral regions and difficult to be tuned to

other spectral regions due to the challenges in nanofabrication. However, an obvious

35

challenging to realize the proposed hyperbolic metafilm pattern is the quality control and

improvement for the multi-layered metal/dielectric films. For instance, 20 and 15 pairs of

metal/dielectric thin films were required to realize the broadband absorption band from

mid-IR [20] to near-IR spectral regime [21], respectively, which is extremely challenging

to maintain the flat and continuous films in practice. In the next section, we discuss a multi-

pattern design to minimize the required number of layers without sacrificing the absorption

bandwidth and extend the proposed HMM multi-layers to thinner hyperbolic metasurfaces.

2.3.2 Multi-unit Pattern Array Based on Less Metal/Dielectric Films

In recent years, multiple top pattern units with different dimensions in a single period

were fabricated to support different magnetic resonances and therefore broaden the

absorption band of single-paired planar meta-absorbers [40-43]. An ideal broadband

absorption resonance requires an optimized selection of period and width, which is difficult

to obtain due to the limited tunability of the pattern width within a given period. In addition,

the bandwidth cannot be broadened unlimitedly due to the finite period space, leading to a

trade-off between the absorption peak and its bandwidth [40-43]. To address the intrinsic

limitation imposed by the single-paired meta-absorber design, graded metal-dielectric

patterns were stacked in the vertical direction as we demonstrated in the previous section,

and therefore largely released the restriction of the pattern width tunability. By introducing

tapered or pyramidal multi-layered patterns in a single period, the width of the metal-

dielectric layer-pair can be freely tuned within the given period. In this case, multiple

resonant absorbers with finely tuned dimensions are cascaded in a single unit, leading to a

significantly broadened absorption band. Unfortunately, many more pairs of

36

a b 0.8

§ 0.6 .. e- 0.4 0 VJ

0.2 .c <(

4 6 8 C 1.0

0.8 C: 0 0.6 .. Q. 0 0.4 VJ .c 0.2

<(

0.0 +--~.-------.-----:! 2 4 6

Wavelength (µm)

a 04

0 0.4

E o.~ 2' N o

0.4

e o, 02

0 04

02

E oj _a 02

N o O• 02

·1 --0.5 0 0.!5

X (µm)

·• ... 0 OS X (µm)

A=3.4µm

A=3.8µm

A=4.2µm

A=4.6µm

•!l!t1n• = = JI!.,,.

metal/dielectric layers are required to realize broader absorption bands, which is

challenging in practice, as we explained in Section 2.3.1. Here we combine the multi-unit

pattern array proposed for single-paired perfect absorber and the multi-layered HMM

waveguide taper in a single structure to minimize the required number of layers and realize

an ultra-broad absorption band.

As shown in Fig. 2.19a (sample 7), a 2-unit HMM waveguide taper array was fabricated

Fig. 2.19 a) 54˚-tilted SEM images of super absorptive meta-films with multiple patterns in a

single period. The scale bar is 500 nm. Images (b-c) show measured and modeled absorption

spectra of these 2 samples, respectively. For comparison, the measured and modeled absorption

spectra of sample 3 with 8-pair Ag/SiO2 layers are plotted by solid red curves. (d) and (e) are

modeled |E|-field distributions in the (d) 1D two-pattern structure and (d) 2D four-pattern HMM

waveguide taper structure. The cross-sectional mode distribution shown in (e) is modeled along

the x or y axis with corresponding x- or y-polarized incident light.

on the 4-paired Ag/SiO2 film. The period of the pattern unit is 2.26 μm, and the top and

bottom widths of two units increase from 580 nm to 860 nm and from 790 nm to 1.2 μm,

respectively, similar to the width range of the tapered structure fabricated on the 8-paired

Ag/SiO2 film shown in Fig. 2.14a (sample 3, from 480 nm to 1.14 μm). One can see that

the FWHM of the absorption band ranges from 2.50 μm to 5.57 μm in experiment (see the

solid black curve in Fig. 2.19b) and from 2.90 μm to 5.31 μm in modeling (see the black

curve in Fig. 2.19c), which is equivalent to the one achieved by sample 3 in Fig. 2.14a.

37

Considering the obvious geometrical difference between sample 3 and sample 7 (i.e. the

spatial discontinuity between the two graded patterns and different period), the absorption

band of sample 7 is slightly narrower than that for sample 3 due to the larger period, which

was already predicted in Fig. 2.11b. To interpret this remarkable absorption property, we

model the mode distribution in this 1D two-pattern system as shown in Fig. 2.19d. One can

see that different wavelengths are trapped at different positions in these two patterns,

similar to the light trapping phenomenon obtained in the single unit HMM pattern array

(i.e. sample 3). It should be noted that the dimension of these two patterns was designed

with an overlap (i.e. the widths of the bottom and top of the small and large patterns are

860 nm and 790 nm, respectively) so that the potential effect of the discontinuity between

the bottom and the top of the two patterns can be minimized.

As shown by the second panel of Fig. 2.19d, the wavelength of 3.8 μm is trapped in

both small and large patterns. Furthermore, the polarization dependence of these 1D pattern

arrays can be overcome by introducing 2D distributed multi-unit patterns, as shown in Fig.

2.19a (sample 8). In this fabrication, the periods along two directions are both 2.26 μm,

and the square pyramidal widths of the four units increase from 630 nm - 860 nm (i.e. a1-

a2) and 790 nm - 1.20 μm (i.e. b1-b2), respectively. In this case, a polarization insensitive

absorption band is obtained with an FWHM from 2.60 μm to 5.56 μm. The slight

wavelength mismatch between the two polarization responses (see dotted lines in Fig.

2.19b) is introduced by the fabrication error along the x and y directions. As shown in Fig.

2.19e, the cross-sectional mode distribution along x or y direction is plotted using three-

dimensional modeling, confirming the polarization-insensitive vertical “rainbow” trapping

phenomenon in the 2D hyperbolic metafilm patterns. Importantly, the required number of

38

1.0 1.0 1.0 1.0

0.8 0.8 0.8 0.8

S 0.6 ~ "' 0.4 (1) = ~ 0.2

.§ 0.6

g 0.4

~ 0.2 (2)

.§ 0.6

g 0.4 = ~ 0.2

(3)

.§ 0.6

g 0.4 = ~ 0.2

0.0 0.0 0.0 0.0 2 4 6 8 2 4 6 8 2 4 6 8 2 4 6 8

1.0 1.0 1.0 1.0

0.8 0.8 0.8 0.8 C C C C 0 0.6 (5) o 0.6 (6) 0 0.6 (7) 0 0.6 :.:, :.:, :.:, :.:,

l;l 0.4 l;l 0.4 l;l 0.4 l;l 0.4 = ~ 0.2

= ~ 0.2

= ~ 0.2

= ~ 02

0.0 0.0 0.0 0.0 0.9 12 1.5 1.8 2 4 6 8 2 4 6 8 2 4 6 8

Wavelength (µm)

metal/dielectric layers is reduced by half, therefore simplifying the sample preparation and

experimental realization of the on-chip broadband super absorptive metafilms significantly.

Although the structure reported in this article was fabricated using FIB milling technique,

the multi-patterned structure is promising to be extended to a larger scale based on recently

reported nanofabrication methods including micro/nanosphere mask lithography and

nano/micro-stencil patterning [44, 45], and will enable the development of practical

optical/thermal technologies.

2.3.3 Scattering Property of HMM Waveguide Taper Array

It is necessary to analyze the scattering property of the proposed HMM waveguide

taper array due to the finite numerical aperture of the collection lens in our experiment

system (i.e. NA=0.4 corresponding to the collection angle of 23.6˚). If a significant part of

the light is scattered into higher order modes beyond the collection angle, the measurement

result cannot describe the absorption properties of the structure accurately. As shown in

Fig. 2.20 Comparison between the zero-order reflection spectra (see dots) and total reflection

spectra (see solid curves) for all 8 samples.

Fig. 2.20, we model the zero-order reflection spectra of all 8 samples (see dots) and

compare them with their corresponding total reflection spectra (see solid curves). One can

39

see that these two spectra are approximately identical, indicating that the high order

scattering/reflection are negligible for all samples analyzed in this work.

2.4 Summary

In conclusion, due to the strong attenuation during the mode conversion process

occurring in the HMM waveguide constructed by metal/dielectric multi-layers, the super

absorptive hyperbolic metafilm is realized with the tunable absorption band in near, mid

and far IR spectral regions. By cascading resonant metal-dielectric-metal perfect absorber

elements with gradually tuned widths along the vertical direction, the absorption band of

the patterned HMM film is extended significantly. Multi-patterned HMM metafilms have

been demonstrated to reduce the required number of metal/dielectric layers, and therefore

simplify the sample preparation and experimental realization of on-chip broadband super

absorbers. This work represents a major breakthrough in our understanding of the compact

photonic chip for photon harvesting, which will pave the way for future investigations of a

broad range of energy technologies, such as solar photovoltaics [46, 47], thin-film thermal

absorbers/emitters [48], and plasmon-mediated surface/localized photocatalysis [49]. In

addition, the spatial control of the localized dispersion properties of multi-layered HMM

patterns can also provide a practical platform for prolonged light-matter interactions [50].

Importantly, the thickness and width of each layer can be controlled to finely engineer the

absorption profile to mimic absorption properties of other materials for novel

stealth/camouflage applications. In addition, according to Kirchhoff law of thermal

radiation, the emissivity of a material is equal to its absorptivity at equilibrium. Due to the

spectrally tunable slow-light principle, the effective refractive index of the super absorptive

hyperbolic metafilm pattern is very large, particularly for mid-far IR wavelengths, which

40

is not naturally available. Therefore, being able to create a high index super

absorptive/emissive material for mid-far IR wavelengths will provide a technological

foundation that will revolutionize a variety of thermal applications, including extraction of

more thermal energy from a more compact thermal emitter [51], miniaturizing the

dimension and improving the performance of conventional heat-to-light converters,

thermophotovoltaic cells and radiative coolers/heaters [52]. This absorption engineering

will lead to the development of revolutionary, controllable, effective media, and improve

our ability to manipulate light in man-made metasurfaces that do not exist in the natural

world [53].

41

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47

Chapter 3

Extreme Light Confinement with Sub-5nm-

Gap Assisted Metamaterial Super Absorber

3.1 Introduction

Due to the diffraction limit of conventional optics, coupling and confinement of light

into deep-subwavelength volume is usually very challenging, resulting in difficulties in

exploring the light-matter interaction within these ultra-thin (one-dimensional, 1D) or

ultra-small dimensions (two- or three-dimensional, 2D or 3D). The unprecedented ability

of metallic nanostructures with nanometric gaps to concentrate light has attracted

significant research interest in recent years [1, 2]. It has been reported that the optical field

can be concentrated into deep-subwavelength volumes and realize significant localized-

field enhancement using a variety of nanoantenna structures [3], showing promise for the

development of enhanced nonlinear optics [4], surface photocatalysis [5, 6] and vibrational

biosensing spectroscopies [7, 8]. It is generally believed that smaller gaps between metallic

nanopatterns will result in stronger localized-field enhancement due to optically driven free

electrons coupled across the gap. According to previous research, visible light can be

squeezed into a 3 nm metal-dielectric-metal (MDM) plasmonic cavity with both open [9]

and closed ends [10]. In other recent work, an electric field enhancement of 1,000 was

experimentally demonstrated for a non-resonant 70-nm-wide slit in the terahertz regime

[11]. Following the prediction that the field enhancement will keep increasing with

decreasing gap size, much larger enhancement (e.g. 25,000) was observed for a 1 nm gap

at the wavelength of ~4 mm [12]. This increasing enhancement continues until the gap is

48

scaled down into quantum regimes (i.e., 0.3~0.5 nm), where the upper limit for plasmonic

field enhancement can be obtained [13-17]. Therefore, structures with extremely small gap

features are highly desired for light-matter interaction applications based on maximized

field confinement and enhancement. However, it is challenging to fabricate nanophotonic

structures with such small features to squeeze light into these extreme dimensions

efficiently.

Atomic layer lithography pioneered by ref. [12, 18-23] is a new technology to fabricate

deep-subwavelength uniform features. In this manufacturing process, atomic layer

deposition (ALD) is used to define nanogaps between pre-defined nanopatterns and

deposited metal films, giving Angstrom-scale lateral resolution along the entire contour of

structures. In the originally proposed strategy [12], the upper metal patterns have to be

peeled off using standard adhesive tape, which is a critical step of this ALD lithography

process. To realize the final metal patterns with very small gaps, it is crucial to fabricate

vertical sidewalls on the first layer, so that there is a discontinuity between the first layer

and the second, as reported in ref. [12, 18, 19]. Nevertheless, it is challenging to control

the sidewall verticality of the first metal layer and thickness of the second metal film to

obtain the tiny discontinuity. If the second layer is thick and forms a continuous film, the

entire layer will be peeled off. Recently, several groups including our own, developed

modified processes to avoid the challenging control of the side-wall and the second layer

deposition [20, 24]. Instead, the entire three-layered nanopattern (i.e., the first predesigned

nanopattern, the second ALD layer and the third metal deposition) is peeled from the

substrate, demonstrating a strategy to develop nanopatterns with ALD-defined gaps over

large areas that can increase the fabrication quality and yield [24]. However, although the

49

localized field can be enhanced significantly within smaller gaps, the light coupling

efficiency from free-space into these ultra-small volumes is usually very weak due to the

diffraction limit of conventional optics. For instance, the peak light coupling efficiency in

periodic patterns with 3 nm gaps is only 3% [20]. Most incident energy was lost due to the

weak coupling. Therefore, it is essential to develop new structures to improve the light

trapping performance and further enhance the localized field in these extreme volumes.

It was recently recognized that patterned metamaterial super absorber structures provide

a planar photonic platform to control the electromagnetic (EM) fields in ultra-thin/small

dimensions with flexibility and performance that was not previously possible [25]. A

particularly exciting opportunity has emerged in thin-film metamaterial super absorbers

capable of near-perfect light absorption [26]. These resonant on-chip structures provide a

promising platform for the efficient coupling and concentration of incident light into

subwavelength volumes. In this chapter, we will combine the super absorbing metamaterial

structure with modified ALD lithography to develop a super absorbing nanogap

metamaterial with sub-5-nm gaps.

3.2 Interaction Between Adjacent Patterns in Planar MDM Structures

As illustrated in Fig. 3.1, a typical three-layered planar metal-dielectric-metal (MDM)

metamaterial super absorber structure is constructed by a continuous metal ground plane,

a dielectric spacer layer and a top (periodic [26] or non-periodic [27, 28]) nanopattern array.

According to the microscopic description of the physical operating mechanism [11], when

the distance between each nanopattern is sufficiently large, the interaction between

50

-500

400

E 300 C: -c, 200

100

1

0

3 5 7 9

Wavelength (µm)

adjacent nanopatterns is negligible, the three-layered unit can be treated as an optical

analogue of a grounded patch antenna, with

a fixed spectral resonance. The position of

this absorption resonance is mainly

determined by geometric parameters of an

individual grounded patch antenna rather

than the period [28]. However, when the Fig. 3.1 Conceptual illustration of

gaps are reduced to sub-10-nm scales, metamaterial structure with 1D periodic

distributed patterns on the top surface.

adjacent modes will strongly interact with

each other and result in extreme localized field with an absorption peak that also depends

strongly on gap size.

3.2.1 Theoretical Analysis of Planar MDM Structure

To demonstrate this mechanism, we plot the absorption spectra of a 1D MDM

metamaterial super absorber as the

function of the gap distance, g. All

other geometric parameters are

fixed [i.e., the width (D), the

thickness of the top pattern (tm), the

thickness of the spacer layer (td) and

the thickness of the bottom layer (tb)

are fixed at 700 nm, 50 nm, 20 nm

and 100 nm, respectively]. As Fig. 3.2 Preliminary modeling of the absorption

spectra of patterned MDM super absorber structures. shown in Fig. 3.2, one can see that

51

a b C 6000 14000 35000

70 -E £: -N

20

0 0 0 0

-20 0 20 -20 0 20 -20 0 20

X(nm)

the perfect absorption peak (close to 100%) is fixed in the range of 3.5~3.7 µm when the

gap between ajacent patterns, g, is larger than 50 nm. However, in the small gap-distance

region, the absorption resonance will significantly shift towards the long wavelength region

due to the interaction between adjacent patterns (see the inset of Fig. 3.2). Specifically,

when g is reduced to 10 nm, the perfect absorption resonance is tuned to 4.52 μm, with an

enhancement factor (i.e., |E/E0|2) of >6,000 (Fig. 3.3a). If g is reduced to 5 nm, the perfect

absorption is shifted to 5.29 μm and the localized enhancement factor is increased to

>14,000, as shown in Fig. 3.3b. If g is further reduced to 2-nm, the strong absorption (over

71 %) is still realizable at 7.16 μm and the localized-field enhancement factor is enhanced

to >35,000, as shown in Fig. 3.3c. These modeling data indicate the potential to efficiently

concentrate the light into extremely deep subwavelength volumes for enhanced light-

matter interaction, which has not been realized by previously reported nanostructures.

To interpret the shifted resonance in mid-IR spectral region, here we employ the optical

nanocircuit theorem [29-32] to analyze the resonance condition, as illustrated in Fig. 3.3.

Fig. 3.3 Localized-field enhancement distribution (i.e., |E/E0|2) within the a) 10-nm-wide, b) 5-

nm-wide and c) 2-nm-wide gaps.

52

Le t C,

The resonance condition for the fundamental magnetic resonance mode can be obtained by

canceling the total impedance [29]:

𝐿𝑚+𝐿𝑒 2𝑍𝑡𝑜𝑡(𝜔) = 𝑗𝜔 ∙ [ − + 𝐿𝑚 + 𝐿𝑒] (3.1).

1−𝜔2𝐶𝑔(𝐿𝑚+𝐿𝑒) 𝜔2𝐶𝑚

Here 𝐿𝑚 = 0.5𝜇0𝑡𝑑𝐷/𝑙 accounts for the parallel-plate inductance; 𝜇0 is the vacuum

permeability; l is the length along the groove direction; 𝐶𝑚 = 𝑐1휀𝑑휀0𝐷𝑙/𝑡𝑑 represents the

parallel-plate capacitance. Parallel-plate capacitance 𝐶𝑔 = 𝑐2휀𝑔휀0𝑡𝑚𝑙/𝑔 is used to describe

the gap capacitance between neighboring patterns. Constants 𝑐1 = 0.21 is related to the

non-uniform charge distribution caused by magnetic resonance [33], 𝑐2 = 2.4 is the

correction factor due to fringing effect of capacitance [34]. 휀𝑑, 휀𝑔, and 휀0 are the relative

permittivities of dielectric spacer material,

gap material, and the vacuum, respectively.

A general form of kinetic inductance 𝐿𝑒 =

′ )−𝐷/(𝜔2𝑡𝑚𝑒𝑓𝑓𝑙휀0휀𝑚 is employed by

considering the real part of dielectric

′ function (휀𝑚) of Al. The effective thickness

(tmeff) for electr ic currents is defined as the Fig. 3.4 Effective circuit model for MDM

super absorber structure. power penetration depth δ if δ < tm (𝛿 =

√𝜌/(𝜋𝑓𝜇), where ρ is the resistivity of the conductor, f is the frequency, μ is the absolute

magnetic permeability of the conductor). Otherwise, tmeff = tm. The resonant condition is

mainly determined by Cg and (Lm + Le), simultaneously (Cm is independent on g). To further

reveal their respective contributions, the impedance values of Cg and (Lm + Le) at the

resonant wavelength as the function of g are plotted in Fig. 3.4. When the gap size is

53

sufficiently large, the absolute impedance of Cg (red curve) is much larger than that of (Lm

+ Le) (blue curve). Since Cg and (Lm + Le) are in parallel, the impedance induced by Cg can

be neglected, i.e., the resonant wavelength is insensitive to the gap distance, g, and only

determined by the impedance of (Lm + Le), which is almost a constant (see the dashed line

in Fig. 3.5). In this case, the corresponding wavelength set the lower limit of the resonant

wavelength for the MDM super absorber structure (see the white dashed line in Fig. 3.2).

This is consistent with the previously reported conclusion [28]: i.e., when the distance

between each nanopattern is so large that the interaction between adjacent nanopatterns is

negligible, the resonant wavelength is mainly determined by the geometric parameters of

the individual optical patch antenna.

On the other hand, as g decreases, Cg becomes non-negligible. As shown in Fig. 3.5, the

two curves for Cg and (Lm + Le) get close to each other, and therefore determine the resonant

wavelength of the circuit simultaneously. As shown by empty triangles in Fig. 3.2, the

resonant wavelength for different gap distance

is plotted using Equation 1, agreeing well with

the numerical modeling (including the small g

region, as shown in the inset of Fig. 3.2).

Therefore, this nanogap MDM does provide a

way to enhance the light-matter interaction

1Imp

ed

an

ce (

oh

m)

x10-5

1 10 100g (nm)

10

100

Fig. 3.5 Impedances of Cg (red curve) and within extremely small volumes that approach

(Lm+Le) (blue curve) at different gap

distance. The dashed line shows the the theoretical upper limit [14] (it should be

impedance of (Lm+Le) at resonant

wavelength for a single grounded patch noted that the quantum limit identified by ref.

antenna.

[13] cannot be predicted accurately using this

54

classical model). However, this planar MDM structure is extremely difficult to fabricate

using the originally proposed ALD lithography process [12]. Instead, here we propose an

alternative corrugated metamaterial structure to overcome those challenges in fabrication

to realize the extremely enhanced field within extremely small gaps over large areas.

3.2.2 Spectral Tunability in Terahertz (THz) Domain

It should be noted that these “nanogap” super absorber structures can be scaled up for

operation in THz regimes in order to achieve strong field confinement and enhancement

for use in THz spectroscopy and detection. In order to show this, we designed a nanogap

super absorbing structure for operation at 1 THz. The metal used was aluminum (Al),

which was chosen due to its lower cost and near equivalent performance to silver and gold

at THz frequencies [35]. Silicon (Si) was chosen as the spacer material due to its

transparency in THz. In the model geometry (shown in Fig. 3.6a)), the patterned upper Al

thickness (tp) was 100 nm. The Si spacer thickness (ts) was 2 µm, and the Al reflector plate

thickness (tb) was 200 nm. The period (P) was fixed at 26.2 µm, while the gap (g) was

varied from 15 nm – 65 nm. The Drude parameters for Al used in the modeling were taken

from reference [36], while Si has constant n= 3.42 and k= 0. The absorption peak at 1 THz

(see Fig. 3.6b)), for which this geometry was optimized, corresponds to a gap size of 15

nm. As shown in Fig. 3.6b), the absorption peak blue shifts as a function of increasing gap

size, asymptotically approaching the absorption peak of a single, isolated metal pattern.

55

C d e 4x106

g = 65 nm g = 55 nm g = 45 nm

f g h

I g = 35 nm g = 25 nm g = 15 nm 0

Wavelength (µm)

This behavior agrees well with the result shown in Figs. 3.2. In terms of field enhancement

and gap size, Figs. 3.6c – 3.6h show an inverse relationship, where stronger localized field

Fig. 3.6 a) Schematic illustration of the model. b) Absorption curves for gap sizes from 15 nm

to 65 nm in the THz regime. Period was fixed at 26.2 µm (need other geometric parameters and

materials). Note that reducing the gap by 50 nm induces an asymptotic red shift in the resonance

from 259 µm (g= 65 nm) to 300 µm (g= 15 nm), while maintaining absorption greater than

90%. Therefore, the gap-induced tunability discussed in Section 3.2.1 is also observed in the

THz regime. Maps of electric field enhancement (|E|/|E0|)2 are shown in figs. c) – h) for gap

sizes decreasing from 65 nm to 15 nm in a step of 10 nm, at resonant wavelengths of 259 µm,

262 µm, 267 µm, 274 µm, 283 µm and 300 µm, respectively (corresponding to the resonance

peaks in the curves shown in a). The peak field enhancement in fig. g was over 1.38×107 near

the corners of the structure. The scale of the color bar was chosen for clarity across all of figs.

c) – h).

strengths are obtained within smaller gaps as expected. Again, this agrees well with Figs.

3.3a – 3.3b in Section 3.2.1. The maximum obtained field enhancement (|E|/|E0|)2 was over

1.38×107 near the corners of the Al pattern with an average of approximately 4×106 within

the gap. The scale of the color bar used in Figs. 3.6c – 3.6h was chosen for clarity across

all sub-figures. Thus, the super absorber structures described in Section 3.2.1 can also be

scaled to THz frequencies, with a nanogap dependent tunability in this region as well.

3.3 Efficient Light Trapping in Corrugated MDM Structure with ALD-defined Gaps

3.3.1 Theoretical Analysis of Corrugated MDM Structure

56

1. 0 ..------,......------,

c: 0.8 0 :;::. 0.6 C. 0 0.4 ,,, .C 0.2 <(

0.0= '--,--------,-------1 4 6 8

Wavelength (µm)

c, c,

p

The schematic diagram of the new structure is illustrated in Fig. 3.7. The ground plate

is a corrugated grating with a top antenna

pattern embedded in the trench of the grating

and isolated by very narrow gaps. The top

surface of the structure is flat. By selecting

Fig. 3.7 Schematic illustration of the

MDM metamaterial structure with

corrugated ground plate.

suitable parameters (e.g. P= 600 nm, D= 300

nm, tm = 40 nm, td= 60 nm, g= 5 nm, tb=100

nm), a resonant perfect absorption at 5.54 μm

can be obtained, as shown in Fig. 3.8. ThisFig. 3.8 Modeled absorption peak of a

designed structure with the geometric resonant wavelength can also be explained parameters of (P= 600 nm, D= 300 nm, tm =

40 nm, td= 60 nm, g= 5 nm, tb=100 nm). using the optical nanocircuit theorem, as

illustrated in Fig. 3.9. In this case, the resonant wavelength condition can be determined by

zeroing the total impedance of this circuit:

1 ′ −𝜔2+𝐶𝑔(𝐿𝑚+𝐿′

𝑒) 𝑍𝑡𝑜𝑡(𝜔) = 𝑗2𝜔 [ + (𝐿𝑚 + 𝐿𝑒)] (2)′ ′ )(𝐶𝑚+𝐶𝑔)−𝜔2𝐶𝑚𝐶𝑔(𝐿𝑚+𝐿𝑒

Fig. 3.9 Effective circuit model for MDM structure with corrugated ground plate.

57

a 50

e .S 30 Cl

10

b 110

e .s N 0

2

-150

a

6 10 Wavelength (µm)

4000

0 150 O X (nm)

_ , ___ ___.n 8 _ _ _,

′ where 𝐿𝑚 = 0.5𝜇0(𝐷 + 2𝑔)(𝑡𝑚 + 𝑡𝑑)/𝑙 is the mutual inductance caused by the parallel-

′ ′ plate inductance; 𝐿𝑒 = −(𝑡𝑚 + 𝑡𝑑)/(𝜔2𝑡𝑚𝑒𝑓𝑓𝑙휀0휀𝑚) is the kinetic inductance of the side-

wall of the second metal layer. Using this equation, the

resonant wavelength is plotted by empty triangles in

Fig. 3.10a, agreeing very well with the numerical

modeling results. Due to the significantly increased Cg

in the ultra-small gaps, the resonance will redshift as

the ga p size decreases. In this case, the light is

squeezed into the 5-nm-wide gaps leading to a field

enhancement factor of 1.55×104 at the resonant

wavelength (Fig. 3.10b). Importantly, this corrugated

Fig. 3.10 a) Modeling of the MDM structure with ALD-defined nanogaps is

absorption spectra of structure in

3.7. b) Modeled electric field realizable from a fabrication standpoint.

enhancement distribution around

the ultra-small gap. The peak

value of the scale bar is set to

4000 to show the localized field 3.3.2 Experimental realization of corrugated more clearly. The actual peak

value is 1.55×104 . MDM structure

To demonstrate the feasibility, we first deposited a Ag/Ti/SiO2 layer on a glass substrate

and then fabricated the periodic patterns with focused ion beam (FIB) milling. The thin Ti

Fig. 3.11 a)-c) Manufacturing procedure to fabricate corrugated MDM super absorbers with

ultra-narrow gaps.

58

600nm -

C C: 0 :.::

0.4

C. ,_ o 0.2 VI .c <(

· • ... 0.0+--~~--~------,


film functions as the adhesion layer between Ag and SiO2. Next, this pattern was coated

with an ALD-defined ultra-thin dielectric film (Fig. 3.11a) and another thick Ag film (Fig.

3.11b). Finally, the entire three-layered structure was peeled off to obtain the proposed

Fig. 3.12 a) Top-view and b) cross-sectional SEM images of a fabricated structure with the

parameter of P= 600 nm, D= 300 nm, tm = 40 nm, td= 60 nm, g= 5 nm, and tb= 100 nm. c)

Measured absorption spectrum of the fabricated structure (blue solid curve) and the modeled

absorption curve (red dotted curve) by considering real parameters extracted from the SEM

image.

corrugated super absorber structure (Fig. 3.11c). According to the calibration of our

commercial ALD system (Ultratech/Cambridge Nanotech Savannah S100), ~0.089 nm

thick dielectric films can be produced for each cycle reaction under 80 °C, indicating the

capability to accurately control the gap size. Following this procudure, a corrugated MDM

structure with deep-subwavelength gaps (P= 600 nm, D= 300 nm, tm = 40 nm, td= 60 nm,

g= ~5 nm fabricated by 56 cycles ALD reactions, and tb= 100 nm) was obtained

successfully as shown in Fig. 3.12a (top view) and 3.12b (cross-sectional view). In this

experiment, the FIB milling area is ~ 50 μm × 50 μm. Its resonant wavelength is at ~5.3

µm with the absorption peak of 45% (blue curve in Fig. 3.12c), agreeing well with the

numerical modeling based on the extracted geometric parameters (red dots in Fig. 3.12c).

Although the geometry of this structure was not optimized yet, the absorption peak is

significantly higher than that obtained previously with no super absorber cavity (i.e., 3%

as reported in ref. [20]). One can see that the side wall of the metal/SiO2 pattern is not

59

al j 11111 f I sooti,m ' -r-

500 nm -

1.0 C

0.8 C: 0 0.6 :s_ ... 0 0.4 IJl SJ < 0.2

0.0 2 3 4 5 Wavelength (µm)

vertical to the substrate plane, demonstrating that one of the major advantages of our

corrugated MDM super absorber: i.e., the verticality of the sidewalls of metal patterns and

thickness control of second metal layer are no longer critical for fabrication. In addition,

this resonant peak can be optimized by suitably designing and fabricating the geometric

parameters. For instance, another structure was fabricated successfully (Fig. 3.13a (top

view) and 3.13b (cross-sectional view)) with optimized parameters of P= 500 nm, D= 250

nm, tm = 30 nm, td= 60 nm, g= ~5 nm, and tb= 150 nm, realizing a higher absorption

peak >81% at the resonant wavelengths of 3.31 μm (blue curve for experimental results

and red dots for modeling results in Fig. 3.13c). The resonant wavelength can be controlled

by tuning the geometry of the nanopatterns. Intriguingly, the dependence of the resonant

Fig. 3.13 a) Top-view and b) cross-sectional SEM images of a structure with the parameter of

P= 500 nm, D= 250 nm, tm = 30 nm, td= 60 nm, g= 5 nm, and tb= 150 nm. c) Measured absorption

spectrum of the fabricated structure (blue solid curve) and the modeled absorption curve (red

dotted curve) by considering real parameters extracted from the SEM image.

wavelength on nanogap, as defined by ALD thickness, provides a unique spectral tunability

while maintaining fixed lateral dimensions of the first nanopatterns.

3.4 Spectral Tunability with Fixed Lateral Dimensions

60

In most reported nanophotonic structures (including photonic crystals, plasmonics and

metamaterial structures), period is one of the most important parameters to tune the

resonant wavelength. However, for this lateral-dimension-dependent spectral tenability

(e.g. from Fig. 3.12a to Fig. 3.13b), advanced top down lithography technologies were

mostly required. Even high throughput techniques, such as photolithography and nano-

imprint lithography, require different mask/stamp profiles for different lateral dimensions,

imposing a significant cost barrier for these types of nanostructure fabrication. Here we

will demonstrate a new strategy to realize the spectral tunability based on the same lateral

dimension.

As demonstrated in Fig. 3.2 and 3.10a, due to the strong interaction between adjacent

nanopatterns (i.e., the contribution of Cg in Equation 3.1 and 3.2), the resonance can be

redshifted using the same lateral dimensions of the metal patterns by using different gap

distances defined by ALD processes. To demonstrate this unique spectral tunability, we

fabricated a set of three sample with identical lateral dimension, as shown in Fig. 3.14a (P=

300 nm, D= 150 nm, td= 40 nm, i.e., the first layer pattern illustrated in Fig. 3.11a). On top

of these structures, we introduced three different ALD-controlled gaps of 3.03 nm (34

cycles), 4.98 nm (56 cycles) and 7.03 nm (79 cycles), respectively. The ALD film thickness

and uniformity was confirmed using a spectral ellipsometer (J. A. Wollam) at 9 different

areas on the same reference Si substrate coated on the same ALD process. Finally, we

deposited the second 200-nm-thick metal film to form the complete super absorber

structure. One cross-sectional SEM image with the gap of ~5 nm is shown in Fig. 3.14b.

As a result, we obtained three different absorption resonance centered at 2.96 μm, 2.74 μm

and 2.48 μm, respectively (solid curves in Fig. 3.14c), agreeing reasonably well with our

61

J

r:r, I !Ii l

- - -

C 1.0 ....

.... .. 0.8 ..

s: 0 0.6

:,;::; Q. ~ 0.4 0 ti) .Q

< 0.2

0.0 2 3 4

Wavelength (µm)

numerical modeling results (dots in Fig. 3.14c). The relatively large difference in the

absorption spectrum for the 3-nm-gap sample should be attributed to the fabrication error

and intrinsic roughness of the

actual structure. These

experimental data

demonstrated the feasibility of

this method for realizing a

resonant field enhancement

that can be tuned over a wide

spectral range with structures

that have identical preliminary

fabrication steps and patterns

(i.e., Fig. 3.11a).

3.5 Summary Fig. 3.14 a) SEM image of the first layer grating with P=300

nm and D=150 nm. b) Cross-sectional SEM image of a

fabricated structure (tm = 40 nm, td= 40 nm, and tb=200 nm)

with the gap size of ~5 nm. c) Absorption spectra of three In conclusion, we proposed samples with different gap sizes of ~3 nm (blue curve), ~5

nm (black curve) and ~7 nm (red curve), respectively. a metamaterial super absorber Insets: Schematic illustration of the MDM metamaterial

structures with different gaps. structure with sub-5-nm gaps.

Due to the strong interaction

between adjacent patterns, the resonant wavelength can be manipulated by controlling the

gap size based on fixed lateral dimensions of major patterns. Using modified ALD-

processes, a novel metamaterial super absorber structure with corrugated ground plate was

realized. Strong light trapping resonances were obtained in the mid-IR spectral range.

62

Remarkably, these highly efficient trapped light modes are confined within sub-5-nm gaps,

resulting in significantly enhanced fields, which are particularly promising for surface

enhanced light-matter interaction. This structure is amenble to larger area manufacturing

methods like optical interference patterning and nano-imprint lithography. This type of

nanogap metamaterial super absorber is particularly attractive for the development of

practical nanophotonic platforms for optoelectronic, energy harvesting, conversion and

biosensing applications within extreme volumes approaching the plasmonic quantum limit

[13, 16, 37].

63

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67

Chapter 4

Surface Enhanced Infrared Absorption

Spectroscopy Using Nanogap MDM Super

Absorber

4.1 Surface enhanced sensing around ultra-small gaps

Infrared (IR) vibrational spectroscopy is one of the most important techniques for

chemistry, medicine, and biology, since it can identify molecular composition by analyzing

“fingerprints” of signature functional groups [1-5]. However, due to the small intrinsic

cross-section of a molecular vibration for IR spectroscopy, the sensitivity of this technique

is rather limited. In order to obtain vibrational information from extremely small amount

of molecules, SEIRA spectroscopy has been developed to improve the detection

performance relying on patterned metal surfaces with localized-field enhancement [2, 4-7].

Particularly, it is a complementary sensing technique to surface enhanced Raman

spectroscopy (SERS): i.e., absorption peaks of SEIRA generally correspond to Raman

scattering peaks of SERS. Signals generated by these two technologies could be more

sensitive at different spectral regions, complementing each other further. Therefore, an

ideal situation is to measure the same sample using these two techniques simultaneously.

However, since the vibrational absorption signal of SEIRA is proportional to |E/E0|2 in

contrast to |E/E0|4 for SERS, the enhancement factor for SEIRA is usually orders of

magnitude lower than SERS [8]. This weakness significantly restricts the application of

SEIRA in ultra-sensitive applications. Recently, various nanopatterns with extremely small

gaps were developed to demonstrate enhanced sensitivity for SEIRA applications. For

68

instance, photochemical metal deposition method was employed to fabricate a SEIRA

substrate with a 3-nm gap between two nano-rod antennas, achieving a signal enhancement

over 2×105 experimentally [5]. However, the scalability, uniformity and reproducibility of

nanogaps fabricated by electron beam (e-beam) lithography over small areas remain

challenging, something that can be addressed using our proposed corrugated MDM super

absorber structure with nanogaps over large areas [9]. In this chapter, we demonstrate our

structure can obtain extremely enhanced light fields that are particularly useful for

enhanced light-matter interaction by squeezing mid-infrared (mid-IR) light into nanogaps

efficiently, as demostrated using surface enhanced infrared absorption spectroscopy

(SEIRA).

4.2 SEIRA for PMMA

4.2.1 Experimental Results for PMMA Molecules Sensing

To demonstrate the feasibility, here we

employed the structures in Fig. 3.12 and

3.13 as the SEIRA substrates to iden tify the

infrared fingerprints of chemical molecules.

When the chemical molecules bind on top of

the nanogap and interact with the locally

enhanced field (Fig. 4.1), its infrared

absorption signal should be enhanced

Fig. 4.1 Conceptual illustration of SEIRA

accordingly. In this experiment, we first sensing using nanogaps.

69

1.0-===========

C 0.8 0

u Q)

'$ 0.6 0::

: VIMA on I g : I I I I

! w/o PMMA

:

i I I

PM MA on MOM I I I I

0.4 ............ -~-~------·---·~-~--1 5 6 7 Wavelength (µm)

0.04

0.00

0 Cl'.'.

I

Cl'.'. -0.04

-0.08

5 6 7 Wavelength ~1m)

selected Poly(methyl methacrylate) (PMMA) as the sensing target since its absorption

finger prints overlap with the absorption band of the fabricated sample in Fig. 3.12. We

spin-coated a ~100-nm-thick PMMA layer on our corrugated MDM structure. For

comparison, a reference sample was

prepared with the same PMMA layer on a

flat Ag substrate. Their reflection spectra

with and without PMMA coating are plotted

in Fig. 4.2. Since the fabricated one-

dimensional structure is polarization

dependent, the resonance can only be

observed under transverse magnetic (TM)

polarized incidence, while under transverse

electric (TE) polarization, there is negligible structural contribution to the response and the

reflection is close to 100%. With TM

polarization, a dip at ~5.5 μm can be

observed on the two samples, corresponding

to the absorption bands of a carbonyl group

(1718.3 cm -1) and poly(vinyl acetate)

(PVAc) segments (1726.9 cm -1) (i.e.,

signatures of PMMA molecules in SEIRA

sensing [10], indicated by the green dashed

lines in Fig. 4.2, 4.3). One can see that the

amplitude of the signal from the MDM structure is obviously stronger than that from the

Fig. 4.2 Experimental reflection spectra of

nanogap-assisted MDM super absorber with

(red curve) and without (blue curve) PMMA

coating, and PMMA film directly spin-

coated on bare Ag film (orange curve).

Fig. 4.3 Reflection differences for both the

nanogap-assisted MDM super absorber

sample (red curve), and bare Ag film (blue

curve). R and R0 are the reflection of bare Ag

film/ MDM super absorber with and without

PMMA, respectively.

70

reference sample. For clarity, the difference between the spectra with and without PMMA

coating is plotted in Fig. 4.3, showing that the amplitude of the signature on the MDM

structure is enhanced by 11.1. Considering the strongly localized field within the nanogap

and the selection rule for SEIRA (i.e. only molecules parallel to the dipole moment of the

localized field can be preferentially enhanced) [11], this enhanced signal is actually

contributed by a region at the side wall of the first metal pattern that is close to the PMMA-

MDM interface. It should be noted that the mid-IR field is strongly localized around the

nanogap and decay exponentially away from the interface. Therefore, by analyzing the

field distribution obtained by numerical modeling, the minimum enhancement factor for

PMMA layer is estimated from ~1.2×105 to 1.8×10 , which is two orders of magnitude

stronger than the previously reported data for PMMA layers on gold strip grating structures

[12].

4.2.2 Enhancement factor calculation for PMMA coatings

The estimation of the EF of SEIRA characterization is dependent on both experimental

results and data processing methods. In particular, selection rule of vibrational

spectroscopy has to be considered: i.e., only molecules parallel to the dipole moment of

the localized field can be preferentially enhanced [11]. Other molecules do not contribute

to the localized enhanced light-matter interaction. This consideration was widely

implemented in other references. For instance, in ref. [12], although a 100-nm-thick

PMMA was coated on top of the structure, only the surface area of the side wall of metal

patterns with localized field enhancement was considered. In ref. [13], only the surface

area of the side wall at the tip of metal nanorods was considered. However, it should be

71

a

E 100 C .__..

N 60

-180 -150 -120 x (nm)

b MAX

MIN -180 -150 -120

x (nm)

noted that these data processing procedures are all approximation by assuming the

localized field are uniform at the side walls.

In our calculation, it is important to determine the effective sensing area in the

corrugated MDM structure. Since the Al2O3 filled in the nanogap was not etched away,

Fig. 4.4 |EX|2 and |EZ|2 distributions around the 5 nm gap.

chemical molecules can only attach to the top surface of the MDM structure. It should be

noted that the spin-coated PMMA molecules are randomly distributed around the gaps.

Therefore, both |EX|2 and |EZ|2 field components will contribute to the enhanced absorption

signal. As shown in Fig. 4.4a and 4.4b, the |Ex|2 and |Ez|

2 field intensity distributions at

MDM/PMMA interface are modeled. By plotting the field intensity distribution across the

nanogap at the MDM/PMMA interface (Fig. 4.5a for |Ex|2 and Fig. 4.5b for |Ez|

2), one can

determine the effective sensing area, which was usually defined by the decay length when

the intensity decreases to 1/e2 over both the lateral and vertical directions [10]. In this case,

the effective sensing width and height can be estimated to ~0.81 nm ×1.7 nm for |Ex|2 (Fig.

4.6a) and ~0.4 nm ×0.23 nm for |Ez|2 (Fig. 4.6b), respectively. Therefore, the enhancement

factor can be expressed as:

∆𝑅𝑠𝑡𝑟𝑢𝑐 𝑉𝑟𝑒𝑓 𝐸𝐹 = × (4.1)∆𝑅𝑟𝑒𝑓 𝑉𝑒𝑓𝑓

72

a 1.0

2!-0.8

·.;; C $ 0.6 C

'O Q)

0.4· .'::! .; E ~ 0.2· 0 z ~------- " - . 1/e2 _______ .,

J\,J\.... 0.0 +-- - --,.-===:..........,,_L..,-.....::::--- ...... ~ -170 -160 -150 -140

x (nm)

a 1.0~-----~----~

2!·.;; C

0.8·

$ 0.6· C

al .'::! .; § 0 z

0.4

0.2 ~------- ,.. _ 1/e2 _______ .,

..I\ 1\. 0.0 +-- - ----,.-===::.........,,_.L,.-=--- --.--_j -170 -160 -150 -140

x (nm)

b 1.0..--.--------------,

0.8 2!-'iii C $ 0.6· C

al .'::! .; § 0 z

0.4

0.2 1/e2

--- ----------------o.o.l-~ ..........:::;::==-=-----~-~ --l

100 101 102 103 104 105

z (nm)

b 1.0..--.--------------,

0.8 2!-'iii C $ 0.6 C

al .'::!

~ 0 z

0.4

0.2 1/e2

--- ----------------o.o+-~ ~ ::;::===;=-.--.-~-~ --1

101 102 103 104 100 105

z (nm)

where ∆𝑅𝑠𝑡𝑟𝑢𝑐 (=0.06) is the reflection difference of our MDM sample with and without

Fig. 4.5 a) and b) are |EX|2 distribution along x and z directions, respectively. Blue dotted lines

indicate the 1/e2 intensity position.

PMMA coating; ∆𝑅𝑟𝑒𝑓 (=0.0054) is the reflection difference of bare silver film with and

without PMMA coating, as shown in Fig. 4.3; 𝑉𝑟𝑒𝑓 (=50 μm ×50 μm × 100 nm) is the

PMMA volume measured with Fourier-transform infrared (FTIR) spectroscopy; and 𝑉𝑒𝑓𝑓

Fig. 4.6 a) and b) are |EZ|2 distribution along x and z directions, respectively. Blue dotted lines

indicate the 1/e2 intensity position.

(=0.81 nm × 1.7 nm × 50 μm × 4 × 83 for |Ex|2 and 0.4 nm × 0.23 nm × 50 μm × 4 × 83 for

|Ez|2) is the effective sensing volume.

Here we consider two ideal cases to estimate the enhancement factor: (1) If PMMA

molecules are all oriented along x-axis, the enhanced signal is fully contributed by |Ex|2 (i.e.

73

a b MAX

E4o C .__.. N 0

M IN -1140 -1050 -960 -1140 -1050 -960

x (nm) x (nm)

Fig. 4.5a and b). In this case, the enhancement factor is 1.2 ×105. (2) If PMMA molecules

are all oriented along z-axis, the enhanced signal is contributed by |Ez|2 (i.e. Fig. 4.6a and

b). The corresponding enhancement factor can be calculated as 1.8 × 106. However, it

should be noted that PMMA molecules oriented along y-axis (i.e. along the nanogap

direction) will not contribute to the enhanced absorption signal due to the selection rule.

Therefore, the minimum enhancement factor obtained by the nanogap super absorber

structure should be between 1.2 ×105 and 1.8 ×106 (i.e. one to two orders of magnitude

higher than the previously reported result [12]). A more accurate estimation will require

the understanding on the actual orientation of PMMA molecules within the sensing area,

which is challenging based on available characterization technologies.

4.2.3 Comparison of sensing area

Due to the sub-10-nm nanogaps, the enhanced field is tightly confined around the

nanogap, which is one of the most significant unique features of the proposed nanogap

Fig. 4.7 a) b) |EX|2 and |EZ|2 distributions around the grating structure.

super absorber. To further demonstrate this unique feature, we simulated a 40 nm Ag

grating array placed on a glass substrate for comparison. The resonance peak was tuned to

74

a 1.0 C 1.0

0.8 0.8 z- z-·;;; ·;;; C C Q) 0.6 2 0.6 E C

'O 'O Q)

0.4 Q)

0.4 .!,! .!,! cij cij

E 0.2 1/e2 E

0.2 0 0 z -------- -------- z

0.0 0.0 -1060 -1050 -1040 -1060 -1050 -1040

x (nm) x (nm)

b 1.0 d 1.0

0.8 0 .8 z- z-·;;; ·;;;

C C: $ 0.6 Q) 0.6 c .f: 'O 'O Q)

0.4 Q)

0.4 .!,! .!,! cij cij

E 0 .2

E 0.2 1/e2

0 0 z z -------- - ------

0.0 40 50 30 40 50

z (nm) z (nm)

the same wavelength as our nanogap MDM structure shown in Fig. 3.13. As we can see

Fig. 4.8 a) and b) are |EX|2 distribution along x and z directions, respectively. c) and d) are |EZ|2

distribution along x and z directions, respectively. Blue dotted lines indicate the 1/e2 intensity

from the field distribution (Fig. 4.7a and 4.7b), the enhanced area for |Ex|2 = 1.6 nm ×8 nm

(as shown in Fig. 4.8a and 4.8b), and for |Ez|2 = 10 nm ×1.75 nm (as shown in Fig. 4.8c

and 4.8d), which are ~10 and 190 times larger than the effective area for nanogap MDM

structure along lateral and vertical directions, respectively.

4.3 SEIRA for ODT

4.3.1 Experimental results for ODT monolayer sensing

To further demonstrate this improved surface enhancement effect, we then coated our

sample with a monolayer of 1-Octadecanethiol (ODT) molecules to perform the second

75

a 1.0 b 0.08 ' '

0.8 ODTon A~ ! 0.04

C: ! 0 0.6 ! u 0

w/o OD~ 0::: Q) I

to::: 0.4 0::: Q) ! 0.00

0::: ! '

0.2 -0.04

3.0 3.5 4.0 3.0 3.5 4 .0 Wavelength (µm) Wavelength (µm)

experiment since their signature fingerprints overlap with the resonance of the structure

shown in Fig. 3.13. According to the ellipsometer characterization, the effective thickness

Fig. 4.9 a) Experimental reflection spectra of nanogap-assisted MDM super absorber with (red

curve) and without (blue curve) ODT coating, and ODT film directly spin coated on bare Ag

film (orange curve). b) Reflection differences of nanogap-assisted MDM super absorber

sample.

of our sample is ~ 2.6 ±0.2 nm, corresponding to a monolayer ODT molecules [14]. As

shown by the orange curve in Fig. 4.9a, the absorption signature signal on the reference Ag

sample (i.e. a monolayer of ODT molecules on a flat Ag film) is not resolvable. In contrast,

an obvious signal change at 3.42 μm and 3.5 μm (indicated by the green dashed lines in

Fig. 4.9a, b) was observed, corresponding to the signature fingerprints of ODT molecules

[4]. The difference between the spectra with and without ODT molecules is plotted in Fig.

4.9b. Since the estimated enhancement factor of SEIRA characterization was dependent on

the calculation methods, we then followed two different data processing procedures [13,

15, 16] and obtained the enhancement factor of 8.5×106 ~1.0×107.

4.3.2 Enhancement factor calculation for ODT monolayer

76

a b

C: 0

0.0002~---------~

e- 0.0001 0 (/)

.0 <(

o.oooo'-- - --~ =!C!:;:.11:l.i.o.£:l~ 10 15 4~

Wavelength (µm)

In this section, we provide details to calculate the EF of ODT samples following two

different data processing methods used in previously reported literature. Before we perform

this calculation, the absorption spectrum of a monolayer ODT molecules on a metal

reflector is required as the reference.

A. Characterization of the reference sample: a monolayer of ODT molecules

As shown in Fig. 4.10a, the MDM structure surface is coated by an ODT monolayer.

Different from PMMA, the ODT monolayer can only be adsorbed on metal surface.

Importantly, the orientation of these molecules is fixed. Therefore, only the Ez component

will contribute to the molecular absorption signal. In our experiment, the absorption

spectrum of a monolayer of ODT molecules on a silver film was measured using

polarization modulation – infrared reflection absorption spectroscopy (PM-IRRAS, Bruker

PMA 50) at the incident angle of 83˚, as shown in Fig. 4.10b. The light spot is an ellipse

with semi-minor and semi-major axis lengths of 1 mm and 1.5 mm, respectively. The peak

absorption is 0.018% at the wavelength of 3.42 μm, which is consist with previously

reported results [16, 17]. This data is required in the estimation of the enhancement factor

of SEIRA.

Fig. 4.10 a) Schematic illustration of ODT molecules bond on metal surface around nanogap. b).

Absorption spectrum of ODT molecules on bare silver film measured with PM-IRRAS.

77

B. Method 1 from ref. [13]

Based on the method proposed by Ref. [13], the EF can calculated using the equation

below:

∆R𝑆𝑡𝑟𝑢𝑐 sin2φ 𝑆0𝐸𝐹 = × ( ) × 2 × (1 + 𝑛𝑠) × (4.2)A𝑟𝑒𝑓 cosφ 𝑆𝑆𝑡𝑟𝑢𝑐

where ∆R𝑠𝑡𝑟𝑢𝑐 is the reflection difference of their structure with and without ODT coating.

A𝑟𝑒𝑓 represents the maximum signal intensity of IRRAS measurement, which was obtained

from the single layer ODT adsorbed on a metal film. Since the IRRAS spectrum was

sin2φ measured under a grazing incident angle of φ = 83°, is the additional enhancement

cosφ

factor due to the larger illumination sample area. The constant factor 2 is introduced by the

mirror dipole effect. The factor 1/(1+ns) was introduced by the nanostructure employed in

ref. [13] (i.e. a single metal nanowire on a dielectric substrate with the refractive index of

𝑆0 ns). is the ratio of the IRRAS illumination area to the effective sensing area. In their 𝑆𝑆𝑡𝑟𝑢𝑐

calculation, ∆R𝑠𝑡𝑟𝑢𝑐=0.01, A𝑟𝑒𝑓=0.0034, ns=1.22 (as indicated in line 6 of the right column

𝑆0 1 on page 2 of ref. [13]), = . Therefore, the EF is calculated as 1.82×105, which

𝑆𝑆𝑡𝑟𝑢𝑐 5.76×10−4

is consistent with the reported data in ref. [13].

In our nanogap MDM, the ODT molecules are still coated on top of the MDM structure

surface, which is different from the situation in ref. [13]. Therefore, we did not consider

this enhancement factor (1+ns) to avoid over-estimation. Then the equation becomes:

∆R𝑛𝑎𝑛𝑜𝑔𝑎𝑝 sin2φ 𝑆0𝐸𝐹 = × ( ) × 2 × (4.3)A𝑟𝑒𝑓 cosφ 𝑆𝑛𝑎𝑛𝑜𝑔𝑎𝑝

78

https://R=0.01

1.0~-------------

0.8 .ii!' ·u; C

"E 0 .6

~ .t::! 0.4 -.; E o 0 .2 z 1/e2

\ ) o.o.J---=:::_~,.___.~_::=..---J -140 -130

x(nm)

-120

where ∆R𝑛𝑎𝑛𝑜𝑔𝑎𝑝 =0.04 (see Fig. 4.9b), A𝑟𝑒𝑓 =1.8×10 -4 (from our direct measurement

shown in Fig. 4.8). The effective width is 0.53 nm, as shown in Fig. 4.11. 𝑆0 = 50 μm × 50

μm, 𝑆𝑛𝑎𝑛𝑜𝑔𝑎𝑝 = 0.53 nm × 50 μm × 4 × 100 = 10.6 μm2. Therefore, the enhancement factor

is 8.5 × 106.

Fig. 4.11 |EZ|2 distribution across the nanogap indicating the effective sensing width for the ODT

sample.

C. Method 2 from ref. [15]

Based on the calculation method proposed in Ref. [15], the EF can be calculated using

the equation:

∆𝑅𝑛𝑎𝑛𝑜𝑔𝑎𝑝/𝑁𝑛𝑎𝑛𝑜𝑔𝑎𝑝 𝐸𝐹 = (4.4)

𝐴𝑟𝑒𝑓/𝑁𝑟𝑒𝑓

Here ΔRnanogap is the absorption in the gaps; Aref is the chemical molecules absorption

on bare silver film; Nnanogap is the number of chemical molecules (in ref. [15], they are BZT

molecules) contributing to the SEIRA signal in the nanogaps (according to [15],

𝐿 𝑁𝑛𝑎𝑛𝑜𝑔𝑎𝑝 = 𝐷 × × 4𝑤𝐿, where L=130 μm, P=3 μm, w=3 nm); Nref is the number of

𝑃

chemical molecules contributing to the absorption on a bare silver film (according to [15],

𝐷 × 𝑆0 × 𝑠𝑖𝑛83°, where S0=π×1 mm×1.5 mm). Using the data reported in ref. [15] (i.e.,

79

ΔRnanogap =7.52×10 -3; Aref =3.3×10 -4 with a correction factor of sin83˚ introduced by the

collection angle of the lens; Nnanogap = D×67.6 μm2; Nref = D×4.68×106 μm2), one can

calculate the EF of 1.58×105 at the absorption peak of 1473 cm -1, which is consistent with

the data provided in their supporting information.

In our case, ΔRnanogap is 0.04 (see Fig. 3.13), which is 5.3 fold of that obtained in ref.

[15]. Aref =1.8×10 -4 (from our direct measurement shown in Fig. 4.4), L=50 μm, w=5 nm,

S0= π×1 mm×1.5 mm. Therefore, the EF is calculated as 1.0 ×107, which is approximately

two orders of magnitude better than the one reported in ref. [15]. This enhancement factor

is better than previously reported results based on small area metallic nano-rods fabricated

by e-beam lithography (e.g. 3.3×105 obtained from a single nano-rod with the dimension

of 1.4 μm ×100 nm [13]; 1.2×105 obtained from a fan-shaped gold nanoantenna with a

~20 nm ×20 nm sensing area over a 1.7 μm ×1 μm pattern) [18] and much larger than

most reported nanopatterned structures for SEIRA sensing [4, 19]. Importantly, the

interaction area on top of these nanogaps (e.g. 𝑆𝑛𝑎𝑛𝑜𝑔𝑎𝑝 = 10.6 μm2 for the 50 μm ×50 μm

structure, see Sec. 4.3.2B) is much larger than previously reported nano-rods (i.e., at the

two ends of each rod) [13] and nanoantenna structures (i.e., in the gap area between two

metallic tips) [5]. Therefore, the signal to noise ratio of our SEIRA result is superior to

previously reported results. For instance, for the fan-shaped nanoantenna measured in a

similar facility setup as ours [18], the signal is less than 0.1%, which is ~40 times smaller

than our signal shown in Fig. 4.9. Due to the weak scattering from the single nano-rod [13],

a synchrotron light source was employed to resolve ~1% signal change. Therefore, a long

time scan was required (i.e., taking an average of 125 spectra with 100 scans), ~60X longer

than our measurement. For our current setup, a regular spherical emitter (SiC bar heated at

80

1.0

0.8

C: 0 0.6 :g_ .... 0 0.4 rJ)

.0 <l'.

0.2

0.0 2 3 4 5

Wavelngth (µm)

1300 K) was used as the light source, which provides far less intensity than the synchrotron

source and is much more inexpensive and therefore, more accessible for regular sensing

applications. As expected, the sensing area can be increased further by reducing the period

of the first step patterning while using a smaller gap to obtain the same resonance

overlapping with the vibrational mode of molecules.

4.4 Increasing the area occupied by nanogaps

The black curve in Fig. 4.12 is the simulated absorption spectrum for the structure in

Fig. 3.13 in Section 3 (i.e., P= 500 nm, D= 250 nm, tm = 40 nm, td= 40 nm, g= 5 nm, and

tb= 150 nm). When the gap size is reduced to 3 nm, with the pattern width and period of

115 nm and 230 nm, respectively, one can obtain a very similar absorption spectrum (i.e.,

the red curve) as the one shown in Fig. 3.13 in Section 3 (i.e., the black curve). However,

by decreasing the pattern size and period, the effective sensing areas (or “hotspots”)

approximately increases from 100 periods to 217 periods, and therefore, resulting in a

higher signal to noise ratio.

Fig. 4.12 Simulated absorption spectra for the structure with the parameters of (P= 500 nm, D=

250 nm, tm= 40 nm, td= 40 nm, g= 5 nm, and tb= 150 nm) (black curve) and (P= 230 nm, D= 115

nm, tm= 40 nm, td= 40 nm, g= 3 nm, and tb= 150 nm) (red curve).

81

It should be noted that in ref. [15], the Al2O3 within the nanogap was etched so that more

molecules can get into the gaps for enhanced light-matter interaction. However, in our

experiment, the ALD-layer was not etched. Therefore, larger sensing areas/volumes are

expected (corresponding to higher signal-to-noise ratios) in the future study by removing

the ALD-layer within the nanogap. More importantly, combined with large area optical

interference patterning methods (e.g. 2 cm ×2 cm as we reported in ref. [9] and 10 cm ×

10 cm in ref. [20]), the proposed structure is easy to be scaled up over larger areas for the

development of inexpensive nanostructured substrates for practical sensing applications. It

should be noted that if the ALD-induced Al2O3 filled in the gap can be removed using

etching [15], more areas/volumes in the gap with strong localized field can be used for

extremely enhanced light-matter interaction, which is still under investigation.

4.5 Summary

According to our experiment demonstration of SEIRA, a sensing enhancement factor over

105 to 106 was obtained using PMMA and ODT layers. Due to the large sensing area on

top of the nanogaps, the absolute value and signal-to-noise-ratio for SEIRA signal is

improved significantly compared with previous reports. Additionally, the nanogap density

(i.e., the sensing area) can be further increased by reducing the basic pattern dimension and

the gap size simultaneously.

82

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enhanced infrared absorption using individual cross antennas tailored to chemical moieties,

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[5] C. Huck, F. Neubrech, J. Vogt, A. Toma, D. Gerbert, J. Katzmann, T. Hartling,A. Pucci,

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83



[9] B. Chen, D. Ji, A. Cheney, N. Zhang, H. Song, X. Zeng, T. Thomay, Q. Gan,A.

Cartwright, Flat metallic surface gratings with sub-10 nm gaps controlled by atomic-layer

deposition, Nanotechnology 2016, 27, 374003.

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International Journal of Polymeric Materials 2008, 57, 969-978.

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Resonant plasmonic and vibrational coupling in a tailored nanoantenna for infrared

detection, Physical review letters 2008, 101, 157403.

[14] M. J. Tarlov, Silver metalization of octadecanethiol monolayers self-assembled on

gold, Langmuir 1992, 8, 80-89.

[15] X. Chen, C. Ciraci, D. R. Smith,S. H. Oh, Nanogap-enhanced infrared spectroscopy

with template-stripped wafer-scale arrays of buried plasmonic cavities, Nano Letters 2015,

15, 107-113.

[16] C. Liang, C. Yang,N. Huang, Tarnish protection of silver by octadecanethiol self-

assembled monolayers prepared in aqueous micellar solution, Surface and Coatings

Technology 2009, 203, 1034-1044.

84

[17] M. R. Anderson, M. N. Evaniak,M. Zhang, Influence of solvent on the interfacial

structure of self-assembled alkanethiol monolayers, Langmuir 1996, 12, 2327-2331.

[18] L. V. Brown, X. Yang, K. Zhao, B. Y. Zheng, P. Nordlander,N. J. Halas, Fan-shaped

gold nanoantennas above reflective substrates for surface-enhanced infrared absorption

(SEIRA), Nano letters 2015, 15, 1272-1280.

[19] W.-C. Shih, G. M. Santos, F. Zhao, O. Zenasni,M. M. P. Arnob, Simultaneous

Chemical and Refractive Index Sensing in the 1–2.5 μm Near-Infrared Wavelength Range

on Nanoporous Gold Disks, Nano letters 2016, 16, 4641-4647.

[20] T. Siegfried, Y. Ekinci, H. Solak, O. J. Martin,H. Sigg, Fabrication of sub-10 nm gap

arrays over large areas for plasmonic sensors, Applied Physics Letters 2011, 99, 263302.

85

Chapter 5

Conclusions

In this chapter, we first summarize the results achieved in this dissertation and then

propose future research directions.

We employed HMM waveguide taper constructed by metal/dielectric multilayers to

realize a novel broadband metamaterial super absorber. The broad absorption band can be

tuned freely in near, mid and far IR spectral region. Due to the eigenmode conversion

between |f> and |b> modes with significantly different optical properties, broadband slow

light resonances can be supported in the HMM waveguide taper, which is called “rainbow

trapping” effect. This proposed universal HMM waveguide taper design is not limited by

those severe theoretical constraints required in previously reported dielectric-metal-

dielectric, metal-dielectric-metal, and dielectric-negative-index-dielectric waveguide

tapers, and therefore representing a significant promise to realize the rainbow trapping

structure practically.

Following the theoretical prediction, we experimentally demonstrate broadband HMM

super absorber in near, mid and far IR spectral region. Multi-patterned HMM super

absorbers are also demonstrated to reduce the required number of metal/dielectric layers,

and therefore simplify the sample preparation and experimental realization of on-chip

broadband super absorber.

86

As contrary side of broadband absorption, extremely confined electromagnetic field is

highly desired for practical applications including enhanced nonlinear optics, surface

photocatalysis, and vibrational biosensing spectroscopies. In order to realize nanometric

gaps for extremely enhanced localized field, we proposed an improved procedure to

fabricate metamaterial super absorber with sub-5-nm features based on ALD processes. By

performing a strip-off procedure of the entire layered structure from the substrate, this

avoids the need for accurate control of the sidewall profile and uniformity. Light trapping

efficiencies up to 81% are experimentally demonstrated at mid-infrared wavelengths. By

coating these structures with chemical/biological molecules, it is successfully

demonstrated that the fingerprints of molecules in the mid-infrared absorption

spectroscopy are enhanced significantly with the enhancement factor up to 106 –107,

representing a record for surface enhanced infrared absorption spectroscopy.

87

Publications

Journal Article:

[13] D. Ji, H. Song, B. Chen, F. Zhang, A. R. Cheney, N. Zhang, X. Zeng, J. D. Atkinson,

C. Zhou, A. N. Cartwright, Q. Gan, Frozen “Tofu” Effect: Engineered Pores of Hydrophilic

Nanoporous Materials, ACS Omega 2, 4838 (2017).

[12] D Ji, A. R. Cheney, N. Zhang, H. Song, J. Gao, X. Zeng, H. Hu, S. Jiang, Z. Yu, Q.

Gan, Efficient mid-infrared light confinement within sub-5-nm gaps for extreme field

enhancement, Adv. Opt. Mater., accepted (2017).

[11] Z. Liu, H. Song, D. Ji, C. Li, A. Cheney, Y. Liu, N. Zhang, X. Zeng, B. Chen, J. Gao,

Y. Li, X. Liu, D. Aga, S. Jiang, Z. Yu, Q. Gan, Extremely cost-effective and efficient solar

vapor generation under non-concentrated illumination using thermally isolated black paper,

Global Challenges 1, 1600003 (2017).

[10] B. Chen, D. Ji, A. Cheney, H. Song, N. Zhang, X. Zeng, T. Thomay, Q. Gan and A.

Cartwright, Flat metallic surface gratings with sub-10-nm gaps controlled by atomic-layer

deposition, Nanotechnology 27, 374003 (2016).

[9] L. Zhou, Y. Tan, D. Ji, B. Zhu, P. Zhang, J. Xu, Q. Gan, Z. Yu, and J. Zhu, Self-

assembly of highly efficient, broadband plasmonic absorbers for solar steam generation,

Sci. Adv. 2, e1501227 (2016).

[8] N. Zhang, Z. Dong, D. Ji, H. Song, X. Zeng, Z. Liu, S. Jiang, Y. Xu, A. A. Bernussi,

W. Li, and Q. Gan, Reversibly tunable coupled and decoupled super absorbing structures,

Appl. Phys. Lett. 108, 091105 (2016).

88

[7] Z. Liu, D. Ji, X. Zeng, H. Song, J. Liu, S. Jiang, Q. Gan, Surface dispersion engineering

of Ag–Au alloy films, Appl. Phys. Express 8, 042601 (2015).

[6] H. Song, S. Jiang, D. Ji, X. Zeng, N. Zhang, K. Liu, C. Wang, Y. Xu, Q. Gan,

Nanocavity absorption enhancement for two-dimensional material monolayer systems, Opt.

Express 23, 7120 (2015).

[5] D. Ji, H. Song , X. Zeng , H. Hu , K. Liu , N. Zhang, Q. Gan, Broadband absorption

engineering of hyperbolic metafilm patterns, Sci. Rep. 4: 4498 (2014).

[4] H. Song, L. Guo, Z. Liu, K. Liu, X. Zeng, D. Ji, N. Zhang, S. Jiang, Q. Gan, Nanocavity

enhancement for ultra-thin film optical absorption, Adv. Mater. 26, 2737 (2014).

[3] T. Moein, D. Ji, X. Zeng, K. Liu, Q. Gan, A. Cartwright, Holographic photopolymer

linear variable filter with enhanced blue reflection, ACS Applied Materials & Interfaces

6, 3081 (2014).

[2] H. Hu, D. Ji, X. Zeng, K. Liu, Q. Gan, Rainbow Trapping in Hyperbolic Metamaterial

Waveguide, Scientific Reports 3: 1249 (2013).

[1] H. Hu, X. Zeng, D. Ji, L. Zhu, Q. Gan, Efficient End-fire Coupling of Surface

Plasmons on Flat Metal Surfaces for Improved Plasmonic Mach-Zehnder Interferometer,

J. Appl. Phys. 113, 053101 (2013).

Conferences and Proceedings:

[11] Z. Liu, H. Song, D. Ji, et al., Extremely Cost-effective and Efficient Solar Vapor

Generation Using Thermally Isolated Black Paper, CLEO 2017, AM1B.1.

[10] Z. Liu, H. Song, D. Ji, et al., Extremely cost-effective and efficient solar vapor

generation, Frontiers in Optics 2017, FTh4B.5.

89

[9] D. Ji, H. Song, B. Chen, et al., Engineered Pores of Hydrophilic Nanoporous

Materials Using Wet-drying and Freeze-drying, CLEO 2017, SM4K. 6.

[8] D. Ji, H. Song, B.Chen, et al., Reversibly tunable hydrophilic nano/microporous

polymer photonic crystal, Frontiers in Optics 2016, FTu1F.6.

[7] K. Liu, N. Zhang, D. Ji, et al., Lithography-free visible metasurface absorbers with

tunable dielectric spacers, Frontiers in Optics 2015, FW3A-2.

[6] D. Ji, B. Chen, X. Zeng, et al., Atomic-layer lithography of sub-10-nm plasmonic

nanogaps on flat metallic surface, Frontiers in Optics 2015, FTh3F-3.

[5] X. Zeng, Y. Gao, D. Ji, et al., On-chip Plasmonic Interferometer Array for Portable

Multiplexed Biosensing System, CLEO 2014, FM3K-3.

[4] D. Ji, H. Song, X. Zeng, et al., Broadband absorption engineering of hyperbolic

metafilm patterns, CLEO 2014, FM1C.4.

[3] K. Liu, H. Hu, D. Ji, et al., Super Meta-Absorber for Ultra-Thin OPV Films. Asia

Communications and Photonics Conference 2013, AW4K-3.

[2] H. Hu, D. Ji, X. Zeng, et al., Rainbow Trapping in Hyperbolic Metamaterial

Waveguide, CLEO 2013, QTu2A.4.

[1] K. Liu, H. Song, D. Ji, et al., Super absorption in ultra-thin photovoltaic films based

on strong interference effects, CLEO 2013, JTu4A.64.

Book Chapter:

[1] Q. Gan, D. Ji, H. Hu, X. Zeng, Rainbow Trapping Effect in Horizontal and Vertical

Directions. Integrated Nanophotonic Resonators: Fundamentals, Devices, and

Applications, 257 (2015).

90

https://JTu4A.64

Dengxin Ji

[email protected] 1337 Millersport Hwy. Buffalo, NY 14221

cell: (716) 235-0250

EDUCATION

University at Buffalo, School of Engineering and Applied Science, Buffalo, NY

Ph.D. in Electrical Engineering, GPA: 3.51/4.00

2012.02~Est. 2017.12

University at Buffalo, School of Engineering and Applied Science, Buffalo, NY

M.S. in Electrical Engineering, GPA: 3.65/4.00

2010.08~2012.02

Yangzhou University, College of Energy and Power Engineering, Yangzhou, Jiangsu, China

B.S. in Electrical Engineering, GPA: 92.82/100

2006.09~2010.06

PROJECT EXPERIENCE

Ultra Broadband Metamaterial Super Absorber UB

2012.05~2015.01

Explore the feasibility of rainbow trapping based on a multi-layered metal-dielectric (i.e.

hyperbolic metamaterials) film stack supporting broadband slow light resonances;

Design on-chip broadband super absorber structure based on hyperbolic metamaterial

waveguide taper array with strong and tunable absorption profile from near-infrared to mid-

infrared spectral region.

Employ FIB to fabricate 2D and 3D tapered grating/pyramid structure to demonstrate the

design concept.

Portable Plasmonic Interferometers Biosensing System UB

2014.09~Present

Design and fabricate plasmonic interferometers to integrate with microfluidic channels,

which delivers target biomolecules to the sensor surface;

Develop cellphone based microscope to integrate with plasmonic interferometer chips

for biosensing applications;

Develop algorithms to track transmission light spots whose intensities are extracted in real

time.

Sub-5-nm Nanogap Assisted Surface Enhanced Infrared Absorption Spectroscopy UB

2014.03~Present

91

https://2012.05~2015.01

https://2006.09~2010.06

https://2010.08~2012.02

https://3.65/4.00

https://3.51/4.00

mailto:[email protected]

Design and fabricate a metamaterial super absorber structure with sub-5-nm gaps using

modified atomic layer deposition lithography method;

Apply the nanogap super absorber chip for surface enhanced infrared absorption spectroscopy

application with extremely high sensitivity.

Graded Holographic Photopolymer Reflection Gratings UB

2011.08~2014.06

Develop a one-step and low-cost method to produce graded rainbow-colored

holographic reflection grating based on porous holographic polymer dispersed liquid-

crystal materials (H-PDLC);

The total internal reflection limitation at short wavelength was overcome and resulted in an

improved fringe contrast by introducing a highly reflective surface in the photopatterning

process;

Tune the pore size of H-PDLC use wet-drying and freeze-drying method.

PUBLICATIONS

Journal Article:

[13] D. Ji, H. Song, B. Chen, F. Zhang, A. R. Cheney, N. Zhang, X. Zeng, J. D. Atkinson, C. Zhou,

A. N. Cartwright, Q. Gan, Frozen “Tofu” Effect: Engineered Pores of Hydrophilic Nanoporous

Materials, ACS Omega 2, 4838 (2017).

[12] D Ji, A. R. Cheney, N. Zhang, H. Song, J. Gao, X. Zeng, H. Hu, S. Jiang, Z. Yu, Q. Gan,

Efficient mid-infrared light confinement within sub-5-nm gaps for extreme field enhancement, Adv.

Opt. Mater., accepted (2017).

[11] Z. Liu, H. Song, D. Ji, C. Li, A. Cheney, Y. Liu, N. Zhang, X. Zeng, B. Chen, J. Gao, Y. Li, X.

Liu, D. Aga, S. Jiang, Z. Yu, Q. Gan, Extremely cost-effective and efficient solar vapor generation

under non-concentrated illumination using thermally isolated black paper, Global Challenges 1,

1600003 (2017).

[10] B. Chen, D. Ji, A. Cheney, H. Song, N. Zhang, X. Zeng, T. Thomay, Q. Gan and A. Cartwright,

Flat metallic surface gratings with sub-10-nm gaps controlled by atomic-layer deposition,

Nanotechnology 27, 374003 (2016).

[9] L. Zhou, Y. Tan, D. Ji, B. Zhu, P. Zhang, J. Xu, Q. Gan, Z. Yu, and J. Zhu, Self-assembly of

highly efficient, broadband plasmonic absorbers for solar steam generation, Sci. Adv. 2, e1501227

(2016).

[8] N. Zhang, Z. Dong, D. Ji, H. Song, X. Zeng, Z. Liu, S. Jiang, Y. Xu, A. A. Bernussi, W. Li, and

Q. Gan, Reversibly tunable coupled and decoupled super absorbing structures, Appl. Phys. Lett.

108, 091105 (2016).

[7] Z. Liu, D. Ji, X. Zeng, H. Song, J. Liu, S. Jiang, Q. Gan, Surface dispersion engineering of Ag– Au alloy films, Appl. Phys. Express 8, 042601 (2015).

[6] H. Song, S. Jiang, D. Ji, X. Zeng, N. Zhang, K. Liu, C. Wang, Y. Xu, Q. Gan, Nanocavity

absorption enhancement for two-dimensional material monolayer systems, Opt. Express 23, 7120

(2015).

[5] D. Ji, H. Song , X. Zeng , H. Hu , K. Liu , N. Zhang, Q. Gan, Broadband absorption engineering

of hyperbolic metafilm patterns, Sci. Rep. 4: 4498 (2014).

[4] H. Song, L. Guo, Z. Liu, K. Liu, X. Zeng, D. Ji, N. Zhang, S. Jiang, Q. Gan, Nanocavity

enhancement for ultra-thin film optical absorption, Adv. Mater. 26, 2737 (2014).

92

https://2011.08~2014.06

[3] T. Moein, D. Ji, X. Zeng, K. Liu, Q. Gan, A. Cartwright, Holographic photopolymer linear

variable filter with enhanced blue reflection, ACS Applied Materials & Interfaces 6, 3081 (2014).

[2] H. Hu, D. Ji, X. Zeng, K. Liu, Q. Gan, Rainbow Trapping in Hyperbolic Metamaterial

Waveguide, Scientific Reports 3: 1249 (2013).

[1] H. Hu, X. Zeng, D. Ji, L. Zhu, Q. Gan, Efficient End-fire Coupling of Surface Plasmons on

Flat Metal Surfaces for Improved Plasmonic Mach-Zehnder Interferometer, J. Appl. Phys. 113,

053101 (2013).

Book Chapter:

[1] Q. Gan, D. Ji, H. Hu, X. Zeng, Rainbow Trapping Effect in Horizontal and Vertical Directions.

Integrated Nanophotonic Resonators: Fundamentals, Devices, and Applications, 257 (2015).

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Metamaterial Super Absorber for Light

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