Interference of Light in Multilayer Metasurfaces: Perfect Absorber and Antireflection Coating

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Interference of Light in Multilayer Metasurfaces:Perfect Absorber and Antireflection CoatingKhagendra Prasad BhattaraiUniversity of South Florida, [email protected]

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Interference of Light in Multilayer Metasurfaces: Perfect Absorber and Antireflection Coating

by

Khagendra Prasad Bhattarai

A dissertation submitted in partial fulfilment of the requirements for the degree of

Doctor of Philosophy with a concentration in Department of Physics

College of Arts and Sciences University of South Florida

Major Professor: Jiangfeng Zhou, Ph.D. Myung K Kim, Ph.D.

Zhimin Shi, Ph.D. Manh-Huong Phan, Ph.D.

Date of Approval: March 29, 2017

Keywords: Metamaterials, perfect absorber, antireflection coating, three layer model

Copyright © 2017, Khagendra Prasad Bhattarai

DEDICATION

To

My Parents( Dataram Bhattarai and Tulasa Bhattarai)

My Grandparents( Pratiman Bhattarai and Bishnumaya Bhattarai)

ACKNOWLEDGEMENT

Firstly, I would like to express my sincere gratutude to my advisor Dr. Jiangfeng Zhou for the

continuous support of my Ph.D study and related research, for his patience, motivation, and

immence knowledge. His guidance helped me in all the time of research and writing of this

thesis. I could not have imagined having a better advisor and mentor for my Ph.D study. I am

thankful and indepted to Dr. Zhou for the knowledge he has transferred to me for my professonal

and personal development.

I would like to thank the rest of my thesis committee: Dr. Myung K Kim, Dr. Zhimin Shi, Dr.

Manh-Huong Phan, and Dr. Manoj Ram (Chairperson of the examination committee) for their

insightful comments and encouragement. I am grateful to Dr. Zahyun Ku, Dr. Sang Jun lee, Dr.

Diyar Talbayev, Dr. Augustine Urbas, Dr. Kun Song, Myung-Soo Park, Jiyeon Jeon and other

collaborators for fruitful collaboration and instructive guidance. I am in particular thankful to Dr.

Zahyun Ku for his valuable advice, instruction, quick response, and fascinating skills he has

taught me.

I am delighted to my lab colleagues Rishi Sinhara Silva and Clayton Fowler for research

collaboration, valuable discussions, sharing experiences, and helping me whenever needed. I am

appreciative to the Former department chair Dr. Pritish Mukherjee, the present chair Dr. David

Rabson, the former and present graduate directors Dr. Lilia Woods and Dr. Sarath Witanachchi

for continuous support. I would like to thank all the faculty and staff members in the department

of Physics for their assistance throughout my time at USF.

Finally, I would be delighted to thank my family: parents, grandparents, brothers, sisters, and

friends for their constant support, love and inspiration throughout my journey. I would specially

like to thank my brother- in- law, Binod Prasai for his contribution to my degree. Last but not

least, I would like to thank my lovely wife Ranju, for helping me find my passion and devotion

towards my career while I was progressing through my journey of completing my Doctoral

degree. I would also like to show courtesy to my considerate daughters who helped me relax and

feel ease at the times when I was feeling down or stressed out. Because of them, I got through

my hardships and found a way to advance.

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TABLE OF CONTENTS LIST OF FIGURES ....................................................................................................................... iii ABSTRACT ................................................................................................................................... xi 1. INTRODUCTION TO METAMATERIALS: PERFECT ABSORPTION AND ANTIREFLECTION COATING.....................................................................................................1

1.1 Metamaterials .................................................................................................................1 1.1.1 Development of Metamaterial Concept ..........................................................2 1.1.2 Classification of Materials ..............................................................................4 1.1.3 Realization of LHMs.......................................................................................5 1.1.4 Effective Medium Theory .............................................................................10

1.2 Surface Plasmon Resonance ........................................................................................11 1.3 Modelling and Simulation of Metamaterials ...............................................................13 1.4 Antireflection Coating .................................................................................................13 1.5 Perfect Absorber ..........................................................................................................16 1.6 Organization of the Dissertation ..................................................................................21

2. METAMATERIAL PERFECT ABSORBER ANALYZED BY A META-CAVITY MODEL CONSISTING OF MULTILAYER METASURFACES ..............................................................24

2.1 Introduction ..................................................................................................................25 2.2 Three Models of Perfect Absorber ...............................................................................25 2.3 Single Layer Effective Medium Model .......................................................................26 2.4 Metafilm Model (Modified Retrieval Method) ............................................................30 2.5 Circuit Model and Transmission Line Theory .............................................................36 2.6 Transfer Matrix Analysis: Three Layer Model ............................................................39 2.7 Angular Independence of Reflection ...........................................................................45 2.8 Currents and Fields for Higher Order FP Resonances .................................................46 2.9 Density of States Calculation .......................................................................................48 2.10 Analysis of Multiple Resonances ...............................................................................51 2.11 Summary: ...................................................................................................................55

3. A LARGE-AREA MUSHROOM-CAPPED PLASMONIC PERFECT ABSORBER: REFRACTIVE INDEX SENSING AND FABRY-PEROT CAVITY MECHANISM ................56

3.1 Introduction ..................................................................................................................57 3.2 Fabrication and Measurement ......................................................................................59

3.3 Mushroom-Capped Plasmonic Optical Cavity Reinterpreted by a Fabry-Perot Cavity Resonance ..........................................................................................................................66

3.4 Mushroom-Capped Structure as the Refractive Index Sensor .....................................70 3.5 Summary ......................................................................................................................73

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4. VERSATILITY OF ANTIREFLECTION USING LOW LOSS METAL DISK ARRAY METASURFACE ..........................................................................................................................74

4.1 Introduction ..................................................................................................................74 4.2 Results and Discussion ................................................................................................75 4.3 Theory: Three Layer Model .........................................................................................79 4.4 Angular Independence of Reflection ...........................................................................84 4.5 Summary ......................................................................................................................85

5. ENHANCED TRANSMISSION DUE TO ANTIREFLECTION COATING LAYER AT SURFACE PLASMON RESONANCE WAVELENGTHS .........................................................86

5.1 Introduction ..................................................................................................................87 5.2 Device Structure and Fabrication for Antireflection ...................................................88 5.3 Experiments .................................................................................................................90 5.4 Analysis Using Three-Layer Model .............................................................................92 5.5 Summary ......................................................................................................................98

6. A LOW-LOSS METASURFACE ANTIREFLECTION COATING ON DISPERSIVE SURFACE PLASMON STRUCTURE .........................................................................................99

6.1 Introduction ................................................................................................................100 6.2 Results ........................................................................................................................100

6.2.1 Metasurface Antireflection Coating ............................................................100 6.2.2 Transmission Enhancement due to Meta-AR Coating ................................105 6.2.3 Antireflection Condition at SPP Resonances ..............................................107 6.2.4 Designer Metasurface using Thin-film AR Coating Mechanism ...............110

6.3 Summary ....................................................................................................................116 7. ANGLE-DEPENDENT SPOOF SURFACE PLASMONS IN METALLIC HOLE ARRAYS AT TERAHERTZ FREQUENCIES ............................................................................................117

7.1 Introduction ................................................................................................................117 7.2 Physics of Spoof SPP Modes .....................................................................................119 7.3 Discussion of Simulation and Experimental Results .................................................121 7.4 Summary ....................................................................................................................131

8. CONCLUSION AND FUTURE WORKS ..............................................................................132 9. REFERENCES ........................................................................................................................136 APPENDICES .............................................................................................................................143 Appendix A: List of Publications ....................................................................................144

Appendix B: Conference Presentations ...........................................................................146 Appendix C: Copyright Permissions ...............................................................................147

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LIST OF FIGURES

Figure 1.1 (a) RHMs: Vectors , , and form right handed vector systems. Wave vector ( ) and poynting vector ( ) are in the same direction. (b) LHMs: Vectors , , and form left handed vector systems. Wave vector ( ) and poynting vector ( ) are in the opposite direction ...................................................................................................... 3 Figure 1.2 Schematic of and coordinate system. In I and III quadrants, wave propagates due to the real value of refractive index ( ) whereas wave decays exponentially in the II and IV quadrants due to the imaginary value of ...................................................... 5 Figure 1.3 (a) Continuous metallic wires arrays with diameter d and separation between the wires . (b) Real part (Green line) and imaginary part (blue dotted line) of permittivity ( ) as a function of frequency. Real part has a small and negative value below the plasma frequency ...................................................................................................... 7 Figure 1.4 (a) Split ring resonators (SRRs) array with lattice constant a. Magnetic field ( ) is applied perpendicular to the plane of SRRs. (b) Real (blue line) and imaginary (brown dotted line) part of effective permeability ( ) as a function of Frequency .................................................................................................................................. 8 Figure 1.5 (a) The Composite of LHMs consisting of thin wires and split ring resonators (SRRs) employed by Smith et al. (b) The Transmission coefficient of thin wires only (blue line), SRR only (black line) and the composite of thin wire and SRRs (black dotted line).SRR has stop band in between the two red dotted lines. When thin wire is combined to the SRR, pass band appears .............................................................................................................................. 9 Figure 1.6 Schematic view of (a) Dipole resonance of metallic wire (b) Split ring resonator (SRR) and (c) Metal Hole Arrays (MHA ................................................................ 12 Figure 1.7 Schematic diagram of Antireflection showing destructive interferences ............................... 14 Figure 1.8 First metamaterial perfect absorber designed by Landy et al. (a) Two split ring resonators connected by a common straight wire. (b) Cut wire and (c) Unit cell of the MPA (d) Spectra for reflection (green), transmission (blue) and absorption (red .................................................................................. 18

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Figure 1.9 (a, b) First simulated and experimental MPA in Microwave regime and unit cell. (c d) First MPA demonstrated in THz regime. (e, f) First MPA demonstrated in millimeter wave regime and unit cell. (g) First wide angle MPA. (h, i) First MPA simulated in IR regime and unit cell. (j) First experimental demonstration of MPA at MIR regime. (k, l) One of the first experimental demonstrations of MPA in NIR regime. (m, n) Demonstration of MPA operating in visible regime .......................................................................................................................... 19 Figure 1.10 (a) Numerical simulation of the Infrared MPA (structure is shown in inset of figure (b). Reflection (blue), transmission (green) and absorption (red). (b) Optical constants of the MPA extracted from the retrieval results. Real and imaginary parts of effective permittivity (red solid and dotted lines) and effective permeability (blue solid and dotted lines) .................................................................................................... 20 Figure 2.1 Schematic diagram of (a) perfect absorber with entire structure as a metamaterial (MM) and its (d) equivalent single-layer film characterized by effective and . (b) perfect absorber with cross wire, spacer and metal ground plate considered as a three-layer structure and the equivalent three-layer film model (e), where the cross wire is considered by a homogenous film with ε and μ . (c) View of perfect absorber along wave propagation direction. The MPA is surrounded by vacuum and a dielectric substrate with optical impedances and at two interfaces, respectively. (f) A transmission line model uses a two port network describes the MPA, where and are the impedances of vacuum and substrate, and and are input and output impedances of , respectively ............................................................... 26 Figure 2.2 (a) Real and imaginary parts of effective permittivity of MPA retrieved by using single-layer thin film model; (b) Real and imaginary parts effective permeability for single-layer thin film model; (c) Real and imaginary parts effective impedance calculated by single-layer thin film model ( ,solid curves) and effective circuit model ( ,dash curves); (d) Simulated reflectance spectra of the actual MPA, a single-layer effective film (blue dash) and three-layer effective film (red dash) ........................................ 29 Figure 2.3 (a), (b) Real part of and of the MDA metasurface for the thickness 0.05 (Red) and 0.10 (blue). (c),(d) Real part of and of the MDA metafilm, where the solid curves are calculated by the retrieval method and the dashed curves are calculated by / and / ......................................................................................................... 32 Figure 2.4 (a) Schematic model of a 50 thick dielectric film with 30, 1 on a 0.5 thick BCB layer. (b) The transmission and reflection coefficients, , , and at the air-film-dielectric (BCB) interfaces can be calculated in CST simulation using the model in (a). (c) , , and at the interfaces of air-film-air are calculated by a transfer matrix method. (d), (e) The effective permittivity and permeability calculated using the transmission and reflection coefficients shown in (b) (blue curves) and (c) (red curves ....................................................................................... 35

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Figure 2.5 Simulated phase of transmission and reflection coefficients through MDA structure (solid) and metafilm (dashed .................................................................................... 36 Figure 2.6 (a) Real part (red) and Imaginary part (blue) of effective permittivity ( ). (b) Real part (red) and imaginary part (blue) of effective permeability ( ). (c) Amplitude terms, | |(red) and | | (blue), in the amplitude condition. The inserting figure depicts the transmission and reflection coefficients. (d) Phase terms in the phase condition: (red), (blue), 2 , (black) and (orange). The shadows of green color show two perfect absorption regions at wavelength of 5.94 and 1.79 ..................................................................... 44 Figure 2.7 Color plot of angular dependence of reflection from crosswire-spacer-MGP structure for (a) TE mode (b) TM mode, from entire single layer thin film structure for (c) TE mode (d) TM mode, and from thin film-spacer-MGP structure for (e) TE mode (f) TM mode .................................................................................. 46 Figure 2.8 (a) Reflection of crosswire-spacer-MGP structure for the 1st order (black), 2nd order (red) and 3rd order (blue) Fabry-perot (FP) resonances. (b) Reflection of thinfilm-spacer-MGP structure for the 1st order (black), 2nd order (red) and 3rd order (blue) Fabry-perot (FP) resonances. Current distributions on the top and bottom layers and X-component of Electric fields (Ex) in the spacer for crosswire-spacer-MGP structure at (c) 1st order (d) 2nd order (e) 3rd order and for Thinfilm-spacer-MGP structure at (f) 1st order (g) 2nd order (h) 3rd order .................................................................................... 48 Figure 2.9 Density of states of (a) Crosswire absorber (b) Crosswire resonator only. (c) Enhancement of density of states of absorber over resonator .......................................................................................................................... 50 Figure 2.10 Color plot of Reflection of wire-spacer-MGP absorber with sweeping the spacer thickness. Each of the resonant peak is assigned with the indices (i,j), where i represents the order of Fabry-perot (FP) resonance and j represents the order of the plasmonic resonance. (-) and (+) sign in FP resonance

represents the mode with less than 4 and more than 4.Currents profile on the resonator for the first two peaks at 1st FP resonance are shown with arrows at the bottom of the figure and Ex field for the 1st, 2nd and 3rd order FP resonances are shown to the right ...................................................................................... 52 Figure 2.11 (a) reflection of the absorber at the 2nd order spacer thickness at 2.07 . X-component of the electric field (Ex) profile in the dielectric spacer along Z-direction in between the top surface of MGP and bottom surface of resonator at the resonant wavelengths of (b) 5.88 µm (c) 3.57 µm (d) 2.73 µm (e) 2.46 µm and (f) 1.85 µm. Here incident electric field is applied along X-direction ............................................................................................ 54

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Figure 3.1 (a) Geometry of a unit cell of metamaterial perfect absorber (MPA) structure without etching dielectric spacer.( b) A unit cell of mushroom-capped MPA with over-etched dielectric spacer (corresponding to the sample shown in (f)). Scanning electron miscroscopy (SEM) images of the samples etched by O2 plasma reactive-ion-etch for (c) 0 s, (d) 45 s, (e) 90 s, and (f) 135 s ....................................... 59 Figure 3.2 Schematic view of fabrication ................................................................................................ 61 Figure 3.3 FTIR-measured reflectance of structures with different RIE etching times for (a) x-polarized, (b) y-polarized and (c) unpolarized incidence. The corresponding simulated reflectance with a variety of etch-depth Δt and etch-bias Δx under (d) x-polarized, (e) y-polarized and (f) unpolarized illumination. The over-etched sample (135s etching, structure shown in Figure 1f) was used to measure the reflectance for unpolarized light before (magenta) and after (cyan) applying water to the sample ............................................ 63 Figure 3.4 At the resonance wavelength, the simulated current density distribution

(a) on the elliptical disk, (b) on the Au film. The positive (red plus sign) and (b) negative (blue negative sign) charges accumulate at two ends. (c) The (c) amplitude of the electric field at the resonance wavelength ............................................. 66

Figure 3.5 (a) Reflectances calculated (balck dashed line) by Equation 1and simulated using the whole MPA structure (red solid line). (b) The amplitude of r12 (blue)

and (red). (c) The phase terms in Equation 3: θ ϕ r ϕ α 2β (blue), (green), (red), and 2β (black), respectively ...................................................... 69

Figure 3.6 (a) Simulated reflectance spectra for the sample in air (black), water (blue) and in glucose solution (red to orange) environment; (b) Calculated FOM* as the refractive index of glucose solution changes from 1.312 (blue) to 1.322 (red) ........................................................................................................................... 72 Figure 4.1 Illustration of (a) Anti reflection coating (ARC) with BCB layer on GaAs substrate. (b) Metal Disk Array (MDA) coated on the top of BCB. (c) MDA

replaced by thin film characterized by its effective permittivity ε and effective permeability μ . Reflection (black), transmission (blue) and loss (red) corresponding to (d) structure a (e) structure b and (f) structure c respectively ....................................................................................................... 77

Figure 4.2 Real (black) and imaginary (blue) part of (a) Effective Permittivity ε and (b) effective permeability μ of Metal Disk Array (MDA) deposited on the top of BCB using retrieval procedure. .......................................................................... 78

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Figure 4.3 Numerical results of the three layer structure (MDA-BCB-GaAs) using three layer model satisfying amplitude and phase conditions to get antireflection. (a) Reflection of the entire structure (MDA-BCB-GaAs) simulated (black line), calculated from effective impedances of the multilayer films (red dot line), simulation of the effective thin film-BCB-GaAS structure (blue dash-dot line) with the thin film described by ε , and μ and simulation of thin film-BCB-GaAS with the thin film described by constant dielectric permittivity of 18.4. (b) The amplitude of r (black) and r (blue). (c) The phase term in equation (3) :θ ϕ r ϕ α. R 2β (red), Phase of r (pink), phase of R (black) and the propagation phase term in BCB, 2β (blue). The brown dotted line shows the resonant wavelength (6.2 μm). ......................... 81 Figure 4.4 (a) Schematic diagram of reflections and transmissions through each of the MM layer, BCB and GaAs. R and R are the effective total reflection from the combined MM and BCB layer from the front side and back side respectively calculated by equation 4.4 using Impedances of Air (Z ), MM layer (Z ) and BCB (Z ).(b) R is calculated by using impedances of BCB (Z ) and GaAs (Z ................ 84 Figure 4.5 (a) Colorplot of reflection from MDA-BCB-GaAS structure with increased oblique incidence from 00 to 800 for (a) TE mode and (b) TM mode ...................................... 85 Figure 5.1 Schematic view of structures and dimensions for (a) PGF and (b) Si3N4:PGF. The pitch p and Si3N4 thickness td are varied from 1.8 µm to 3.2 µm with a step of 0.2 µm and from 150 nm to 750 nm with a step of 200 nm, respectively. The circular aperture size (d) and Au thickness (tm) are fixed at 0.5·p and 50 nm, respectively. The scanning electron microscope (SEM) images (side view) of (c) PGF structure with p = 2.6 µm and (d) Si3N4: PGF structure with p = 1.8 µm; td = 750 nm. Insets show the tilted SEM images .................................................. 89 Figure 5.2 FTIR-measured normal incidence transmission spectra of PGF (Gray) and Si3N4:PGF (Color) samples with variable pitches (p = 1.8 – 3.2 µm) and thicknesses of Si3N4 layer, (a) td = 150 nm, (b) td = 350 nm, (c) td = 550 nm and (d) td = 750 nm .................................................................................................................. 90 Figure 5.3 Transmission enhancement factor as a function of the periodicity (p) for different thickness of Si3N4 layer (td) placed on top of PGFs at (a) the first-order and (b) the second-order SPP resonance wavelengths ................................................................... 92 Figure 5.4 (a) Numerical reflection (red line) and transmission (blue line) for the structure with p = 1.8 µm and td = 750 nm obtained from 3D full field EM simulation of the whole structure (all three layers together) while circles show the calculated reflection (red) and transmission (blue) using a three-layer model. Black line represents the transmission without Si3N4 coating layer. (b) The amplitude of r12 and r23, i.e. |r12| (red line) and |r23| (blue line). Magenta dashed line is drawn at the first SPP resonance. (c) The phase terms in Eq. (4), 2 , where and are the phase of r12 (red) and r23 (blue), respectively and the propagation phase in the silicon nitride coating layer is 2β (green ........................................................................................................ 95

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Figure 5.5 The effective normalized impedance of Si3N4 coating layer (Z2: gray) and PGF (√Z3: black), and the amplitude of r12 (|r12|: light blue) and r23 (|r23|: blue). The resonance region is highlighted ........................................................................................ 97 Figure 6.1 Illustrations of (a) MHA, (b) BCB layer coated MHA and (c) MHA coated with MDA atop the BCB layer. (d–f) distribution in x = 0.36 m plane of a unit cell (x = 0, the center of the unit cell) for structures shown in (a-c), respectively. The interface between MHA and GaAs substrate is set to zero in z-axis (z = 0). (g) Simulated reflection colormap for structure displayed in (b) as a function of wavelength and the BCB thickness . is varied from 0.35 m to 1.55 m with a step of 0.2 m. Colormaps of simulated reflection at (h) the first-order and (i) the second-order SPP resonance wavelengths for structure as shown in (c) as a function of BCB thickness and the ratio ⁄ . increases from 0.35 m to 1.55 m by a 0.2 m step and ⁄ varies from 0.5 ( = 0.9 m) to 0.8 ( = 1.44 m) by a 0.05 (0.09 m) step ........................................................................................................ 102

Figure 6.2 Scanning electron microscope (SEM) images of three samples (MHA, a BCB layer coated MHA, MHA coated with an array of circular metal disks atop the BCB layer) and BCB coating condition. (a) A periodic circular post photoresist (PR) pattern defined by standard photolithography. (b) E-beam deposition (5 nm of Ti and 50 nm of Au in sequence) and a liftoff processing, which leads to MHA structure. (c) Measured BCB thickness as a function of spin-coating speed and dilution ratio between BCB and rinse solvent. (d) BCB coated on MHA sample showing the flat-top surface. (e) A periodic circular hole PR pattern on the BCB layer shown in (d). Consecutive e-beam evaporations were used to deposit Ti (5 nm) / Au (50 nm) after (e), followed by a lift-off step. (f) Completed Meta-AR coated MHA (an array of circular metal disks atop the BCB coated MHA). Insets display the magnified MHA and MDA in Meta-AR coating ............................................................. 105 Figure 6.3 (a) Colormap of simulated transmission for BCB layer coated MHA as increases from 0.35 m to 1.55 m with 0.2 m step. Simulated transmission for MHA with Meta-AR coating at (b) the first-order and (c) second-order SPP resonance wavelengths when is varied from 0.9 m 0.5 ∙ to 1.44 m 0.8 ∙ with a step of 0.09 m 0.05 ∙ and is changed in the same manner as (a). Experimental (sphere) and simulated (cross) transmission enhancement ratio for BCB (blue) and Meta-AR (red) coating at (d) the first-order and (e) second-order SPP resonance wavelengths ................................................................ 107 Figure 6.4 Colormaps of amplitude and phase AR-conditions around the first-order SPP resonance wavelength. Difference in amplitudes of reflection coefficients, ∆| | | | | ∙ | and the phase term, ∙ 2 with (a),(b) various BCB thicknesses and (c),(d) MDA sizes, respectively ...................................................................................... 110

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Figure 6.5 The real (red) and imaginary (blue) parts of (a) effective permittivity and (b) permeability of the MDA metasurface. Inset shows the real part of effective permittivity, (red) and the loss tangent, tan (green) around the first-order ( 6.25 m) and second-order ( 4.38 m) SPP resonances of MHA. (c) Diagram of the reflection and transmission coefficients of MDA and MHA. (d) Simulated reflection of the entire structure (MDA-BCB-MHA-GaAs) (black line), calculated reflection (blue line) from Eq. 1 and simulated reflections of MDA Metasurface-BCB-MHA-GaAs structure with wavelength-dependent (red dash line: and ) and wavelength-independent (green dash-dot line: 30.8 ∙ 0.147

and 0.86 ∙ 0.012) effective parameters. (e) The amplitude

of (blue) and ∙ (red) in Eq. 2. (f) The phase terms (Eq. 3) ∙ 2 (red), the phase of ∙ (blue), the phase of (black), and the propagation phase term in the BCB layer 2 (green) ............................ 115 Figure 7.1 (a), b) Schematic layout and (b) SEM image of MHA which consists of perforated. gold layer on a fused silica substrate. (c) and (d): Configurations of (c) transverse electric (TE) wave and (d) transverse magnetic (TM) wave, where θ and ϕ denote polar angle and azimuthal angle for incident wave vector k, respectively. For TE (or TM) wave, E (or H) field is always in the xy-plane, while H ( or E) field lies in the plane of incidence (indicated by the light-blue dash-dot triangle) with an angle ϕ from the x-axis. ........................................................................................................ 120 Figure 7.2 (a), (b): Transmission spectra for normally incident TE (a) and TM (b) waves. (c), (d): Real part of E field of SPP waves at the first-order (c) and the second- order (d) resonances excited by incident TE wave. (e), (f): Real part of E field of SPP waves excited by incident TM wave. (g)-(h): Phase of E for corresponding SPP waves shown in (c)-(f) ..................................................................... 122 Figure 7.3 (a) Simulated and (b) measured transmission spectra for TE mode when. θ increases from 0 to 20° and keep ϕ 0. The dotted and solid lines are the analytical resonance frequencies for different SPP resonance modes as shown in the legend. The real part (c)-(e) and phase (f)-(h) of E field for SPP waves. ............................................................................................................................ 124 Figure 7.4 (a) Simulated and (b) measured transmission spectra for TM wave. The dotted and solid lines are the analytical resonance frequencies different resonance modes as listed in the legend. (c)-(f): The real part and (g)-(j) the phase of field of SPP waves. ..................................................................................................... 127 Figure 7.5 (a) Simulated and (b) measured transmission spectra for TE wave for θ 10 , 0 ϕ 270 . The dotted and solid lines are the analytical resonance frequencies for SPP resonance modes listed in the legend. (c)-(j): The real part of E field for SPP waves. The purple dash-lines show equiphase lines calculated analytically using Eq. 7.3 ............................................................ 128

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Figure 7.6 (a) Simulated and (b) measured transmission spectra for TM wave. (c) Transmission peak value taken at resonance frequencies shown as dash lines in (a) for (+1, 0), (-1, 0) and (0, +1) modes. (d) After a mirror-image transform at 180 degree for (-1, 0) mode and a -90 degreetranslational shift for (0, +1) mode, the resulting curves exactly overlap with (+1, 0) mode. ........................... 130

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ABSTRACT

We have studied several metamaterials structures with multiple layers by explaining them

theoretically and verifying experimentally. The engineered structures we have designed work

either as a perfect absorber or antireflection coating. The multilayer model as we call it Three

Layer Model (TLM) has been developed, which gives the total reflection and transmission as a

function of reflection and transmission of individual layers. By manipulating the amplitude and

phase of the reflection and the transmission of the individual layers, we can get the required

functionality of the optoelectronic devices. To get zero reflection in the both perfect absorber and

the antireflection coating, the amplitude and phase conditions should be satisfied simultaneously.

We have employed the numerical simulation of the structures to verify those conditions for all of

the work presented here. As the theoretical retrieval method to extract the effective permittivity

and effective permeability of the metamaterial contains air on the both side of the structure, we

have dielectric at least on one side practically, that gives a little bit deviated result. We have

modified the retrieval method to better fit with the multilayer structure by introducing air on the

both side of the resonator using transfer matrix method and use it throughout all the works.

We have explained the perfect absorption of the EM wave through Fabry-Perot cavity bounded

by the resonator mirror and the metallic film. The metallic film acts as the close boundary

whereas the resonator acts as the quasi-open boundary with very high effective permittivity,

which leads to the characteristic feature of subwavelength thickness. We have shown

numerically that the ultra-thin thickness makes the perfect absorber angular independent. We

have also explained the phenomenon of perfect absorption through Impedance Matched Theory

xii

and Transmission Line Theory, and showed their matching with TLM. We have also developed

the Meta Film Model by considering the resonator as a homogeneous thin film characterized by

the effective permittivity and permeability giving rise to the same behavior as the original

multilayer structure. We have shown that the resonance of the metamaterial resonator is very far

from the resonance of the absorber, it behaves as the medium of high refractive index and very

low loss. We have also shown that the density of states of the absorber is increased as compared

to the resonator itself. We have investigated that the resonance peaks of the absorber arise from

the combination of Fabry- Perot cavity modes and surface plasmon resonance modes. All the

modes with increased spacer thickness are assigned with specific names describing the mode

profiles. We have shown the application of perfect absorber as a refractive index sensor. It is

used as a plasmonic sensor to detect the refractive index change of the chemical and biological

samples. To increase the sensitivity, we have etched the dielectric spacer below the resonator,

where electric field is localized and enhanced. We have found that the sensitivity (wavelength

shift per refractive index change) and the Figure of Merit (FOM*) as an indicator of performance

of the device both are enhanced significantly.

We have employed metamaterial (MM) anti-reflection (AR) coating to avoid the shortcomings of

the conventional thin film coating in three different cases of the structures. At first, we have

deployed metamaterial Metal Disk Array (MDA) on the top of conventional coating material

(BCB) with homogeneous substrate to enhance the transmission of EM wave. Then conventional

AR coating is employed to the dispersive media (metal Hole Array) to enhance the transmission.

We have shown that Impedance matched condition has been satisfied not only for homogeneous

media, but for dispersive media also. At the end, we have employed the MM AR coating to the

MM dispersive media (MHA). The two MM layers may interact with each other and may

xiii

degrade the SPP wave of the MHA, which is essential to enhance the performance of the devices.

To investigate the effect of interaction, we perform the simulation of the MDA, which shows that

the resonance of the MDA is far from the antireflection resonance and hence the electric field of

the SPP is significantly increased (~30%). With an improved retrieval method, the metasurface

is proved to exhibit a high effective permittivity ( ~30) and extremely low loss

( ~0.005). For all of the three AR structures, a classical thin film AR coating mechanism is

identified through analytical derivations and numerical simulations. The properly designed

and of the meta surface lead to the required phase and amplitude conditions for the AR

coating, thereby paving the way for the improved performance of the optoelectronic devices.

We have used MHA as a dispersive media to get extraordinary optical transmission (EOT). To

understand the behavior of the SPP peaks, we have investigated the shifting and splitting of the

spoof SPP resonance by varying the polar angle and azimuthal angle. The amplitude of

extraordinary optical transmission also shows angle dependence and exhibits mirror-image or

translational symmetries. Our measurements and simulations of the THz spoof SPP waves match

very well with the theoretical predictions. The angle dependence results provide the important

information for designing THz plasmonic devices in sensor and detector applications.

1

1. INTRODUCTION TO METAMATERIALS: PERFECT ABSORPTION AND

ANTIREFLECTION COATING

1.1 Metamaterials

Electromagnetic metamaterials (MMs) are man-made, they are also typically periodically-

arranged metallic resonant structures with unit cell size (P) much smaller than the EM

wavelength (λ) [1-4]. When P<λ, MMs behave as homogeneous media with effective electric

permittivity (ε) and effective magnetic permeability (μ). With appropriately engineered ε and μ

values, MMs can realize fascinating EM properties that do not exist in nature, such as a negative

refractive index [5, 6], diffraction-unlimited optical imaging [7, 8], quantum levitation [9], and

EM invisibility cloaking [10, 11]. The unique EM properties of MMs have inspired applications

including high resolution photolithography [12], compact antennas [13], THz [14] and infrared

[15] sensors, high frequency magnetism [16], analog signal processing [17], perfect absorbers

[18, 19], and polarizers [20, 21]. Since first proposed by Pendry [22, 23], MMs have been

demonstrated in a wide range of EM spectrum from radio [24], microwave [25, 26], terahertz

(THz) [27], up to infrared [16, 28-32] and optical frequencies [33]. MMs have been regarded as

one of the most important breakthroughs in optics and electromagnetics in the past decade [34].

MMs related to quantum optics (single photon devices), nonlinear optics, optical magnetism, and

semiconductor optics (efficient solar cells and light emitting devices) are surging research areas

in this field.

2

1.1.1 Development of Metamaterial Concept

Although the foundation of metamaterial research begin early, Veselago in 1968 has published

his work [35] that made theoretical breakthrough on metamaterial by introducing hypothetical

Left handed materials(LHMs) having negative refractive index(NIMs), √ with

simultaneously negative values of permittivity( ) and magnetic permeability( ) over a same

wavelength range. To investigate the existence of LHMs electromagnetically, the source free

Maxwell’s equations in an isotropic medium can be written as:

(1.1)

with

(1.2)

For a plane wave in which all fields are proportional to , the equations (1.1) and (1.2)

are reduced to

(1.3)

Equation (1.3) shows that the Electric field ( ), Magnetic field ( ) and Wave vector ( )

form right handed triplets of vectors when 0, 0 and left handed system for NIMs when

both 0, 0.

Poynting vector, is defined as the energy flux and gives the direction of energy flow.

It always forms a right handed coordinate system with and , whatever be the sign of and .

Since

same dire

in the op

LHMs.

Figure 1.poynting systems. W

Another

and grou

where

be derive

where

velocity

refractive

is right han

ection. But

pposite direc

1 (a) RHMs:vector ( ) arWave vector (

basic differ

p velocity. P

| | is the

ed as:

1

always acts

e index ( )

nded in norm

is left han

tion. Figure

Vectors , e in the same( ) and poyn

ence betwee

Phase velocit

unit vector a

has the sam

along the w

) of the med

mal material,

nded in LHM

(1.1) shows

, and foe direction. (b

nting vector (

en RHMs an

ty ( ) and g

|

along k dire

me sign as

wave vector

dium. For RH

3

, Poynting v

Ms, the Poyn

s the directio

orm right hanb) LHMs: Ve) are in the o

nd LHMs is

group veloci

| and

ction. From

,

. From the a

r whereas

HMs, is p

vector ( ) an

nting vector

ons of , ,

nded vector ectors , , opposite direc

s the relative

ity ( ) are d

| | ,

m dispersion

above relatio

s group velo

positive there

nd wave vect

( ) and wav

, and in

systems. Waand form

ction.

e direction o

defined as:

relation,

ons, one can

ocity depend

eby making

tor ( ) are i

ve vector (

n both RHM

ave vector (left handed v

of Phase vel

| | ,

n infer that p

ds on the sig

phase and g

in the

) are

s and

) and vector

locity

(1.4)

can

(1.5)

phase

gn of

group

4

velocity in the same direction. But for LHMs, is negative that makes the group velocity in the

opposite direction to the phase velocity.

The application of Snell’s law for NIMs brings about the propagation of the light in opposite side

of the Normal [36]. This amazing property of material was ignored by the scientific community

for about 35 years due to unavailability of material with negative until Pendry suggested the

possibility of creating artificial magnetism with negative using structure called Splitting Ring

Resonator(SRR) in 1999 [37] followed by theoretical and experimental demonstrations of NIMs

by Smith in 2000 and 2001 [5, 6].

1.1.2 Classification of Materials

For an isotropic medium of permittivity ( ) and permeability ( ), dispersion relation can be

written as:

(1.6)

Depending on the signs of and , the wave can propagate or decay exponentially in the

medium. If ∙ 0, √ , then the wave propagates. If ∙ 0, | | , then

the wave decays exponentially into the medium. Figure (1.2) shows the plane of and and

summarizes their possible combination in four quadrants. In I quadrant, and are both

positive; therefore and are real numbers. Hence, wave propagates through the medium.

Majority of the dielectrics belongs to this group. In the II quadrant, is negative thereby creating

imaginary and and hence the wave decays exponentially. Metals and ionized gas have

negative below the plasma frequency, so they belong to this group. Some ferrites can have

negative near the resonance, so they belong to IV quadrant and wave decays exponentially in

those media. The III quadrant belongs to the material which have both and negative. They

can’t be

and realiz

a branch

Figure 1.2value of rimaginary

1.1.3 Rea

Even if s

be exper

permittiv

Pendry r

below th

found in nat

zed experim

of metamate

2 Schematic orefractive indy value of .

alization of

scientists exp

imentally re

vity ( ) and

eported that

e plasma fre

ture. But rec

mentally [5] a

erials.

of and coodex ( ) wher

LHMs

plained the p

ealized for a

negative pe

t negative pe

equency and

cently, those

and opens up

ordinate systereas wave dec

possibility of

a long time d

rmeability (

ermittivity (

in 1999, he

5

types of ma

p the road to

em. In I and IIcays exponen

f getting LH

due to the la

), at the de

) can be tu

reported tha

aterials are p

a new class

II quadrants, ntially in the

HMS theoreti

ack of techn

esired freque

uned with th

at negative p

proposed the

s of materials

wave propagII and IV qu

ically long a

nique on how

ency range. I

he continuou

permeability

eoretically [6

s called LHM

gates due to thuadrants due

ago, they cou

w to get neg

In 1996, Sir

us wire array

y ( ) can be t

6, 38]

Ms as

he real to the

uldn’t

gative

r J. B.

y [38]

tuned

6

with Split ring resonators (SRRs) [39]. By designing the composites of the SRRs and wires

together, negative refractive index ( ) can be realized.

Metals can be described by the Drude model of dielectric constant, modelled as free quasi

electrons given by

1 (1.7)

where is the damping frequency, is the concentration of free electrons (number of electrons

per unit volume) and m is the effective mass of electron. is the plasma frequency defined by

= (1.8)

It is obvious from the above relation that negative permittivity can be obtained from metals

below the plasma frequency ( ). Plasma frequency is very high in metals. For example, gold

(Au) has = 13700 THz and = 40.5 THz. As a result, absolute value of is too large to

apply for LHMs in the applicable frequency range from microwave to optical. So to bring the

value of down in the applicable range ( 1 , one has to decrease the by decreasing the

concentration of free electrons ( ). Pendry proposed to use wire array to achieve low that can

be tuned by changing its geometrical parameters [38].

Figure 1.3Real part Real part

As shown

separatio

permittiv

( ) and

arrays ca

/

volume

increased

inductanc

two param

3 (a) Continu(Green line) has a small an

n in figure 1

on, a, are u

vity of the w

d lower perm

an be expla

, which is d

occupied by

d by the self

ce is related

meters, plasm

uous metallic and imaginarnd negative v

1.3(a), period

used to form

wire arrays i

mittivity ( ).

ained by tw

diluted due t

y the wire

f-inductance

to the magn

ma frequenc

wires arrays ry part (blue dvalue below th

dically arran

m wire arr

is similar to

The mechan

wo paramete

to the large

itself. Othe

of the wires

netic energy

cy can be wr

7

with diametedotted line) ohe plasma fre

nged infinitel

ray structure

the bulk m

nism of the

ers. One is

volume occu

er parameter

s by slowing

, which is pr

ritten as:

er d and sepaof permittivityequency.

ly long wire

es. Figure

metal except

decreased p

the effectiv

upied by the

r is the eff

g down the m

roportional t

aration betweey ( ) as a func

es with diam

1.3(b) show

the lower p

plasma frequ

ve electron

e unit cell as

fective mass

motion of ele

to ln ( /r).

en the wiresction of frequ

meter, d, and w

ws that effe

plasma frequ

uency of the

density,

s compared t

s ( ) th

ectrons. The

Combining

. (b) uency.

wires

ective

uency

e wire

to the

hat is

e self-

those

(1.9)

Since the

the wires

be contro

Negative

negative

proposed

narrow f

periodica

lattice co

electric c

field. Ch

circuit,

Figure 1.4perpendiceffective p

e plasma freq

s (r), by cont

olled.

e refractive

permeability

d a design ca

frequency r

ally arranged

onstant a. W

currents are

harges are ac

with induct

4 (a) Split rincular to the ppermeability

quency depe

trolling the p

index mater

y at the desi

alled split ri

range with

d double sp

When magnet

induced in

ccumulated a

tance (L)

ng resonatorsplane of SRR( ) as a func

ends only on

parameters

rials cannot

red frequenc

ng resonator

certain pol

plit ring reso

tic field ( )

the both ou

at the gap of

of the ring

s (SRRs) arraRs. (b) Realction of freque

8

n the two val

, and r, plas

t be realized

cy, since the

rs (SRRs) w

arization of

onators (SR

) is applied p

uter and inne

f both the rin

g and capa

ay with lattic(blue line) a

ency.

lues, lattice c

sma frequenc

d until one

ey do not exi

which produc

f EM wave

RRs) made o

perpendicul

er rings due

ngs. Each of

acitance (C

ce constant a.and imaginar

constant (a)

cy and hence

has to find

ist in nature

ce negative

e. Figure 1

of metal(cop

ar to the pla

e to the alte

f the SRR ac

C) between

. Magnetic firy (brown do

and the radi

e permittivit

d the way to

. In 1999, Pe

permeability

.4(a) shows

pper, gold)

ane of the S

ernating mag

cts as RLC s

the two r

ield ( ) is apotted line) p

ius of

ty can

o get

endry

y at a

s the

with

SRRs,

gnetic

series

rings.

pplied art of

In figure

which th

narrow fr

After fin

frequency

SRRs to

interact w

experime

transmiss

shown in

transmiss

Figure 1.employedline) and red dotted

As soon

represent

e 1.4(b), ver

e real and im

requency ran

nding the w

y range, sci

gether to ac

with each ot

entally by d

sion of wire

n figure 1.5(b

sion of SRR

5 (a) The Cd by Smith et the composit

d lines. When

as the SRR

ted by the bl

rtical red do

maginary pa

nge above th

way to creat

ientists starte

chieve negat

ther. In 200

designing th

e alone, SRR

b). Transmis

s has a stop

Composite ofal. (b) The Tre of thin wirethin wire is c

is combined

lack dotted l

otted line rep

arts of the pe

he resonant f

te both perm

ed to work

tive refracti

0, Smith et

he structure

Rs alone an

ssion of wire

band in betw

f LHMs consransmission ce and SRRs (combined to t

d with the wi

line. This ev

9

presents the

ermeability h

frequency, th

mittivity an

on composi

ive index, a

al. demonst

e as shown

nd the comp

e alone coinc

ween the two

sisting of thcoefficient of black dotted the SRR, pass

ires, the stop

vidence prov

e resonant fr

have highly

he real part o

nd permeabi

ites combini

assuming tha

trated negat

in figure

posites of w

cides with th

o vertical red

hin wires andf thin wires online).SRR ha

s band appear

p band is con

ved that the p

requency of

dispersive m

of permeabil

lity negativ

ing both the

at the two s

tive refractiv

1.5(a). The

wires and SR

he noise leve

d dotted line

d split ring rnly (blue lineas stop band irs.

nverted into

permittivity

f the resonat

magnitude. I

lity is negativ

ve in the de

e wire arrays

structures do

ve index ma

ey measured

RR separate

el at -52dBm

es.

resonators (S), SRR only (in between th

o the pass ba

and permea

tor at

In the

ve.

esired

s and

o not

aterial

d the

ely as

m and

SRRs) (black he two

and as

ability

10

of the composite are both negative in this region, thereby creating LHMs and hence the wave

propagates through it.

1.1.4 Effective Medium Theory

As we discuss that wires can possess negative permittivity, SRR can possess negative

permeability and the composites of wire and SRR can possess negative refractive index, one

question arises that can these structures produce the medium of those values. To understand this

question, we need to understand the concept of permittivity and permeability. The permittivity

and permeability are defined originally to represent the homogeneous view of the

electromagnetic properties of the medium, which are derived from the macroscopic electric and

magnetic properties of the materials (Polarization and magnetization). The polarization and

magnetization are the average behavior of electrons and atoms under the external electric and

magnetic fields of EM wave. In this regard, normal materials are also the composites with

electrons and atoms as the individual ingredients. Here, one important thing to consider is that

size of the ingredients (electrons and atoms) is very small as compared to the wavelength of the

incident wave.

If we apply this concept to the periodic array of unit cells with size a, metamaterial can be

considered as a homogeneous medium. Effective response of the unit cell as a whole gives the

total electromagnetic properties of the structure. The restriction to consider the medium as a

homogeneous is that the unit cell size, ≪ . If the structure obeys this condition, the incident

EM wave does not recognize the fine detail of the structure and considers it as a homogeneous

medium. Hence, considering effective permittivity and effective permeability of the metamaterial

is a reasonable concept.

11

1.2 Surface Plasmon Resonance

Most of the metamaterial structure consists of thin metallic part combined with the dielectrics.

The incident light excites the electrons on the metal surface. The collective oscillation of

conduction electrons on metal surface when interacting with the incoming electromagnetic wave

is called Surface Plasmon. Copper is generally used in the microwave regime because it is the

standard material for PCB fabrication. Gold and silver are preferred in the infrared regime. Gold

is stable against environmental degradation such as Oxidation and easy for nanofabrication.

However, Silver is preferable in the visible regime due to its lower loss than any other metal at

that frequency. There are two types of Surface Plasmon; Localized surface Plasmon (LSPR) and

Surface Plasmon Polariton (SPP). LSPR are non-propagative excitations in nature and confined

to nanostructure smaller than the wavelength of light used to excite the plasmon. As a result of

LSPR, local electric field is greatly enhanced around the vicinity of the structure and decays

quickly exponentially. Due to this property, LSPR has been emerged as a very powerful

technique in many fields of research from life science to environmental safety enabling high

sensitivity, label free detection, electrochemical analysis, food safety etc. This technique is easy

to perform and cost effective. Examples of nanostructures producing LSPR consist of circular

elliptical and rectangular disk, single wire, cross wires, SRR, fishnet structure, etc. The Physics

behind the resonance in the straight wire is the dipole resonance by accumulating oscillating

positive and negative charges at the two edge of the wire. Since, electric field , it has

highest value at the edge of the wire along the electric field and minimum at the center. Since,

current , it is maximum at the center and minimum at the edge. The resonance

wavelength at which current is maximum is given by / 2 / , where and are

the resonant wavelength in the air and the substrate respectively. The metallic disks can also be

considere

before, S

producin

Figure 1.6(c) Metal

Surface

interface

wave wit

importan

exponent

periodic

huge rang

and photo

SPP wav

where,

vectors a

scattering

Dipole mo

+ +

(a) Wire

ed as the wir

SRR produc

ng the circula

6 Schematic vHole Arrays

Pasmon Po

separating

th the oscilla

nt characteri

tially away f

nano-holes

ge of applica

onics [41] B

ve on MHA

is the wav

associated w

g events that

oment, P = q

‐ ‐

e

re that produ

es resonanc

ar current

view of (a) Di(MHA).

olaritons (SP

metal and d

ation of elect

istics of the

from the me

on the meta

ations includ

Bio sensing [4

can be descr

ve vector inc

ith the x and

t couples inc

.

uce electric r

ce due to th

ipole resonan

PP) are the

dielectric me

trons. Unlik

e SPP are t

etal. SPP are

al surface ov

ding extraord

42] etc.

ribed by mom

||

cident at azim

d Y direction

cident light.

(b) SRR

12

resonance an

he varying m

nce of metallic

e electroma

edia due to t

e LSPR, SPP

that its Z-co

realized exp

ver the subst

dinary optic

mentum mat

=

muthal angle

ns, i and j ar

nd follow the

magnetic fie

c wire (b) Spl

agnetic exci

the coupling

P are the pro

omponent o

perimentally

trate as show

al transmiss

tching condi

e , and

re the intege

(

e same Phys

eld which ac

lit ring resona

itations prop

g of incident

opagating su

of electric f

y by creating

wn in figure

sion [40], me

ition [43] as

,

are the B

ers indicating

c) MHA

sics. As desc

cts as LC c

ator (SRR) an

pagating on

t electromag

urface waves

field ( ) de

g sub-wavele

e 1.6(c). SPP

erging electr

shown below

(

Bragg’s recip

g the order o

cribed

circuit

nd

n the

gnetic

s. The

ecays

ength

P has

ronics

w

(1.10)

procal

of the

13

1.3 Modelling and Simulation of Metamaterials

Computational work is necessary in the field of metamaterials before experimental work. Since

solving Maxwell’s equation analytically is very difficult for composite irregular structures, they

are generally solved by using numerical techniques. We use commercially available software

called Computer Simulation technology Microwave Studio (CST MSW) that works on the

principle of Finite integration technique (FIT) to design the metamaterial structure and retrieve

scattering parameters(S-parameters), fields, currents etc. From the S-parameters, it is possible to

retrieve reflectance, transmittance, permittivity, permeability etc. CST has several solvers

including time and frequency domain that are applied according to the requirement needed. For

example, T-solver takes less memory than f-solver whereas f- domain gives better accuracy than

t-domain. Several boundary conditions are available in CST including PEC/PMC and periodic. If

we need to show the angular dependence of the light, unit cell boundary (periodic boundary) is

preferred. CST gives the freedom to choose the material from its library, define ourselves by

either conductivity or constant permittivity and insert user friendly dispersive permittivity. Hence

CST has provided freedom to design a wide variety of materials.

1.4 Antireflection Coating

When electromagnetic waves encounter the interface between two media with different

refractive indices, the energy of incident light is partially reflected while the rest propagates into

the second medium. The undesired reflection can severely limit the performance of modern

optoelectronic devices, such as photovoltaics cells, light-emitting diodes, and infrared detectors,

etc. Extensive efforts have been made to develop antireflection (AR) techniques to reduce the

amount of reflective losses. Conventionally, a layer of quarter-wavelength-thick ( /4)

dielectric coating has been used to suppress the reflection at certain wavelength owing to the

destructiv

and is

transmitt

.

Figure 1.7

To comp

and a

coating m

relative

dielectric

condition

lack of c

perfect e

structure

varying

ve interferen

the thicknes

ted through t

7 Schematic d

pletely elimi

and

are permittiv

material and

impedance,

c materials

n c

coating mat

elimination o

d materials t

their geome

nce as shown

ss of the coa

the top surfa

diagram of An

inate the ref

, where

vities, and

substrate, r

1, the

found on n

can be writte

erial with a

of reflection

that provide

etric design

n in figure 1

ating materia

ace after trav

ntireflection s

flection, the

,

, and

espectively.

e AR condi

nature have

en in terms o

accurate imp

n is usually

e the tunable

n, thereby c

14

.7, where

al. Here the w

velling throu

showing destr

dielectric c

an

are perm

Generally, t

ition can be

e relative p

of refractive

pedance at w

unachievabl

e effective pe

capable of

is the wavel

waves reflec

ugh the film

ructive interfe

coating has

nd

meabilities o

the backgro

e simplified

ermeability

index as

wavelengths

le. Metamat

ermittivity a

achieving th

length in the

cted from th

have the ph

erences.

to satisfy th

are the im

of the back

und materia

d as

equal to 1

. How

s of practica

terials (MM

and effective

he required

e coating ma

he top surfac

hase differen

he AR cond

mpedances,

kground mat

al is air for w

. Most o

1. Therefore

wever, due t

al applicatio

s) are artific

e permeabili

d AR imped

aterial

e and

nce of

dition,

,

terial,

which

of the

e AR

to the

ons, a

cially

ity by

dance

15

matching conditions. Recent progress in MMs has demonstrated AR coating on non-dispersive

semiconductor surfaces [44-46]. It has been shown that a metallic-resonator/dielectric/metallic-

mesh sandwich-type MM can be used as AR coating on a gallium arsenide (GaAs) substrate

[44]. In this work, destructive interference of light reflected by two metallic structure layers

eliminates the overall reflection within certain wavelength range in the THz regime. A more

recent work has demonstrated that an array of metallic nanoantenna buried between an

amorphous silicon (-Si) film and crystalline silicon substrate can effectively reduce the

reflection between air and silicon substrate [45]. An array of metallic cross-wires on top of a low

refractive index magnesium fluoride (MgF2) dielectric film can also dramatically reduce the

reflection from germanium (Ge) substrate [46]. In these reports, MM based AR coatings were

applied to homogenous material (GaAs, Si or Ge) with nearly constant impedance. However, it

has not been clarified to date whether the MM based AR coating can be applicable to the

resonant metallic structures fabricated on substrate and by extension, integrated with

optoelectronic devices [47-50]. MMs are typically made from metallic resonators. Accordingly,

MM based AR coating may cause the AR impedance matching to malfunction due to unwanted

resonance coupling [51] with metallic structures underneath. In addition, the expected

functionality resulting from metallic structures on substrate or devices (e.g. extraordinary optical

transmission (EOT), improved device performance) may be affected.

One example of metallic structures integrated with substrate or optoelectronic devices [47-50] is

a metallic hole array (MHA) which exhibits strong surface plasmon polarition (SPP) resonances.

SPPs are the collective oscillations of electron plasma in the metallic structure excited by

electromagnetic (EM) radiation [52]. The SPP resonances occurring on various types of periodic

arrays of subwavelength holes in the metallic film lead to EOT[40]. At the resonance

16

wavelengths, SPPs help to concentrate light into subwavelength scale beyond the diffraction

limit and also assist in significantly enhancing the EM field. These characteristic features have

been utilized in many applications including surface-enhanced Raman spectroscopy[53], bio- or

chemical-sensors [54], photonic circuits [41, 55] and photovoltaic devices [56]. In particular, for

the metallic hole array (MHA) structure on a dielectric substrate, when the wave vector of the

normally incident light matches the reciprocal lattice of the array, strong SPP resonances occur

and produce evanescent waves that tunnel through subwavelength apertures, resulting in

extraordinary transmission of light on the other side [40, 57]. However, not all incident light

contribute to the SPP resonances due to the impedance mismatch at the air-MHA interface (i.e. a

part of incident light can be reflected). It has been recently demonstrated that a thin dielectric

film used as an AR coating can effectively improve the transmission through the MHA at the

resonant wavelengths [58]. However, the resonance wavelength is tunable with MHA geometry

(e.g. periodicity or aperture size), so it is impossible to find a common material with appropriate

impedance that matches the AR condition, , for different wavelengths in various

applications. Furthermore, the effective impedance of the MHA, , exhibits strong dispersion

around the SPP resonance wavelength. As previously stated, MM based AR coating can provide

great flexibility to solve these challenges, but the resonance of the MM may be able to generate

the interaction with the SPP resonance of MHA, leading to the shift of SPP resonance

wavelength and damping or degradation of surface wave [51].

1.5 Perfect Absorber

Recently, the metamaterial perfect absorber (MPA) consisting of a few-layer metasurfaces has

attracted tremendous interest. The MPA is a recently developed branch of metamaterial which

exhibits nearly unity absorption within a narrow frequency range [59-64]. The MPA possesses

17

characteristic features of angular-independence, high Q-factor and strong field localization that

have inspired a wide range of applications including electromagnetic (EM) wave absorption [61,

65, 66], spatial [64] and spectral [63] modulation of light [67], selective thermal emission [67],

thermal detection [68] and refractive index sensing for gas [69] and liquid [70-72] targets. The

MPA is typically made of three layers. The first layer is composed of periodically arranged

metallic resonators layer, e.g. cross-type resonators [15, 67], split-ring resonators [61] or metallic

nanoparticles [73]. The parameters of the resonator should be very carefully designed to avoid

the reflection, fulfilling the impedance matching condition required for perfect absorption. The

second layer is the subwavelength-thick dielectric film (spacer) which provides the space for the

electromagnetic wave to dissipate and also makes the cavity to prolong the time for multiple

reflection of the EM wave. The third layer is a highly reflective layer, e.g. metallic film [15, 61,

67, 73] or metallic mesh grid [61] which blocks the remaining EM wave to pass through. The

impedance matching between MPA and free space, and high attenuation inside the MPA result in

the perfect absorption [61]. The mechanism of MPA has been explained through a number of

models including impedance matching [61, 65, 74] and destructive interference [75]. In the

impedance matching mechanism, the entire three-layered structure is considered as a

homogeneous medium. At the perfect absorbing wavelength, the effective permittivity and the

effective permeability reach the same value, μ , so that the impedance (both the real

part and the imaginary part) matches to the free space, 1. Meanwhile, the

effective refractive index ′′ exhibits a large imaginary part, ≫ , thus the

incident EM wave propagates through the first interface (air-resonator) without reflection and

then decays rapidly to zero inside the MPA. In the destructive interference mechanism, the

resonator

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21

dispersive and has very large value at the resonant wavelength. The high refractive index of the

metamaterial is responsible to reflect large part of the incident wave and high value of imaginary

part of effective permittivity is responsible to absorb the wave efficiently.

1.6 Organization of the Dissertation

In this thesis, we start with the introduction of metamaterial and its development after Veselago

predicted negative refractive index theoretically in 1968. We describe the properties of Left

handed material and the methods how to realize them. After discussing the surface plasmon

resonance of wire, Split ring resonators (SRRs) and Metal hole array (MHA), we briefly review

the phenomenon of perfect absorbers and antireflection coating.

In chapter 2, we discuss the phenomenon of metamaterial perfect absorber with three different

theoretical models; Impedance matched theory, transmission line theory and meta cavity

bounded between a resonator and metal thin film. The Fabry-Perot cavity model of the perfect

absorber explains the unique properties of ultra-thin thickness, angular independence and strong

field localization. We also find that such a meta-cavity exhibits very low ohmic loss at the

perfection absorption wavelength because of the off-resonance of the metasurface. In

combination of these features, metamaterial perfect absorber can be redefined as a meta-cavity

exhibiting high Q-factor and extreme high density of states. The zero reflection is explained by

multiple layer model satisfying amplitude and phase condition simultaneously. Further, we have

developed an improved retrieval method to extract the permittivity and permeability of the

resonator, which can be useful to design optoelectronic devices.

In chapter 3, we discuss about the plasmonic perfect absorber used as a refractive index sensor.

In the previously designed absorber, only the surface of the sensor is accessible to the gas or

22

liquid as the sensing target. We have designed a large area mushroom capped plasmonic perfect

absorber whose dielectric spacer is partially removed by a reactive-ion-etch process, thereby

enabling the liquid to permeate into the sensitive region to a refractive index change. We

demonstrate experimentally and numerically that etching the spacer below the metamaterial

resonator increases the spectral shift of the resonance wavelengths as the surrounding refractive

index changes. The sensitivity and the figure of merit (FOM*), as the measure of the sensor

performance are significantly improved. We show that the plasmonic perfect absorber can be

understood as a Fabry-Perot cavity bounded by a “resonator” mirror and metallic film, where the

former exhibits a “quasi-open” boundary condition and leads to the characteristic feature of

subwavelength thickness. Zero reflection of the absorber is explained by multiple layer model

satisfying amplitude and phase condition simultaneously.

In chapter 4, we introduce metamaterial antireflection coating by depositing metal Disk Array

(MDA) on the top of a conventional antireflection coating film. The structural parameters of the

MDA can be adjusted to get antireflection at any desirable wavelength, thereby illuminating the

drawback of conventional antireflection coating. With an improved retrieval method, the

metasurface is proved to exhibit a high effective permittivity and extremely low loss. A classical

thin-film AR coating mechanism is identified through analytical derivations and numerical

simulations.

In chapter 5, we employ metasurface antireflection coating (Si3N4) on the top of dispersive

media (perforated gold film (PGF)). We present experiments and analysis on enhanced

transmission due to dielectric layer (Si3N4) deposited on a metal film perforated with two-

dimensional periodic array of subwavelength holes. We develop and demonstrate the concept of

AR condition based on the effective parameters of PGF. In addition, the maximum transmission

23

(zero reflection) condition is analyzed numerically by using a three-layer model and a transfer

matrix method is employed to determine the total reflection and transmission. Destructive

interference conditions for amplitude and phase to get zero reflection are well satisfied.

In chapter 6, we employ metal disk arrays (MDA) on the top of dispersive media (perforated

gold film (PGF)) separated by dielectric to get zero reflection/maximum transmission. In order to

enhance the SPP of MHA, a single-layer metasurface-based AR coating is shown to operate at

off-resonance wavelengths and to avoid the resonant coupling with the MHA layer. The SPP

resonance wavelengths are unaffected whereas the electric field of surface wave is significantly

increased. With an improved retrieval method, the metasurface is proved to exhibit a high

effective permittivity (ϵ_eff~30) and extremely low loss (tanδ~ 0.005). A classical thin-film AR

coating mechanism is identified through analytical derivations and numerical simulations. The

properly designed effective permittivity and effective permeability of the metasurface lead to

required phase and amplitude conditions for the AR coating, thereby paving the way for

improved performance of optoelectronic devices.

In chapter 7, we demonstrate the angle dependence of spoof surface plasmon on metallic hole

arrays in terahertz regime. By varying polar angle and azimuthal angle, we have observed

frequency shifting and splitting of resonance modes. The nature of the individual resonance peak

(standing wave or propagation wave) is also explored. The amplitude of extraordinary optical

transmission also shows angle dependence and exhibits mirror-image or translational

symmetries.

In chapter 8, conclusion of the work and the works needed to be done in the future are presented.

24

2. METAMATERIAL PERFECT ABSORBER ANALYZED BY A META-CAVITY

MODEL CONSISTING OF MULTILAYER METASURFACES

Note to Reader

Portions of this chapter have been previously published in peer reviewed journal paper (J. Jeon,

K. Bhattarai, D.-K. Kim, J. O. Kim, A. Urbas, S. J. Lee, et al., "A Low-loss Metasurface

Antireflection Coating on Dispersive Surface Plasmon Structure," Scientific Reports, vol. 6, p.

36190, 11/02/online 2016) and have been reproduced with the permission from the publisher.

In this chapter, metamaterial perfect absorber is modeled by a meta-cavity bounded between a

resonator metasurface and metallic thin film. The perfect absorption is achieved by the Fabry-

Perot cavity resonance via the multiple reflections between the two boundaries. Unique features

of angle independence, ultra-thin thickness and strong field localization can be well explained by

this model. We find that the perfect absorption occurs at off-resonance of the metasurface, so

that such meta-cavity exhibits very low ohmic loss. In combination of these features,

metamaterial perfect absorber can be redefined as a meta-cavity exhibiting high Q-factor and

extreme high density of states.

25

2.1 Introduction

In this work, we use a transfer matrix method to assemble the MPA from three functional layers

and obtain the phase and the amplitude conditions for the perfect absorption. Analying these

conditions, we reinterpret the MPA structure as a meta-cavity bounded by a “resonator” mirror

and a metallic film. The Fabry-Perot (FP) resonance is responsible for the perfect absorption.

The meta-cavity model can explain characteristic features of MPA including the ultra-thin

thickness, angular independence and strong field localization. With an improved retrieval

method, we find that the resonator metasurface operates at off-resonance wavelengths, so that the

meta-cavity has very low ohmic loss. These combined features redefine MPA as a meta-cavity

with high Q-factor and extremely high photonic density of states (PDOS) where the FP modes

are easily tailoered by the geometric parameters of metasurfaces, paving the way for novel

photonic, optoelectronic and cavity quantum electrodynamic (QED) applicaitions [85].

2.2 Three Models of Perfect Absorber

Our perfect absorber consists of three layers: an array of cross-wire resonators, a dielectric

spacer ( 2.28) and a metal ground plane (MGP) as shown in Fig. 2.1(a). We carry out full-

wave simulation of the structure by Computer Simulation Technology Microwave Studio (CST

MSW) that uses finite element method (FEM) to solve Maxwell’s equations and obtains

numerical solutions [86]. The parameters used in the simulation are as follows: period of cross

wire array, 2 , length and width of the cross wire, 1.7 and 0.4 ,

permittivity of GaAs substrate and dielectric spacer 11.56, and 2.28, thickness of

the dielectric spacer, 0.09 , the gold cross wire and ground plane, 0.1 . Gold

used for cross wire and MGP are described by the Drude model with plasma frequency,

1.37 10 / and collision frequency 4.08 10 / . We use three

different

structure

character

layer ef

homogen

spacer an

as a two

Figure 2.1(d) equivawire, spacfilm modeperfect absubstrate wmodel usesubstrate,

2.3 Sing

Since the

obtained

2.2(d). A

models to d

(Figure 2

rized by the

ffective med

nous metafilm

nd MGP; (ii

port network

1 Schematic dalent single-lacer and metal el (e), where tbsorber along with optical ies a two port nand and

le Layer Ef

e MGP pre

when the r

Among three

describe the p

.1(a)) is co

effective pe

dium mode

m (Figure 2

i) a transmis

k (Figure 2.1

diagram of (a)ayer film charground plate

the cross wirewave propagmpedances network de

are input

ffective Med

vents the E

reflection re

e models sho

perfect absor

onsidered a

ermittivity

el- the cros

2.1(e)) with

ssion line m

1(e)) with in

) perfect absoracterized by considered ae is consideregation directio

and at escribes the Mt and output im

dium Model

EM wave fr

eaches zero

own in Figu

26

rber: (i) sing

as a layer

ϵ and ef

ss wire res

and

model – the m

nput impedan

orber with enteffective

as a three-layeed by a homogon. The MPA two interface

MPA, where mpedances of

l

om propaga

at waveleng

ure 2.1, the

gle-layer effe

of homoge

ffective perm

sonator (Fig

on top of

multiple-lay

nce, , and

tire structure a and . (b

er structure angenous film wis surrounded

es, respectivel and are t

f , respectiv

ating throug

gth of

single-layer

ective mediu

enous layer

meability

gure 2.1(b)

f two layers

er optical sy

d output impe

as a metamatb) perfect absnd the equivawith ε and μd by vacuum ly. (f) A tranthe impedancvely.

gh, the perfe

6 as

r effective m

um model - e

(Figure 2.

; (ii) a t

)) is consid

of real films

ystem is mo

edance,

erial (MM) ansorber with cralent three-layμ . (c) Viewand a dielectsmission linees of vacuum

fect absorpti

shown in F

medium mod

entire

.1(d))

three-

dered

s, the

deled

.

nd its ross yer w of tric

m and

on is

Figure

del is

27

widely used in various MPA work [59, 61, 65, 74], where the electric and magnetic resonances

of the three-functional layer leads to the impedance matching condition, / 1,

and large imaginary effective refractive index, ≫ , at the perfect absorption wavelengths.

To verify this fact, we use effective medium theory [87] to retrieve the effective permittivity( )

and effective permeability ( ) from the complex transmission , , and reflection as described

in section 2.4 with modification. Due to the asymmetry of the structure, the transmission and

reflection from the front (vacuum) and back (substrate) side of MPA are different. Strictly

speaking, such structure cannot be considered as a medium with homogenous permittivity and

permeability. However, since we only consider the interaction of MPA with incident light from

the front side, here we use the and for impinging light from the vacuum side to obtain

and . Figure 2.2(a) shows a Lorentzian type resonance of at wavelength of 5.5 . This

is the first-order dipole resonance mode of the cross wire driven by electric field of incident

light, where the amplitude of oscillating current exhibits a half period of cosine function along

the length of cross wire. At long wavelength 6 , Re 0 due to the Drude type

response of MGP. The effective permittivity, , in Figure 2.2(c) also shows a resonances at

wavelength of 6.0 , driven by the magnetic field of the incident wave. This magnetic

resonance is indicated by the anti-parallel current on the cross-wire and ground plane [65], and

can be qualitatively explained by the method of image theory.

The real and imaginary parts of the effective permittivity, , the effective permeability, ,

and the effective impedance, , of single-layer thin film model are shown In Fig. 2(a)-

(c). At the perfect absorption wavelength 5.94 , 2.432 24.175 and

1.003+25.517i, this leads to 1.02 0.03 , which matches with the impedance of air

28

1 very well. The light impinging onto the air-MPA interface enters effective thin film

representing MPA shown in Fig. 2.1(d) without any reflection. Meanwhile, the effective

refractive index, 1.736 24.849 has a large imaginary part 24.849.

So that the intensity of light decays quickly following , where

26.28 is the absorption coefficient, making decays to 1/ for every

0.019 distance traveling inside the MPA. When the reflected light at MPA-MGP interface

reaches the air-MPA surface again, the intensity reduced to / ⋅ 7.8 10 . Thus

the single-layer thin film model very well describes the perfect absorption property of MPA.

Another absorption peak show up at 1.79 , when the impedance 1.022 0.006

matches again, where 0.3008 7.157 , 0.378+7.833i and 0.338

7.49 . This absorption peak is less studied in the past, as will be shown later; it results from the

second-order dipole resonance of the cross-wire.

Using the retrieved effective and , we performed full-wave simulation for the

single-layer effective thin film (Fig. 1(d)). Obtained reflection spectra, shown as blue dash curve

in Fig. 2(d), completely overlaps the reflection from the original absorber structure (black solid

curve) as expected. This further confirms the single layer effective medium model provides a

complete description of the reflection and transmission properties for MPA. However, this

model has certain drawbacks: (i): To achieve the impedance matching condition, , both

electric and magnetic resonances are required to simultaneously modify and values. The

magnetic resonances of MPA structure result from anti-parallel current on the cross-wire and

MPG, which creates strong magnetic moment along the direction of the incident field. This

mechanism has been deployed to explain the magnetic resonances of short-wire pair structure,

where the coupling of dipole resonances of two wires results in symmetric and anti-symmetric

modes w

does not

Figure 2.2thin film Real and iand effecsingle-lay

Other st

condition

an

optimal

applicatio

cannot be

with parallel

apply to MP

2 (a) Real anmodel; (b) Rimaginary pactive circuit m

yer effective f

tudies show

ns, which d

nd e

geometric

ons, e.g. sen

e well expla

and anti-par

PA structure

d imaginary peal and imag

arts effective imodel ( ,da

film (blue das

w that the a

does not ne

exhibit strong

parameters

nsors [71, 72

ained by the

rallel current

because of M

parts of effecinary parts efimpedance caash curves); (h) and three-l

anti-parallel

ecessarily in

gly dispersiv

to achieve

2, 88], the ab

impedance

29

ts, respectiv

MGP do not

ctive permittivffective permalculated by s(d) Simulatedlayer effectiv

current ca

ndicating a

ve features w

e

bsorption pe

condition

vely. Howeve

support any

vity of MPA meability for s

ingle-layer thd reflectance

ve film (red da

an also resu

magnetic r

which make

at target

eak does not

. (

er, such coup

y dipole reso

A retrieved bysingle-layer thhin film mode

spectra of thash).

ult from th

resonances

it very diffic

wavelength

t necessary r

(iv) The imp

pling mecha

onance mode

y using singlehin film modeel ( ,solid cuhe actual MP

e EM boun

[75]. (ii)

cult to predic

h. (iii) In

reach 100%,

pedance matc

anism

e.

-layer el; (c) urves) PA, a

ndary

Both

ct the

some

, thus

ching

30

conditions in single-layer effective medium model has difficulties to explain some important

features such as ultra-thin thickness.

2.4 Metafilm Model (Modified Retrieval Method)

The disk-type plasmonic resonator can be considered as a metasurface since the induced electric

current only resides at the surface of the structure due to the skin effect. The electromagnetic

properties of the metasurface can be described by the effective surface electric susceptibility

and the effective surface magnetic susceptibility , which can be calculated from the

transmission and reflection coefficients [76, 89]. For normal incidence, and can be

calculated by the following equations:

(2.1)

(2.2)

where is the wavevector in vacuum, and and are complex transmission and reflection

coefficients, respectively. Typically, and do not change with physical thickness of the

metallic resonant structure. However, in the infrared regime, the conductivity of metal decreases

diametrically, so that the electric current flows through the entire volume of the metallic

structure. Thus, and show clear dependence on the thickness of the disk , as shown

in Figure 2.3(a,b). In this work, since the electromagnetic properties of the disk-type resonator

depend on the thickness, we model it as a thin film (metafilm) with effective permittivity ,

and effective permeability . and of the metafilm can be calculated by using the

well-known retrieval method [90] or by the relations of / and / . As

31

shown in Figure 2.3(c, d), and calculated by two methods match very well. The

retrieval method using the following equations to calculate and :

(2.3)

(2.4)

(2.5)

/ (2.6)

(2.7)

where and are the effective impedance and effective refractive index, respectively,

and is the thickness of the metamaterial. The sign of and are determined respectively

by the fact that 0 and 0 for any passive medium. The integer in

Equation 2.4 is usually determined by the continuity of as a function of the wavelength.

Figure 2.3(Red) andsolid curv

/

Both the

2.3-2.7 a

configura

transmiss

configura

MM use

to calcul

modeled

3 (a), (b) Read 0.1ves are calcula

.

metasurfac

assume that

ation. Howe

sion and ref

ation as sho

the transmi

ate and

as a metafil

al part of 0 (blue).ated by the re

e model Equ

the metama

ver, in realit

flection coef

wn in Figur

ssion and re

d , whic

lm with thick

and of t (c),(d) Real etrieval metho

uations 2.1

aterial is bo

ty MM struc

fficients are

re 2.4(b). To

eflection coe

ch cause ina

kness 5

32

the MDA mepart of

od and the da

& 2.2 and t

ounded by a

ctures are us

obtained at

o the best o

efficients of

accurate valu

0 . The e

etasurface for and of

ashed curves a

the effective

air at both s

sually made

t the interfa

of our knowl

air-MM-die

ues. In our

extremely th

the thicknesf the MDA mare calculated

e retrieval m

sides formin

on a dielectr

aces of an a

ledge, most

electric confi

structure, th

hin thikness

s 0.0metafilm, wher

d by /

method Equa

ng an air-MM

ric substrate

air-MM-diele

works relat

figuration dir

he metasurfa

magnifies

05 re the

and

ations

M-air

e. The

ectric

ted to

rectly

ace is

error

33

signaficantly because exists in the denominator in Equations 2.4 & 2.5. To obtain the correct

and , we develop a method to obtain the transmission and reflection coefficients of the

air-MM-air configuraiton (Figure 2.4(c)), , , and , from , , and of the

air-MM-dielectric configuation (Figure 2.4(b)). The results of , , and shown in

Figure 2.3 & 2.4 are calculated from , , and of the air-MM-air configuration by

using this improved metasurface model and effective thin-film retrieval method. The transfer

matrix at the interface of two dielectric media with impedance and is given by

12

Therefore, the transfer matrix of the air-MM-dielectric configuration can be written as

(2.8)

(2.9)

00

(2.10)

(2.11)

where and are the effective impedance and effective refractive index of the MM,

respectively, is the wave number in vaccum, and are the impedance of air ( 1) and

dielectric ( 1/ ) layer, respectively. If we insert an infnite-thin ( 0) air layer between

the MM and the dielectric layer, the transfer matrix of the resulting air-MM-air-dielectric

configuration is given by

34

where and are the transfer matrices of the MM-air and air-dielectric interfaces,

respectively

12

12

It is easy to prove that

12

Thus we obtain

Note that this result proves inserting an infinite-thin air layer does not change the transfer matrix

of the overal all structure. So that

(2.12)

The matrix is the transfer matrix for the air-MM-air configuration (Figure 2.4c). In

Equation 2.12, can be obtained from simulated or measured transmission and reflection

coefficients as shown in Figure 2.4(b) using Equation 2.17 and is given by

(2.13)

The transmission and reflection coefficients of air-MM-air configuration (Figure 2.4c),

, , and , can be calculated from using Equation 2.17. In our work, we use

, , and to calculate , (Equations S2.2 & S2.3), and (Equations 2.3-

2.7). To validate the method shown in equation 2.12, we simulated a 50 nm thick dielectric film

with

2.4(a). Th

configura

10 .

Equation

coefficien

for both

air-MM-

Figure 2.4thick BCBdielectric , ,

effective pin (b) (blu

By mode

through a

30 and

he transmiss

ation are ob

Meanwhile,

n 2.16. We

nts as shown

30 a

dielectric co

4 (a) SchemaB layer. (b)

(BCB) inteand at t

permittivity aue curves) and

eling the MD

and reflected

1 on a B

sion and refl

btained direc

, ,

calculated

n in Figure 2

and

onfiguration

atic model ofThe transmis

erfaces can the interfacesand permeabild (c) (red curv

DA as a meta

d by the met

BCB (

ection coeff

ctly from sim

and for

and

2.4(d,e). The

1 over the e

results in ve

f a 50ssion and refbe calculate

s of air-film-ality calculatedves).

afilm, the EM

tafilm. This

35

2.3716,

ficients, ,

mulation wit

the air-MM

using tw

e air-MM-ai

entire wavel

ery large erro

thick dieleflection coeffed in CST air are calculad using the tra

M wave accu

phase corre

1) su

, and

thin the wav

M-air config

two sets of

ir configurat

length range

or and incorr

ectric film wificients, ,simulation

ated by a transansmission an

umulate pha

ectly represe

ubstrate as

, for the a

velength ran

guration is

transmissio

tion produce

e from 2

rect dispersi

ith 30,, and

using the msfer matrix mnd reflection

se when the

nts the abru

shown in F

air-MM-diele

nge from 2

calculated u

on and refle

es accurate v

to 10 , w

on.

1 on a 0 at the air

model in (a)method. (d), (e

coefficients s

wave propa

upt phase cha

Figure

ectric

to

using

ection

values

while

.5 r-film-). (c) e) The shown

agates

anges

when the

simualtio

where th

the phase

actual M

Figure 2.5metafilm

2.5 Circ

The effe

2.1(f) sho

element

calculate

In circuit

e EM wave

on for air-M

e metafilm i

es of transm

DA structur

5 Simulated p(dashed).

uit Model a

ctive imped

ows an effec

in conne

d based on t

t theory, S-p

e propagates

MDA-spacer

is defined by

mission and

e.

phase of trans

and Transm

dance of the

ctive circuit

ction with l

transmission

arameters ar

s through an

structure an

y a 50nm-thi

reflecction c

smission and r

mission Line

MPA can a

model for th

loads (ai

n line theory

re defined as

,

36

nd reflects

nd the corre

ick film with

coefficients

reflection coe

Theory

also be obta

he MPA, wh

ir) and (

as described

s

, ,

by the MD

esponding a

h and

of the meta

efficients thro

ained by eff

here the MPA

(substrate).

d below

,

DA. We perf

ir-Metafilm-

. As show

afilm perfect

ough MDA st

fective circu

A is conside

The input i

fomed full

-spacer struc

wn in Figure

tly match th

tructure (solid

uit model. F

ered as a two

impedance

(

wave

cture,

e 2.5,

hat of

d) and

Figure

o-port

is

(2.14)

37

Where , and , are the incoming and outgoing voltage (current) from the front and

back surface as shown in figure 2.1(f).

1

1

Where and are the reflection coefficients between Vacuum- MM and MM -Substrate

interfaces.

We can compare the circuit model with the optic structure. In optic structure, and can be

written in terms of S-parameters as

1

1

S-parameters can be obtained from the simulation of the absorber structure. But It is difficult to

calculate and using above equation because of the presence of both and terms in both

the equations. Therefore, we process the equations further leading into the final form as shown

below. Since these expressions contain only the s-parameters, they can be easily extracted from

the simulation.

38

12

2 1 1

4 1 2 1

12 2 1

2 1 1

4 1 2 1

and can also be written in terms of impedance as:

(2.15)

Where and are the impedances of the front and back surfaces of the metamaterial.

Solving the above expressions, the impedances and can be written as:

11

(2.16)

The input impedance calculated is plotted in as dashed curves in Figure 2.2(b), showing

perfect match with effective impedance obtained from single-layer thin film model.

39

2.6 Transfer Matrix Analysis: Three Layer Model

In our crosswire-spacer-MGP structure, the incident light is reflected at the two interfaces;

crosswire/spacer and spacer/MGP. Zero reflection from the absorber structure can be interpreted

by using a multiple-layer model in which each layer is considered as homogeneous meta-layer

with effective electric permittivity and magnetic permeability . A transfer matrix

method is adopted to obtain the overall transmission and reflection coefficients using a transfer

matrix of each layer. The transfer matrix of the air-crosswire-spacer structure can be described

by

/ // 1/ (2.17)

where , , and are the transmission and reflection coefficients obtained from the

numerical simulation. The transmission coefficient is defined as the S-parameter and the

reflection coefficient is defined as the S-parameter , where the subscript i (j) represents the

waveguid port at i-material (j-material). Specifically, and are the transmission coefficients

along forward (air-crosswire-spacer) and backward (spacer-crosswire-air) directions,

respectively. and are the reflection coefficients at front (air) and back (spacer) sides of

crosswire. The transfer matrix for the dielectric spacer layer is given by

00

(2.18)

where is the propagating phase term in the spacer layer ( : ) is

the refractive index of the spacer, is the wave vector in vaccum and is the thickness of

the spacer layer). Also, the transfer matrix for the spacer-MGP-GaAs configuration can be

written as given below,

40

/ /

/ 1/ (2.19)

where the subscript 2(3) represents the waveguide port at spacer (GaAs). As mentioned above,

the overall reflection coefficient of crosswire absorber on GaAs substrate can be calculated by

multiplying the transfer matrix of each layer,

1 ∙ 00

∙ 1

The matrix in the above Matrix is calculated as

∙ ∙ ∙ ∙

1

∙ ∙1

∙ ∙1

∙ ∙ ∙

∙

Since the overall reflectrion is defined as,

∙ ∙ ∙

∙

∙ ∙ ∙∙

∙ ∙

1 ∙

41

∙ ∙

∙ (2.20)

where .

To understand the mechanism light travel and decay inside the MPA, we have studied the

transmission and reflection of light at each constituting layers of MPA and used a transfer matrix

method to obtain the overall reflection/absorption property of MPA. Our Perfect absorber

consists of three layers: cross wire, dielectric spacer and MGP. We consider the cross-wire as a

metasurface and describe it as a homogenous thin film with effective permittivity, , and

effective permeability, . The effective parameter can be calculted from transmisison and

refleciton coefficients of a air/cross-wire/spacer configuration by using an improved retrieval

method to take account of the asymmetric boundary of air and spacer [91]. The effective

permittivity of cross-wire shows a Lorentzian type electric resonance at wavelength of

4.75 , which is shorter than the resonance (5.94 ) in single-layer model. This resonance is

purely electric since the effective permeability takes a constant value of Re 0.8except a

typical anti-resonance at due to the periodicity effects [92]. With those value of and μ ,

we use a thin film of the same thickness to replaces the cross-wire in the absorber structure. Full-

wave simulation of the three-layer thin film absorber shown in Figure 2.1(e) is carried out and

the reflection(red curve) spectra is plotted in Figure 2.2(d). The reflection matches very well with

simulation of actual MPA struture (black line) at the first absorption wavelength ( 5.94 )

and is off slighlty at the second absorption wavelength ( 1.79 ). We believe the small

mismatch at 1.79 is due to inaccurcy of simulaitons which is typcially more notable for

shorter wavelengths.

The perfect matching of three-layer thin film model suggestes that the cross-wire layer and the

42

MGP layer are decoupled. Therefore, we use the transfer matrix method, a common approch to

study layered medium, to study the mechanism of MPA. The overall reflection of the three-layer

structure(Crosswire-Spacer-MGP) is calculated using equation 2.20, where and are the

reflection coefficients of the cross-wire from front (air) and back (spacer) side, respectively.

is the reflection coefficient of the MGP. ⋅ ⋅ is the propagating phase term in the

dielectric layer, where , and k are the refractive index, thickness of the spacer, and the wave

vector in vacuum, respectively. , where and are the transmission

coefficients through the cross-wire along forward (air-crosswire-spacer) and backward (spacer-

crosswire-air) directions, and and are the reflection coefficients from the crosswire to air

and spacer, respectively. Although is strictly equal to 1 at the interface between two

homogenous medium, 1 for the cross-wire around the resonance wavelength. This is caused

by the structral asymmetry in forward and backward directions of the air-crosswire-spacer

structure. To achieve complete absorption, according to Equation (2.20) the overall reflectance,

0, requires the following conditions for the amplitude and the phase:

| | | ⋅ | (2.21)

2 2 1 ,| | 0,1,2,…. (2.22)

The coefficients , , and are obtained from simualtion of the air/cross-wire/spacer

configuration and is obtained from the simulation of the spacer/MGP configuration.

The calculated reflection from the Equation (2.20) matches very well with the reflection obtained

from simulation of entire structure as evident from the amplitude and phase condition for zero

reflection in Figure 2.2(d). At around the perfect absorption wavelength 5.94 , both the

amplitude condition in Equation (2.21) (| | | ⋅ | and the phase condition term )

43

are stasified simultaneously as shown in Figure 2.6(d). As the wavelength decreases, the phase

term decreases and reach at 1.79 . Meanwhile, the amplitude condition

| | | ⋅ | matchs again at the same wavelength. This leads to the second absoprtion peak

mentioned eariler in Fig. 2.2(d). A closer look at Fig. 2.6(d) shows that the ampltitude conditon

(| | | ⋅ | at 5.61 ) and the phase condtion at 5.88 ) does not

match at the exact same wavelengths. This explains the fact that the reflectance in Figure 2.2(d)

does not reach absolute zero (min 3.68 10 5.94 ). The phase and amplitude

condition reveal a Fabry-Perot cavity-like mechanism. The cross-wire acts as a “mirror” that

reflects light due to its high effective permittivity and forms a cavity together with the MGP.

When the incident light passing through the cross-wire layer, it is reflected multiple times

successively by MGP and cross-wire. The Fabry-Perot cavity modes establish when the round-

trip phase fullfil the following condition:

2 2 ,| | 0,1,2, …. (2.23)

where and are the phases of reflection coefficients at the spacer/cross-wire

interface and the spacer/MGP interface, respectively. When reaches 2 , the waves reflected

by cross-wire and MGP are in phase and hence interfere constructively, leading to resonant

cavity modes. Blue curve in Fig. 2.6(d) shows the increase monotonically as wavelength

decreases and reaches 0 at 5.96 and 2 at 1.82 , repectively, matching very well

with two perfect absorptions wavelengths. Note that the phase condition of Equation (2.23) only

guarantees Fabry-Perot cavity modes, which leads to absorption peaks. However, to achieve

perfect absorption, the amplitude condition in Equation (2.21) needs to be stastisfied at the same

wavenegth as well. Nevertheless, Equation (2.22) and Equation (2.23) well explains the

absorptio

sensing a

The ultra

Figure 2

0, i

extremly

Figure 2.6and imagiin the amp(d) Phase shadows o

on peaks of

applications

a-thin thickn

.6(d), at th

and

it requires

and thus

y thin compar

6 (a) Real parinary part (bluplitude conditterms in the p

of green color

a varity of r

[70, 72, 88]

ness of MPA

he first perfe

is slig

/2, thu

, whi

red to a regu

rt (red) and Imue) of effectivtion. The insephase conditir show two pe

resonator-sp

], where the

A can also be

ect absorptio

ghtly less th

s we can ob

ich is close

ular Fabry-P

maginary part ve permeabilierting figure don: (red), erfect absorpt

44

pacer-MGP s

e absorption

e well expla

on wavelenth

han , i.e.

btain

to the real th

erot cavity w

(blue) of effeity ( ). (c) Adepicts the tra (blue), 2 ,

tion regions a

strcutures th

peaks does

ained by the

th 5.88

/4 ≪ . I

hickness

with size of

ective permittAmplitude teansmission an

(blackat wavelength

hat have bee

not necessa

cavity mod

where

with

In our simul

0.09

/2.

tivity ( ). (erms, | |(rend reflection ck) and

h of 5.94

en widely us

arily reach 1

del. As show

0, the p

≪ . To ach

ations, we o

/66, whi

(b) Real part (ed) and | | (bcoefficients. (orange). Th

and 1.79

sed in

00%.

wn in

phase

hieve

obtain

ich is

(red) blue),

he .

45

2.7 Angular Independence of Reflection

One of the very important characteristics of our perfect absorber is the angular independence of

the reflection with incident light that is very useful in variety of applications. WE have carried

out 3D simulation of the perfect absorber by changing the polar angle θ from normal incidence to

800 for both TE and TM mode. The reflection spectrum is shown as a color plot for TE mode in

figure 2.7(a) and for TM mode in figure 2.7(b). From the color plot, it is evident that the first

order resonance peak is not shifted at all at 6um in the whole range of θ for TE mode. The

simulation of angular dependence is also carried out for entire single layer thin film structure

called one layer film (figure 2.1(a)) and thin film-spacer-MGP structure called three layer film

(figure 2.1(c)) for both TE and TM modes. For TE mode of both one and three layer films,

reflection is entirely constant at 6 µm as shown in figure 2.7(c) and (e) respectively, which

matches with the original simulation of the perfect absorber (crosswire-spacer-MGP). For TM

mode, the reflection of the crosswire-spacer-MGP structure is blue shifted with increase in polar

angle from 00 t0 800 by around 4% as shown in figure 2.7(b). For entire single layer thin film

structure (one layer film), reflection is blue shifted by 7.75%. For thin film-spacer-MGP

structure (three layer film) also, reflection is blue shifted (figure 2.7(f)) as in the original

structure (figure 2.7(b)) but the shift is increased to 9.8%.

Figure 2.7TE mode from thin

2.8 Curr

Since the

eg. quant

resonanc

FP reson

spacer. i.

first orde

simulatio

are calcu

2.28

thickness

zero for

the top cr

7 Color plot (b) TM modfilm-spacer-M

rents and Fi

e spacer thic

tum dots) w

e peaks at h

nances are ob

e. thickness

er thickness,

on, 1st order

ulated to be

8. Full 3D S

s is perform

all orders. T

rosswire stru

of angular dde, from entirMGP structur

ields for Hi

ckness of the

with it. Hence

higher order

btained by i

of the nth or

is the wa

spacer thick

2.07

imulation of

med and refle

The discrepa

ucture and th

dependence ore single layere for (e) TE m

gher Order

e MPA is ver

e, we need t

FP resonan

increasing th

rder FP reson

avelength in

kness, 0

and

f Crosswire-

ection spectr

ancy in reson

he MGP. Sin

46

f reflection frer thin film stmode (f) TM

r FP Resona

ry thin, it is

thicker space

nces with thi

he spacer thi

nance,

n free space,

0.09 . Th

4.057

-spacer-MGP

rum is show

nant Wavele

nce the cross

from crosswirtructure for (cmode.

ances

impossible

er. Therefor

icker spacer

ickness by h

is the perm

herefore 2nd a

respectivel

P structure w

wn in figure

ength arises

swire resona

re-spacer-MGc) TE mode (

to integrate

re it is impor

r thickness.

half of the w

√

mittivity of t

and 3rd order

ly by taking

with all 1st,

2.8. The re

due to the c

ator is model

GP structure f(d) TM mode

some device

rtant to stud

The higher

wavelength i

, where

the spacer. I

r spacer thick

g 6

2nd and 3rd

flection is n

coupling bet

lled as a thin

for (a) e, and

e (for

dy the

order

in the

is the

In our

kness

and

order

nearly

tween

n film

47

with effective permittivity and permeability, the Thinfilm-spacer-MGP structure is also

simulated for 1st, 2nd and 3rd order FP resonances and plotted the reflection as shown in figure

2.8(b). The reflections have similar behavior as the crosswire-spacer-MGP structure which

verifies the concept of resonator as the thinfilm. Currents in the resonator and MGP at 1st order

thickness are in opposite direction as shown in figure 2.8(c) which indicates that the phase of Ex

field on the top and bottom layers are in opposite direction. Ex field in the spacer along z-

direction is the standing wave having node at MGP (closed boundary) and higher amplitude at

resonator but not the antinode because the resonator acts as quasi-open boundary instead of open

boundary. The currents are in the same direction for the 2nd order thickness on the top and

bottom layer as shown in figure 2.8(d) which indicates that the Ex field is in opposite phase on

Figure 2.83rd order (order (blatop and bostructure a(g) 2nd ord

the top a

resonator

thickness

8 (a) Reflectio(blue) Fabry-pack), 2nd orderottom layers aat (c) 1st orderder (h) 3rd ord

and the bott

r (higher am

s as shown i

on of crosswiperot (FP) resr (red) and 3rd

and X-compor (d) 2nd ordeder.

tom layer. E

mplitude). T

in figure 2.8

re-spacer-MGsonances. (b) d order (blue) onent of Electer (e) 3rd orde

Ex field has

The currents

8(e), where E

48

GP structure fReflection ofFabry-perot (

tric fields (Exer and for Thi

s one more

are again

Ex has the s

for the 1st ordf thinfilm-spa(FP) resonanc

x) in the spaceinfilm-spacer

node in be

in the same

same phase

der (black), 2n

acer-MGP struces. Current der for crosswir-MGP structu

etween the M

e direction

on the top a

nd order (red) aucture for thedistributions oire-spacer-MGure at (f) 1st o

MGP (node)

for the 3rd

and bottom l

and e 1st on the GP rder

) and

order

layer.

49

One more node of Ex field is included in between MGP (node) and resonator (higher amplitude).

We investigate the behavior of currents and Ex fields in thinfilm-spacer-MGP structure as shown

in figure 2.8(f, g, h). Both the currents and Ex fields show the similar behavior as that of the

crosswire-spacer-MGP structure except the amplitude of the Ex field. Ex field in the thinfilm-

spacer-MGP structure is less than that of crosswire-spacer-MGP because crosswire is the

resonator where as thinfilm is the homogeneous media.

2.9 Density of States Calculation

Density of state of cavity, which is the function of frequency, is defined as:

∆

∆ (2.24)

Where ∆ is the full width of half maximum (FWHM) of the resonance peak, is the Volume of

the cavity, is the resonant frequency of the cavity and is the incident frequency. For

absorber, ∆ 2 ∆ 2 5.29 33.6 , 2 2 50.54

317.6 and 2 2 0.09μ ^3, Where period of the structure is 2 μm . To find the

density of state of the resonator only, after removing the metal ground plane (MGP), the

crosswire resonator with thick dielectric is simulated and its thickness for which electric field is

decreased to less than 10% is measured to be 0.5μm. Hence for the resonator, ∆ 2 ∆

2 38.8 243.8 , 2 2 66.97 420.8 and 2

2 0.09μ ^3. The density of states for the absorber, resonator and the enhancement factor due

to the cavity are shown in figure 2.9. The enhancement in the density of states is found to be 80

at the resonance of the absorber.

Figure 2.9density of

9 Density of f states of abs

states of (a) Csorber over re

Crosswire absonator.

50

sorber (b) Crrosswire reson

nator only. (cc) Enhancement of

51

2.10 Analysis of Multiple Resonances

There are two types of resonances occurring at the perfect absorber; one is the FP resonance

produced by the cavity and another is the plasmonic resonance produced by the oscillating

current of the resonator. Therefore it is important to investigate the type of resonances involved

to create the particular resonance peaks. To achieve this goal, we perform the simulation of the

absorber by sweeping the spacer thickness from 0.09 μm to 4.59 μm. Figure 2.10 shows the

colorplot of reflection of the absorber as a function of spacer thickness. To determine the

plasmonic modes, Currents on the resonator surface are plotted by applying the incident electric

field along X-direction. To determine the FP modes, Ex fields are plotted along z-direction in the

spacer cavity. From the results of the mode profiles, the resonant peaks are assigned with the

indices (i,j), where i and j represent the FP mode and plasmonic modes respectively. The same

order of FP modes is of two types; one has the Ex field less than 4 in one of the section

denoted by (-) sign and other has Ex field more than 4 in one of the section which is denoted

by (+) sign. For the ultrathin thickness of 0.09um, perfect absorption is achieved for our

absorber. At this spacer thickness, Current mode and FP modes for the first two peaks are shown

in the figure 2.10. The current on the resonator at first peak around 6 um is the dipole mode with

maximum current at the center and zero current at the edges described by 2 mode. X-

component of electric field (Ex) shows standing wave with node at MGP and higher amplitude at

the resonator which is called 1st order FP mode (1-). Hence this peak is represented by the mode

((1-), 2 ). The second peak has 3 2 plasmonic mode and 1st order FP mode, so it is represented

by ((1-),3 2 ) mode. As the spacer thickness increases, ((1-), 2 ) mode is red shifted and

quickly disappears. The second peak also red shifted but the amplitude decreases slowly,

disappear at around 0.7 um and reappear ((1+), 2 ) mode. From 0.81 µm to 1.35 µm,

Figure 2.1Each of th(FP) reson

representstwo peaks2nd and 3rd

The first

((1+), 2

resonanc

found as

order res

µm. Tha

10 Color plothe resonant pnance and j r

s the mode ws at 1st FP resd order FP res

three peaks

2 ) mode d

e peak. If w

((2- ), 2 )

onance peak

at peak app

t of Reflectiopeak is assignrepresents the

with less than sonance are ssonances are s

are assigne

disappears an

we follow th

), ((2+), 2

k ((2+), 2 )

ears as ((3-

on of wire-spned with the e order of the

4 and moshown with arshown to the

d as ((1+),

nd ((2- ),

he resonance

), ((3- ), 2

) becomes w

- ), 2 ) af

52

pacer-MGP abindices (i,j), e plasmonic r

re than 4.Crrows at the bright.

2 ), ((2-),3

2 ) mode

e modes for

), ((3+), 2

weaker as the

fter 3.3

bsorber with where i reprresonance. (-

Currents profibottom of the

2 ) and ((2

appears for

2.07

2 ) as shown

e increases

33 µm and

sweeping theresents the or-) and (+) sig

file on the rese figure and E

2+),3 2 ). A

r 1.53

µm, the firs

n in figure 2

s and disapp

becomes s

e spacer thickrder of Fabry-gn in FP reso

sonator for thEx field for th

At 1.53

µm as the

st four mode

2.10. The se

pears at

stronger whe

kness. -perot nance

e first he 1st,

3 µm,

first

es are

econd

3.15

en

53

increases. The first four resonance peaks at third order thickness 4.05 µm are found as ((3-

), 2 ), ((3+), 2 ), ((4- ), 2 ), and ((4+), 2 ). All those resonance peaks are summarized in

figure 2.10.

To understand the detail behavior of the resonance peaks, the mode profiles of the peaks are

studied at various thickness of the spacer in the cavity of the absorber. X-components of the

electric field (Ex) are plotted along the Z-direction in the dielectric spacer from the bottom

surface of the resonator to the top surface of the MGP. As a representative mode profile, spacer

thickness 2.07 µm is taken. Reflection of the absorber as a function of wavelength is

plotted in the figure 2.11(a). The first five resonance peaks are at the resonant wavelengths of

5.88 µm, 3.57 µm, 2.73 µm,2.46 µm and 1.85 µm respectively. At 5.88 µm, X-

component of electric field (Ex) has completed one 2 mode and extra very small mode

corresponding to the ultrathin 1st order spacer thickness as shown in figure 2.11(b). Hence we

call it 2nd (-) order FP resonance. From the current profile, all the peaks show 2 behavior.

Therefore, the resonance peak at 5.88 µm is represented by ((2- ), 2 ) mode. At 3.57

µm, Ex has completed one 2 mode and an extra mode with more than 4 as shown in figure

2.11(c). This mode is designated as ((2+), 2 ). At 2.73 µm, Ex has completed two 2

modes and an extra mode with less than 4 as shown in figure 2.11(d). This mode is designated

as ((3- ), 2 ). At 2.46 µm, Ex has completed two 2 modes and an extra mode with more

than 4 as shown in figure 2.11(e). This mode is designated as ((3+), 2 ). At 1.85 µm, Ex

has completed three 2 modes and an extra mode with less than 4 as shown in figure 2.11(f).

This mode is designated as ((4- ), 2 ). In this way, we can investigate the mode profile of the all

the peaks.

Figure 2.1of the eleMGP and(d) 2.direction.

11 (a) reflectiectric field (Ed bottom surfa.73 µm (e)

ion of the absEx) profile in ace of resona

2.46 µm a

sorber at the 2the dielectric

ator at the resand (f) 1

54

2nd order spacc spacer alonsonant wavele1.85 µm. Her

cer thickness ng Z-directionengths of (b) re incident el

at 2.07n in between

5.88 µmlectric field is

7 . X-compthe top surfa

m (c) 3.5s applied alon

ponent ace of 57 µm ng X-

55

2.11 Summary:

In this work, we investigate the mechanism of perfect absorber by using three layer model and

describe the propagation of EM wave through each of the multilayer structure. The resonance

mode is verified as a Fabry-perot (FP) cavity mode and the perfect absorption condition is

explained by satisfying the amplitude and phase condition simultaneously. We are able to extract

the effective permittivity of the Single layer thin film which works on impedance matching

condition and Circuit model, and both the values are precisely overlap each other. However,

these models cannot explain the ultrathin spacer of the absorber but we are able to explain it by

using three layer model. Hence three layer model has helped to design the perfect absorber

precisely and can explain its mechanism theoretically. Furthermore, the resonator is modelled as

a homogeneous thin film characterized by the effective permittivity and effective permeability

and produced the same result as the original structure. We found that the density of states of the

absorber is enhanced by the factor of 80 compared to the resonator. We verified the angular

independence of the absorber for the original structure as well as single layer entire film and

thinfilm-spacer-MGP structure for both TE and TM EM wave. This modelling can be used to

design the optoelectronic devices such as photodetector, Infrared sensors, etc.

56

3. A LARGE-AREA MUSHROOM-CAPPED PLASMONIC PERFECT ABSORBER:

REFRACTIVE INDEX SENSING AND FABRY-PEROT CAVITY MECHANISM

Note to Reader

Portions of this chapter have been previously published in peer reviewed ojurnal paper(K.

Bhattarai, Z. Ku, S. Silva, J. Jeon, J. O. Kim, S. J. Lee, et al., "A Large-Area, Mushroom-Capped

Plasmonic Perfect Absorber: Refractive Index Sensing and Fabry-Perot Cavity Mechanism,"

Advanced Optical Materials, vol. 3, pp. 1779-1786, 2015 2015) and have been reproduced with

the permission from the publisher.

In most plasmon resonance based sensor to date, only the surface of the sensor is accessible to

the gas or liquid as the sensing target. In this work, we have demonstrated an interferometric-

lithographically fabricated, large-area mushroom-capped plasmonic perfect absorber whose

dielectric spacer is partially removed by a reactive-ion-etch process, thereby enabling the liquid

to permeate into the sensitive region to a refractive index change. Our findings demonstrate

experimentally and numerically that etching the spacer below the metamaterial resonator

increases the spectral shift of the resonance wavelengths as the surrounding refractive index

changes. The sensitivity and the figure of merit (FOM*), as the measure of the sensor

performance are significantly improved. We show that the plasmonic perfect absorber can be

57

understood as a Fabry-Perot cavity bounded by a “resonator” mirror and metallic film, where the

former exhibits a “quasi-open” boundary condition and leads to the characteristic feature of

subwavelength thickness.

3.1 Introduction

Recently, using localized surface plasmon resonance (LSPR) for biochemical sensing has

attracted tremendous interest [93-97]. The LSPR rises from collective oscillations of electrons

when the incident light interacts with metallic nanoparticles or patterned planar nanostructures

[41, 98, 99]. The resonance wavelength depends on the size, shape and composition of the

nanostructure, and is sensitive to the refractive index of surrounding material. When the LSPR

structures are placed in liquid or gas environment, the change of surrounding refractive index

causes the spectral shift of the resonance wavelength. In particular, most organic molecules have

a higher refractive index than buffer solution, thus as the concentration of these molecules rises,

the local refractive index increases, thereby red-shifting the resonance wavelength. The spectral

shift of resonance results in the change of the transmission, reflection or absorption spectrum,

which can be monitored by inexpensive spectrometry [70, 93-96, 100-102]. However, strong

induced electric current in these plasmonic resonators also leads to significant ohmic loss [41,

98, 99], which gives rise to the broadening of the resonance spectrum with low quality factor (Q-

factor) and thus degrade the performance of the sensor characterized by a figure of merit FOM*.

Over the years, numerous efforts have been made to improve the performance of plasmon based

sensor, for example using high Q-factor Fano resonance induced by coupling of surface plasmon

polariton and LSPR [102] and reducing the substrate effect by lifting the LSPR resonators [103].

Among the efforts, it has been demonstrated that the metamaterial perfect absorbers (MPA) can

be used to significantly increase the Q-factor and thus improve the FOM* [70, 80]. The MPA is

58

a recently developed branch of metamaterial which exhibits nearly unity absorption within

certain frequency range [60, 62-64, 77, 104]. The optically thin MPA possesses characteristic

features of angular-independence, high Q-factor and strong field localization that have inspired a

wide range of applications including electromagnetic (EM) wave absorption [65, 66, 77], spatial

[64] and spectral [63] modulation of light [105], selective thermal emission[105], thermal

detecting[68] and refractive index sensing for gas [69] and liquid [70, 80] targets. The MPA is

typically comprised of three layers: a metallic resonators layer, e.g. cross-type resonators [84,

105], split-ring resonators [77] or metallic nanoparticles [73], and a highly reflective layer, e.g.

metallic film [73, 77, 84, 105] or metallic mesh grid [77], separated by a subwavelength-thick

dielectric film (spacer). The impedance matching between MPA and free space, and high

attenuation of light inside the MPA result in the perfect absorption [77]. In the sensing

application, the spectral shift of perfect absorption peak is attributed to the refractive index

change of gas [69] or liquid [70, 80]. However, the gas or liquid used as the sensing target has

been so far only on the surface of the MPA-based sensors [69, 70, 80], which implies that we

have overlooked the space under the resonators - the most sensitive region responding to a

refractive index change of surrounding medium. It has been shown that the spectral shift of

LSPR can be effectively increased by lifting the resonator from the substrate through a dielectric

pillar [103]. Following the similar concept, we demonstrate that the sensing performance of

MPA-based sensor, both the sensitivity and the FOM*, can be largely improved by using a

mushroom-capped architecture created by etching away the dielectric spacer along lateral

direction. Thus the most sensitive region inside the MPA structure can be accessible to gas or

liquid sensing target.

Figure 3.1dielectric (corresponetched by

3.2 Fab

The unit

layer san

fabricatin

thick bla

(mirror).

radiation

followed

define a

one-dime

Au was

1 (a) Geometrspacer.( b) Anding to the

y O2 plasma re

brication and

cell of the

ndwiched by

ng the large

anket layer o

A bottom

n) lithograph

d by a layer

periodic ell

ensional exp

deposited o

ry of a unit ceA unit cell of m

sample showneactive-ion-et

d Measurem

MPA is illu

y a layer of

-area (1×1 i

of Au was d

anti-reflecti

hy was spun

of negative-

iptical hole

posures with

on the devel

ell of metamamushroom-can in (f)). Scantch for (c) 0 s

ment

ustrated in F

f gold (Au)

in2), uniform

deposited on

on coating

n onto a 10

-tone photor

pattern in th

different do

loped sampl

59

aterial perfect apped MPA wnning electron, (d) 45 s, (e)

Figure 3.1(a)

elliptical di

m mushroom

n cleaned B

(BARC) lay

00 nm thick

resist. Interfe

he photoresi

oses. After ex

le using e-b

absorber (MPwith over-etchn miscroscop90 s, and (f)

). It consists

isks and an

m-capped MP

BK7 glass su

yer for i-lin

k layer of A

ferometric lit

ist layer wit

xposure and

beam evapor

PA) structurehed dielectric py (SEM) ima

135 s.

s of three la

Au film. Th

PA is as fol

ubstrate as t

ne (365 nm

Au as the d

thography [

th two succe

d developme

ration, follo

e without etchspacer

ages of the sam

ayers: a diele

he procedur

llows. A 10

the ground p

wavelength

dielectric sp

106] was us

essive orthog

ent, a 30 nm

owed by a l

hing

mples

ectric

re for

0 nm

plane

h UV

pacer,

sed to

gonal

thick

liftoff

60

processing. This resulted in an array of elliptical Au disks atop the BARC layer, which leads to

the MPA structure (p =800 nm, a = 570 nm, b = 375 nm, tm = 30 nm, ts = 50 nm, tgnd = 100 nm)

as shown in Figure 3.1(a,c). Starting from this conventional MPA structure, we create a

mushroom-capped structure (as illustrated in Figure 3.1(b)) by additional fabrication processing:

a predominately anisotropic O2 plasma reactive-ion-etch (RIE) with slight isotropic component

was carried out to remove the BARC-spacer laterally at a slower speed than that of etching

downward. Various etching time was used to remove different amount of spacer depicted in

Figure 3.1(d-f). Specifically, Figure 3.1(d) represents a sample with ≈50% etch-depth (vertically-

etched spacer) and a small etch-bias (laterally-etched spacer) after an etch time of 45 s. As

shown in Figure 3.1(e), ≈100% etch-depth and evident etch-bias were developed after 90 s,

namely that the spacer between the disks has been completely removed and the remaining spacer

only exists under the disk. With longer etching time (135 s), the remaining spacer under the disks

becomes narrower due to more etch-bias shown in Figure 3.1(f). As will discuss later, filling the

liquid into the RIE-etched spacer region between Au elliptical disk and Au film allows to

increase the spectral shift of resonance wavelength, thereby improving the sensitivity. The

detailed processing sequence is explained below.

The processing steps for the large-area mushroom capped metasurfaces were as follows. (A)

BK7 glass substrate (1×1 in2) was cleaned with piranha solution with a volume concentration

ratio of H2SO4/H2O2 of 4:1 to remove any residual organic contamination, followed by

dehydration processing on 150°C on hotplate for 6 min. (B) A 100 nm thick blanket layer of gold

(Au) was deposited on cleaned BK7 glass substrate as ground plane or mirror. (C) A bottom anti-

reflection coating (BARC) (Brewer Science: i-CON-7, i-CON-16) for i-line lithography was

spun onto a 100 nm thick layer of Au at 3K rpm or 5K rpm for 30 s and oven baked at 175°C for

3 min; ne

for 30 s a

3rd harmo

layer wit

doses for

post-bake

(E) a 30

followed

elliptical

was used

bias (70 V

different

egative-tone

and hotplate

onic YAG:N

th two succe

r asymmetric

ed sample w

nm thick A

d by liftoff p

Au disks at

d to etch thro

V). Various

structure of

e photoresist

e-baked at 15

Nd3+ laser sou

ssive orthog

cal aperture

was develope

Au was depos

rocessing w

top the BAR

ough the BA

etching time

f BARC betw

Figure 3

t (Futurrex: N

50°C for 1 m

urce produc

gonal one-dim

e shape; a 2

ed (Shipley:

sited using a

with acetone

RC layer. (F

ARC at RF (3

e with const

ween metal p

.2 Schematic

61

NR7-500P)

min. (D) Inte

ed a periodic

mensional ex

min post-ba

MF-702) fo

an e-beam e

to remove th

F) An anisot

30W), O2 ga

ant time step

plates.

view of fabri

was spread

erferometric

c elliptical h

xposures wi

ake at 110°C

or 13 s and

evaporator at

he PR layer

tropic O2 pla

as (10 sccm),

p, e.g. 45 s,

ication proce

atop BARC

c lithography

hole pattern

ith power 50

C was used;

rinsed with

t ~10-7 mTo

r. This result

asma-reactiv

, pressure (9

90 s, 135 s w

dure

C layer at 4K

y using a 35

in the photo

0 mJ and diff

the exposed

deionized w

orr and 0.01

ted in an arr

ve ion etch (

9 mTorr) and

was used to m

K rpm

55 nm

oresist

ferent

d and

water.

nm/s

ray of

(RIE)

d DC-

make

62

The samples with different etching time were measured through a Nicolet Fourier transform

infrared spectrometer (FTIR). Figure 3.3(a,b) show the measured reflectance spectra for

normally incident x-polarized (incidence light polarized with the E-field parallel to the major

axis of elliptical disk) and y-polarized (incidence light polarized with the E-field parallel to the

minor axis of elliptical disk) light for the samples etched by 0 s (black), 45 s (red), 90 s (green),

and 135 s (blue). Because of the presence of 100 nm thick Au film, the transmission is totally

eliminated across the entire wavelength regime of interest. Therefore, strong resonances with low

reflectance observed for all samples imply the high absorption of incident light by the MPA, A =

1 – R. It is shown in Figure 3.3(a) (Figure 3.3(b)) that the resonance shifts towards shorter

wavelength from ~2.52 μm to ~2.09 μm (from ~1.8 μm to ~1.47 μm) as the RIE-etching time

increases. As the spacer is gradually removed, the refractive index of this region decreases from

1.7 (spacer) to 1 (air). The resulting large blue-shift indicates that the resonance wavelength is

very sensitive to the refractive index change of materials filled in the etched region. The

spectrally-shifting trend (blue-shift) can be understood using the LC-circuit model for the disk

resonator [107], where the resonance wavelength is proportional to the square root of the

dielectric constant of surrounding material. As the dielectric spacer is gradually etched away, the

effective capacitance decreases, resulting in the blue-shift of resonance wavelength. Another

interesting property seen in Figure 3.3(a,b) is the rate of the blue-shift (the amount of spectral

shift Δλ per unit etching time), which is initially large but becomes smaller as the etching time

increases. In Figure 3.3(a) the resonance wavelengths for 0 s, 45 s, 90 s and 135 s etching time

are ≈2.52 μm, ≈ 2.33 μm, ≈2.14 μm and ≈ 2.09 μm, respectively. The corresponding spectral

shifts Δλ caused by every 45 s etching time are ≈ 0.19 μm, ≈ 0.19 μm, and ≈ 0.05 μm,

respectively. The decreasing blue-shift rate is due to the strong localization of the resonant

63

electric field under the edge of the disk, as will be discussed later in Figure 3.4, thereby making

this region more sensitive to the refractive index change than the central region. Thus, as the

dielectric spacer around and under the edge of the disk is removed by 45s and 90s etching

(Figure 3.1(d, e)), the resonance wavelength shifts more than the etching between 90s and 135s

(Figure 3.1(f)), which only laterally removes remaining spacer in the central region of the unit

cell.

Figure 3.3 FTIR-measured reflectance of structures with different RIE etching times for (a) x-polarized, (b) y-polarized and (c) unpolarized incidence. The corresponding simulated reflectance with a variety of etch-depth Δt and etch-bias Δx under (d) x-polarized, (e) y-polarized and (f) unpolarized illumination. The over-etched sample (135s etching, structure shown in Figure 1f) was used to measure the reflectance for unpolarized light before (magenta) and after (cyan) applying water to the sample.

To better understand the resonance behavior of the mushroom-capped MPA structure we

performed numerical simulations using CST Microwave Studio [108] for various etch-depth

(vertically-etched spacer, Δt) and etch-bias (laterally-etched spacer, Δx). In our simulations, we

implemented the structure illustrated in Figure 3.1(b) with the unit cell boundary condition. The

simulations use a finite element method to solve Maxwell‘s equations and provide results

y-polarization

0 s45 s90 s135 sb 0.6

0.7

0.8

0.9

1.0 Unpolarized light

c0.0

0.2

0.4

0.6

0.8

1.0

x-polarization

a

1.0 1.5 2.0 2.5 3.0

0.0

0.2

0.4

0.6

0.8

1.0

Ref

lect

ance

d1.0 1.5 2.0 2.5 3.0

Wavelength (m)

t = 0; x = 0 nmt = 25; x = 5 nmt = 50; x = 15 nmt = 50; x = 25 nme

1.0 1.5 2.0 2.50.0

0.2

0.4

0.6

0.8

1.0

fairwater

64

including the electromagnetic field and scattering parameters. The geometrical parameters of the

structure are as follows: periodicity (p) = 800 nm, major axis (2a) = 570 nm, minor axis (2b) =

375 nm, thickness of gold disk (tm) = 30 nm, thickness of dielectric spacer (ts) = 50 nm, thickness

of gold mirror (tgnd) = 100 nm. The dielectric constant of the spacer is taken as ϵ 2.89with

loss tangent tanδ ϵ /ϵ 0.04 (ϵ and ϵ are the real part and the imaginary part of the

permittivity, respectively). The Au is defined by a Drude model with plasma frequency ωp = 9.02

eV and scattering frequency ωc = 0.027 eV [109]. The overall agreement between experimental

and simulated reflectance is apparent from Figure 3.3, however the discrepancy in reflectance

intensity is probably due to imperfections and variations of the structure size in the fabrication.

To test the response of the sample under unpolarized light, we measured the reflectance spectra

of the over-etched sample (Figure 3.1(f)) by a Perkin Elmer Lambda 950 UV/Vis

spectrophotometer with an installed de-polarization module. The measured results and

corresponding simulations are shown in Figure 3.3(c) and 3.3(f), respectively. The magenta and

cyan curves (as results of a proof of concept) show the reflectance before and after dipping the

sample into water. We carefully removed residual water on the surface by covering the sample

with a Kim wipes under a coverslip for 10 minutes, so that no water on the surface can be

visually observed. With water applied, the resonance wavelength under the x (y)-polarization is

shifted by Δλ ≈ 210 nm (≈ 160 nm), respectively, which is increased by a factor of ≈1.88 (≈1.43)

compared to the shift of Δλ ≈ 112 nm reported in ref. [70], where the dielectric spacer is not

etched. The relative spectral shifts, (Δλ /λair)x ≈ 0.106 and (Δλ /λair)y ≈ 0.107 are improved by a

factor of ≈1.51 and ≈1.53 compared to (Δλ /λair) ≈ 0.07 from ref. [70]. The improvement of the

spectral shift attributes to the mushroom-capped MPA design, which allows water to enter the

65

etched region around and under the disk edges, i.e. the most sensitive region for the refractive

index change.

The elliptical Au disks act as dipole resonators and result in LSPR as they interact with the

incident EM wave [41, 110]. Figure 3.4(a) shows the electric current on the Au disk and the Au

film at the resonance wavelength for normally incident x-polarized light. Here the current refers

to the polarization current, 1 / where is the relative permittivity

of Au given by the Drude model. The current on the Au disk shows a typical half-wavelength

dipole resonance mode with the maximum amplitude at the center and the minimum at the ends

of the disk. Correspondingly, the surface charge density reaches the maximum at the ends and

the minimum at the center. The current on the Au film (Figure 3.4(b)) also shows a dipole

resonance mode but with opposite phase. The opposite charges (depicted as +/- in Figure 3.4

(a,b)) maximized at the ends excite strong localized electric field along the vertical direction,

/ ), where is the dielectric constant of the region between Au disk and Au film.

The amplitude of excited electric field follows the same distribution as the surface charges,

which is maximized at the ends and decreases quickly to almost zero towards the center as

shown in Figure 3.4(c). Since the localized electric field is mainly along the vertical direction,

the Au disk and the Au film form a parallel capactior with the capacitance of /

where is the effective area to take account for the effect of nonuniform distributions of the

charge and the electric field. Since both charge and the electric field are maximum at the edges

of the disk, the area of this region dominates the effective capacitance. Therefore, when liquid or

gas sensing target enter the region under the edge of the disk, the capacitance changes

significantly due to the change of , and thereby shifting the resonance wavelength.

Figure 3.4disk, (b) oaccumulat

3.3 Mus

Resonan

The mec

matching

the entir

absorbing

value, ε

to the fre

exhibits a

interface

destructiv

two deco

surfaces

4 At the resonon the Au filmte at two ends

hroom-Cap

nce

hanism of M

g [65, 74, 77

re three-laye

g wavelengt

μ , so

ee space,

a large imag

(air-resonat

ve interferen

oupled surfa

lead to zer

nance wavelenm. The positivs. (c) The amp

pped Plasmo

MPA has be

7] and destru

ered structu

th, the effec

o that the im

ginary part,

tor) without

nce mechani

aces, and de

ro reflection

ngth, the simuve (red plus siplitude of the

onic Optica

en explained

uctive interfe

ure is consid

ctive permitt

mpedance (bo

1. Mean

≫ , thu

reflection an

ism, the reso

estructive in

n [75, 76].

66

ulated currentign) and negae electric field

al Cavity R

d through a

erence [75].

dered as a

tivity and th

oth the real p

nwhile, the e

us the incide

nd then deca

onator layer

nterferences

By using th

t density distrative (blue negd at the resona

Reinterprete

number of

In the impe

homogeneo

he effective

part and the

effective refr

ent EM wave

ays rapidly to

r and the me

of multiple

he model in

ribution (a) ongative sign) cance wavelen

d by a Fab

models inclu

edance matc

ous medium

permeability

imaginary p

ractive index

e propagates

o zero inside

etallic film a

e reflected

ntroduced in

n the ellipticacharges ngth.

bry-Perot C

uding imped

hing mechan

m. At the pe

y reach the

part [74]) ma

x

s through the

e the MPA. I

are consider

waves from

n the destru

al

avity

dance

nism,

erfect

same

atches

′′

e first

In the

red as

m two

uctive

67

interference mechanism and a transfer matrix method, we obtain the phase and the amplitude

conditions for the perfect absorption. Analying these conditions, we reinterpret the MPA

structure as a Fabry-Perot (FP) cavity bounded by a “resonator” mirror and a metallic film. The

FP model can explain some characteristic features of MPA. In particular, the “quasi-open”

boundary conditon of the “resonator” mirrors leads to ultra-thin thickness of the MPA.

Our MPA structure consists of a disk-tpye resonators layer and an Au film separated by a

dielectric spacer layer. The disk resonators can be considered as a homogenous metasurface with

resoant effective electric and magnetic surface susceptibilities [76]. Using a transfer matrix

method, the overall reflection of the MPA can be obtained by multiplying the transfer matrix of

each layer, M = M1 · M2 · M3, as given below and with more detail shown in ref. [76]. The same

equation is also obtained in ref. [75] through a multiple reflection approach.

(3.1)

In equation (1), and are the reflection coefficients of the Au disk metasurface from front

(air) and back (dielectric spacer) side, respectively. 1 is the reflection coefficient of the

Au film (mirror). β = ns · k · ds is the propagating phase term in the spacer, where ns, ds and k are

the refractive index, thickness of the spacer, and the wave vector in vacuum, respectively.

, where t12 and t21 are the transmission coefficients through the Au disk along

forward (air-disk-spacer) and backward (spacer-disk-air) directions, and and are the

reflection coefficients from the Au disk to air and spacer, respectively. Figure 3.5(a) shows that

the simulated reflectances using the entire MPA structure and calculated by Equation 3.1 match

very well, where r12, r21, t21 and t12 in Equation 3.1 are obtained from the simualtion of the air-

disk-spacer structure. Although α is strictly equal to 1 at the interface between two homogenous

68

medium, 1 for the metasurface (especially around the resonance wavelength) as shown in

Figure 3.5(b). This is caused by the structral asymmetry in forward and backward directions of

the air-disk-spacer structure. The perfect absorption, i.e. r = 0, requires the following phase and

amplitude conditions:

| | | | (3.2)

2 2 ,| | 0,1,2, … (3.3)

The phase and the amplitude terms of above equations are numerically simulated and plotted in

Figure 3.5(b,c). We can see from Figure 3.5(b) that the amplitude of r12 and α reach the same

value at the resonance wavelength, satisfying the amplitude condition. Figure 3.5(c) shows that

the phase term, 2 , reaches zero (gray line) as predicted in the phase

condition for 0. Note that an absorption peak always shows up when the the phase condition

is reached, but the perfect absorption only occurs when both amplitude and phase conditions are

fulfilled simultaneously.

69

Figure 3.5 (a) Reflectances calculated (balck dashed line) by Equation 1and simulated using the whole MPA structure (red solid line). (b) The amplitude of r12 (blue) and (red). (c) The phase terms in Equation 3: θ ϕ r ϕ α 2β (blue), (green), (red), and 2β (black), respectively.

Equation (3.3) shows that the absorption peak reappears at the same wavelength when the

propagating phase term β increases by . This has been confirmed by numerical simulaiton (not

showing here). Increasing the phase term by corresponds to an increment of the spacer

thickness by half of the wavelength, /2 / 2 , where is the real part of the

refractive index of the spacer, λ0 and λs are the resonance wavelengths in the free space and the

spacer, respectively. The characteristic /2 increment indicates that the MPA is a FP cavity

bounded by the resonator metasurface and Au film where the former can be viewed as a

2 3 4 5 6-0.5

0.0

0.5

1.0

1.5

Wavelength (m)

c

Ph

ase

, , ,

Ref

lect

ance

0.0

0.2

0.4

0.6

0.8

1.0

a

Whole structureCalculated

0.2

0.4

0.6

0.8

1.0

b

Am

pli

tud

e

,| |

70

“resonator” mirror [111] at wavelengths around its resonance. Specifically, the resonator

metasurface can be considered as a surface with very large electric surface susceptibility [76],

which leads to high reflection with phase in contrast to a metallic mirror with reflection

phase of . The EM waves reflected at metasurface and Au film form resonant standing waves

inside the cavity and thereby leading to the complete absorption. The general expression for the

size of the cavity, i.e., the thickness of the spacer, can be written as /2, where m

is the order of the FP resonance modes and ts0 is the thickness for the first order resonance.

Remarkably, the first order thickness in a MPA is much smaller than the distance between two

mirrors in a typical FP cavity. For instance, in the unetched structure with resonace at 2.5 μm

shown in Figure 3.3(a,c), ts0 = 50 nm ≈ λs/30. The reason for the ultra-thin thickness is that, as

mentioned above, the “resontor” mirror in MPA forms a “quasi-open” boundary condition with

the reflection phase of (see red curve in Figure 3.5(c)), which is slightly larger than

, i.e., ≪ . According to the phase condition in Equation 3.3, at the

pefect absorbing wavelength, /2. So the thickness can be

derived as /2 /4 . The first order thickness for 0 is given by

/4 ≪ /4, which is much smaller than the size of /2for a regualr Fabry-Perot cavity

boundary between two metallic mirrors.

3.4 Mushroom-Capped Structure as the Refractive Index Sensor

We perform numerical simulations to examine the feasibility of our mushroom-capped MPA

structure operating as the refractive index sensor. We find that the spectral shift of resonance is

larger when the dielectric constant of the spacer is low. Our simulations show that the sensitivity

η = Δλ /Δn (in nm per refractive index unit [93]) increases from ≈ 2000 nm/RIU to ≈2500

nm/RIU as the dielectric constant of the spacer decreases from 9 to 1.9. In the following

71

discussion, we take MgF2 (with the dielectric constant of 1.9 and a loss tangent 0.0027) as the

spacer in simulations, which is also used elsewhere [74, 112] when low dielectric constant is

preferred. The perfect absorption for x-polarized light is obtained with parameters p = 875 nm,

2a = 850 nm, 2b = 300 nm, tm = 20 nm, ts = 60 nm, and tgnd = 100 nm. Considering the feasibility

of current nanofabrication technique, we use Δx = 90 nm and Δt = 60 nm as the laterally- and

vertically-etched amount for the mushroom-capped structure. As shown in Figure 3.6(a), our

simulation shows that the resonance wavelength shifts ≈ 29% (from the black to the blue curves)

after applying water onto the surface and inside the etched region between Au disk and Au film.

This leads to the sensitivity of η ≈2513 nm/RIU. This value is significantly larger than the

sensors based on circular disk (400 nm/RIU) [70], isotropic spiral metamaterials (410 nm/RIU)

[113], complementary split ring resonators (210 nm/RIU) [114], nanohole rectangular array (396

nm/RIU) [115], sensor based on EIT metamaterial (588 nm/RIU) [116], but less than nanorod

sensor (more than 30,000 nm/RIU) [117]. In addition to the spectral shift, our plasmonic cavity

sensor can also detect the relative intensity change Δ / . When air (n = 1) is replaced by

water (n = 1.312), reflectance increases from ~ 0 to ≈ 0.88 at wavelength ≈ 2.71 μm, denoted by

a dash-dot black line in Figure 3.6(a), which is ~190% improvement as compared to the result

(reflectance increases from ≈ 0 to ≈ 0.46 at wavelength ≈ 1.6 µm) reported in ref. [70]. Using

water as a reference medium, reflectance increases from ≈ 0 to ≈ 0.94 at the resonance

wavelength ≈ 3.49 μm, denoted by a dash-dot blue line in Figure 3.6(a).

This structure can be also used to detect small changes in the refractive index of liquid such as

glucose solutions. The blue to the orange curves in Figure 3.6(a) show the simulated reflectance

spectra of 0% to 25% glucose solutions whose refractive indices vary from 1.312 to 1.352 with a

step of 0.01, when water is used as the reference medium. When we compare water (n = 1.312)

72

and glucose solution (n = 1.352), the sensitivity is ≈ 2508 nm/RIU and the reflectance increases

from ≈ 0 to ≈ 0.13 at ≈ 3.49 μm and from ≈ 0 to ≈ 0.14 at ≈ 3.59 µm (compared to around 0.02 at

≈1.71 μm in ref. [70]).

A figure of merit introduced by J. Becker, ∗ max| Δ / /Δ | [118], can be used to

describe the performance of detecting the intensity change. To avoid unrealistic large FOM*

values due to ~0 around the perfect absorbing wavelength, we use the average intensity on

two curves for n=1.312 and n=1.322. However, this treatment, also used in ref. [70], imposes an

upper limit to the FOM*, i.e., ∗ ⋅ max/

. Figure 3.6(b) shows the

FOM* as the refractive index changes from 1.312 (blue curve) to 1.322 (red curve), where

0.01 and the upper limit for FOM* is 200. We obtain the FOM* value of 179.23 (the

maximum value of the dashed curve), which is close to the upper limit and is improved

compared to previous result of FOM∗ 120 reported in ref. [70].

Figure 3.6 (a) Simulated reflectance spectra for the sample in air (black), water (blue) and in glucose solution (red to orange) environment; (b) Calculated FOM* as the refractive index of glucose solution changes from 1.312 (blue) to 1.322 (red).

3.40 3.45 3.50 3.55 3.60

0.00

0.04

0.08

0.12

0.16

-200

-100

0

100

200

b

Wavelength (m)

FO

M*

2.5 3.0 3.5 4.0 4.5 5.0

0.0

0.2

0.4

0.6

0.8

1.0

Re

fle

cta

nc

e

Wavelength (m)

n=1 n=1.312 n=1.322 n=1.332 n=1.342 n=1.352

3.45 3.50 3.55 3.60

0.00

0.04

0.08

0.12

0.16

a

Re

fle

cta

nc

e

73

3.5 Summary

We have fabricated a large-area, uniform, low-cost plasmonic optical cavity based liquid

refractive index sensor by interferometric lighography and a reactive-ion-etch process. With the

dielectric spacer partially etched away to allow sensing target enter the etched region, the

spectral shift induced by the refractive index change is significantly increased. This largely

improves the sensitivity compared to the existing MPA based sensors. We have also developed a

Fabry-Perot model to reinterpret the perfect absorption. Our simulations show that Q-factor is

also increased and thereby improving the FOM*.

74

4. VERSATILITY OF ANTIREFLECTION USING LOW LOSS METAL DISK ARRAY

METASURFACE

Conventionally, antireflection on a homogeneous media is achieved by depositing quarter

wavelength thick dielectric coating of appropriate refractive index. But it is very difficult to find

the appropriate dielectric at all the wavelength region required. We have proposed metal disk

array (MDA) as a metasurface deposited on the top of dielectric coating with arbitrary refractive

index to get zero reflection. The size and shape of the MDA can be adjusted to get antireflection

at any desirable wavelength. Resonance of the resonator is always associated with the loss that

decreases the performance of the optoelectronic devices. But we have proved numerically that

the loss of the MDA at resonant wavelength is zero. With an improved retrieval method, the

metasurface is proved to exhibit a high effective permittivity 18.4 and extremely low

loss 0.005 . A classical thin-film AR coating mechanism is identified through

analytical derivations and numerical simulations.

4.1 Introduction

Whenever there is a difference of refractive index between two media, some fraction of the

incident wave is reflected. The performance of the optoelectronic devices is reduced by the

undesired reflection. To reduce the reflection, a layer of quarter-wavelength-thick dielectric

coating has been used conventionally. The destructive interference of the light reflected from the

top and bottom surfaces of the coating layer results to the antireflection at specific wavelength.

75

Two Antireflection (AR) conditions have to be satisfied to completely eliminate the reflection,

and /4, where is the thickness of the coating layer, is the wavelength in the

coating material, / and / are the impedances, and are permittivities,

and and are permeabilities of the coating material and substrate, respectively. However,

due to the lack of coating material with accurate impedance at wavelengths of practical

applications, a perfect elimination of reflection is usually unachievable. Metamaterials (MMs)

are artificially structured materials that provide the tunable effective permittivity and effective

permeability by varying their geometric design, thereby capable of achieving the required AR

impedance matching conditions. In this work, in addition to the dielectric coating, a metallic disk

array (MDA) is added on the top of dielectric coating thereby producing destructive interference

of light. Here the MDA acts as the resonator and generates dispersive refractive index.

4.2 Results and Discussion

To get antireflection, we start the numerical simulation of the BCB layer as Anti-reflection

coating material on GaAS substrate. We performed numerical simulations using CST

Microwave Studio[108], which utilizes a finite integration technique to obtain the solutions of

the Maxwell’s equations. The advantages of BCB include, highly transparent, a lower dielectric

constant, low tangent loss at high frequency, good adhesion to substrate and metal conductor,

high-planarization level and lower dissipation factor. It also possesses low water absorption, low

stress formation, a shorter cure time and a lower cure temperature[119]. Those properties of BCB

make it very reliable and advantageous dielectrics in electronic industry for many applications

such as multichip modules, optical interconnect micro machines, flat panel display, interlayer

dielectrics etc. The optimized Parameters used in the numerical simulation to get minimum

reflection at resonance of 6 are as follows: periodicity 1.8 , thickness of

76

BCB 0.95 , permittivity of BCB 2.3716 , permittivity of GaAs substrate

11.56, and the thickness of GaAs 1 as shown in figure 4.1(a). Since,

√ . √ .

), antireflection condition is not satisfied. Numerical simulation of

BCB-GaAs structure with those parameters achieves the minimum reflection ~20% as shown in

figure 4.1(d). Only the BCB layer is not sufficient to get zero reflection because the change in

thickness of the BCB changes the phase of the light only but not the amplitude. To change the

amplitude, we propose Metal Disk Array on the top of BCB as shown in figure 4.1(b),

which acts as a dipole resonator thereby adding extra layer equivalent to the resonant high

refractive index[91]. That very high refractive index material is unavailable in nature. The

diameter of the MDA has the ability to change the amplitude and synchronizing with the BCB

thickness, both amplitude and phase conditions are satisfied to get zero reflection. The optimized

Parameters used in the numerical simulation to get zero reflection are as follows:

periodicity 1.8 , thickness of the MDA 0.05 , Diameter of the

MDA 0.66 ∙ , thickness of BCB 0.55 , thickness of GaAs

1 . The reflection (black) and transmission (blue) and loss (red) are plotted in figure 4.1(e).

Since the reflection is reduced, the transmission is obviously increased compared to bare MDA.

Figure 4.1Disk Arraeffective ploss (red)

To und

permeabi

modified

4.2(b) res

around 0

dielectric

thereby d

Importan

from the

figure 4.1

1 Illustration oay (MDA) coapermittivity εcorrespondin

derstand the

ility o

d by introdu

spectively. T

0.9(close to 1

c material fo

decreasing t

nt fact in this

e resonance

1(e).

of (a) Anti reated on the toε and effeng to (d) struc

e mechani

of the meta

ucing air on

The resonanc

1) and imagi

for the magn

the perform

s design is th

of the MDA

flection coatiop of BCB. (c)ective permeacture a (e) stru

sm of an

llic layer (M

both sides

ce of the MD

inary part is

netic respon

mance of the

hat the reson

A(3 the

77

ing (ARC) wi) MDA replac

ability μ . ucture b and (

ntireflection,

MDA) are o

of the reson

DA is at 3

zero, our M

nse. Resona

e device; for

nance wavele

ereby produ

ith BCB layerced by thin fiReflection (b

(f) structure c

Effective

obtained fro

nator[91] as

. Real part

MDA (resona

ance is alwa

r example d

ength of the

ucing nearly

r on GaAs subilm characteriblack), transmc respectively.

Permittivi

om retrieval

s shown in f

of is n

ator) is beha

ays associat

decreasing t

e ARC(6

y zero loss(r

bstrate. (b) Mized by its

mission (blue).

ity

procedure

figure 4.2(a)

nearly consta

aving as a no

ted with the

the transmis

is extreme

red) as show

Metal

and

and

[120]

) and

ant at

ormal

e loss

ssion.

ly far

wn in

Figure 4.2permeabil

The MDA

and

0.05

permittiv

(blue) of

shown in

2 Real (black)lity μ of M

A is modelle

d simulation

as that of M

vity and per

f the thin film

n figure 4.1(

) and imaginaMetal Disk A

ed as the thin

n is perform

MDA (figure

rmeability. T

m exactly ov

(f). In most

ary (blue) partArray (MDA)

n film on the

ed replacing

4.1(c)). The

The simulat

verlap with

of the appli

78

t of (a) Effectdeposited on

e top of BCB

g MDA by

e thin film n

tion results

the original

ication, the r

tive Permittivthe top of BC

B, characteri

the thin film

now acts as t

for reflectio

l reflection a

resonance b

vity ε andCB using retr

ized by the r

m having sa

the dielectri

on (black) a

and transmis

behavior of t

d (b) effectiveieval procedu

retrieved

ame thickne

c with dispe

and transmi

ssion of MD

the nanostru

e ure.

and

ess of

ersive

ission

DA as

ucture

79

has drawbacks due to the loss part involved at the target wavelength. In this work, to avoid the

resonance of the MDA with the ARC wavelength, the size of the MDA is so adjusted that the

resonance of the MDA 3 is very far from the resonance 6 of the Antireflection

coating (ARC). As a result, loss of the thin film (red) is very low (nearly to zero) at the

resonance resembling with the loss of MDA.

To make our understanding of the resonator (MDA) more relevant; for example, why the size of

MDA has to be a particular value of 0.66 ∙ , the thin film is modelled as a dielectric of

constant permittivity. Numerical simulation by sweeping several permittivity values has revealed

that zero reflection at 6 is matched when the permittivity value of 18.4(black) as shown in

figure 4.3(a). Then we analyze the permittivity of MDA in the retrieval result (figure 4.2(a)) at

6 , its value come to be exactly 18.4. Hence, it explains that to get the zero reflection, the

MDA size on the top of BCB has to be exactly fitted that retrieves the necessary permittivity at

the resonance wavelength required. The mismatch of the reflection at off resonance with

dielectric (permittivity=18.4) is obvious because the permittivity of the MDA and thin film is

dispersive and great discrepancy in the region of resonance of the MDA 3 . However, the

discrepancy is very low on the right side of the resonance 6 10 because permittivity of

the dispersive MDA and thin film is almost constant being far side of the resonance of MDA.

4.3 Theory: Three Layer Model

Our MM based ARC consists of three layers; MDA, BCB and GaAS.We assume that Reflection

takes place effectively at the two interfaces;Air-BCB and BCB-GaAS. Zero reflection through

MM based ARC can be interpreted by using three layer model in which each layer is considered

as homogeneous meta-layer with effective electric permittivity and magnetic permeability.

Transfer Matrix method is adopted to write the transmission and reflection properties of each of

80

the layer Air, BCB and GaAS referred by the indeces 1, 2 and 3 respectively.

By using a transfer matrix method, the overall reflection of the three layers can be obtained by

multiplying the transfer matrix of each layer, ∙ ∙ , as given below with more detail

shown in (Ref). Overall reflection , calculated from the final transfer matrix leads to the

final expression

(4.1)

where, and are the reflection coefficients of the MDA metasurface from the front (air) and

back (BCB layer) side respectively. is the reflection coefficient of the GaAS. ∙ ∙

is the propagating phase term in the BCB layer,where is the refractive index of the BCB layer,

is the wave vector in vacuum and is the thickness of the BCB. , where

and are the transmission coefficients of MDA metasurface along forward (air-disk-BCB)

and backward (BCB-disk-air) directions. For a homogenous medium 1 strictly, for

metasurface, however, 1, around the resoance frequency. The same equation is also obtained

in [121] through a multiple reflection approach. Similar equation is derived in ref.[75]using

destructive interference. Other theories explaining Antireflection condition is the impedence

matching[122] and transmission Line model[45]. At antireflection condition, overall reflectance,

0 requires the following conditions for amplitude and phase:

| | | . | (4.2)

. 2 2 1 ,| | 0,1,2,…. (4.3)

where the coefficients , , and are obtained from simualtion of the air-MDA-BCB

structure

Figure 4.3satisfying(MDA-BC(red dot lifilm descrconstant dterm in eqthe propagμm).

Reflectio

the Equa

4.3(b), w

. Similarly,

3 Numerical rg amplitude anCB-GaAs) simine), simulatioribed by ε , dielectric permquation (3) :θgation phase t

on obtained b

ation 4.1 (gre

we can see

is obtain

results of the nd phase condmulated (blacon of the effeand μ and

mittivity of 18θ ϕ rterm in BCB,

by the simul

een) match v

clearly tha

ed from the

three layer strditions to get ck line), calcuective thin filmd simulation o8.4. (b) The aϕ α. R

, 2β (blue). T

lation of the

very well at

at the ampl

81

simulation o

ructure (MDAantireflection

ulated from efm-BCB-GaASof thin film-BCamplitude of r2β (red), Ph

The brown dot

entire struct

t the resonan

itude of

of the BCB-G

A-BCB-GaAsn. (a) Reflectiffective impedS structure (bCB-GaAS wir (black) an

hase of r (pitted line show

ture(black l

nce as show

and .

GaAS struct

s) using threeion of the entidances of the blue dash-dot ith the thin filnd r (blue). ink), phase of

ws the resonan

line) and the

wn in Figure

are equal

ture.

e layer model ire structure multilayer filline) with thelm described (c) The phase

f R (black) nt wavelength

e calculation

4.3(a). In F

at the reso

lms e thin by e and

h (6.2

from

Figure

onant

82

wavelength, satisfying the amplitude condition(equation 4.2). As shown in Figure 4.4(c), the

phase term, . 2 crosses (gray line), as predicted in the phase

condition (equation 3). It is important to point out that the phase condition can be matched by

changing the thickness of BCB only, since manupulating the thickness of BCB layer ( ) can

arbitarily change the term ∙ ∙ to meet the phase condition but perfect zero reflection

can be achieved only when both amplitude and phase conditions are fulfilled simultaneously.

That can be achieved by changing the diameter of MDA (that changes the effective refractive

index of the coating) synchronized with the BCB thickness.

For normal non-magnetic dielectrics, permeability (μ) is equal to 1 but our metamaterial

structure contains resonator, μ is deviated from exactly one. Hence, it is noteworthy to explain

the zero reflection by introducing impedance of the each layer of the multi-layered structure.

Since we have 3 layers, thin film-BCB-GaAs enclosed in the air medium as shown in figure

4.1(c), condition for antireflection can’t be applied. Hence, we assume the thin film

and BCB as a single layer with the equivalent reflection coefficient and for the first two

layers (thin film-BCB compound structure) as shown in figure 4.4(a) by using equation 1 in the

form shown below.

,

(4.4)

Where, , and . , and are the impedances of the air,

MM layer and BCB respectively. Here lower case r represents the reflection coefficient from the

individual layer and upper case R represents the reflection coefficient from the combined thin

film and BCB layer. 1 For homogeneous media and propagation phase term in MM layer,

83

∙ ∙ .

Reflection coefficient for the BCB-GaAs surface (figure 4.4(b)) is calculated as:

(4.5)

Where, is the impedance of the GaAs layer.

Using calculated , and above, total reflection from the entire structure R is

calculated using equation 4.1 as

, where ∙ ∙ as shown in

figure 4.3 (a) (red dotted line). It is matched with the reflection obtained from the numerical

simulation of MDA (black line) in the entire wavelength region (2-10µm), even in the resonant

region of the MDA. It explains that our retrieval result of the permittivity, permeability and the

impedance of the MM layer are precisely correct and calculation of the reflection using three

layer model works perfectly not only for the homogeneous media but also for the resonant

structure.

Figure 4.4and GaAsfront side (Z ) and B

4.4 Angu

The inci

applicatio

incidence

polar ang

respectiv

TE and TM

4 (a) Schemats. R and Rand back sid

BCB (Z ). (b)

ular Indepe

dent electro

ons. Therefo

e. Numerica

gle ( ) from

vely. From the

M mode. But

tic diagram of are the effec

e respectively) R is calcu

endence of R

omagnetic w

ore, it is im

al simulation

m 00 to 800 fo

e figures, it c

t the intensity

f reflections active total refy calculated blated by using

Reflection

wave may n

mportant to in

n is perform

or both TE a

an be inferred

of the reflect

84

and transmissflection from by equation 4.g impedances

not be alway

nvestigate h

med to the a

and TM mod

d that the reso

tion increases

sions through the combined.4 using Impes of BCB (Z )

ys normal t

how the anti

antireflection

des as shown

onant wavelen

s significantly

each of the Md MM and BCedances of Ai) and GaAs (Z

to the struc

ireflection w

n structure b

n in figures

ngth is almos

y beyond

MM layer, BCCB layer fromir (Z ), MM laZ ).

cture in pra

works for ob

by increasin

4.5(a) and 4

st constant for

50 .

CB m the ayer

ctical

blique

ng the

4.5(b)

r both

Figure 4.5from 00 to

4.5 Sum

We deve

on the to

resonator

resonanc

its resona

phenome

simultane

resonator

refractive

5 (a) Colorploo 800 for (a) T

mmary

lop a versati

op of conven

r by changin

e of the reso

ance is nearl

enon by the

eously. Furth

r as the hom

e index

ot of reflectionTE mode and (

ile technique

ntional diele

ng its size,

onator is far

ly zero at the

e three laye

hermore, mu

mogeneous t

n from MDA(b) TM mode

e to get low

ectric coatin

make it fle

from the an

e anti-reflect

er model b

ulti-layered e

thin film the

85

A-BCB-GaAS e.

loss antirefl

ng. The flexi

exible to use

ti-reflection

tion region. W

by satisfying

effective me

ereby produ

structure wit

lection by de

ibility of ch

e at any de

resonance,

We are able

g the ampl

edium theory

ucing a disp

th increased o

epositing a m

hanging the

esired wavel

possible los

e to explain t

itude and p

y is also adop

ersive medi

oblique incide

metallic reso

resonance o

length. Sinc

s originated

the anti-refle

phase condi

pted to mode

ium of very

ence

onator

of the

ce the

from

ection

itions

el the

high

86

5. ENHANCED TRANSMISSION DUE TO ANTIREFLECTION COATING LAYER AT

SURFACE PLASMON RESONANCE WAVELENGTHS

Note to Reader

Portions of this chapter have been previously published in peer reviewed journal paper (M. S. Park, K.

Bhattarai, D. K. Kim, S. W. Kang, J. O. Kim, J. F. Zhou, et al., "Enhanced transmission due to

antireflection coating layer at surface plasmon resonance wavelengths," Optics Express, vol. 22, pp.

30161-30169, Dec 1 2014) and have been reproduced with the permission from the publisher.

In chapter 4, we employed the antireflection on the homogeneous media but the antireflection on

dispersive media is not known yet. Therefore we choose perforated gold film (PGF) as the

dispersive medium and employed meta-surface antireflection on the top of it. We present

experiments and analysis on enhanced transmission due to dielectric layer deposited on a metal

film perforated with two-dimensional periodic array of subwavelength holes. The Si3N4

overlayer is applied on the perforated gold film (PGF) fabricated on GaAs substrate in order to

boost the transmission of light at the surface plasmon polariton (SPP) resonance wavelengths in

the mid- and long-wave IR regions, which is used as the antireflection (AR) coating layer

between two dissimilar media (air and PGF/GaAs). It is experimentally shown that the

transmission through the perforated gold film with 1.8 µm (2.0 µm) pitch at the first-order

(second-order) SPP resonance wavelengths can be increased up to 83% (110%) by using a 750

87

nm (550 nm) thick Si3N4 layer. The SPP resonance leads to a dispersive resonant effective

permeability (μeff ≠ 1) and thereby the refractive index matching condition for the conventional

AR coating on the surface of a dielectric material cannot be applied to the resonant PGF

structure. We develop and demonstrate the concept of AR condition based on the effective

parameters of PGF. In addition, the maximum transmission (zero reflection) condition is

analyzed numerically by using a three-layer model and a transfer matrix method is employed to

determine the total reflection and transmission.

5.1 Introduction

In this study, we investigate the effect of a silicon nitride (Si3N4) layer for enhancement of

transmission (or suppression of reflection) through a two-dimensional square array of

subwavelength circular holes penetrating a gold layer (perforated gold film) at the first- and

second-order SPP resonance wavelengths in the IR region. A rigorous coupled wave analysis

based simulation was preliminarily carried out to confirm the resonance wavelengths of the

perforated gold film (PGF). The experimental results indicate that transmission through the

fabricated PGFs on GaAs substrates by standard optical lithography can be enhanced by Si3N4

layers under certain conditions. An analytical model based on homogenized effective materials

was developed to study the antireflection (AR) coating between two dissimilar media – air and

PGF/GaAs. In our model, the PGF is considered as a homogeneous thin film with the resonant

effective parameters (refractive index, impedance, permittivity and permeability). Then, using

the transmission and the reflection coefficient equations for layered homogeneous media, the

amplitude and phase conditions for zero reflection can be achieved through the destructive

interference between the EM waves reflected at the interfaces – air/Si3N4 and Si3N4/PGF. We

further calculate the effective impedance of the PGF, and find the impedance matching condition

88

required for AR coating on the resonant structure, which is different from the refractive index

matching condition for the conventional AR coating on a dielectric surface.

5.2 Device Structure and Fabrication for Antireflection

Figure 5.1(a) illustrates the PGF structure which consists of a gold (Au) layer perforated with a

2D square array of circular holes on top of a GaAs substrate. On the other hand, Figure 5.1(b)

displays a Si3N4 layer deposited atop the PGF structure (Si3N4: PGF). In brief, the fabrication

steps for the PGF and Si3N4:PGF samples are as follows: (A) Hexamethyldisilazane (HMDS) as

an adhesion layer was spun onto a semi-insulating double-polished GaAs (100) substrate,

followed by a negative-tone photoresist (PR); (B) A periodic circular post pattern in the PR layer

was produced using standard optical lithography; (C) 5-nm thick adhesion layer of titanium and

50-nm thick layer of Au were deposited using e-beam evaporation, followed by a lift-off process

with acetone to remove the PR layer; (D) After the lift-off process, the PGF structure was

obtained; (E) In order to obtain the Si3N4:PGF structure, the Si3N4 layer was deposited on the

PGF structure using plasma enhanced chemical vapor deposition (PECVD). For the experiment,

samples have been fabricated with various pitches (p = 1.8 – 3.2 µm with an interval of 0.2 µm)

of the PGF and four different thicknesses of the Si3N4 layer (td) with 150, 350, 550, 750 nm. The

scanning electron microscope (SEM) images of fabricated PGF and Si3N4: PGF are also

provided in Figures 5.1(c) and 5.1(d).

Figure 5.1Si3N4 thicwith a stepand 50 nmstructure wtilted SEM

5.3 Expe

The trans

spectrom

under a

incidence

unpolariz

holes in P

variable p

1 Schematic vckness td are vp of 200 nm,

m, respectivelwith p = 2.6 µ

M images.

eriments

smission spe

meter with a K

nitrogen en

e to the sa

zed FTIR be

PGF structur

pitches (p) a

view of structvaried from 1.respectively.y. The scanniµm and (d) Si

ectra were r

KBr beam sp

nvironment.

amples and

eam was use

res. The FTI

and thickness

tures and dim.8 µm to 3.2 µ The circular ing electron mi3N4: PGF stru

recorded wit

plitter and a

The transm

normalized

d to measur

IR-measured

s of Si3N4 la

89

ensions for (aµm with a steaperture size

microscope (Sucture with p

th a Nicolet

MCT detect

mission mea

d to the spe

e the transm

d transmissio

ayer (td) are p

a) PGF and (bep of 0.2 µm ae (d) and Au tSEM) images = 1.8 µm; td

6700 Fouri

tor in the wa

asurement w

ectrum of a

mission of th

on spectra o

plotted in Fi

b) Si3N4:PGFand from 150thickness (tm) (side view) o= 750 nm. In

er transform

avelength ran

was carried

a bare GaA

he 2D square

of PGFs and

gure 5.2.

. The pitch p0 nm to 750 nm

are fixed at 0of (c) PGF sets show the

m infrared (F

nge of 4 – 1

out at a no

As substrate

e array of cir

Si3N4:PGFs

and m 0.5·p

e

FTIR)

5 µm

ormal

e. An

rcular

s with

90

Figure 5.2 FTIR-measured normal incidence transmission spectra of PGF (Gray) and Si3N4:PGF (Color) samples with variable pitches (p = 1.8 – 3.2 µm) and thicknesses of Si3N4 layer, (a) td = 150 nm, (b) td = 350 nm, (c) td = 550 nm and (d) td = 750 nm.

As expected, the experimentally measured SPP resonances change clearly with the pitch p

(specifically, ~ . / , where i, j are integers indicating the order of SPP resonance

coupling, is the real part of permittivity for the substrate) [4,5]. We observed two significant

peaks that correspond to the first- and second-order SPP modes at the Au-GaAs interface. For

each periodicity p, the peak at the longer wavelength (first-order) is associated with fourfold

degenerate (±1, 0) and (0, ±1) SPP modes resulting from nearest-aperture coupling and normally

incident unpolarized light while another peak at the shorter wavelength (second-order) is related

to (±1, ±1) SPP modes due to next-nearest-aperture coupling (all four modes are also degenerate)

[10]. The (1, 0) and (1, 1) peaks for PGFs with pitches (p = 1.8, 2.0, 2.2, 2.4, 2.6, 2.8, 3.0, 3.2

µm) were detected at 6.2 (4.44), 6.9 (4.91), 7.5 (5.37), 8.2 (5.87), 8.8 (6.32), 9.5 (6.81), 10.1

(7.26), and 10.9 (7.79) µm, respectively. Figure 5.2 also shows the obvious changes of

transmission spectra due to Si3N4 layers placed on top of PGFs. In order to estimate the influence

of Si3N4 layer, the transmission enhancement factor (EF) is defined as : / with

0.0

0.5

0.0

0.5

0.0

0.5

0.0

0.5

0.0

0.5

0.0

0.5

0.0

0.5

0.0

0.5

4 5 6 7 8 9 10 11 12 13 14

4 5 6 7 8 9 10 11 12 13 14

4 5 6 7 8 9 10 11 12 13 14

4 5 6 7 8 9 10 11 12 13 14

4 5 6 7 8 9 10 11 12 13 14

4 5 6 7 8 9 10 11 12 13 14

0.0

0.5

0.0

0.5

0.0

0.5

0.0

0.5

0.0

0.5

0.0

0.5

0.0

0.5

4 5 6 7 8 9 10 11 12 13 14 150.0

0.5

4 5 6 7 8 9 10 11 12 13 14 15

Wavelength (m)

Tra

nsm

issi

on

td = 150 nm td = 350 nm td = 550 nm td = 750 nm

p = 1.8 m

p = 2.0 m

p = 2.2 m

p = 2.4 m

p = 2.6 m

p = 2.8 m

p = 3.0 m

p = 3.2 m

(a) (b) (c) (d)

91

: being the transmission of Si3N4: PGF (PGF). As the thickness of Si3N4 layer

(td) increases, the transmission EF at the first-order SPP resonance wavelengths is increased for

the pitch p varying from 1.8 µm to 2.4 µm. On the contrary, the transmission EF is decreased for

the pitch p varying from 2.6 µm to 3.2 µm. This tendency can be interpreted by the optical

property of Si3N4 deposited onto PGF samples and the presence of Si3N4 layer acting as the AR

coating layer: The absorption loss of Si3N4 (k, imaginary part of refractive index) is very low in

the IR range up to ~7 µm whereas it increases rapidly beyond ~7 µm [123]. For a smaller

periodicity (p = 1.8 – 2.4 µm) and the first-order SPP resonance wavelengths, an optimal

thickness of Si3N4 layer is found to be 750 nm for the thickness range we considered and the

measured EF is found to be ~1.83 (6.2 µm), ~1.79 (6.9 µm), ~1.3 (7.5 µm) and ~1.04 (8.2 µm).

However, for a larger periodicity (p = 2.6 – 3.2 µm), EFs less than unity, ~0.85 (8.8 µm), ~0.6

(9.5 µm), ~0.4 (10.1 µm), ~0.23 (10.9 µm), were measured due to the 750 nm thick Si3N4 layer

presenting significant absorption at the resonant wavelength. Also, we find that the transmission

at the second SPP resonance is obtained with ~79% (4.4 µm), ~110% (4.9 µm), ~72% (5.4 µm)

increase for the 550 nm thick Si3N4 layered PGFs (p = 1.8 µm – 2.2 µm) and ~101% (5.9 µm),

~102% (6.3 µm), ~78% (6.8 µm), ~76% (7.3 µm), ~31% (7.8 µm) enhancement for the 750 nm

thick Si3N4 layered PGFs (p = 2.4 µm – 3.2 µm). Note that a dip around 4.6 µm is attributed to a

Si-H vibration (PECVD grown silicon nitride) [124]. Figure 5.3 shows the transmission EF as a

function of the periodicity p for different thickness of Si3N4 layer td. Again, we clearly see a

general trend; for the first-order SPP resonance wavelength, the rate of enhancement change is

steeper for thicker Si3N4 layer as explained above. Compared with the EF at the first-order SPP

resonance wavelength, the second order SPP resonance shows the higher EF due to relatively

92

low transmission with the absence of Si3N4 coating layer, thus a greater EF is shown with the

same amount of increase in transmission.

Figure 5.3 Transmission enhancement factor as a function of the periodicity (p) for different thickness of Si3N4 layer (td) placed on top of PGFs at (a) the first-order and (b) the second-order SPP resonance wavelengths.

5.4 Analysis Using Three-Layer Model

Transmission enhancement through Si3N4: PGF can be theoretically understood by using a three-

layer model (Air - Si3N4 - PGF), in which reflection and transmission occur on two interfaces,

air/Si3N4 and Si3N4/PGF. In this model [121, 122], each layer is regarded as a homogeneous

medium for which a transfer matrix can be defined in terms of S parameters, and the overall

reflection coefficient (r = S11) and transmission coefficient (t = S21) of the three-layer structure

can be obtained by multiplying the transfer matrix of each layer as given below (The details of

this transfer matrix analysis can be found elsewhere [121]),

12 23 12 23

12 23 12 23

exp 2 exp,

1 exp 2 1 exp 2

r r i t t ir t

r r i r r i

(5.1)

where r12 is the reflection coefficient of the air/Si3N4 interface and r23 is the reflection coefficient

of the Si3N4/PGF interface, which are obtained from the numerical simulation of a Si3N4-PGF-

1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.20.0

0.5

1.0

1.5

2.0

Pitch (m)

(a) (b)

Si3N4: 150 nm

Si3N4 : 350 nmSi3N4 : 550 nmSi3N4 : 750 nm

1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.20.5

1.0

1.5

2.0

2.5

En

han

cem

ent

fact

or

En

han

cem

ent

fact

or

(1,0) (1,1)

93

GaAs sandwich structure as illustrated in the inset of Figure 5.4. The t12 and t23 are the

transmission coefficients through interfaces – air/Si3N4 and Si3N4/PGF, respectively.

∙ ∙ is the propagating phase term in the Si3N4 layer, where is the refractive

index of the Si3N4, k is the wave vector, and is the thickness of the Si3N4 layer. We apply this

model to study the enhanced transmission at the first-order SPP resonance for the structure with

p = 1.8 µm and td = 750 nm, whose EF reaches the maximum as shown in Figure 5.3(a).

Reflection and transmission obtained from 3D full field EM simulations based on the finite

integration technique [125] of the entire structure and the three-layer model match very well as

shown in Figure 5.4(a). Note that r23 is obtained at far-field where the localized EM field decays

to zero and thereby the reflected wave recovers to a plane wave. This indicates that PGF can be

considered as a homogeneous thin film with effective parameters. At the minimum of reflection,

more energy of the incident wave enters the Si3N4: PGF structure and is coupled to SPP

resonances. As a result, the transmission is greatly enhanced as compared to the uncoated PGF

structure. Figure 5.4(a) verifies numerically that the transmission obtained with the Si3N4 coating

layer (blue line) is enhanced as compared to that without the coating layer (black line), which is

consistent with the experimental result. From Eq. (5.1), r = 0 requires the following conditions

for amplitude and phase:

| | | | (5.2)

2 2 1 , | | 0,1,2…. (5.3)

Equation (5.3) is the typical condition for destructive inference of reflected waves at two

interfaces, air/Si3N4 and Si3N4/PGF. Satisfying Eq. (5.3) will guarantee a minimum of r, however

Eq. (5.2) is also needed to get r = 0. In the conventional antireflection coating (e.g., a thin

94

coating layer on a lossless dielectric material), the reflection coefficients can be calculated by

Fresnel’s equation / and / , where n1, n2

and n3 are the refractive indices of air, coating layer and dielectric layer, respectively. For a

lossless system, the reflection coefficients (r12 and r23) shown in Eq. (5.1) are real values, so the

reflection R = r2. The minimum of R is achieved when the coating layer has the refractive index

of and the thickness of λ/4, where λ is the wavelength of light inside the coating

layer [126]. It is straightforward to verify that both Eqs. (5.2) and (5.3) are satisfied with this

choice of the coating layer. Note that and 2

2 /4 because the refractive indices are all real values due to the lossless media and

n1 < n2 < n3. However, for a Si3N4-PGF-GaAs sandwich structure, r23 is generally complex value

because the PGF exhibits the loss near its resonance wavelengths (the phase of reflection

coefficient of the Si3N4/PGF interface is not equal to , ). The thickness of the Si3N4

layer cannot be chosen to λ/4. Furthermore, as will be shown later, the effective permeability of

PGF is dispersive ( 1), so the AR condition should be discussed by means of the

impedance instead of the refractive index. The conventional AR condition (the refractive index

and the thickness of coating layer are and λ/4, respectively) cannot be applied to our

system. In the following, we will use the amplitude and the phase condition shown in Eqs. (5.2)

and (5.3) to analyze the AR condition.

95

Figure 5.4 (a) Numerical reflection (red line) and transmission (blue line) for the structure with p = 1.8 µm and td = 750 nm obtained from 3D full field EM simulation of the whole structure (all three layers together) while circles show the calculated reflection (red) and transmission (blue) using a three-layer model. Black line represents the transmission without Si3N4 coating layer. (b) The amplitude of r12 and r23, i.e. |r12| (red line) and |r23| (blue line). Magenta dashed line is drawn at the first SPP resonance. (c) The phase terms in Eq. (4), 2 , where and are the phase of r12 (red) and r23 (blue), respectively and the propagation phase in the silicon nitride coating layer is 2β (green).

1.0

4

0.8

0.4

0.2

0.6

1.0

0.0

0.8

0.4

0.2

0.6

5 7 8 9 106

1.6

1.2

1.4

0.8

0.0

Re

flec

tio

n, T

ran

smis

sio

nA

mp

litu

de

Ph

ase

,

Wavelength (m)

(a)

(b)

(c)

Air Si3N4 GaAs

PGF

96

The parameters used for three-layer model are as follows: Periodicity (p) = 1.8 µm, diameter of

aperture in PGF (d) = 0.9 µm, thickness of PGF (tm) = 0.05 µm, thickness of Si3N4 layer (td) =

0.75 µm, Si3N4 permittivity ( ) = 5.84, and GaAs permittivity ( ) = 11.56. The phase and

amplitude terms of the above equations are calculated numerically and plotted as shown in

Figures 5.4(b) and 5.4(c). Figure 5.4(b) clearly shows that the amplitudes of r12 and r23 are equal

at the first SPP resonant wavelength, satisfying the amplitude condition for zero reflection as

indicated by Eq. (5.2). The phase term, 2 2 1 crosses nearly π

(red line) for the first-order thickness at the resonant wavelength as shown in Figure 5.4(c). The

small mismatch on the phase π results in the reflection not reaching zero. In general, Eqs. (5.2)

and (5.3) impose two independent conditions on complete antireflection (r = 0). Manipulating

the thickness of the Si3N4 layer (td) can arbitrarily change ∙ ∙ to meet the phase

condition (Eq. (5.3)). However, to simultaneously satisfy both the amplitude and phase

conditions, we need to control two independent parameters, such as refractive index and

thickness of dielectric layer (Si3N4). The phase of r12 is very close to π as shown in Figure 5.4(c),

so the phase condition in Eq. (5.3) can be further simplified to 2 for m = 0. For instance,

the phase term 2β gradually increases as the thickness of coating layer for p = 1.8 µm is varied

from 150 nm to 750 nm. The simplified equation 2 is eventually satisfied by the 750 nm

thick Si3N4 layer, thereby suppressing the reflection (enhancing the transmission). This

explanation makes clear why the EF increases experimentally with thickness as shown in Figure

5.3(a).

Moreover, it is worth analyzing the AR condition through the effective parameters (refractive

index, impedance, permittivity and permeability) by considering the PGF as a homogeneous thin

film with the thickness of 50 nm (i.e., same as the thickness of the PGF, tm) [121]. The effective

permittiv

simulated

index,

cannot

(i.e.,√

not equa

equation

and PGF

using th

effective

Figure 5.5and the am

If we ne

amplitud

condition

vity and

d transmissi

apply

l to 1 (

, respectivel

he impedanc

impedance

5 The effectivmplitude of r1

eglect the lo

de condition

n

d permeabilit

ion and refl

and im

the c

) b

1). Thus

/

ly. Instead, t

ce,

of Si3N4 and

ve normalized12 (|r12|: light b

oss in the PG

shown in

(i.e.,

ty can

lection coeff

mpedance,

conventional

because the

s, the reflect

, where

the reflection

/

d PGF, respe

d impedance oblue) and r23 (

GF (i.e., onl

Eq. (5.2) c

/

97

be obtained

ficients (t23

l antiref

effective pe

tion coefficie

e n2 and n3 a

n coefficient

, w

ectively.

of Si3N4 coatin(|r23|: blue). T

ly consider

an be writt

/ /

through a r

and r23). T

/ can

flection

ermeability o

ent cannot b

are (effective

t from interf

where

ng layer (Z2: The resonance

the real par

ten as

/ ). As

etrieval proc

Then, the eff

be calculat

condition

of the PGF

be calculated

e) refractive

face, Si3N4/P

1/

gray) and PGe region is hig

rt of the im

, so we

shown in

cedure [87] u

ffective refra

ed. Note tha

is dispersive

d using Fres

e indices of S

PGF is calcu

and Z3 are

GF (√Z3: blackghlighted.

mpedance Z3)

e obtain the

Figure 5.5

using

active

at we

e and

snel’s

Si3N4

ulated

e the

k),

), the

e AR

, the

98

normalized effective impedance for the Si3N4 and the square root of the normalized effective

impedance of PGF are matched at the first-order SPP resonance wavelength, i.e.

required for AR condition. Additionally, the amplitude condition, | | | | for destructive

interference is satisfied.

5.5 Summary

We demonstrated that the incorporation of a dielectric top layer significantly improves the

transmission at the surface plasmon (SP) resonance wavelengths of a perforated metal film in the

infrared. Using this dielectric layer serves to match the effective impedance between the different

media, in this case air and the perforated gold film in order to reduce reflection. We used Si3N4

as the material of the antireflection (AR) coating layer placed on top of the perforated gold film.

Through several iterations in design and experiment, we found that 750 nm (550 nm) thick Si3N4

layered perforated gold film with 1.8 µm (2.0 µm) pitch provided the best impedance matching

at the first-order (second-order) SP resonance wavelengths having an 83% (110%) increase in

transmission. The conventional AR condition (the refractive index of and the thickness of

λ/4) cannot be applied to the SP resonant structure such as PGF due to the dispersive resonant

effective permeability. The impedance matching condition for AR coating ( ∙ ) and

more accurate amplitude and phase conditions (Eqs. (5.2) and (5.3)) are established, which may

offer general guidelines for the optimization of the AR coating for resonant structures. Our next

step is to realize the antireflection effect at the detector level, such as in a plasmonic integrated

infrared detector or imager. The results drawn from this work could be used as a basis to improve

the overall performance of a perforated metal film integrated infrared detector and provide a new

perspective for the application of antireflection coatings in plasmonic optoelectronics.

99

6. A LOW-LOSS METASURFACE ANTIREFLECTION COATING ON DISPERSIVE

SURFACE PLASMON STRUCTURE

Note to Reader

Portions of this chapter have been previously published in peer reviewed journal paper (J. Jeon,

K. Bhattarai, D.-K. Kim, J. O. Kim, A. Urbas, S. J. Lee, et al., "A Low-loss Metasurface

Antireflection Coating on Dispersive Surface Plasmon Structure," Scientific Reports, vol. 6, p.

36190, 11/02/online 2016) and have been reproduced with the permission from the publisher.

In this work, we demonstrate an off-resonance, disk-type MM operating as the AR (Meta-AR)

coating for a MHA layer fabricated on a GaAs substrate. The Meta-AR coating can effectively

reduce the reflection at both first-order and second-order SPP resonances, thereby increasing the

transmission. Additionally, our results do not show the resonance shift or damping of the SPP

because the MM does not couple with the SPP resonance. Instead, the surface wave is enhanced

as compared to the uncoated MHA (no AR coating atop MHA). Furthermore, we demonstrate

that the MM layer works as a homogenous thin film with high dielectric constant (~30) and

extremely low loss (loss tangent ~0.005). Thus the Meta-AR coating can be understood as well-

known thin-film AR coating, which provides an intuitive purely optical model compared to the

electrical transmission-line model used in previous work2. We also validate through simulation

that such thin-film model can be generally applicable to other MM-based AR coating structures

[44, 45].

100

6.1 Introduction

Over the years, there has been increasing interest in the integration of metal hole array (MHA)

with optoelectronic devices, as a result of enhanced coupling of incident light into the active

layer of devices via surface plasmon polariton (SPP) resonances. However, all incident light is

unlikely to contribute to the SPP resonance due to unachievable impedance match (i.e., perfect

elimination of reflection) at the interface between incident medium and MHA, which is

responsible for a non-existing material satisfying the antireflection (AR) condition and strong

dispersion of MHA’s effective impedance around SPP resonances. In order to enhance the SPP

of MHA, a single-layer metasurface-based AR coating is shown to operate at off-resonance

wavelengths and to avoid the resonant coupling with the MHA layer. The SPP resonance

wavelengths are unaffected whereas the electric field of surface wave is significantly increased.

With an improved retrieval method, the metasurface is proved to exhibit a high effective

permittivity ( ~30) and extremely low loss (tan). A classical thin-film AR coating

mechanism is identified through analytical derivations and numerical simulations. The properly

designed effective permittivity and effective permeability of the metasurface lead to required

phase and amplitude conditions for the AR coating, thereby paving the way for improved

performance of optoelectronic device.

6.2 Results

6.2.1 Metasurface Antireflection Coating

Our metamaterial based antireflection (Meta-AR) coating consists of a planar metallic disk array

(MDA) on top of a cured layer of benzencyclobutene (BCB). For comparison of Meta-AR

coating with conventional AR coating (a BCB layer only), we designed three types of samples,

101

namely the uncoated MHA, a BCB layer coated MHA and MHA coated with an array of circular

gold (Au) disks (MDA) atop the BCB layer. Figures 6.1(a-c) illustrates three structures on GaAs

substrates, respectively. In all structures, the orthogonal pitches of MHA, (pitch along x-axis)

and (pitch along y-axis), are both fixed at 1.8 μm ( = = ) and the diameter of the

circular aperture ( ) and thickness of Au ( ) are 0.9 µm (a half of pitch, 0.5·p) and 0.05

μm, respectively. We performed numerical simulations using CST Microwave Studio[108],

which utilizes a finite integration technique to obtain the solutions of the Maxwell’s equations. In

our simulation, the dielectric constant for BCB and GaAs are = 11.56 and = 2.37,

respectively. Au is described by a Drude model with the plasma frequency, ωp = 9.02 eV and the

collision frequency, ωc = 0.038 eV [127]. Figures 6.1(d-f) show the simulated Ez distribution in a

plane parallel to yz-plane through the center of the unit cell (the distance between the parallel

planes is 0.36 µm) when x-polarized light is incident along the normal direction. The surface

waves are observed in all three structures, evidenced by the exponential decay of Ez along z-

direction. This indicates that the SPP waves is confined to MHA-GaAs interface and propagates

along the lateral direction. As compared with uncoated MHA (Figure 6.1(d): = 1.8 µm, =

0.9 µm), z component-electric field Ez of the SPP waves for BCB coated MHA (Figure

6.1(e): = 0.95 µm) and Meta-AR coated MHA (Figure 6.1(f): = 0.5 µm, = 1.8

µm, = 1.4 µm) are enhanced by ~20% and ~33%, respectively. The intensity of surface

wave, ∝ | | , are remarkably increased by ~44% and ~77%, respectively. Without AR

coating, the reflection of MHA at the first-order ( 6.25 µm) and the second-order (

4.38 µm) SPP resonances are 0.45and 0.67, respectively. This indicates that ~45%

and ~67% of incident light do not contribute to the surface waves at the two lowest-order SPP

resonances.

Figure 6.1BCB layestructuresaxis (z = 0and the Bsimulatedas shown to 1.55 m0.05 (0.09

Figure 6.

with thic

the reflec

complete

1 Illustrationser. (d–f) di shown in (a-0). (g) SimulaCB thickness

d reflection at in (c) as a fun

m by a 0.2 m9 m) step.

.1(g) shows

ckness v

ction is redu

ely eliminate

s of (a) MHA,stribution in x-c), respectiveated reflections . is(h) the first-o

nction of BCBm step and

the simulate

varying from

uced as com

ed with onl

, (b) BCB layx = 0.36 m pely. The interfn colormap fos varied from order and (i) tB thickness

⁄ varies

ed reflection

m 0.35 µm t

mpared with

ly BCB coa

102

yer coated MHplane of a uniface between or structure di

0.35 m to 1the second-or

and the rafrom 0.5 (

of a BCB la

to 1.55 µm.

the uncoate

ating becaus

HA and (c) Mit cell (x = 0, tMHA and G

isplayed in (b1.55 m with rder SPP resonatio ⁄ .= 0.9 m)

ayer coated

In the regio

ed MHA. Ho

se the impe

MHA coated wthe center of

GaAs substrateb) as a functio

a step of 0.2 nance wavele. increas) to 0.8 (

MHA sampl

on enclosed

owever, refl

dance of th

with MDA atothe unit cell) e is set to zeroon of wavelenm. Colorma

engths for struses from 0.35 = 1.44 m)

le (Figure 6.

by black cu

lection cann

he BCB (

op the for

o in z-ngth aps of ucture m by a

.1(b))

urves,

not be

103

1/ ) does not match the AR condition ( ) at these resonance wavelengths.

The minimum values of reflection for the first-order and the second-order SPP resonances,

and reach 0.136 and 0.388 with 0.95µm and 0.75 µm, respectively.

These optimal thicknesses can be well explained by the destructive interference of light reflected

at the top (air-BCB interface) and bottom (BCB-MHA interface) surfaces of BCB layer. At the

resonance wavelengths, the impedance of BCB layer is smaller than the impedance of air but

larger than the effective impedance of MHA structure[58], i.e. 1 . So

both the lights reflected by the air-BCB and the BCB-MHA interfaces exhibit phase shift with

respect to the corresponding incident light at each interface. This leads to the condition for

destructive interference, /4 = ~1.02 µm and ~0.71µm, at the first and the second-

order SPP resonances, respectively. With a properly designed MDA on top of the BCB layer, the

reflection can be further reduced and reach nearly zero at SPP resonance wavelengths. Figures

6.1(h, i) show the reflections taken at the SPP resonance wavelengths ( and ) for the MHA

structures with a MDA layer added on top of the BCB layer. In order to investigate the geometry

dependence, and are varied from 0.35 µm to 1.55 µm and from 0.5·p to 0.8·p,

respectively. The contour lines in black show the minimum reflection of only BCB layer coated

MHA ( 0.136and 0.388). In between these lines shows a large region

that the Meta-AR coating outperforms the BCB coating. For the first SPP resonance (Figure

6.1(h)), the white contour line shows a wide range of 0.35μm 0.55μm and 0.65 ∙

0.8 ∙ that reduces the reflection below 0.01 ( 0.01). This shows that our Meta-AR

(MDA atop BCB layer) coating is robust against possible fabrication tolerance, i.e. variations of

BCB thickness and MDA size . Reflections reach the minimum values,

1.21 10 and 3.16 10 when 0.55μm& 0.75 ∙

104

and 0.35μm & 0.65 ∙ at two resonance wavelengths, respectively. Two

regions of minimum values of and do not overlap perfectly. For this reason, we mainly

focus on AR coating designs that eliminate the reflection at the first-order SPP resonance ( ),

which can also substantially reduce the reflection at the second-order SPP resonance ( ). Based

on the simulation results, three type of structures illustrated in Figures 6.1(a-c) have been

fabricated.

The structure of all samples discussed here consists of a semi-insulating double-polished GaAs

(100) substrate with MHA, BCB layer coated MHA, or Meta-AR (MDA atop BCB layer) coated

MHA. In brief, the processing steps to fabricate the aforementioned samples are as follows. (i)

Conventional photolithography was used to produce periodic circular post arrays in the

photoresist (PR) layer (Figure 6.2(a)). (ii) 5-nm-thick adhesion layer of titanium and 50-nm-thick

layer of Au were deposited using e-beam evaporation and a liftoff processing, resulting in MHA

structure (Figure 6.2(b)). (iii) Based on the colormap of measured BCB film thickness (Figure

6.2(c)) depending on spin-coating speed and dilution ratio between BCB and rinse solvent

(Cyclotene 3022-35 and T1100, The Dow Chemical Company), BCB was spin-coated on MHA,

whose top-surface is flat and smooth (Figure 6.2(d)). (iv) A periodic circular hole pattern in the

PR layer was defined by photolithography once again (Figure 6.2(e)), followed by e-beam

deposition of a 50-nm-thick layer of Au. (v) After the lift-off processing to remove the PR layer,

the Meta-AR coated MHA was finally obtained as shown in Figure 6.2(f). The detailed

fabrication is included in Supporting Information.

Figure 6.2MHA, MH(a) A peridepositionstructure. BCB and circular hodeposit Ti(an array MDA in M

6.2.2 Tra

As discu

resonanc

(no AR c

first-orde

transmiss

c)) as

and

2 Scanning elHA coated wiiodic circular n (5 nm of Ti (c) Measuredrinse solventole PR patterni (5 nm) / Au of circular meMeta-AR coat

ansmission

ussed in Figu

e wavelengt

coating atop

er and secon

sion of MHA

and

0.8 ∙ . Not

d to th

ectron microsith an array opost photoresand 50 nm o

d BCB thickn. (d) BCB coan on the BCB(50 nm) afteretal disks atopting.

Enhanceme

ure 6.1, the

ths, which le

p MHA) exh

nd-order SPP

A with the B

vary wit

te that the m

he minimum

scope (SEM) f circular metsist (PR) pattef Au in seque

ness as a functated on MHA

B layer shownr (e), followedp the BCB co

ent due to M

Meta-AR c

eads to signi

hibits low tr

P resonance

BCB coating

thin the ran

maximum v

values of r

105

images of thrtal disks atopern defined byence) and a liftion of spin-c

A sample shown in (d). Consed by a lift-off

oated MHA).

Meta-AR Co

coating can

ificant increa

ransmission

s, respective

(Figure 6.3(

nges of 0.3

values of tra

eflection as

ree samples (p the BCB layy standard phftoff processinoating speed

wing the flat-tecutive e-beaf step. (f) ComInsets display

oating

effectively r

ase of transm

where

ely. Figures

(a)) and Met

35μm

ansmission

shown in F

(MHA, a BCByer) and BCB hotolithographng, which leaand dilution rtop surface. (

am evaporatiompleted Metay the magnifi

reduce the r

mission. The

0.39 and

6.3(a-c) sho

ta-AR coatin

1.55μm

are achieve

Figures 6.1(g

B layer coatedcoating cond

hy. (b) E-beamads to MHA ratio betweene) A periodic

ons were useda-AR coated Med MHA and

reflection at

e uncoated M

0.12, a

ow the simu

ng (Figures 6

m and 0.5

ed with iden

g-i). Specific

d dition. m

n c d to MHA d

t SPP

MHA

at the

ulated

6.3(b,

∙

ntical

cally,

106

the regions enclosed by the black contour lines in Figure 6.3(a) indicate the enhanced

transmission due to BCB coating. Within these regions, transmission reaches the maximum

values, 0.618 when 0.95µm and 0.208 when 0.75µm at the first-

order and second-order SPP resonances, respectively. Owing to additional MDA design on top of

the BCB layer, the transmission can further be improved up to = 0.717 and 0.318 when

0.35µm and 0.7 ∙ , as shown in Figures 6.3(b, c). The regions where the Meta-

AR coating (MDA-BCB coating) outperforms the BCB coating are enclosed by black contour

lines (Figures 6.3(b, c)). Figures 6.3(d, e) show the measured and simulated enhancement ratio

(ER) of transmission for seven samples with various thickness of BCB layer ( is varied from

0.35 µm to 1.55 µm with a step of 0.2 µm), however pitch p and disk size are fixed at

1.8 µm and 1.26 µm (0.7·p), respectively. Here the ER is calculated by

/ , where i’s are the BCB and Meta-AR (MDA+BCB). The overall agreement

between experimental (solid lines) and simulated (dashed lines) ERs at the first-order SPP

resonance is apparent from Figure 6.3(d). We find the maxima of measured ERs for BCB and

Meta-AR coating are obtained with 58% and 88% when 0.95 µm and 0.55 µm,

respectively. Remarkably, with the Meta-AR coating, the ER is improved by 30% as compared

with only BCB coating, but on the contrary the thickness of BCB is reduced by 42%. The

significant reduction of the thickness is beneficial in the low frequency regime (e.g. THz), where

the thickness of AR coating is normally in the order of ~50 µm, which gives rise to great

challenge in film deposition. The transmission at the second-order SPP resonance exhibits even

higher ER with both BCB and Meta-AR coating due to the relatively low transmission for the

bare MHA structure (as compared with at the first-order SPP resonance). Accordingly, the

maximum ERs are found to be 106% for BCB ( 0.75 µm) coating and 99% for Meta-AR

( 0

simulatio

specifica

Figure 6.30.35 m tfirst-order1.44 m ExperimeAR (red)

6.2.3 An

To under

layer mo

0.35 µm) co

on for Meta

ally the misal

3 (a) Colormato 1.55 m wir and (c) seco0.8 ∙ with

ental (sphere) coating at (d)

tireflection

rstand the u

odel based o

oating (Figu

a-AR coatin

lignment bet

ap of simulateith 0.2 m ste

ond-order SPPa step of 0.09and simulate

) the first-orde

Condition a

underlying m

on a transfer

ure 6.3(e). N

ng is proba

tween MDA

ed transmissioep. SimulatedP resonance w9 m 0.05 ∙d (cross) traner and (e) sec

at SPP Reso

mechanism o

r matrix me

107

Note that th

ably due to

A and MHA.

on for BCB lad transmissionwavelengths w

and insmission enhcond-order SP

onances

of our Meta

ethod[128]. O

he discrepan

o the imper

ayer coated Mn for MHA wwhen is is changed in

hancement ratPP resonance

a-AR coating

Our Meta-A

ncy between

rfections in

MHA as ith Meta-AR varied from

n the same matio for BCB (bwavelengths.

g, we devel

AR coated M

n experiment

the fabrica

increases fromcoating at (b)0.9 m 0.5 ∙

anner as (a). blue) and Me.

loped a mul

MHA structu

t and

ation,

m ) the ∙ to

ta-

ltiple-

ure is

108

composed of three layers: MDA, BCB and MHA on a GaAs substrate. Using a transfer matrix

method, the overall reflection coefficient r of the three-layer structure can be obtained by

multiplying the transfer matrix of each layer, ∙ ∙ , as given below and further

details on the derivation are presented in the Supporting Information.

212 23

221 231

i

i

r r er

r r e

(6.1)

The transmission and reflection coefficients involved in Eq. 6.1 are illustrated in Figure 6.5(c). In

particular, and are the reflection coefficients of the MDA from front (air) and back (BCB)

side, respectively. is the reflection coefficient of the MHA. ⋅ ⋅ is the

propagating phase term in the BCB layer, where , and k are the refractive index, the

BCB thickness, and the wave vector in vacuum, respectively. , where

and are the transmission coefficients through the MDA along forward (air-MDA-BCB)

and backward (BCB-MDA-air) directions, respectively. Although is strictly equal to 1 at the

interface between two homogenous media, 1 for the MDA around the resonance

wavelengths because of the structural asymmetry in forward and backward directions (air-MDA-

BCB structure). In order to achieve perfect antireflection, 0 (Eq. 6.1) requires the following

conditions for amplitude and phase:

| | | ⋅ | (6.2)

∙ 2 2 1 ,| | 0,1,2,…. (6.3)

where the coefficients , , and are obtained from numerical simualtion of the air-

MDA-BCB structure and is obtained from the simulation of the BCB-MHA-GaAs structure.

109

To find the appropriate geometric paramters of MDA that simultaneously stasify amplitude (Eq.

6.2) and phase (Eq. 6.3) conditions, we carried out a series of simulaitons by varying the BCB

thickness, and the diameter for MDA, . Specifically, the complex reflection

coefficients, and , are obtained from simulations of two different configurations, air-

MDA-BCB and BCB-MHA-GaAs, respectively. For the variation of BCB thickness, is

fixed at 0.7 ∙ (1.26 µm) and is changed from 0.35 µm to 1.55 µm. For the variation of

MDA size, is fixed at 0.5 µm, and is changed from 0.3 ∙ (0.54 µm) to 0.8 ∙ (1.44

µm). The circular aperture size of MHA, is kept at 0.5 ∙ (0.9 µm). Figure 6.4 shows the

difference of amplutides, Δ| | ≡ | | | ∙ |(Figures 6.4(a, c)) and the phase term

(Figures 6.4(b, d)) for wavelengths around the first-order SPP resoannce. Figure 6.4 represents

the minimum value of Δ| | and satisfying phase condition (i.e. ). Figure 6.4(a) suggests

that the amplitudes of reflection coefficients, | |and| |, are independent of the BCB

thickness for all values in the range of 0.35 µm to 1.55 µm, so that Δ| |can always reach

the minimum value ofΔ| |, ∆| | 0.081 at the first-order SPP resonance

wavelength 6.25μm. The phase condition is satisfied when the BCB thickness is within a

range of 0.35μm 0.6μm around the white dash line as indicated in Figure 6.4(b). In

combination, we find the amplitude and phase conditions are satisfied simultaneously when

0.5μm at the first-order SPP resonance wavelength 6.25μm. In contrast, the size

of the MDA is strongly correlated to both the amplitude and phase as shown in Figure 6.4(c, d).

In the region of0.75 ∙ 0.8 ∙ , both the amplitude Δ| | 0 and the phase

conditions are satisfied simultaneously. Using the strategy of geometric parameter ( , )

sweep, we find the optimal AR coating structure with 0.5μm and 0.78 ∙ (1.4

µm) that is able to completely eliminate the reflection at the first SPP resonance 6.25μm,

and furth

4.3

experime

Figure 6.wavelengtterm, respective

6.2.4 Des

The role

theory. T

hermore is c

8μm. The

ental results

0.7 ∙ show

4 Colormapsth. Differenc

ely.

signer Meta

of MDA in

The MDA ex

capable of g

optimized M

s shown in

ws the best tr

s of amplitudce in amplitu

∙ 2

asurface (

n the Meta-A

xhibits local

greatly reduc

Meta-AR coa

Figure 6.3;

ansmission e

de and phasudes of reflec2 with (a),(

& ) u

AR coating

ized surface

110

cing the refl

ating design

; the fabric

enhancemen

e AR-conditiction coeffici(b) various B

using Thin-

can be und

e plasmon re

flection at

n (via our st

ated sample

nt among all

ions around ients, ∆| |BCB thickne

-film AR Co

derstood by

esonances at

t the second

trategy) agre

e with

samples.

the first-ord| | | ∙

esses and (c

oating Mech

using the e

t wavelength

d-order reson

ees well wit

0.55μm

der SPP reso| and the

c),(d) MDA

hanism

effective me

hs determine

nance

th the

m and

nance phase sizes,

edium

ed by

111

its geometric size and the refractive indices of surrounding materials[41]. The plasmon

resonances induce abrupt amplitude and phase changes to the light reflected by or transmitted

through the MDA layer. Such phase and amplitude discontinuities have been used to reshape the

beam profile to achieve negative refraction and beam steering [129, 130]. These single layer

plasmonic resonator arrays are typically regarded as two-dimensional metasurfaces instead of

bulk metamaterial since they only consist of single “meta-atom” layer. The electromagnetic

properties of the metasurface can be described by the effective surface electric susceptibility

and the effective surface magnetic susceptibility , which are calculated from the transmission

and reflection coefficients [76, 89]. Due to the skin effect, the induced electric current in the

plasmonic resonators only flows within extreme thin region under the surface of the structure (in

the order of the skin depth 2/ , where is the conductivity of metal). Therefore,

and are typically independent of the physical thickness of the resonators. However, at

infrared regime, the conductivity of metal decreases dramatically, so that the skin effect is less

pronounced and the electric current distributes throughout the entire volume of the resonator. As

a result, we observe that the surface susceptibilities and increases as the thickness of the

MDA increases (see Supporting Information). To address the thickness dependence, in this work,

we model the MDA metasurface as a thin film (metafilm) with the same thickness as the MDA

( ). The effective permittivity and effective permeability of the metafilm can be

calculated from simulated transmission and reflection coefficients of an air-MDA-BCB

configuration by using the well-known retrieval method[90] or alternatively by /

and / [76, 89]. With and , the metafilm model considers the MDA layer as

an effective thin film, which provides a more intuitive description compared to effective surface

susceptibilities and . The meta-AR coating consists of two thin flims, i.e. MDA metafilm

112

and BCB layer.

Both the effective surface susceptibilities, and in the metasurface model [76, 89] and

and in the retrieval method [90] are calculated using the transmission and reflection

coefficients of an air-MM-air configuratoin. In reality, MM structures are usually made on a

dielectric substrate, so the transmission and reflection coefficients are obtained at the interfaces

of an air-MM-dielectric configuration. To the best of our knowledge, many MM related works

use the transmission and reflection coefficients of air-MM-dielectric configuration directly to

extract and , which cause inaccurate values. In our structure, the metasurface is

modeled as a metafilm with thickness = 50 nm. The extremely thin thikness magnifies the

error greatly because the effective refractive index of the metafilm, , is inversely

proportional to . To obtain correct effective parameters of the metafilm, we develop a

method to obtain the transmission and reflection coefficients of the air-MM-air configuraiton

from that of the air-MM-dielectric configuation. The resutlsing transmission and reflection

coefficients produce accurate , , and . Details of this improved retrieval method

are elucidated in the Supporting Information. Figures 6.5(a,b) show and of MDA

structure calculated from simulation data of an air-MDA-BCB configuration with

0.5μmand 0.78 ∙ , where solid lines show and calculated by the retrieval

method and dash lines show / and / . It can be seen that two methods

give nearly identical values except minor deviation at the resonance wavelength 2.92μm,

where the thin-film retrieval shows typical antiresonance in due to the periodicity

effects[92]. The strong Lorentzian line shaped resonance in indicates the resonance is an

electric response, where the electric field of the incident light induces resonant electric current in

113

the disk. is nearly constant ( 0.86) within entire wavelength range from 2.5 µm to

7.0 µm. The resonance wavelength ( 2.92μm) of MDA is much shorter than the operating

wavelengths of our Meta-AR coating, i.e. the first-order ( 6.25 μm) and second-order

( 4.38 µm) SPP resonances of MHA. Therefore, the imaginary parts (blue lines) of and

at these wavelengths are nearly zero, and hence the loss in MDA is neglegible. Specifically,

as shown in the inset of Figure 6.5(a), the real part of gradually decreases from 40.25 to

30.52 in the wavelength range from 4.2 µm to 6.4 µm. The loss tangent, defined as the ratio

between the imaginary and the real parts of the permittivity (tan / ), also decreases from

0.0097 to 0.0046. The effective permittivity reads values of , 30.79 ∙ 1 0.0049 and

, 38.42 ∙ 1 0.0089 at the first-order and second-order SPP resonance wavelengths

( , ), respectively. Note that the loss tangents, tan 0.0049 and tan 0.0089,

have the same order of magnitude of commonly used low-loss dielectric coating materials such

as polyimide (tan ~0.005) and BCB (tan ~0.001).

With the calculated and , we can replace the MDA layer as a thin film of thickness

. As illustrated in Figure 6.5(c), the AR coating on the MHA comprises two layers of

homogenous films: a MDA metasurface with and and a BCB layer. The numerically

calculated (blue line: using Eq. 6.1) and simulated reflections (black line: using actual MDA

structure; red dash and green dash-dot lines: using homogeneous film with wavelength-

dependent ( , as shown in Figure 6.5(a,b) and wavelength-independent

(.

30.8 ∙ 0.147,.

0.86 ∙ 0.012)

effective parameters, respectively) are shown in Figure 6.5(d). At the first-order SPP resonance

( 6.25 µm), all four curves are matched very well and perfect antireflection is achieved with

114

nearly zero reflection ( 0). However, at the second-order SPP resonance, the simulated

reflection using effective medium model does not match with using actual MDA structure. The

discrepancy attributes to the resonance coupling between the MHA and the MDA (Supporting

Information) because the second-order SPP resonance ( 4.38 µm) is close to the resonance

wavelength ( 2.92μm) of the MDA (Note: the effective permittivity and permeability of

MDA are obtained from simulation of the air-MDA-BCB configuration, where the coupling

between the MDA and the MHA resonances are absent). The phase and amplitude conditions

given in Eq. 6.2 and Eq. 6.3 reveal the underlying mechanism of AR as the destructive

interference of light reflected at the MDA-BCB and BCB-MHA interfaces. In Figure 6.5(e), we

can clearly see that the amplitudes of and ∙ are equal at the first-order SPP resonance

wavelength 6.25 µm (i.e. the amplitude condition is satisfied). Simultaneously, as shown in

Figure 6.5(f), the phase term, ∙ 2 crosses (gray line), as predicted in

the phase condition. At the second-order SPP resonance 4.38 µm, the reflection is reduced

but does not reach zero because only the amplitude condition is satisfied.

Figure 6.5 of th

loss tangeresonanceSimulated(blue line)wavelengt

dash-dot l

parameter

phase term

5 The real (redhe MDA metaent, tan (grees of MHA. (cd reflection of) from Eq. 1 ath-dependent

line:

rs. (e) The am∙

m in the BCB

d) and imaginasurface. Inseten) around thc) Diagram off the entire strand simulated(red dash lin

3

mplitude of 2 (red), the layer 2 (gre

nary (blue) pat shows the re

he first-order (f the reflectioructure (MDAd reflections one:

30.8 ∙ 0.1

(blue) and e phase of ∙een).

115

arts of (a) effeeal part of eff( 6.25

on and transmA-BCB-MHAof MDA Meta

and

47 and

∙ (red) in(blue), the

ective permittfective permitm) and secon

mission coefficA-GaAs) (blacasurface-BCB

) and w

n Eq. 2. (f) The phase of

tivity anttivity, nd-order (cients of MDAck line), calcuB-MHA-GaAwavelength-in

0.86 ∙

he phase term (black), and

nd (b) permeab (red) and 4.38 m) S

A and MHA. ulated reflectis structure wi

ndependent (g

0.012) effect

ms (Eq. 3) d the propagat

bility the

SPP (d)

ion ith green

tive

tion

116

6.3 Summary

In summary, we have experimentally, numerically and analytically investigated the enhanced

transmission due to a metasurface antireflection (AR) coating on a dispersive surface plasmon

(SP) structure in the mid-infrared regime. Our metasurface AR coating (based on MDA) works

at off-resonance wavelengths and can be modeled as a metafilm with high effective permittivity

( ~30). The extremely low loss tangent,tan ~0.005, is comparable to low-loss films used

in AR coating such as polyimide (tan ~0.005) and BCB (tan ~0.001). In addition, the

effective permittivity is easily tunable by changing the geometric size of the MDA, which

provides unprecedented flexibility to fit the different wavelengths for a variety of applications.

With the metasurface coating, the measured transmission through the dispersive SP structure is

greatly increased at both the first-order (58% for 0.35 µm; 88% for 0.55 µm) and

second-order (99% for 0.35 µm; 80% for 0.55 µm) SP resonances. The electric

field and the intensity of surface wave are also enhanced by ~33% and ~77%, respectively, for

the first-order SP resonance. The enhanced electric field of surface wave will benefit to

applications where the local field engineering (strong local field) is demanded, e.g. improving

the performance of optoelectronic devices. Moreover, the metafilm model, transfer matrix

analysis and improved retrieval method developed in our work are generally applicable to multi-

layered metasurface system including antireflection coating and plasmonic perfect absorbers.

117

7. ANGLE-DEPENDENT SPOOF SURFACE PLASMONS IN METALLIC HOLE

ARRAYS AT TERAHERTZ FREQUENCIES

Note to Reader

Portions of this chapter have been previously published in peer reviewed journal paper (K.

Bhattarai, S. Silva, A. Urbas, S. J. Lee, Z. Ku, and J. Zhou, "Angle-dependent Spoof Surface

Plasmons in Metallic Hole Arrays at Terahertz Frequencies," IEEE Journal of Selected Topics

in Quantum Electronics, vol. PP, pp. 1-1, 2016) and have been reproduced with the permission

from the publisher.

In chapter 5 and 6, we employed the antireflection on the dispersive media. We choose

perforated gold film (PGF) as the dispersive medium and employed meta-surface antireflection

on the top of it. It is important to understand the detail properties of spp resonance of PGF

therefore we demonstrate the angle dependence of spoof surface plasmon on metallic hole arrays

in terahertz regime. By varying polar angle and azimuthal angle, we have observed frequency

shifting and splitting of resonance modes. The amplitude of extraordinary optical transmission

also shows angle dependence and exhibits mirror-image or translational symmetries.

7.1 Introduction

Extraordinary optical transmission (EOT) through subwavelength metallic hole-arrays (MHA)

has attracted tremendous interest since it was first reported by Ebbesen et al [40]. Such enhanced

transmission property is due to surface plasmon polariton (SPP) resonance which helps to

118

concentrate light into subwavelength scale beyond the diffraction limit and leads to significantly

enhancement of electromagnetic field. These characteristic features have been utilized in many

applications including surface-enhanced Raman spectroscopy [53], bio- or chemical-sensors

[54], photonic circuits [41, 55] and photovoltaic devices [56], and quantum dot based infrared

detectors [131, 132]. The SPP resonance can be further enhanced by anti-reflection coating [58,

91] to minimize reflection loss of the incident wave. In the infrared and optical regime, free

electrons in metal behaves like a plasma with dielectric function described by Drude model,

which supports SPP as the collective oscillations of electrons bounded to the surface of metal-

dielectric interface [52]. At terahertz frequencies, although the metal behaves as a nearly perfect

conductor, the effective dielectric constant of MHA has a plasma form and therefore spoof SPP

can be achieved [133, 134]. Pendry [133] and Hibbins et al. [134] have shown that spoof plasma

has the same dispersion and therefore exhibits many similar exceptional properties in common

with the electron SPP, which in consequence leads to terahertz devices applications such as

filters, modulators and switches [135-138]. The resonance wavelength of SPPs is determined

by the wave vector matching between incident light and reciprocal lattice of the MHA. Thus it is

sensitive to the direction of the incident light. It has been shown that of electron SPP changes

with both the polar angle and azimuthal angle [139] of vector of incident light. However,

such observation has not been well demonstrated for spoof SPP at terahertz frequencies except a

recent work that reports splitting of resonance peaks due to polar angle [140]. In this work, we

show that the spoof SPP exhibits angle dependence that exactly matches with theoretical

predication. In addition, we show that amplitude of EOT also exhibits angle dependence. We

also demonstrate that both resonance frequency and peak value of transmissions exhibit mirror-

119

image or translational symmetries with respect to azimuthal angle for different SPP resonance

modes.

7.2 Physics of Spoof SPP Modes

Figure 7.1(a) shows the schematic layout of MHA structure which consists of a gold (Au) layer

perforated with a 2D array of circular holes forming a square lattice on the top of a fused silica

substrate, where 150 , 75 , 0.2 , 3.75 are the periodicity,

diameter of the hole, thickness of the gold layer and dielectric constant of the substrate,

respectively. Polar ( ) and azimuthal ( ) angles dependence SPP resonances are simulated by

the finite element method with periodic boundary condition using CST Microwave Studio [86].

Fabrication of MHA structure is done by e-beam deposition of 200 nm thick gold layer above 10

nm thick titanium adhesion layer followed by photolithography and chemical etching to create

the pattern shown in Figure 7.1(b). The transmission measurement is carried out by using a

terahertz time domain spectroscopy (THz-TDS) system and and are controlled through two

motorized rotational stages.

The wave vector of SPP waves excited at the interface between MHA and dielectric substrate are

given by the following equation due to the conservation of momentum [57]:

∥ sin cos sin sin (7.1)

where and ∥ are the incident wave vector and its component in the plane of MHA structure,

2 / and 2 / are the reciprocal lattice vectors of 2-D square lattice along x and y

directions ( for our case 2 / ), and are integers that denote the index of SPP

modes along and directions, respectively. For smooth metallic film, using the continuity of

tangentia

incident l

where

very goo

dispersio

resonanc

Figure 7.1fused silicmagnetic respectivethe plane

al electric fi

light can be

is t

od approxim

on [52, 57,

e can be der

1 (a) Schematca substrate. (TM) wave, w

ely. For TE (oof incidence

field at the

derived as [

the refractiv

mation becau

138]. Thus,

rived as [57]

tic layout and(c) and (d): Cwhere θ andor TM) wave(indicated by

metal-dielec

141]

e index of t

use the exist

the wavelen

d (b) SEM imConfigurationd ϕ denote poe, E (or H) fiey the light-blu

120

ctric interfa

2 /

the substrate

tence of hol

ngth of inci

mage of MHA ns of (c) translar angle and

eld is always e dash-dot tri

ace, the SPP

e. Equation

le has negli

ident wave

/

which consissverse electri

d azimuthal anin the xy-pla

iangle) with a

P wave vec

7.2 also app

igible effect

that excites

sts of perforac (TE) wave ngle for incidane, while H (an angle ϕ fro

tor for norm

ply to MHA

t on the pla

s ( , ) mode

ated gold layeand (d) trans

dent wave vec( or E) field lom the x-axis

mally

(7.2)

A as a

smon

e SPP

(7.3)

er on a sverse ctor k, lies in .

121

where, is the resonance wavelength for normal incidence. It is obvious from the wavelength

relation Eq. 7.3 that there are multiple EOT peaks depending on the order of ( , . In the

following, we demonstrate through simulations and experiments that the dependence of

resonance wavelengths on and exactly follows theoretical prediction of Eq. 7. 3.

7.3 Discussion of Simulation and Experimental Results

We have simulated and measured the transmission spectra through MHA structure for both

transverse electric (TE) and transverse magnetic (TM) polarized incident waves by varying the

polar angle and azimuthal angle of the wave vector . As shown in Figure 7.1(c), the electric

field of the TE polarized wave, , is always in the xy-plane and is perpendicular to the plane of

incidence that contains the wave vector and the surface normal ( z-axis) , thereby orienting

along the direction with an angle of /2 from x-axis. TM polarization is shown in

Figure 7.1(d), where the electric field, , lies in the plane of incidence and has the same

azimuthal angle as the wave vector . The polar angle of is given by /2– , thus the in-

plane component ∥ has an amplitude of ∥ cos and is along the line (black dash line) with

an angle from x-axis.

Figure7.2Realpartbyincideh :Phas

For norm

the xy-pl

Since ∥

2 a , b :TrtofE fieldontTEwave.eofE forco

mal incidence

lane, and

0 for no

and (

ransmissionsfSPPwavese , f :Real

orresponding

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is polarized

rmal incide

1, 0

spectrafornatthefirst‐opartofE fiegSPPwaves

d 0), bo

d along y-ax

nce, two-fo

0) with

122

normallyinciorder c andeldofSPPwashownin c

oth the electr

xis and x-ax

lder degene

,

dentTE a adthesecond‐avesexcited‐ f .

ric field an

xis for TE a

erate SPP m

are excited

andTM b w‐order d rebyincident

nd the magne

and TM mo

modes, (

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waves. c , dsonancesexcTMwave. g

etic field a

ode, respecti

0, 1 )

and TM w

d :cited‐

are in

ively.

with

waves,

123

respectively. The resonance wavelength, 290.5 , and the corresponding

frequency, 1.04THz, can be calculated by Eq. 7.3. Similarly, at the second-order resonance

wavelength, /√2 205.4 (or frequency 1.46THz), four-fold degenerate

modes ( 1, 1) are excited with for both TE and TM waves. Figure 7.2(a)

and 7.2(b) show the transmission spectra for normal incident TE and TM waves, respectively.

Due to the symmetry of MHA lattice, the transmission spectra for TE and TM waves are exactly

the same. Two EOT peaks are observed at the frequencies exactly matching with and

calculated above. For the first-order resonance, the electric field of TE wave is along y-

direction and thereby induces resonant current oscillating along y-direction. This results in two

counter-propagating SPP waves along +y and –y directions for (0, 1) and 0, 1 resonance

modes, respectively. The interference of two SPP waves lead to a standing wave pattern as

shown in Figure 7.2(c), where component of the SPP wave has alternating nodes (| | 0

shown as green color) and anti-nodes (| | reaches the maximum values shown as red or blue

color) along y-direction. The standing wave feature is confirmed by the constant phase along y-

direction shown in Figure 7.2(g). Note the phase of shifts by 180° across the positions of

nodes shown in Figure 7.2(c). Along x-direction, Figure 7.2(c) and 7.2(g) show straight wave

front parallel to x-axis, indicating a plane wave nature of SPP waves. At the second-order

resonance, the four-fold degenerate modes result in four SPP waves propagating along or

directions. The interferences between them lead to a two-dimensional (2D) standing wave pattern

shown in Figure 7.2(d) and 7.2(h). Likewise, for TM wave, similar 2D standing wave pattern

(Figure 7.2(f) and 7.2(j)) for the second-order resonance, and 1D standing wave along x-direction

(Figure 7.2(e) and 7.2(i)) for the first-order resonance are observed.

Figure7.3from0tofordifferE fieldfo

Figure 7.

for TE w

degenera

vector,

exhibit a

3 a Simulato20°andkeeentSPPresoorSPPwaves

.3(a) shows s

wave. Like

ate SPP reson

sin

blue shift w

tedand b mepϕ 0.Thonancemodes.

simulated tra

the norma

nance modes

. D

when polar a

measuredtrahedottedandsasshownin

ansmission s

al incidence,

s (0, 1) at w

Due to the s

angle incre

124

ansmissionsdsolidlinesanthelegend

spectra as

, the y-pola

wavelength

sin / t

eases as sho

pectraforTEaretheanaly.Therealpa

increases fro

arized electr

/ s

term in e

own in Figur

Emodewhenyticalresonanart c ‐ e an

om 0 to 20°

ric field ex

sin /

equation, th

re 7.3(a). Th

nθincreasesncefrequencdphase f ‐

and keeps

xcites a two

1/ , with

he (0, 1) m

he wave vect

sciesh of

0

o-fold

wave

modes

tor of

125

the second-order SPP modes are given by sin . The four-fold

degenerate SPP modes ( 1, 1) for 0 split into two two-fold degenerate modes ( 1, 1)

and ( 1, 1) for 0 with resonance wavelength / 1/ sin / 1/ ,

and / 1/ sin / 1/ , respectively. As increases, the sin / term in

and leads to a red shift for ( 1, 1) modes and a blue shift for ( 1, 1) modes,

respectively, which is confirmed by the simulations and measurements shown in Figure 7.3(a)

and 7.3(b). The wave vector of (0, 1) modes is depicted in Figure 7.3(c), and the wave

equation of SPP wave can be written as:

, , ∥ 2 cos ∥ (7.4)

Thus for 0, 0the parallel wave vector ∥= sin creates a propagation wave ∥

along +x-direction as depicted by the Figure 7.3(c). The phase of decreases when x increases

as shown in Figure 7.3(f), thereby proving that the wave propagates along +x-direction. The

cos term shows that the amplitude of forms a standing wave pattern along y-direction

with node at 1/2 / 1/2 /2 and anti-node at /2, where is an

integer. So the distance between adjacent nodes or adjacent anti-nodes are given by Δ /2,

which exactly matches the distance between the adjacent 0 (green) or adjacent | |

(blue or red) shown in Figure 7.3(c). Equation 7.4 also shows that the phase of SPP wave is

independent of , which is confirmed by the constant phase along y in Figure 7.3(f). Note that

the phase is shifted by across the nodes of because the cos term changes to opposite

sign. The ( 1, 1) modes contain two waves, ( 1, 1) and ( 1, 1), with wave vector along

directions shown by red arrows in Figure 7.3(d). The interference of them results in a

propagating wave along –x-direction with standing wave pattern along y-direction as shown in

126

Figure 7.3(d) and 7.3(g). Similarly, Figure 7.3(e) and (h) shows the wave pattern propagating

along +x-direction for ( 1, 1) mode. Measured transmission spectra in Figure 7.3(b) shows

good agreement with simulations, except for the broadening of resonance peaks. This is due to

the parabolic lens used in our THz-TDS system, which cause the incident terahertz beam

containing a certain range of when it is focused onto the sample.

For TM mode, simulated and measured transmission spectra with increasing at 0 are

shown in Figure 7.4(a) and 7.4(b), respectively. For 0, the parallel wave vector ∥

sin breaks the symmetry of along x-direction, and thereby the degenerate ( 1,0) modes

split into ( 1,0) and ( 1,0) modes with wave vector sin and

sin , respectively. The resonance wavelengths for ( 1,0) and ( 1,0) modes are

given by / 1/ sinθ/λ and / 1/ sinθ/λ , respectively. The

sinθ/λ term in and gives rise to respective red and blue shift as shown in Figure 7.4(a)

and (b). Since the field of incident TM wave is polarized along x, both branches propagate

along x-axis as shown in Figure 7.4(c) and 7.4(d). The increasing (Figure 7.4(g)) and decreasing

(Figure 7.4(h)) phase along +x further confirms that ( 1,0) and ( 1,0) modes propagate along –

x-direction and +x-direction, respectively. Figure 7.4(e), 7.4(f) and 7.4(i), 7.4(g) show the real

part and the phase of Ez field for ( 1, 1) and ( 1, 1) modes, respectively, which exhibit

same behavior as the corresponding modes for TE wave. Measured transmission spectra in

Figure 7.4(b) show exactly same frequency shift as simulations in Figure 7.4(a). In addition, the

measurements also show the same trend of amplitude changes as increases at the first-order

resonance.

Figure 7.4are the anpart and (

In the fo

general c

different

thereby c

and 1

4 (a) Simulatenalytical reson(g)-(j) the pha

ollowing, we

case of

frequencies

can be writte

,0 modes, w

ed and (b) menance frequenase of fiel

e discuss th

0 and 0

s. For TE w

en as

while the y-

easured transmncies differentld of SPP wav

he effect of

0, the resona

wave, the ele

sin

-component

127

mission spectrt resonance mves.

azimuthal a

ance ( ,

ctric field is

cos .

excites 0,

ra for TM wamodes as listed

angle . Ac

) modes are

s polarized a

The x-comp

1 and 0

ave. The dotted in the legen

ccording to

e excited by

along

ponent of

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ed and solid lind. (c)-(f): Th

Eq. (7.3), i

incident wa

/2direction

excites

s. Both x- an

ines he real

n the

ave at

n and

1,0

nd y-

compone

transmiss

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Figure 7.5270 . Thein the legecalculated

All the re

instance,

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ent of c

sion spectra

onance frequ

sion, exactly

5 (a) Simulatee dotted and send. (c)-(j): Td analytically

esonance mo

( 1,0) m

n propa

can excite th

for 10

uency for all

y follow theo

ed and (b) mesolid lines are

The real part ousing Eq. 7.3

odes result in

mode with

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he second-or

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easured transme the analyticaof E field for3.

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128

rder modes

270 show

dicated by th

es (dash or s

mission spectral resonance fr SPP waves.

on SPP wave

or calculate

n between –

1, 1 . I

w that all the

he maxima (

solid lines) p

ra for TE wavfrequencies foThe purple da

es with wave

ed as ,

–x-axis and

In Figure 7.

e modes are

(shown in d

plotted using

ve for θ 10for SPP resonaash-lines show

e vector give

, sin

–y-axis as

5(a) and (b)

e non-degene

dark red colo

g Eq. 7.3.

0 , 0 ϕance modes liw equiphase

en by Eq. 7.1

n cos

shown in F

), the

erate.

or) of

isted lines

1. For

Figure

129

7.5(c). The field shows perfect plane wave pattern with wave fronts exactly parallel to the

theoretical equiphase lines (purple dash lines) calculated from Eq. (7.1). The (+1,0) mode has

wave vector , sin cos sin sin and propagates along a direction

between +x-axis and –y-axis as depicted in Figure 7.5(d). Likewise, all other first-order and

second-order modes form propagation SPP waves as shown in Figure 7.5(c) to 7.5(j).

Figure 7.6(a) and 7.6(b) show simulations and measurements of transmission spectra for TM

modes. Similar to the TE modes, all eight modes for the first-order and second-order resonances

are non-degenerate. The splitting and merging of the peaks are observed as increases, exactly

following the theoretical predication shown in solid- or dash-lines. While the resonance

frequency splits and shifts as the polar angle and the azimuthal angle change, the amplitude of

transmission peaks at resonance frequencies also change. Figure 7.6(c) shows the amplitudes of

transmission peaks, , that are taken from simulation data shown in Figure 7.6(a) at the

resonance frequencies for ( 1,0), ( 1,0) and (0, 1) modes. These resonance frequencies are

calculated using Eq. 7.3 for 10 , 0 360 as shown by the dash lines in Figure

7.6(a). For each mode, varies significantly between 0.3 to 0.5 as changes from 0 to

360 . Due to the symmetry of the MHA lattice, optical responses of SPP modes also exhibit

certain symmetry. For instance, ( 1,0) and ( 1,0) are both excited by x-component of the

electric field. For TM wave, ∥cos , so that exhibits mirror-image symmetry about x-

axis. Consequently, as shown in Figure 7.6(c), the transmission peak values are symmetric

about 180 (or 0 ). Similarly, (0, 1) and (0, 1) are mirror symmetrical about y-axis,

so values are symmetric about 90 or 270 as shown in Figure 7.6(c). In addition,

different SPP modes are also related by certain symmetries. For instance, ( 1,0) mode and

( 1,0) m

transmiss

in Figure

mode. Si

(+1,0) m

understoo

and 7.1(d

Figure 7.6value takeAfter a m+1) mode

mode are m

sion curve fo

e 7.6(d), the

imilarly, a

mode. Thes

od by the sa

d).

6 (a) Simulaten at resonan

mirror-image t, the resulting

mirror-symm

or ( 1,0) m

e new curve

90 transl

se mirror-im

ame types o

ted and (b) mce frequencietransform at 1g curves exac

metrical abo

ode (blue da

of “imaged

lational-shift

mage or tra

f symmetrie

measured tranes shown as d180 degree fotly overlap w

130

out x-axis.

ash curve) in

d” (-1, 0) mo

ted (0, +1) c

anslational s

es of inciden

nsmission spdash lines in (or (-1, 0) mod

with (+1, 0) mo

When we

n Figure 7.6(

ode exactly

curve exactly

symmetry o

nt wave vect

pectra for TM(a) for (+1, 0)de and a -90 dode.

take the

(c) at 1

overlaps the

y overlaps w

of SPP mod

tor shown

M wave. (c) T), (-1, 0) and degreetransla

mirror-imag

180 and rep

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with the curv

des can be

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Transmission(0, +1) mode

ational shift f

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plot it

+1,0)

ve for

well

7.1(c)

n peak es. (d) for (0,

131

7.4 Summary

We have investigated the shifting and splitting of spoof surface plasmon polariton resonance by

varying both the polar angle and azimuthal angle . Both the resonance frequency and the

transmission amplitudes of SPP modes vary with and , and exhibit mirror-image or

translational symmetries. We have found the degenerate modes form standing waves, while the

degeneracy can be fully broken by introducing a parallel wave vector ∥ under oblique

incidence. Our measurements and simulations of THz spoof SPP waves match very well with

theoretical predications. The angle dependence results provide important information for

designing THz plasmonic devices in sensor and detector applications.

132

8. CONCLUSION AND FUTURE WORKS

In conclusion, the multilayer model (Three Layer Model or TLM) of a multilayer metamaterial

structure has been developed in which the total reflection and transmission of the entire structure

are calculated from the reflection and transmission obtained from the individual layer. In this

model, we can obtain the amplitude and phase information of the reflection and transmission

from each of the layer so that we can manipulate them to get the required functionality in

optoelectronic devices. The TLM is applied to a metamaterial perfect absorber and the

Numerical simulation is performed to satisfy the amplitude and phase conditions required to get

zero reflection. The perfect absorption phenomenon is explained through Fabry-Perot cavity

bounded by a “resonator” mirror and metallic film, where the resonator exhibits a “quasi-open”

boundary condition and leads to the characteristic feature of subwavelength thickness. We have

also discussed the perfect absorber from the Impedance Matched Theory and Transmission Line

Theory and showed their matching with the TLM. We have modified the retrieval method (to

extract effective permittivity and permeability) to better fit with the multilayer structure by

introducing air on the both side of the resonator. We have developed the Meta film model by

considering the resonator as a homogeneous thin film characterized by the effective permittivity

and permeability giving rise to the same behavior as the original multilayer structure. One

important characteristic of the resonator is that its resonance is far from the resonance of the

absorber so that it behaves as a medium of high refractive index and very low loss. We have

shown numerically that the resonant wavelength of the reflection spectra is almost constant with

increase in angle of incidence from 0 degree to 80 degree. Hence, the ultra-thin thickness makes

133

the absorber angular independent. We have also shown that the density of states is increased by

the absorber as compared to the resonator itself. We have investigated that the resonance peaks

of the absorber with increased spacer thickness arise from the combination of Fabry-perot cavity

modes and the surface plason resonance modes. All the different modes are assigned with

specific names describing the mode profiles. To demonstrate the application of the perfect

absorber, we have designed an absorber structure consisting of three layers: elliptical Metal Disk

Array (MDA), dielectric Spacer, and Metal Ground Plane (MGP). This structure is used as a

plasmonic sensor to detect the refractive index change of the chemical and biological samples.

When the refractive index of the liquid on its surface changes, the frequency and intensity of the

reflection spectra also changes. Therefore, this device is called Refractive Index Sensor. The

sensitivity (wavelength shift per refractive index change) and Figure of Merit (FOM) as an

indicator of performance of the device are enhanced significantly. To achieve the high

sensitivity, we have etched the dielectric spacer below the resonator where the electric field is

maximum. The liquid enters into the etched region of high electric field thereby maximizing the

shifting of the resonant wavelength.

We have also employed the Three Layer Model and Meta Film Model to the multi-layer

structure giving anti-reflection. Conventional antireflection coating consists of a dielectric on the

top of the substrate, whose thickness should be quarter wavelength and the refractive index

follow the condition . Experimentally, it is difficult to deposit very large thickness of

the dielectric and the matching coating material may not be available, metamaterial anti-

reflection coating is required. At first, we have deployed metamaterial anti-reflection (Metal

Disk Array) coating on the top of conventional coating material (BCB) with homogeneous

substrate to enhance the transmission. Then we have applied the conventional anti-reflection

134

coating on the top of dispersive media (Metal Hole Array) to enhance the transmission. We have

proved numerically and experimentally that the metamaterial anti reflection can be applied not

only for homogeneous media but for dispersive media also. The impedance matching condition

is verified numerically by calculating the impedance of the resonator form retrieval method. In

order to enhance the SPP of MHA, a single-layer metasurface-based AR coating is shown to

operate at off-resonance wavelengths and to avoid the resonant coupling with the MHA layer.

The SPP resonance wavelengths are unaffected whereas the electric field of surface wave is

significantly increased (around 30%). With an improved retrieval method, the metasurface is

proved to exhibit a high effective permittivity ( ~30) and extremely low loss (tan). A

classical thin-film AR coating mechanism is identified through analytical derivations and

numerical simulations. The properly designed effective permittivity and effective permeability of

the metasurface lead to required phase and amplitude conditions for the AR coating, thereby

paving the way for improved performance of optoelectronic device.

To understand the detailed properties of spp resonance of metal Hole Array (MHA), we have

investigated the shifting and splitting of spoof surface plasmon polariton resonance by varying

both the polar angle and azimuthal angle . The amplitude of extraordinary optical

transmission also shows angle dependence and exhibits mirror-image or translational

symmetries. We have found that the degenerate modes form standing waves, while the

degeneracy can be fully broken by introducing a parallel wave vector ∥ under oblique

incidence. Our measurements and simulations of THz spoof SPP waves match very well with

theoretical predications. The angle dependence results provide important information for

designing THz plasmonic devices in sensor and detector applications.

135

For future work, we would like to use metasurface to get oblique incidence on Metal Hole Array

(MHA). Since, controlling the direction of EM wave is tedious, metasurface can do this job by

controlling the phase of the wave that passes through it. The metamaterial structures capable of

changing the phase of the incident beam constantly can be deposited on the dielectric medium

kept over the MHA. When the EM wave is incident on the metasurface, transmitted beam passes

obliquely into the dielectric medium and the wave is incident on the MHA structure with certain

angle θ. By designing the proper metasurface, angle of incidence can be controlled precisely.

Then we can investigate the shifting of the resonant peaks and the nature and direction of the

wave propagation depending on the incident direction of EM wave. The second work we would

like to do is the use of MHA resonant peaks in radar detection technique. As we discussed in

chapter 7, there are specific resonant peaks for particular polar and azimuthal angles of the

incident EM wave. Therefore, by analyzing the resonant peaks of the MHA obtained on

impinging the EM wave from unknown source, its direction (polar and azimuthal angles) can be

calculated. The third work we would like to do is the analysis of the resonant peaks of the

metamaterial perfect absorber consisting of the MHA as a resonator. When the spacer thickness

of the absorber increases, multiple peaks of the Fabry-perot resonance modes and Surface

Plasmon Resonance modes arise. To fully understand the mechanism of the absorber, it is

important to understand those peaks.

136

9. REFERENCES

[1] D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science, vol. 305, pp. 788-792, Aug 2004.

[2] C. M. Soukoulis, S. Linden, and M. Wegener, "Negative refractive index at optical wavelengths," Science, vol. 315, pp. 47-49, 2007.

[3] V. M. Shalaev, "Optical negative-index metamaterials," Nature Photonics, vol. 1, pp. 41-48, 2007. [4] C. M. Soukoulis and M. Wegener, "Past achievements and future challenges in the development

of three-dimensional photonic metamaterials," Nature Photonics, vol. 5, pp. 523-530, Sep 2011. [5] R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of

refraction," Science, vol. 292, pp. 77-79, // 2001. [6] D. R. Smith, "Composite medium with simultaneously negative permeability and permittivity,"

Phys. Rev. Lett., vol. 84, pp. 4184-4187, // 2000. [7] J. B. Pendry, "Negative Refraction Makes a Perfect Lens," Physical Review Letters, vol. 85, pp.

3966-3969, 2000. [8] N. Fang, H. Lee, C. Sun, and X. Zhang, "Sub-diffraction-limited optical imaging with a silver

superlens," Science, vol. 308, pp. 534-537, APR 22 2005. [9] U. Leonhardt and T. G. Philbin, "Quantum levitation by left-handed metamaterials," New Journal

of Physics, vol. 9, Aug 2007. [10] D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, et al., "Metamaterial

electromagnetic cloak at microwave frequencies," Science, vol. 314, pp. 977-980, Nov 2006. [11] J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science, vol. 312,

pp. 1780-1782, Jun 2006. [12] T. Xu, Y. H. Zhao, J. X. Ma, C. T. Wang, J. H. Cui, C. L. Du, et al., "Sub-diffraction-limited

interference photolithography with metamaterials," Optics Express, vol. 16, pp. 13579-13584, Sep 2008.

[13] A. Alu, F. Bilotti, N. Engheta, and L. Vegni, "Subwavelength, Compact, Resonant Patch Antennas Loaded With Metamaterials," Antennas and Propagation, IEEE Transactions on, vol. 55, pp. 13-25, 2007.

[14] J. F. O'Hara, R. Singh, I. Brener, E. Smirnova, J. G. Han, A. J. Taylor, et al., "Thin-film sensing with planar terahertz metamaterials: sensitivity and limitations," Optics Express, vol. 16, pp. 1786-1795, Feb 2008.

[15] X. Liu, T. Starr, A. F. Starr, and W. J. Padilla, "Infrared spatial and frequency selective metamaterial with near-unity absorbance," Phys Rev Lett, vol. 104, p. 207403, May 21 2010.

[16] S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science, vol. 306, pp. 1351-3, Nov 19 2004.

[17] S. Gupta and C. Caloz, "Analog Signal Processing in Transmission Line Metamaterial Structures," Radioengineering, vol. 18, pp. 155-167, Jun 2009.

[18] N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, "Perfect Metamaterial Absorber," Phys. Rev. Lett., vol. 100, p. 207402, May 2008.

[19] X. Liu, T. Starr, A. F. Starr, and W. J. Padilla, "Infrared Spatial and Frequency Selective Metamaterial with Near-Unity Absorbance," Phys. Rev. Lett., vol. 104, p. 207403, May 2010.

[20] J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, et al., "Gold Helix Photonic Metamaterial as Broadband Circular Polarizer," Science, vol. 325, pp. 1513-1515, SEP 18 2009.

[21] X. G. Peralta, E. I. Smirnova, A. K. Azad, H. T. Chen, A. J. Taylor, I. Brener, et al., "Metamaterials for THz polarimetric devices," Optics Express, vol. 17, pp. 773-783, Jan 2009.

137

[22] J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," Ieee Transactions on Microwave Theory and Techniques, vol. 47, pp. 2075-2084, Nov 1999.

[23] J. Pendry, A. Holden, W. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Physical Review Letters, vol. 76, p. 4773, Jun 1996.

[24] M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured magnetic materials for RF flux guides in magnetic resonance imaging," Science, vol. 291, pp. 849-851, Feb 2001.

[25] D. Smith, W. Padilla, D. Vier, S. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Physical Review Letters, vol. 84, p. 4184, May 2000.

[26] J. F. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, "Negative index materials using simple short wire pairs," Physical Review B, vol. 73, Jan 2006.

[27] T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, et al., "Terahertz magnetic response from artificial materials," Science, vol. 303, pp. 1494-1496, Mar 2004.

[28] S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science, vol. 306, pp. 1351-1353, Nov 2004.

[29] C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, et al., "Magnetic metamaterials at telecommunication and visible frequencies," Physical Review Letters, vol. 95, Nov 11 2005.

[30] G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, and C. M. Soukoulis, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Optics Letters, vol. 30, pp. 3198-3200, Dec 1 2005.

[31] S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys Rev Lett, vol. 94, p. 037402, Jan 28 2005.

[32] S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys Rev Lett, vol. 95, p. 137404, Sep 23 2005.

[33] G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Low-loss negative-index metamaterial at telecommunication wavelengths," Optics Letters, vol. 31, pp. 1800-1802, Jun 2006.

[34] R. F. Service and A. Cho, "Strange New Tricks With Light," Science, vol. 330, p. 1622, December 17, 2010 2010.

[35] V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of [epsi] and [mu]," Sov. Phys. Uspekhi, vol. 10, pp. 509-514, // 1968.

[36] V. Veselago, L. Braginsky, V. Shkover, and C. Hafner, "Negative refractive index materials," Journal of Computational and Theoretical Nanoscience, vol. 3, pp. 189-218, Apr 2006.

[37] J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE T. Microw. Theory, vol. 47, pp. 2075-2084, // 1999.

[38] J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Physical Review Letters, vol. 76, pp. 4773-4776, Jun 1996.

[39] J. B. Pendry, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech., vol. 47, pp. 2075-2084, // 1999.

[40] T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature, vol. 391, pp. 667-669, Feb 12 1998.

[41] E. Ozbay, "Plasmonics: Merging photonics and electronics at nanoscale dimensions," Science, vol. 311, pp. 189-193, Jan 13 2006.

[42] N. L. D Jones, B. Corbett, P. Lovera, A.J. Quinn, A O’Riordan "Surface Plasmon assisted extraordinary transmission in metallic nanohole arrays and itssuitability as a bio-sensor," Journal of Physics D-Applied Physics, 2005.

138

[43] W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, "Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film," Physical Review Letters, vol. 92, Mar 12 2004.

[44] H. T. Chen, J. F. Zhou, J. F. O'Hara, F. Chen, A. K. Azad, and A. J. Taylor, "Antireflection Coating Using Metamaterials and Identification of Its Mechanism," Physical Review Letters, vol. 105, p. 073901, Aug 9 2010.

[45] A. Kabiri, E. Girgis, and F. Capasso, "Buried Nanoantenna Arrays: Versatile Antireflection Coating," Nano Letters, vol. 13, pp. 6040-6047, 2013/12/11 2013.

[46] B. Zhang, J. Hendrickson, N. Nader, H.-T. Chen, and J. Guo, "Metasurface optical antireflection coating," Applied Physics Letters, vol. 105, p. 241113, 2014.

[47] S. J. Lee, Z. Y. Ku, A. Barve, J. Montoya, W. Y. Jang, S. R. J. Brueck, et al., "A monolithically integrated plasmonic infrared quantum dot camera," Nature Communications, vol. 2, Apr 2011.

[48] C.-C. Chang, Y. D. Sharma, Y.-S. Kim, J. A. Bur, R. V. Shenoi, S. Krishna, et al., "A Surface Plasmon Enhanced Infrared Photodetector Based on InAs Quantum Dots," Nano Letters, vol. 10, pp. 1704-1709, 2010/05/12 2010.

[49] S. C. Lee, S. Krishna, and S. R. J. Brueck, "Quantum dot infrared photodetector enhanced by surface plasma wave excitation," Optics Express, vol. 17, pp. 23160-23168, 2009/12/07 2009.

[50] F. Zhao, C. Zhang, H. Chang, and X. Hu, "Design of Plasmonic Perfect Absorbers for Quantum-well Infrared Photodetection," Plasmonics, vol. 9, pp. 1397-1400, 2014.

[51] J. S. Clausen, E. Højlund-Nielsen, A. B. Christiansen, S. Yazdi, M. Grajower, H. Taha, et al., "Plasmonic Metasurfaces for Coloration of Plastic Consumer Products," Nano Letters, vol. 14, pp. 4499-4504, 2014/08/13 2014.

[52] H. Raether, Surface plasmons on smooth and rough surfaces and on gratings. Berlin ; New York: Springer-Verlag, 1988.

[53] S. Nie and S. R. Emory, "Probing Single Molecules and Single Nanoparticles by Surface-Enhanced Raman Scattering," Science, vol. 275, pp. 1102-1106, February 21, 1997 1997.

[54] J. Homola, S. S. Yee, and G. Gauglitz, "Surface plasmon resonance sensors: review," Sensors and Actuators B: Chemical, vol. 54, pp. 3-15, 1/25/ 1999.

[55] D. K. Gramotnev and S. I. Bozhevolnyi, "Plasmonics beyond the diffraction limit," Nature Photonics, vol. 4, pp. 83-91, Feb 2010.

[56] H. A. Atwater and A. Polman, "Plasmonics for improved photovoltaic devices," Nature Materials, vol. 9, pp. 205-213, Mar 2010.

[57] H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, "Surface plasmons enhance optical transmission through subwavelength holes," Physical Review B, vol. 58, pp. 6779-6782, 09/15/ 1998.

[58] M. S. Park, K. Bhattarai, D. K. Kim, S. W. Kang, J. O. Kim, J. F. Zhou, et al., "Enhanced transmission due to antireflection coating layer at surface plasmon resonance wavelengths," Optics Express, vol. 22, pp. 30161-30169, Dec 1 2014.

[59] C. M. Watts, X. L. Liu, and W. J. Padilla, "Metamaterial Electromagnetic Wave Absorbers," Advanced Materials, vol. 24, pp. 98-120, Jun 19 2012.

[60] M. Hedayati, F. Faupel, and M. Elbahri, "Review of Plasmonic Nanocomposite Metamaterial Absorber," Materials, vol. 7, p. 1221, 2014.

[61] N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, "Perfect metamaterial absorber," Physical Review Letters, vol. 100, p. 207402, May 23 2008.

[62] H. R. Seren, G. R. Keiser, L. Cao, J. Zhang, A. C. Strikwerda, K. Fan, et al., "Optically Modulated Multiband Terahertz Perfect Absorber," Advanced Optical Materials, vol. 2, pp. 1221-1226, 2014.

[63] D. Shrekenhamer, J. Montoya, S. Krishna, and W. J. Padilla, "Four-Color Metamaterial Absorber THz Spatial Light Modulator," Advanced Optical Materials, vol. 1, pp. 905-909, 2013.

[64] S. Savo, D. Shrekenhamer, and W. J. Padilla, "Liquid Crystal Metamaterial Absorber Spatial Light Modulator for THz Applications," Advanced Optical Materials, vol. 2, pp. 275-279, 2014.

139

[65] H. Tao, N. I. Landy, C. M. Bingham, X. Zhang, R. D. Averitt, and W. J. Padilla, "A metamaterial absorber for the terahertz regime: Design, fabrication and characterization," Optics Express, vol. 16, pp. 7181-7188, May 12 2008.

[66] J. Hao, J. Wang, X. Liu, W. J. Padilla, L. Zhou, and M. Qiu, "High performance optical absorber based on a plasmonic metamaterial," Applied Physics Letters, vol. 96, p. 251104, 2010.

[67] X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, "Taming the Blackbody with Infrared Metamaterials as Selective Thermal Emitters," Physical Review Letters, vol. 107, p. 045901, 07/18/ 2011.

[68] T. Maier and H. Brückl, "Wavelength-tunable microbolometers with metamaterial absorbers," Optics Letters, vol. 34, pp. 3012-3014, 2009/10/01 2009.

[69] A. Tittl, P. Mai, R. Taubert, D. Dregely, N. Liu, and H. Giessen, "Palladium-Based Plasmonic Perfect Absorber in the Visible Wavelength Range and Its Application to Hydrogen Sensing," Nano Letters, vol. 11, pp. 4366-4369, Oct 2011.

[70] N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, "Infrared Perfect Absorber and Its Application As Plasmonic Sensor," Nano Letters, vol. 10, pp. 2342-2348, Jul 2010.

[71] G. H. Li, X. S. Chen, O. P. Li, C. X. Shao, Y. Jiang, L. J. Huang, et al., "A novel plasmonic resonance sensor based on an infrared perfect absorber," Journal of Physics D-Applied Physics, vol. 45, p. 205102, May 23 2012.

[72] K. Bhattarai, Z. Ku, S. Silva, J. Jeon, J. O. Kim, S. J. Lee, et al., "A Large-Area, Mushroom-Capped Plasmonic Perfect Absorber: Refractive Index Sensing and Fabry-Perot Cavity Mechanism," Advanced Optical Materials, vol. 3, pp. 1779-1786, 2015 2015.

[73] M. K. Hedayati, M. Javaherirahim, B. Mozooni, R. Abdelaziz, A. Tavassolizadeh, V. S. K. Chakravadhanula, et al., "Design of a Perfect Black Absorber at Visible Frequencies Using Plasmonic Metamaterials," Advanced Materials, vol. 23, pp. 5410-+, Dec 1 2011.

[74] A. Tittl, M. G. Harats, R. Walter, X. Yin, M. Schäferling, N. Liu, et al., "Quantitative Angle-Resolved Small-Spot Reflectance Measurements on Plasmonic Perfect Absorbers: Impedance Matching and Disorder Effects," ACS Nano, vol. 8, pp. 10885-10892, 2014/10/28 2014.

[75] H.-T. Chen, "Interference theory of metamaterial perfect absorbers," Optics Express, vol. 20, pp. 7165-7172, 2012/03/26 2012.

[76] J. Zhou, H.-t. Chen, T. Koschny, A. K. Azad, A. J. Taylor, C. M. Soukoulis, et al., "Application of metasurface description for multilayered metamaterials and an alternative theory for metamaterial perfect absorber," arXiv:1111.0343v1, Jul 2011.

[77] N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, "Perfect metamaterial absorber," Phys. Rev. Lett., vol. 100, p. 207402, // 2009.

[78] !!! INVALID CITATION !!! [79] B. Wang, T. Koschny, and C. M. Soukoulis, "Wide-angle and polarization-independent chiral

metamaterial absorber," Physical Review B, vol. 80, p. 033108, 07/30/ 2009. [80] G. H. Li, X. S. Chen, O. P. Li, C. X. Shao, Y. Jiang, L. J. Huang, et al., "A novel plasmonic

resonance sensor based on an infrared perfect absorber," Journal of Physics D-Applied Physics, vol. 45, May 23 2012.

[81] Y. Ma, Q. Chen, J. Grant, S. C. Saha, A. Khalid, and D. R. S. Cumming, "A terahertz polarization insensitive dual band metamaterial absorber," Optics Letters, vol. 36, pp. 945-947, Mar 15 2011.

[82] B. Zhang, Y. Zhao, Q. Hao, B. Kiraly, I.-C. Khoo, S. Chen, et al., "Polarization-independent dual-band infrared perfect absorber based on a metal-dielectric-metal elliptical nanodisk array," Optics Express, vol. 19, pp. 15221-15228, 2011/08/01 2011.

[83] S. Li, J. Gao, X. Cao, Z. Zhang, Y. Zheng, and C. Zhang, "Multiband and broadband polarization -insensitive perfect absorber devices based on a tunable and thin double split-ring metamaterial," Optics Express, vol. 23, pp. 3523-3533, 2015/02/09 2015.

[84] X. Liu, T. Starr, A. F. Starr, and W. J. Padilla, "Infrared spatial and frequency selective metamaterial with near-unity absorbance," Phys. Rev. Lett., vol. 104, p. 207403, // 2010.

140

[85] K. Tanaka, E. Plum, J. Y. Ou, T. Uchino, and N. I. Zheludev, "Multifold Enhancement of Quantum Dot Luminescence in Plasmonic Metamaterials," Physical Review Letters, vol. 105, Nov 24 2010.

[86] "CST Micwave Studio: A numerical simualtion software for electromagnetic computing, Computer Simulation Technology GmbH, Darmstadt, Germany. URL https://www.cst.com/," ed.

[87] D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B, vol. 65, p. 195104, // 2002.

[88] Y. Shen, J. Zhou, T. Liu, Y. Tao, R. Jiang, M. Liu, et al., "Plasmonic gold mushroom arrays with refractive index sensing figures of merit approaching the theoretical limit," Nature Communications, vol. 4, p. 2381, 2013.

[89] C. L. Holloway, A. Dienstfrey, E. F. Kuester, J. F. O'Hara, A. K. Azad, and A. J. Taylor, "A discussion on the interpretation and characterization of metafilms/metasurfaces: The Two-Dimensional Equivalent of Metamaterials," Metamaterials, vol. 3, p. 100, 2009.

[90] D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Physical Review B, vol. 65, p. 195104, May 15 2002.

[91] J. Jeon, K. Bhattarai, D.-K. Kim, J. O. Kim, A. Urbas, S. J. Lee, et al., "A Low-loss Metasurface Antireflection Coating on Dispersive Surface Plasmon Structure," Scientific Reports, vol. 6, p. 36190, 11/02/online 2016.

[92] T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys Rev E Stat Nonlin Soft Matter Phys, vol. 68, p. 065602, Dec 2003.

[93] J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, "Biosensing with plasmonic nanosensors," Nat Mater, vol. 7, pp. 442-453, 06//print 2008.

[94] A. J. Haes, L. Chang, W. L. Klein, and R. P. Van Duyne, "Detection of a Biomarker for Alzheimer's Disease from Synthetic and Clinical Samples Using a Nanoscale Optical Biosensor," Journal of the American Chemical Society, vol. 127, pp. 2264-2271, 2005/02/01 2005.

[95] K. A. Willets and R. P. Van Duyne, "Localized surface plasmon resonance spectroscopy and sensing," Annual Review of Physical Chemistry, vol. 58, pp. 267-297, 2007.

[96] A. B. Dahlin, J. O. Tegenfeldt, and F. Höök, "Improving the Instrumental Resolution of Sensors Based on Localized Surface Plasmon Resonance," Analytical Chemistry, vol. 78, pp. 4416-4423, 2006/07/01 2006.

[97] C. R. Yonzon, D. A. Stuart, X. Zhang, A. D. McFarland, C. L. Haynes, and R. P. Van Duyne, "Towards advanced chemical and biological nanosensors—An overview," Talanta, vol. 67, pp. 438-448, 9/15/ 2005.

[98] W. A. Murray and W. L. Barnes, "Plasmonic Materials," Advanced Materials, vol. 19, pp. 3771-3782, 2007.

[99] D. K. Gramotnev and S. I. Bozhevolnyi, "Plasmonics beyond the diffraction limit," Nat Photon, vol. 4, pp. 83-91, 02//print 2010.

[100] Y. Gong, L. Chang, K. L. Viola, P. N. Lacor, M. P. Lambert, C. E. Finch, et al., "Alzheimer's disease-affected brain: Presence of oligomeric Aβ ligands (ADDLs) suggests a molecular basis for reversible memory loss," Proceedings of the National Academy of Sciences, vol. 100, pp. 10417-10422, September 2, 2003 2003.

[101] J. Hardy and D. J. Selkoe, "The amyloid hypothesis of Alzheimer's disease: progress and problems on the road to therapeutics," Science, vol. 297, pp. 353-6, Jul 19 2002.

[102] Y. Shen, J. H. Zhou, T. R. Liu, Y. T. Tao, R. B. Jiang, M. X. Liu, et al., "Plasmonic gold mushroom arrays with refractive index sensing figures of merit approaching the theoretical limit," Nature Communications, vol. 4, Aug 2013.

141

[103] A. Dmitriev, C. Hagglund, S. Chen, H. Fredriksson, T. Pakizeh, M. Kall, et al., "Enhanced Nanoplasmonic Optical Sensors with Reduced Substrate Effect," Nano Letters, vol. 8, pp. 3893-3898, Nov 2008.

[104] C. M. Watts, X. Liu, and W. J. Padilla, "Metamaterial electromagnetic wave absorbers," Adv Mater, vol. 24, pp. Op98-120, op181, Jun 19 2012.

[105] X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, "Taming the Blackbody with Infrared Metamaterials as Selective Thermal Emitters," Physical Review Letters, vol. 107, Jul 18 2011.

[106] D. Xia, Z. Ku, S. C. Lee, and S. R. J. Brueck, "Nanostructures and Functional Materials Fabricated by Interferometric Lithography," Advanced Materials, vol. 23, pp. 147-179, 2011.

[107] S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science, vol. 306, pp. 1351-1353, Nov 19 2004.

[108] CST Micwave Studio, Computer Simulation Technology GmbH, Darmstadt, Germany. [109] M. A. Ordal, R. J. Bell, R. W. Alexander, L. L. Long, and M. R. Querry, "OPTICAL-

PROPERTIES OF 14 METALS IN THE INFRARED AND FAR INFRARED - AL, CO, CU, AU, FE, PB, MO, NI, PD, PT, AG, TI, V, AND W," Applied Optics, vol. 24, pp. 4493-4499, Dec 1985.

[110] E. Hutter and J. H. Fendler, "Exploitation of Localized Surface Plasmon Resonance," Advanced Materials, vol. 16, pp. 1685-1706, 2004.

[111] R. Ameling and H. Giessen, "Microcavity plasmonics: strong coupling of photonic cavities and plasmons," Laser & Photonics Reviews, vol. 7, pp. 141-169, 2013.

[112] G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, "Negative-index metamaterial at 780 nm wavelength," Optics Letters, vol. 32, pp. 53-55, Jan 1 2007.

[113] M. X. Ren, C. P. Pan, Q. Q. Li, W. Cai, X. Z. Zhang, Q. Wu, et al., "Isotropic spiral plasmonic metamaterial for sensing large refractive index change," Optics Letters, vol. 38, pp. 3133-3136, Aug 15 2013.

[114] Z. Liu, X. Xia, Y. Sun, H. Yang, R. Chen, B. Liu, et al., "Visible transmission response of nanoscale complementary metamaterials for sensing applications," Nanotechnology, vol. 23, Jul 11 2012.

[115] A. P. Blanchard-Dionne, L. Guyot, S. Patskovsky, R. Gordon, and M. Meunier, "Intensity based surface plasmon resonance sensor using a nanohole rectangular array," Optics Express, vol. 19, pp. 15041-15046, Aug 1 2011.

[116] N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, et al., "Planar Metamaterial Analogue of Electromagnetically Induced Transparency for Plasmonic Sensing," Nano Letters, vol. 10, pp. 1103-1107, Apr 2010.

[117] A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, et al., "Plasmonic nanorod metamaterials for biosensing," Nature Materials, vol. 8, pp. 867-871, Nov 2009.

[118] J. Becker, A. Trugler, A. Jakab, U. Hohenester, and C. Sonnichsen, "The Optimal Aspect Ratio of Gold Nanorods for Plasmonic Bio-sensing," Plasmonics, vol. 5, pp. 161-167, Jun 2010.

[119] H. young-tack, Y. i. Kim, M.-c. Lee, P. sunhee, S. dongha, C. M. Park, et al., "Post-etch residue removal in BCB/Cu interconnection structure," Thin Solid Films, vol. 435, pp. 238-241, 7/1/ 2003.

[120] D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Physical Review E, vol. 71, Mar 2005.

[121] H.-T. C. J. Zhou, T. Koschny, A. K. Azad, A. J. Taylor, C. M. Soukoulis, and J. F. O'Hara, "Application of metasurface description for multilayered metamaterials and an alternative theory for metamaterial perfect absorber," arXiv, 2011.

[122] H.-T. Chen, J. Zhou, J. F. O’Hara, F. Chen, A. K. Azad, and A. J. Taylor, "Antireflection Coating Using Metamaterials and Identification of Its Mechanism," Physical Review Letters, vol. 105, p. 073901, 08/09/ 2010.

142

[123] J. Kischkat, S. Peters, B. Gruska, M. Semtsiv, M. Chashnikova, M. Klinkmüller, et al., "Mid-infrared optical properties of thin films of aluminum oxide, titanium dioxide, silicon dioxide, aluminum nitride, and silicon nitride," Applied Optics, vol. 51, pp. 6789-6798, 2012/10/01 2012.

[124] W. R. Knolle and J. W. Osenbach, "The structure of plasma‐deposited silicon nitride films determined by infrared spectroscopy," Journal of Applied Physics, vol. 58, pp. 1248-1254, 1985.

[125] CST Microwave Studio 2013. [126] E. W. Max Born, Principles of Optics:Electromagnetic Theory of Propagation, Interference and

Diffraction of Light, 1999. [127] M. A. Ordal, R. J. Bell, R. W. Alexander, Jr., L. L. Long, and M. R. Querry, "Optical properties of

fourteen metals in the infrared and far infrared: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, and W," Appl Opt, vol. 24, p. 4493, Dec 15 1985.

[128] K. Bhattarai, Z. Ku, S. Silva, J. Jeon, J. O. Kim, S. J. Lee, et al., "A Large-Area, Mushroom-Capped Plasmonic Perfect Absorber: Refractive Index Sensing and Fabry–Perot Cavity Mechanism," Advanced Optical Materials, vol. 3, pp. 1779-1786, 2015.

[129] A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, "Planar Photonics with Metasurfaces," Science, vol. 339, March 15, 2013 2013.

[130] N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, et al., "Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction," Science, vol. 334, pp. 333-337, Oct 21 2011.

[131] S. J. Lee, Z. Ku, A. Barve, J. Montoya, W.-Y. Jang, S. R. J. Brueck, et al., "A monolithically integrated plasmonic infrared quantum dot camera," Nature Communications, vol. 2, p. 286, 04/19/online 2011.

[132] Z. Ku, W. Y. Jang, J. Zhou, J. O. Kim, A. V. Barve, S. Silva, et al., "Analysis of subwavelength metal hole array structure for the enhancement of back-illuminated quantum dot infrared photodetectors," Optics Express, vol. 21, pp. 4709-4716, Feb 25 2013.

[133] J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, "Mimicking Surface Plasmons with Structured Surfaces," Science, 2004.

[134] A. P. Hibbins, B. R. Evans, and J. R. Sambles, "Experimental Verification of Designer Surface Plasmons," Science, vol. 308, pp. 670-672, 2005.

[135] W. Zhang, A. K. Azad, J. Han, J. Xu, J. Chen, and X. C. Zhang, "Direct Observation of a Transition of a Surface Plasmon Resonance from a Photonic Crystal Effect," Physical Review Letters, vol. 98, p. 183901, 05/01/ 2007.

[136] A. K. Azad, H.-T. Chen, S. R. Kasarla, A. J. Taylor, Z. Tian, X. Lu, et al., "Ultrafast optical control of terahertz surface plasmons in subwavelength hole arrays at room temperature," Applied Physics Letters, vol. 95, p. 011105, 2009.

[137] S. Yin, X. Lu, N. Xu, S. Wang, Y. E, X. Pan, et al., "Spoof surface plasmon polaritons in terahertz transmission through subwavelength hole arrays analyzed by coupled oscillator model," Scientific Reports, vol. 5, p. 16440, 11/09/online 2015.

[138] D. Qu, D. Grischkowsky, and W. Zhang, "Terahertz transmission properties of thin, subwavelength metallic hole arrays," Optics Letters, vol. 29, pp. 896-898, 2004/04/15 2004.

[139] S. Yoon, J. Hwang, J. S. Kim, J. O. Kim, S.-W. Kang, W.-Y. Jang, et al. (2014, Incident angular dependence of surface plasmon polariton modes for thermal imaging. Electronics Letters 50(24), 1862-1864. Available: http://digital-library.theiet.org/content/journals/10.1049/el.2014.3153

[140] L. Chen, Y. Zhu, X. Zang, B. Cai, Z. Li, L. Xie, et al., "Mode splitting transmission effect of surface wave excitation through a metal hole array," Light Sci Appl, vol. 2, p. e60, 03/29/online 2013.

[141] F. Yang, J. R. Sambles, and G. W. Bradberry, "Long-range surface modes supported by thin films," Physical Review B, vol. 44, pp. 5855-5872, 09/15/ 1991.

143

APPENDICES

144

Appendix A: List of Publications

1. K. Bhattarai, Z. Ku, S. Silva, J. Jeon, J. O. Kim, S. J. Lee, et al., "A Large-Area, Mushroom-Capped

Plasmonic Perfect Absorber: Refractive Index Sensing and Fabry–Perot Cavity Mechanism,"

Advanced Optical Materials, pp. n/a-n/a, 2015.

2. K. Bhattarai, S. Silva, A. Urbas, S. J. Lee, Z. Ku, and J. Zhou, "Angle-dependent Spoof Surface

Plasmons in Metallic Hole Arrays at Terahertz Frequencies," IEEE Journal of Selected Topics in

Quantum Electronics, vol. PP, pp. 1-1, 2016.

3. M.S. Park*, K. Bhattarai*, D.K. Kim, S.W. Kang, J. O. Kim, J. Zhou, et al., "Enhanced transmission

due to antireflection coating layer at surface plasmon resonance wavelengths," Optics Express, vol.

22, pp. 30161-30169, 2014/12/01 2014.

* These two authors contributed equally

4. J. Jeon*, K. Bhattarai*, D.-K. Kim, J. O. Kim, A. Urbas, S. J. Lee, Z. Ku & J. Zhou, “A Low-loss

Metasurface Antireflection Coating on Dispersive Surface Plasmon Structure”, Scientific Report,6,

36190, (2016)

* These two authors contributed equally

5. S. Lin, K. Bhattarai, J. Zhou, and D. Talbayev, "Thin InSb layers with metallic gratings: a novel

platform for spectrally-selective THz plasmonic sensing," Optics Express, vol. 24, pp. 19448-19457,

2016/08/22 2016.

6. K. Song, C. Ding, Y. Liu, C. Luo, X. Zhao, K. Bhattarai, and J. Zhou,” Planar composite chiral

metamaterials with broadband dispersionless polarization rotation and high transmission”, Journal of

Applied Physics 120, 245102 (2016)

7. K. Song, M. Wang, Z. Su, C. Ding, Y. Liu, C. Luo, X. Zhao, K. Bhattarai, J. Zhou” Broadband

angle- and permittivity-insensitive nondispersive optical activity based on chiral metamaterials”.

[Submitted]

8. K. Bhattarai, S. Silva, K. Song, A. Urbas, S. J. Lee, Z. Ku, and J. Zhou, “Metamaterial perfect

absorber analyzed by a meta-cavity model consisting of multilayer metasurfaces”. [Submitted]

145

9. K. Bhattarai, Z. Ku, and J. Zhou, “manipulating permittivity of the meta-layer using resonator

for antireflection coating and explanation of its mechanism using multiple reflection

approach”. [In preparation]

10. K. Bhattarai, Z. Ku, and J. Zhou, “A THz plasmonic perfect absorber and Fabry-Perot cavity

mechanism”. [In preparation]

11. S. Silva, K. Bhattarai, K. Sonju and J. Zhou, “Enhancing harmonic generation using nonlinear

metamaterials”. [In preparation]

146

Appendix B: Conference Presentations

1. Khagendra Bhattarai, Sinhara Silva, Jiyeon Jeon, Junoh Kim, Sang Jun Lee, Zahyun Ku,

Jiangfeng Zhou, “A THz plasmonic perfect absorber and Fabry-Perot cavity mechanism

(Invited Paper)”, SPIE (Optics and Photonics) conference, August 28, 2016, San Diego, USA

2. Khagendra Bhattarai, Jiyeon Jeon, Jun Oh Kim, Zahyun Ku, Sang Jun Lee, Jiangfeng Zhou,

“A Metasurface Anti-reflection Coating for Enhancing Surface Plasmon-Polariton of

Metallic Hole Array”, American Physical Society, March.14, 2016, Baltimore, Maryland,

USA.

3. Khagendra Bhattarai, Zahyun Ku, Jiyeon Jeon, Jun Oh Kim, Sang Jun Lee, Jiangfeng Zhou,

6 “Anti-reflection coating using metasurface by enhancing surface plasmon polariton of

metal hole array”, 8th Annual Graduate Student and Post-Doctorate Research Symposium,

March.28, 2016, Tampa, FL, USA.

4. Khagendra Bhattarai, Sinhara R. Silva, Jiangfeng Zhou, “Splitting of the surface Plasmon

transmission peaks with polar and azimuthal angles due to incident of Terahertz wave on

Metal Hole Arrays(MHA)”, 7th Annual Graduate Student and Post-Doctorate Research

Symposium, March.10, 2015, Tampa, FL, USA.

5. Khagendra Bhattarai, Zahyun Ku, Jiangfeng Zhou “A mushroom shaped metamaterial

perfect absorber for refractive index sensing”,

American Physical Society, March.3, 2014, Denver, Colorado, USA.

6th Annual Graduate Student and Post-Doctorate Research Symposium, March.17,

2014, Tampa, FL, USA.

Appendi

J. Jeon, K

Antirefle

36190, 1

ix C: Copyr

K. Bhattarai

ction Coatin

1/02/online

right Permis

i, D.-K. Kim

ng on Dispe

2016

ssions

m, J. O. Kim,

ersive Surfac

147

A. Urbas, S

ce Plasmon

S. J. Lee, et a

Structure,"

al., "A Low-

Scientific R

-loss Metasu

Reports, vol.

urface

6, p.

K. Bhatta

Capped

Mechanis

arai, Z. Ku,

Plasmonic

sm," Advanc

S. Silva, J.

Perfect Ab

ced Optical M

Jeon, J. O.

bsorber: Re

Materials, vo

148

. Kim, S. J.

efractive In

ol. 3, pp. 17

Lee, et al.,

ndex Sensing

779-1786, 20

"A Large-A

g and Fab

015

Area, Mushr

bry-Perot C

room-

Cavity

M. S. Par

due to an

pp. 30161

rk, K. Bhattar

tireflection c

1-30169, Dec

rai, D. K. Kim

oating layer

1 2014

m, S. W. Kan

at surface pl

149

ng, J. O. Kim,

lasmon reson

, J. F. Zhou,

ance wavelen

et al., "Enha

ngths," Optic

anced transm

cs Express, vo

ission

ol. 22,

K. Bhatta

Plasmons

in Quant

arai, S. Silva

s in Metallic

tum Electron

a, A. Urbas,

c Hole Arra

nics, vol. PP,

S. J. Lee, Z

ays at Terah

, pp. 1-1, 20

150

Z. Ku, and J

ertz Frequen

16

J. Zhou, "An

ncies," IEEE

ngle-depende

E Journal of

ent Spoof Su

f Selected T

urface

Topics

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Documents

Interference of Light in Multilayer Metasurfaces: Perfect Absorber and Antireflection Coating