plasmonic optical antennas for enhanced light detection and emission a dissertation submitted to

PLASMONIC OPTICAL ANTENNAS

FOR ENHANCED LIGHT DETECTION AND EMISSION

A DISSERTATION

SUBMITTED TO THE DEPARTMENT OF MATERIALS SCIENCE

AND ENGINEERING

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

Edward Simon Barnard

August 2011

Abstract

Antennas are used across a wide range of frequencies in the electromagnetic spectrum to

concentrate wave energy into electronic circuits. The principles that govern the opera-

tion of conventional radio-frequency antennas can be extended to much higher frequencies

and be applied to produce nano-metallic (i. e. plasmonic) antennas that act as “receivers”

and “transmitters” for visible light. These traits make them excellent candidates for light

trapping in solar cells, light concentration in sub-wavelength photodetectors, or even lo-

calized heating for cancer therapies. The unique optical properties of metals at visible

frequencies makes it difficult to apply traditional antenna design rules. Using full-field

electromagnetic simulations and analytic antenna models, we developed new design rules

for producing optical antennas with a desired set of optical properties. We then apply these

design rules to create antennas that resonantly enhance absorption on thin silicon detectors

as well as enhance emission of cathodoluminescence (CL). Through spatial and spectral

mapping of both photocurrent and CL we clearly show the fundamental and higher-order

resonant modes of these antennas. With CL we are also able to map the spatial distribution

of these resonant modes with nanometer resolution. In addition to these specific demon-

strated applications, the results of this work enables optical engineers to more easily design

a myriad of plasmonic devices that employ optical antenna structures, including nanoscale

photodetectors, light sources, sensors, and modulators.

iv

Acknowledgements

[INCOMPLETE]

Funding: NSF, GCEP, KAUST

Acknowledge support from a National Science Foundation Graduate Research fellow-

ship, the Stanford Global Climate and Energy Project, and the National Science Founda-

tion.

Lizzie

Family

EJ and Toon

Brongersma group members

Mark

Collaborators

v

Contents

Abstract iv

Acknowledgements v

1 Introduction and Overview 11.1 Types of light concentrating antennas . . . . . . . . . . . . . . . . . . . . 2

1.2 Overview of Chapters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 Research Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 Spectral properties of optical antennas 112.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2 Optical properties of metallic films . . . . . . . . . . . . . . . . . . . . . . 13

2.3 Fabry-Perot resonator model . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.4 Local field enhancement . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.5 Determination of reflection amplitude and phase . . . . . . . . . . . . . . . 17

2.6 Fabry-Perot resonances in local field enhancement . . . . . . . . . . . . . . 20

2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3 Photocurrent mapping of near-field antenna absorption resonances 243.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2 Photocurrent measurements of nano-strip antennas . . . . . . . . . . . . . 29

3.3 In-coupling cross-section . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.4 Electromagnetic simulations of nano-strip antennas . . . . . . . . . . . . . 33

3.5 Application of antenna model to absorption resonances . . . . . . . . . . . 35

vi

3.6 Measurement of the optical conductivity of the metals used in an antenna . 37

3.7 Comparison to dark-field scattering . . . . . . . . . . . . . . . . . . . . . . 41

3.8 Photocurrent enhancement from a plasmonic grating . . . . . . . . . . . . 43

3.9 Dielectric Si nanowire antenna resonances . . . . . . . . . . . . . . . . . . 45

3.10 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4 Imaging emission modes of antennas by cathodoluminescence 504.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.2 Cathodoluminescence measurements . . . . . . . . . . . . . . . . . . . . . 52

4.3 Resonance trends of nano-strip antennas . . . . . . . . . . . . . . . . . . . 54

4.4 Resolving the spatial distribution of SPP resonances . . . . . . . . . . . . . 56

4.5 Short- and Long-Range SPP resonances . . . . . . . . . . . . . . . . . . . 58

4.6 Calculation of LDOS near antennas . . . . . . . . . . . . . . . . . . . . . 60

4.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5 Applications and future directions of optical antennas 625.1 Improving the efficiency of thin film solar cells . . . . . . . . . . . . . . . 62

5.2 Phase-coupled plasmon-induced transparency . . . . . . . . . . . . . . . . 65

5.3 Other applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5.4 Conclusions and future directions . . . . . . . . . . . . . . . . . . . . . . 69

A Generalized Design rules: Resonance Maps 70A.1 Resonance maps of strips in a uniform medium . . . . . . . . . . . . . . . 70

A.2 Application of resonance maps . . . . . . . . . . . . . . . . . . . . . . . . 72

B Cavity model derivations 75B.1 Normal-incidence plane-wave Fabry-Perot model . . . . . . . . . . . . . . 75

B.2 Local emitter Fabry-Perot model . . . . . . . . . . . . . . . . . . . . . . . 77

C Electromagnetic simulation methods 81C.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

C.2 Finite Difference Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . 82

C.3 Finite-difference time-domain method . . . . . . . . . . . . . . . . . . . . 83

vii

C.4 Finite-difference frequency-domain method . . . . . . . . . . . . . . . . . 85

C.5 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

D Fabrication of silicon on insulator (SOI) detectors 89

References 94

viii

List of Figures

1.1 Types of plasmonic optical antennas . . . . . . . . . . . . . . . . . . . . . 3

1.2 Overview of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1 Trends in properties of SR-SPPs on silver films . . . . . . . . . . . . . . . 14

2.2 Full-field simulation of an SR-SPP reflection . . . . . . . . . . . . . . . . 18

2.3 Resonance behavior of silver strips . . . . . . . . . . . . . . . . . . . . . . 21

2.4 Field intensity distributions for resonant silver strips . . . . . . . . . . . . . 23

3.1 Near-field SOI detector platform architecture . . . . . . . . . . . . . . . . 26

3.2 Spatial and spectral photocurrent mapping of a wedge antenna. . . . . . . . 31

3.3 Analysis of the resonant behavior using 2-dimensional finite difference fre-

quency domain (FDFD) simulations . . . . . . . . . . . . . . . . . . . . . 34

3.4 Theoretical and Experimental photocurrent enhancement maps. . . . . . . . 36

3.5 Effect of metal-loss on field intensity (|E|2) profiles . . . . . . . . . . . . . 38

3.6 Effect of metal loss on in-coupling cross-section of a Ag optical antenna . . 40

3.7 Comparison of dark-field light scattering experiments and near-field pho-

tocurrent mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.8 Photocurrent enhancement from a periodic plasmonic antenna array . . . . 44

3.9 Photocurrent enhancement from a silicon nanowire optical antenna . . . . . 46

4.1 Cathodoluminescence imaging of wedge antenna . . . . . . . . . . . . . . 53

4.2 Cathodoluminescence resonance trends . . . . . . . . . . . . . . . . . . . 55

4.3 Cathodoluminescence imaging of plasmon standing waves . . . . . . . . . 57

4.4 Plasmon mode profiles and LDOS simulations . . . . . . . . . . . . . . . . 59

ix

5.1 Photon management schemes for photovoltaics . . . . . . . . . . . . . . . 63

5.2 Plasmon-enhanced photovoltaic scheme . . . . . . . . . . . . . . . . . . . 64

5.3 Phase-coupled plasmon-induced transparency schematic . . . . . . . . . . 66

5.4 Phase-coupled plasmon-induced transparency results . . . . . . . . . . . . 67

A.1 Geometry of a strip antenna in a uniform medium. . . . . . . . . . . . . . . 71

A.2 Resonance parameter maps for a strip antenna in a uniform medium. . . . . 73

A.3 Application of resonance maps to finding Au and Ag antennas with similar

resonant properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

B.1 Schematic of the normal-incidence plane-wave Fabry-Perot model. . . . . . 76

B.2 Schematic of the local emitter Fabry-Perot model. . . . . . . . . . . . . . . 77

C.1 Time Stepping in FDTD . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

C.2 Schematic of the Yee cell . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

D.1 Process flow for fabrication of detector platform . . . . . . . . . . . . . . . 93

x

Chapter 1

Introduction and Overview

Antennas are across a wide range of frequencies in the electromagnetic spectrum to con-

centrate wave energy into electronic circuits and vice versa. Examples include televisions,

radios, cell phones, radar and many others. The principles that govern such radio-frequency

antennas can be extended to much higher frequencies and be applied to produce nanoscale

nano-metallic (i. e. plasmonic) antennas that act as “receivers” and “transmitters” for vis-

ible light. As will be shown in this thesis, these plasmonic antennas can efficiently con-

centrate light into a deep-subwavelength volume thus acting as receiving antennas. This

makes them ideally suited for use as light trapping structures in solar cells [1], as optical

couplers to ultra-compact photodetectors [2–6], as localized heaters for cancer therapies

[7], as enablers of single molecule Raman signal detection [8], or as heating elements that

facilitate nanostructure growth [9] and modification [10, 11]. Plasmonic antennas can also

efficiently enhance and redirect the emission of light from nanoscale light sources such as

excited atoms, molecules or quantum dots (thus acting as optical transmitters). However

the unique material properties of metals at visible frequencies makes it difficult to apply

traditional antenna design rules in optical antenna optimization. To address this, this thesis

shows new theoretical (Chapter 2) and experimental (Chapters 3 and 4) methods to un-

derstand, measure and optimize the resonant properties of these antennas. The results of

this work provide a framework for optical antenna designers to create optimized antennas

for their specific application. To that end, many applications of plasmonic antennas such

as solar cell light trapping [12], nanoscale photo-detection [6], Raman spectroscopy [13],

1

CHAPTER 1. INTRODUCTION AND OVERVIEW 2

light modulation [14], light focusing [15] and localized laser heating [16] are explored in

Chap. 5.

1.1 Types of light concentrating antennas

Researchers are investigating the optical properties of an increasing variety of metallic

nanostructures with the hope of effectively concentrating light into or extracting light from

nanoscale volumes. Physically, time-varying electric fields associated with light waves

exert a force on the gas of negatively charged electrons inside a metal and drive them into

a collective oscillation, known as a surface plasmon. At specific optical frequencies this

oscillation is resonantly driven to produce a very strong charge displacement and associated

electromagnetic (light) field concentration. The resonant structures come in two distinct

varieties: quasi-static (deep-subwavelength) or retardation-based (wavelength-scale).

1.1.1 Quasi-static antennas: Localized surface plasmon resonances

The quasi-static approximation for electromagnetics is valid when the size of a nanostruc-

ture is significantly smaller than the free-space wavelength of the incident light, such that

the entire structure experiences a uniform electric field at any instant in time. In this regime,

resonance effects can be determined by solving for the electrostatic potential for a struc-

ture of a given geometry and dielectric constant embedded within a uniform electric field.

Spherical nanoparticles, for instance, exhibit a dipolar plasmonic resonance at wavelengths

where εmetal =−2εdielectric. Although quasi-static resonance frequencies are independent of

particle size, metallic nanoparticles can be made resonant over a wide range of frequencies

by changing the type of metal, particle shape, or dielectric environment (Fig. 1.1a,b). A

number of very general, geometry-independent results can be derived for these resonators.

For instance, plasmon resonance occurs at a frequency where the energy inside the metal

and surrounding dielectric is equal. Furthermore, their resonant quality factor, Q, is solely

determined by the metal losses at the resonant frequency and cannot be changed by modi-

fying geometry [17].


Redshift

a

c d e

b

εm/εd

L

f

g

h

0 200near-eld enhancement

Figure 1.1: Types of plasmonic optical antennas (a) Effects of geometry and materials onelectrostatic resonances of deep subwavelength metal nanostructures. As the surroundingdielectric constant is increased the resonance for a spherical nanoparticle redshifts. Asthe aspect-ratio for a nanorod is increased the longitudinal resonance is redshifted [17]. (b)Resonant condition of the ratio of the dielectric constants in the metal and dielectric (εm/εd)as a function of aspect ratio parameter L for quasi-static spheroidal particles [18]. (c, d,e) Retardation-based strip resonators. Field intensity distributions normalized to incidentintensity for the lowest odd order resonances (m = 1,3,5) of 30 nm thick silver stripsat an illumination wavelength of lambda = 550 nm (Chap. 2). NSOM measurements (f)and FDTD simulations (g) illustrating SPP focusing using a tapered metal strip waveguide[19]. (h) Simulations show a large near-field enhancement in the feed-gap of a gold opticalantenna [20].


1.1.2 Wavelength scale antennas

When nanostructures have one or more dimensions approaching the excitation wavelength,

the optical phase can vary across the structure and it is necessary to consider retardation

(i. e. wave propagation) effects. This type of antenna is the focus of this thesis. The con-

cepts behind many retardation-based plasmonic light concentrators are based on scaled

radio frequency (RF) antenna designs, such as the half-wavelength dipole antenna. Such

scaling is non-trivial as metals exhibit finite conductivity and support more complex wave

propagation behavior at optical frequencies. Wavelength-scale nanometallic structures,

such as metal nanowires [21–23], or strips[24, 25], can be considered as truncated sur-

face plasmon-polariton (SPP) waveguides. SPPs propagate back and forth between the

metal terminations, creating a cavity resonator for SPPs. To first order, the resonant length

of such structures is thus equal to mλspp/2, where m is an integer and λspp is the wavelength

of the supported surface plasmon-polariton mode (Fig. 1.1c-e). In practice the phase pickup

upon reflection from the metal termination is non-neglible and can give rise to substantial

changes in the resonant length (see Chap. 2). These concepts can quite easily be extended

to other plasmonic waveguides consisting of two parallel-running metal structures to real-

ize metal-dielectric-metal (MDM) cavities. Since the MDM modes are not cut off when the

metal-to-metal spacing is reduced, fields can be concentrated effectively in truly nanoscale

volumes [26].

1.1.3 Collective Effects

Because of the small size of the resonators described above, dielectric lenses are typically

required to efficiently couple free-space light to the structure of interest. However, plas-

monic effects can also be used to funnel light from areas that are substantially larger than

the wavelength of light. In a plasmonic lens an engineered grating couples free-space pho-

tons to SPPs that then transport energy toward a central focus [cite whitejs]. If light hits

a grating with a grating constant, G, it can gain a momentum, 2πn/G, in the direction of

the periodicity, where n is an integer. This additional “momentum kick” enables the cou-

pling of normally incident light (with no in-plane momentum) to SPPs when the condition

λsp = 2π/G is satisfied [27, 28]. An example of this grating coupling is demonstrated in


Section 3.8 and used for solar applications in Chap. 5.

1.1.4 Non-resonant concentration

Non-resonant effects can also be used to further enhance light concentration. For instance,

strong subwavelength light localization in retardation-based resonators can be achieved by

introducing a small gap in the metal structure, known as a feedgap (Fig. 1.1h) [29]. Here,

one takes advantage of the fact that SPPs have an appreciable longitudinal electric field

component which jumps in magnitude by the ratio εm/εd of the metal and dielectric permit-

tivities (due to the electromagnetic boundary condition that requires the normal component

of εE to be continuous across the metal-dielectric interface) [25]. A more physical inter-

pretation attributes the high local fields to the build-up of charges of opposite sign across

the gap. Similar broadband dielectric contrast based enhancement of local field intensities

can be achieved via lightning-rod effects. The lightning rod effect occurs at a sharp metal

termination, where field continuity conditions force surface charges into a small area. The

effect can be described with electrostatics [30], but can also be used in unison with other

field enhancement strategies in larger retardation-based structures. Finally, we note that

plasmonic taper structures, such as metal cones or wedges, can also support broadband,

non-resonant enhancements. Such structures support SPP waves that display an increase in

wavevector and decrease in group velocity as they propagate towards their apex [31, 32].

As a result, an SPP launched near the base of a structure experiences considerable field

concentration as it propagates towards the tip (Fig. 1.1f,g).

1.2 Overview of Chapters

Chapter 2: Shrinking antennas to the nanoscale, a resonator model

Using both full-field electromagnetic simulations and analytical optical antenna models,

we first derived simple and intuitive design rules to achieve antennas with a desired set of

optical properties. We found that wavelength-scale antennas in the visible spectrum ex-

hibit similar, but quantitatively different, trends as compared to traditional radio-frequency


Figure 1.2: Overview of results (a) Schematic of the nano-strip antenna on the SOI de-tector platform. (b) Dark-field microscope image of antenna on detector. (c) CL emissionscans of resonant antenna lengths at λ = 700 nm showing experimentally measured plas-mon standing waves. (d) Plasmon standing wave modeled as two simultaneous resonantplasmons, shown with two different shadings.

(RF) antennas. While these two antenna regimes both show periodic length-dependent res-

onances that result from electromagnetic standing waves, they show very different resonant

antenna-length/resonant frequency ratios. This discrepancy is due to the metal’s frequency-

dependent material properties, such as dielectric constant and conductivity, which differ

significantly between visible and RF regimes. By accounting for these differences we were

the first to accurately predict and measure the resonant behavior of nano-strip antennas in

the light detection and emission experiments described below and in subsequent chapters.

Chapter 3: Mapping near-field concentration of receiver antennas forenhanced light detection

When designing a “receiving” optical antenna one needs not only our theoretical meth-

ods, but also experimental tools to measure and optimize the light concentrating ability of

the antenna. The goal was to assist in the antenna design by providing a convenient ex-

perimental platform to rapidly analyze and screen a wide variety of antenna designs. An

ideal platform would be inexpensive, be easy to implement, provide an accurate quanti-

tative measurement of the near-field enhancement produced by an antenna, and allow for


rapid screening of a large number of antennas. We developed such a platform using a

simple, inexpensive, large-area silicon-on-insulator (SOI) photodetector system (Fig. 1.2a

and b). Unlike current far-field methods, our platform allows for direct measurement of

the antenna’s near-field. As an example of its use, we measured the resonant behavior of

a plasmonic silver nano-strip antenna by both spatial and spectral photocurrent mapping.

These enhanced photocurrent maps showed resonance modes in excellent agreement with

our antenna model and demonstrated the antenna’s ability to strongly concentrate light in

the near-field.

Chapter 4: Nanoscale mapping of the transmitter antenna efficiency

The silver nano-strip antenna used on our detector device can also be used to enhance and

redirect light from a nanoscale emitter such as an atom, molecule or quantum dot. To

explore how an emitter’s light emission is affected by our antenna we performed scanning

cathodoluminescence (CL) microcopy to locally excite the antenna with an electron beam

and collect the emitted light. The electron beam excites surface plasmons on the antenna

in the same manner as a nanoscale emitter and thus is an excellent probe of the efficiency

of the antenna. We measured up to four high-order resonances that not only agreed with

our design rules for antenna resonance but also matched the resonances of the “receiving”

antenna. Additionally CL measures the relationship between light emission and emitter

position with 10 nm spatial resolution. This allowed us to both find the optimal emitter

position and clearly show that these antenna resonances are indeed due to electromagnetic

standing waves as illustrated in Fig. 1.2c. Surprisingly these high-resolution scans also

showed that, as a transmitting antenna, the nano-strip has two simultaneous resonances due

to two independent resonant plasmon-mode standing waves as modeled in Fig. 1.2d.

Chapter 5: Applications of optical antennas

In the final chapter we discuss many applications of optical antennas that have been de-

veloped recently including light trapping for photovoltaics, optical modulators, nano-scale

heating, and nano-scale photodetectors.


1.3 Research Outlook

There are a myriad of radio-frequency antenna designs that have been developed over the

past 100 years to fill the requirements of frequency, power, directivity, bandwidth, physical

size for the varied uses of antennas that we see everyday. We can leverage this knowledge

to create antennas that now operate at frequencies orders of magnitude higher in the optical

part of the spectrum (100’s of THz). This thesis shows that there is not a direct corre-

spondence between RF antennas and their optical analogs. But using the shown modeling

and measurement techniques of both antenna emission and collection efficiencies, the op-

timization of antennas for optics becomes possible. New applications of these plasmonic

antennas range from the immediately practical, such as faster photodetectors and more ef-

ficient solar cells, to the more far-reaching goals of on-chip optical networks and quantum

optical circuits.


Published works by the author

Chapter 1

• Jon A. Schuller, Edward S. Barnard, Wenshan Cai, Young Chul Jun, Justin S. White,

and Mark L. Brongersma. Plasmonics for extreme light concentration and manipu-

lation. Nat. Mater., 9(3):193–204, 03 2010.

Chapter 2

• Edward S. Barnard, Justin S. White, Anu Chandran, and Mark L. Brongersma. Spec-

tral properties of plasmonic resonator antennas. Opt. Express, 16(21):16529–16537,

2008.

Chapter 3

• Edward S. Barnard, Ragip A. Pala, and Mark L. Brongersma. Photocurrent mapping

of near-field optical antenna resonances. Accepted in Nat. Nano., 2011.

Chapter 4

• Edward S. Barnard, Toon Coenen, Ernst Jan R. Vesseur, Albert Polman, and Mark L.

Brongersma. Imaging the hidden modes of ultra-thin plasmonic strip antennas by

cathodoluminescence. Submitted to Nano Lett., 2011.

Chapter 5

• Ragip A. Pala, Justin White, Edward Barnard, John Liu, and Mark L. Brongersma.

Design of plasmonic thin-film solar cells with broadband absorption enhancements.

Adv. Mater., 21(34):3504 – 3509, Jun 2009.

• Rohan D. Kekatpure, Edward S. Barnard, Wenshan Cai, and Mark L. Brongersma.

Phase-coupled plasmon-induced transparency. Phys. Rev. Lett., 104(24):243902,

Jun 2010.


Other Related work

• Lieven Verslegers, Peter B. Catrysse, Zongfu Yu, Justin S. White, Edward S. Barnard,

Mark L. Brongersma, and Shanhui Fan. Planar lenses based on nanoscale slit arrays

in a metallic film. Nano Lett., 9(1):235–238, 11 2008.

• Justin S. White, Georgios Veronis, Zongfu Yu, Edward S. Barnard, Anu Chandran,

Shanhui Fan, and Mark L. Brongersma. Extraordinary optical absorption through

subwavelength slits. Opt. Lett., 34(5):686–688, 2009.

• T. Sikola, R. D. Kekatpure, E. S. Barnard, J. S. White, P. Van Dorpe, L. Brınek,

O. Tomanec, J. Zlamal, D. Y. Lei, Y. Sonnefraud, S. A. Maier, J. Humlıcek, and

M. L. Brongersma. Mid-IR plasmonic antennas on silicon-rich oxinitride absorbing

substrates: Nonlinear scaling of resonance wavelengths with antenna length. Appl.

Phys. Lett., 95(25):253109, 2009.

• Rohan D. Kekatpure, Aaron C. Hryciw, Edward S. Barnard, and Mark L. Brongersma.

Solving dielectric and plasmonic waveguide dispersion relations on a pocket calcu-

lator. Opt. Express, 17(26):24112–24129, 2009.

• Linyou Cao, Pengyu Fan, Edward S. Barnard, Ana M. Brown, and Mark L. Brongersma.

Tuning the color of silicon nanostructures. Nano Lett., 10(7):2649–2654, 2010.

• Jung-Sub Wi, Edward S. Barnard, Robert J. Wilson, Mingliang Zhang, Mary Tang,

Mark L. Brongersma, and Shan X. Wang. Sombrero-shaped plasmonic nanoparti-

cles with molecular-level sensitivity and multifunctionality. Accepted in ACS Nano,

2011.

Chapter 2

Spectral properties of plasmonic opticalantennas†

In this chapter we derive a simple cavity model that describes the optical resonances of

wavelength nano-strip antennas. To do this we use full-field electromagnetic simulations to

visualize the interaction of light with these antennas. By doing this we are able to extract

two components of the antenna’s resonance: surface plasmon polariton propagation and

plasmon reflection. These strip antennas exhibit retardation-based resonances resulting

from the constructive interference of counter propagating short-range surface plasmon-

polaritons (SR-SPPs) that reflect from the antenna terminations. Here we formulate a

Fabry-Perot cavity model that successfully predicts both the peak position and spectral

shape of their optical resonances. These quantities were first estimated using an intuitive

Fresnel reflection model and then calculated exactly using full-field simulations based on

the finite-difference frequency-domain (FDFD) method. With only three dimensionless

scaling parameters, the Fabry-Perot cavity model provides simple design rules for engi-

neering resonant properties of such plasmonic optical antennas.

†This Chapter follows closely the text and results published in Optics Express [33]

11

CHAPTER 2. SPECTRAL PROPERTIES OF OPTICAL ANTENNAS 12

2.1 Introduction

Recent advances in nanofabrication techniques have enabled the realization of a wide va-

riety of metallic nanostructure shapes and sizes [34]. Such structures provide a unique

and effective means to concentrate and manipulate light at the nanoscale through the ex-

citation of collective electron oscillations known as surface plasmons (SPs). In order to

take full advantage of this class of objects, it would be desirable to formulate simple de-

sign rules that can capture the essence of their operation, while hiding much of the internal

complexity [35, 36]. Deep subwavelength metallic nanoparticles exhibit localized SP exci-

tations which are electrostatic in nature and fairly well understood [17, 37]. Such particles

are already extensively used to concentrate light and have enabled a wide variety of optical

sensing and spectroscopy techniques, most notably Surface Enhanced Raman Spectroscopy

(SERS) [38–40].

More recently, metallic waveguide structures, such as wires and strips, have also gained

significant interest for their ability to support propagating SPs known as surface plasmon-

polaritons (SPPs). These SPPs are electron density waves propagating at a metal-dielectric

interface that exhibit a strong coupling to electromagnetic fields. The metallic nanos-

tructures that support SPPs thus can serve as miniature optical waveguides and their use

for chipscale optical information transport has been suggested [23, 41–44]. In addition,

it has recently been shown that retardation-based optical resonators can be constructed

by truncating such waveguides to wavelength-scale dimensions [21, 22, 45]. Local field-

enhancements can be achieved in these truncated structures through the excitation and con-

structive interference of SPP waves that propagate back and forth between the terminations

[45]. Because of their high radiation efficiency, these resonators can also be thought of

as optical analogs to traditional microwave antennas [46]. As these structures behave as

both resonators and antennas, they can logically be termed plasmonic resonator antennas

(PRAs) in analogy to dielectric resonator antennas [47]. This type of resonator antenna has

effectively been used for Raman spectroscopy and non-linear optics applications [20, 29].

The resonant lengths of these PRAs are strongly dependent on the SPP wavelength and

reflection phase [48]. While the calculation of the SPP wavelength can be accomplished

using well-established techniques [49, 50], the direct calculation of reflection phase has


only been performed more recently for the case of SPPs on thick metal films and for gap

SPPs [51, 52]. In addition, recent work has provided indirect estimates of reflection phase

for SPPs on strips from their resonant response to optical excitation [48, 53].

In this Chapter, we directly calculate both the reflection amplitude and phase for thin

metal film terminations using an intuitive Fresnel reflection model and full-field electro-

magnetic simulations. To our knowledge this is the first direct calculation of these re-

flection parameters for an SR-SPP reflecting off a terminated thin metal film. We then

develop a Fabry-Perot model that uses these parameters to predict the peak position and

spectral shape of the field-intensity resonances for metallic strips (truncated films) of dif-

ferent width, thickness, and optical material properties.

2.2 Optical properties of metallic films

A thin metallic film supports two distinct types of SPP modes: a long range SPP (LR-

SPP) and a short range SPP (SR-SPP) [49]. These two modes result from the coupling of

the SPPs supported by the two individual surfaces. In this study our focus is on the SR-

SPPs, which exhibit substantially increased mode indices and increased field-confinement

for films that are much thinner than the wavelength of light. These characteristics naturally

give rise to strong reflections off metal film terminations and can result in large local field

enhancements in wavelength-scale structures due to constructive interference effects. To

illustrate these useful properties of SR-SPPs we start by investigating their behavior on ex-

tended films of a thickness, t, with a metal dielectric constant, εm, which is embedded in a

dielectric with εd . Fig. 2.1(a) shows the significant increase in the real part of the SR-SPP

effective index, n′spp, with decreasing film thickness for a silver film in air. This increase in

n′spp for thinner films is related to a reduced mode size and increased overlap of the SR-SPP

mode with the metal. The plot shows similar trends in t/λo for three different free-space

wavelengths (λo = 500 nm, 600 nm, and 700 nm). With decreasing excitation wavelength

n′spp increases; the SR-SPP is slowed down due to a decrease in the magnitude of the the

metal dielectric constant and an increase in the mode overlap with the metal. Fig. 2.1(b)

shows the rapid decrease in the SR-SPP mode size with decreasing film thickness. Here,


0

1

2

3

4

5

n′ eff

(a)(a)(a)

εm =−7.8 +0.779i (Ag at 500 nm)

εm =−12.7 +1.08i (Ag at 600 nm)

εm =−18.3 +1.44i (Ag at 700 nm)

0.00 0.05 0.10 0.15 0.20

thickness (t/λo )

0.0

0.5

1.0

1.5

2.0

mod

esi

ze/λ

o (b)(b)(b)

0.0

0.5

1.0

|r|

(c)(c)(c)

0.00 0.05 0.10 0.15 0.20

thickness (t/λo )

0.0π

0.2π

0.4π

0.6π

φ(r

adia

ns) (d)(d)(d)

Figure 2.1: Trends in the guiding and reflection properties of short range surface plasmon-polaritions (SR-SPPs) supported by truncated silver films with normalized metal thickness,t/λo. The blue dotted, green dashed, and red solid curves show the trends for εm valuesthat correspond to silver at 500, 600, and 700 nm free-space wavelengths respectively. (a)Real part of the effective index, n′spp, of SR-SPP mode. (b) Mode size of the SR-SPP. (c)Reflection amplitude for an SR-SPP reflecting off of a silver film truncation. (d) Phasepickup for an SR-SPP reflecting off of a silver film truncation. (c) & (d): The thin lineswere calculated with the Fresnel reflection model and the thick lines were obtained fromfull-field simulations.


mode size is defined as the distance between the points in the two dielectric cladding re-

gions where the electric field decays to 1/e of its peak value. The calculations are based

on the analytic solutions to the SR-SPP mode [49] and the optical properties of silver are

taken from experimental data [54].

In contrast to SR-SPPs, the LR-SPP modes are poorly confined, exhibit low mode in-

dices, and provide little field enhancement [45]. LR-SPPs are ideally suited for the realiza-

tion of low-loss plasmonic components [55], but not for strip PRAs and thus these modes

are not further considered in this paper.

2.3 Fabry-Perot resonator model

A metallic strip, such as shown in Fig. 2.3(a), can be generated by truncating a silver

film of thickness t to a width w. When top-illuminated with the electric field polarized

along the x-direction, SR-SPPs will be excited at the truncations and start propagating

back and forth between the antenna end-faces. When the SR-SPP encounters an end-face

it will partially reflect and partially scatter into free-space modes. For a properly chosen

strip width, constructive interference of multiply-reflected SR-SPPs will occur and generate

resonantly enhanced fields in the vicinity of the strip.

It was recently suggested that the metal strip can be treated as a Fabry-Perot resonator

for SR-SPPs where the reflection phase can dramatically affect the resonance condition

[45]. In this study we will provide further evidence that wavelength-scale metallic struc-

tures behave as SR-SPP resonators. This is a valuable conclusion as it allows for a more

intuitive way of thinking about this class of structures. Since the properties of SR-SPPs

can be captured in just a few normalized geometric and materials parameters (w/λo, t/λo,

and εm/εd), it also enables a complete description of the resonant optical properties of

metal strips in terms of these normalized quantities. For example, the resonant width of

a metal strip can be written in terms of the SR-SPP wavelength (λspp = λo/n′spp) and re-

flection phase which only depend on t/λo and εm/εd . On resonance, the round trip phase

must be equal to an integer multiple of 2π . For the case of the metal strip this implies that


(2π/λspp)2wres,m +2φ = m2π where m is the order of the resonance. This then leads to

wres,m =mπ−φ( t

λo, εm

εd)

2π

λo

n′spp(t

λo, εm

εd)

(2.1)

From the equation, it is clear that a larger n′spp or a larger φ will result in a shorter wres,m. It is

worth noting that for structures exhibiting large reflection phases, our microwave intuition

that suggests wres,1 = λo/2 is insufficient to predict their resonant widths. Below we will

show that reflection phases exceeding π/2 can be expected in this system which can cause

shifts in the resonance width, wres,1, from λspp/2 to less than λspp/4.

2.4 Local field enhancement

One of the most exciting characteristics of nano-strip resonators is their ability to generate

local field enhancements for the resonant widths, wres,m. With the Fabry-Perot model,

the dependence of the field intensity at the end-faces, |Eend|2, can be found by summing

contributions from the multiply-reflected SR-SPPs that were launched onto the strip. A

simple addition of these fields gives

|Eend|2 ∝

∣∣∣∣∣(1−|r|eiφ eiksppw)(1− eiksppw)

1−|r|2ei 2φ ei 2ksppw

∣∣∣∣∣2

. (2.2)

In this equation we express |Eend|2 as a proportionality rather than an equality since the

(possibly frequency-dependent) coupling efficiency of the incident wave into SR-SPPs is

unknown. Note that for symmetry reasons only odd modes (m = 1,3,5...) can be excited

in the considered top-illumination geometry. Through a careful comparison to full-field

simulations, we will show that the frequency dependence of the coupling efficiency is weak

and the Fabry-Perot resonances occur where exp[i 2ksppw+ i2φ ] is close to unity, i.e. where

Eq. (2.1) holds, and the quantity in Eq. (2.2) is maximized. Note that the numerator in

Eq. (2.2) gives rise to an asymmetric line-shape as a function of w and slightly shifts (by

less than 5%) the resonance maximum from the wres,m predicted by Eq. (2.1). Interestingly,

the weak frequency dependence of the coupling also enables an accurate prediction of the


resonant line-shape and thus the quality factor, Q.

2.5 Determination of reflection amplitude and phase

2.5.1 Fresnel reflectivity model

In order to test the validity of the Fabry-Perot model, we first estimate the amplitude and

phase of SR-SPP reflection off of a film truncation using a Fresnel reflectivity model. In

this simple estimate, we treat the metal film as a uniform medium with an effective com-

plex refractive index nspp = kspp/ko, where kspp is the in-plane wave vector of the SR-SPP

supported by the film. Reflections from a termination are then obtained by considering a

plane wave propagating in a uniform medium of nspp and reflecting off a dielectric with an

index equal to that of the embedding medium (n = 1 in our case). The reflection amplitude,

|r|, and phase pickup, φ , for the SR-SPP wave can now be calculated based on this effective

index contrast using the well-known Fresnel equations [56]:

r = |r|eiφ =nspp−1nspp +1

. (2.3)

The thin lines in Fig. 2.1(c) show the dependence of the reflection amplitude on thick-

ness for the same εm values as in Fig. 2.1(a) and (b). For sufficiently thick films, the

reflection parameters asymptote as the SR-SPP becomes more like a SPP on a semi-infinite

metal film. However, as the film thickness is decreased, the increase in the SR-SPP mode

index leads to a larger reflection amplitude that tend towards unity for films that are thinner

than just a few percent of the free-space wavelength. Within the confines of the Fresnel re-

flection model, the reflection phase would be equal to zero for the case of a lossless metal.

However, real metals exhibit loss and give rise to a non-negligible phase pickup. For low-

loss noble metals this Fresnel reflection model predicts a small phase pickup as seen in

Fig. 2.1(d) for silver.


xo xm xe

Ei Er

x

y

z

Figure 2.2: Full-field simulation of an SR-SPP reflecting off of a metal film truncation. (a)Schematic of the simulation geometry showing the truncated metal film with the SR-SPPlaunch point (xo), end-face (xe), and measurement point (xm). (b) Incident, (c) total, and(d) reflected (total minus incident) tangential electric field, Ex, for a 30 nm thick silver filmexcited with a SR-SPP mode with a wavelength of λspp = 465 nm (free-space λo = 550nm).


2.5.2 Numerical simulations of reflection parameters

The Fresnel reflection model (Eq. (2.3)) is expected to underestimate the reflection ampli-

tude and phase because it does not take into account the significant mode mismatch between

the SR-SPP mode and the free-space modes it couples to at the end-faces. Fig. 2.1(b) shows

that the mode size can drop well below the free-space wavelength and modifications of the

reflection properties should be expected. To analyze these effects and more accurately pre-

dict the end-face reflection properties, we performed full-field finite-difference frequency-

domain (FDFD) simulations [57] to calculate the reflection amplitude and phase. FDFD

allows for the use of frequency-dependent optical constants determined from experiments

[54]. Fig. 2.2(a) shows the simulated geometry consisting of a semi-infinite metal film

with an abrupt truncation at which the SR-SPP will partially reflect and partially scatter

into free-space modes. To calculate |r| and φ at a frequency and film thickness of interest,

we launch an analytically-derived SR-SPP mode [49] from xo towards the end-face of the

slab at xe and monitor its reflection at xm.

To illustrate the procedure, Fig. 2.2(b) shows the tangential electric field distribution

of the incident, forward-propagating wave, Ex,i(x,y) for a 30 nm thick silver film at an

excitation (free-space) wavelength of 550 nm. Upon reaching the end-face, the SR-SPP

scatters and produces a total field Ex,tot(x,y) as shown in Fig. 2.2(c). Fig. 2.2(d) shows that

near the strip the difference field, Ex,tot(x,y)−Ex,i(x,y), is dominated by contributions from

a backward-propagating, reflected SR-SPP, as is expected for such a strongly bound mode.

For this reason we call this difference field the reflected field Ex,r(x,y). Sufficiently far from

the end-face and within the metal film Ex,r only has contributions from the reflected SR-

SPP wave. In those locations, (xm,ym), the phase and amplitude of the SR-SPP reflections

can be directly computed from our simulated field patterns. To determine the reflection

amplitude, |r|, and phase, φ , we first write out the incident, Ex,i, and reflected, Ex,r, SR-

SPP fields:

Ex,i(x,y) = Ex,o(y) eikspp(x−xo) (2.4)

Ex,r(x,y) = Ex,o(y) |r|eikspp(xe−xo)eiφ eikspp(xe−x). (2.5)

It is then straightforward to show that the complex reflection coefficient, r, for the SR-SPP


is given by the ratio of the incident and reflected fields as

r = |r|eiφ =Ex,r(xm,ym)

Ex,i(xm,ym)ei2kspp(xm−xe). (2.6)

The thick lines in Fig. 2.1(c) and (d) show the dependence of the simulated reflection

amplitude and phase on film thickness. These curves exhibit similar qualitative behavior

as those obtained from the Fresnel reflection model (thin lines). However, the full-field

simulations properly take into account the significant decrease in mode size with decreasing

film thickness (Fig. 2.1(b)) and thus predict stronger reflections and substantially larger

reflection phases. The rapid decrease in |r| with increasing film thickness can be explained

by both the decrease in the SPP effective index and the concurrent spreading of the SR-SPP

mode into the surrounding dielectric. The increased mode overlap of the now larger SR-

SPP mode gives rise to better coupling to free-space modes and thus a reduced reflection.

Unlike the Fresnel reflection model, these full-field simulations show a very significant

φ , in some cases exceeding π/2. Similar to the Fresnel reflection model, the reflection

phase pickup again tends towards zero as the metal thickness is decreased. This limit can

be explained by the fact that the reflection becomes almost perfect (r → 1). For large

film thicknesses (t/λo) the reflection phase increases and approaches the phase pickup of a

single-interface (semi-infinite) SPP reflection as the surface modes decouple.

2.6 Fabry-Perot resonances in local field enhancement

Using the methods to determine in |r| and φ in the previous section we can now assess

the usefulness of the Fabry-Perot model for predicting the spectral response of metallic

strips. To this end we will directly compare full-field simulations of the field enhancement

near strips with the Fabry-Perot model. For our simulations we consider a generic silver

strip, shown schematically in Fig. 2.3(a), with a given thickness (t = 30nm) in y, a width

(w) in x, and is infinite in z. The strip is top-illuminated under normal incidence by a

plane wave with an E-field parallel to the x-axis. Fig. 2.3(f) shows the simulated local field

intensity enhancement, |Eend/Eo|2, 4 nm outside of the end of the strip as a function of


/

x

y

z

Figure 2.3: Resonance behavior of 30 nm thick silver strips and comparison with Fabry-Perot models. Dashed blue lines correspond to the Fresnel reflection Fabry-Perot model andsolid red lines correspond to Fabry-Perot model with phase and reflection coefficient fromfull-field simulations. The dashed green indicates cuts from the full-field strip resonancemap. (a) Schematic of the simulated strip geometry. (b) Slice of resonance map and (c)Fabry-Perot model vs. strip width, w, at λo = 550 nm. (d) Slice of resonance map and(e) Fabry-Perot model vs. excitation wavelength, λo, at w = 0.8µm. (f) Resonance mapof 30 nm thick silver strips from full-field simulations. |Eend|2 is shown as a density plot,overlayed with predicted resonance peaks from Fabry-Perot models.


the strip width and incident wavelength. As predicted by the Fabry-Perot model, this near-

field intensity map indeed shows first-, third- and fifth-order resonances. Representative

horizontal and vertical cuts of this resonance map (dashed green lines in Fig. 2.3(c) and

(e) respectively) were made for a detailed comparison to the Fabry-Perot model. The field

intensity distributions corresponding to the resonant peaks in Fig. 3(c) show the odd order

resonant modes and the high field enhancement at the PRA end-faces (Fig. 2.4).

Figure 2.3(c) shows three resonances in the local field enhancement. From Eq. (2.1)

the spacing between these odd order resonances in wres,m is expected to match the SR-SPP

wavelength of λspp = 465 nm for the considered excitation wavelength of λo = 550 nm.

The differences between wres,1 and wres,3 is 445 nm, just 4.3% smaller than the SR-SPP

wavelength. This similarity to the surface plasmon wavelength was used previously to

argue that metal strips behave as SR-SPP resonators [58]. It is worth noting that the differ-

ence between the m = 3 and m = 5 resonance widths is less than 1 nm from the SR-SPP

wavelength. This indicates that for wide strips the local field intensity enhancement can

fully be attributed to resonating SR-SPPs and that narrow strips are dominantly, but not

purely SR-SPP resonators.

In Fig. 2.3(b) and (d) we have also calculated the local intensity enhancement obtained

the Fabry-Perot model (Eq. (2.2)). The dashed blue lines were calculated using |r| and

φ from the Fresnel reflection model. For this simple model the Fabry-Perot resonance

peaks occur at too large a width or too short a wavelength when compared to the full-

field simulations because this model significantly underestimates the phase pickup upon

reflection. The solid red curves in these Figs. were obtained by taking |r| and φ from

full-field reflection simulations as shown in Fig. 2.2. With these more accurate reflection

parameters the Fabry-Perot model predicts peak positions and spectral shapes that are in

agreement with full-field simulations of strips. The small observed deviations in the line-

shape and peak position may be attributed to minor contributions on the local intensity from

other modes as well as to the frequency-dependence of the coupling efficiency for free-

space waves into SR-SPPs. The close agreement between the full-field simulations and the

Fabry-Perot model further confirm that wavelength-scale strips behave as resonators for

SR-SPPs. It also shows that intuitive Fabry-Perot models can effectively be used to predict

not only the resonance positions, but also their line-shapes.


520

(c)

w=1040 nm0

4

12

1

20

2

2

Figure 2.4: Field intensity distributions (|E|2/|Eo|2) for the lowest order resonances(m = 1,3,5) of 30 nm thick silver strips at an illumination wavelength of λo = 550 nm.For this excitation wavelength wres,1 = 130 nm is shown in (a), wres,3 = 575 nm is shownin (b), and wres,5 = 1040 nm is shown in (c).

2.7 Conclusions

This study on the optical properties of metallic strips has provided further evidence that

wavelength-scale metallic structures behave as SR-SPP resonators. This is a valuable con-

clusion as the properties of SR-SPPs can be captured in terms of just a few normalized

geometric and materials parameters (w/λo, t/λo, and εm/εd). Moreover, it allows for the

SR-SPP reflection amplitudes and phases to be described in terms of these parameters. This

in-turn enables the construction of an intuitive Fabry-Perot model capable of predicting the

position and line-shapes of resonant metallic structures for a wide variety of choices for the

metal, surrounding dielectric, and structure geometries. Although we have only verified

applicability for strips, it is expected that these models can effectively be extended to other

wavelengths-scale structures of different cross-sectional shape. We anticipate that the pre-

sented concepts will provides optical engineers with a powerful framework for designing

the properties of this exciting new class of resonators.

Chapter 3

Photocurrent mapping of near-fieldoptical antenna absorption resonances†

In the previous chapter we derived a model that help us understand the resonances of op-

tical antennas. The question then arises, how do these antennas behave in the real world?

To validate our understanding of optical antennas, it is imperative to have experimental

methods to confirm the predictions of this model and to characterize effects that cannot be

simply modeled. This chapter shows the development and use of a photodetector platform

that allows one to measure the near-field light concentrating ability of optical antennas. The

resonant properties of such antennas are conventionally characterized by far-field light scat-

tering techniques. However, many applications require quantitative knowledge of the near-

field behavior and existing local field measurement techniques provide only relative, rather

than absolute, data. Here, we demonstrate a photodetector platform that uses a silicon-on-

insulator substrate to spectrally and spatially map the absolute values of enhanced fields

near any type of optical antenna by transducing local electric fields into photocurrent. We

are able to quantify the resonant optical and materials properties of nanoscale (∼ 50 nm)

and wavelength-scale (∼ 1 µm) metallic antennas as well as high refractive index semi-

conductor antennas. The data agree well with light scattering measurements, full-field

simulations and the intuitive resonator models seen in the previous chapter.

†This Chapter follows closely the text and results to be published in Nature Nanotechnology [59]

24

CHAPTER 3. NEAR-FIELD ANTENNA ABSORPTION RESONANCES 25

3.1 Introduction

Optical antennas, either plasmonic [20, 60–64] or dielectric [65, 66], can efficiently con-

centrate light into a deep- subwavelength volume. This makes them ideally suited for use

as light trapping structures in solar cells [1], as optical couplers to ultra-compact photode-

tectors [2–6], as localized heaters for cancer therapies [7], as enablers of single molecule

Raman signal detection [8], or as heating elements that facilitate nanostructure growth [9]

and modification [10, 11]. For these applications it is critical to quantify the absolute effi-

ciency with which light is concentrated in the vicinity of the antenna. Unfortunately, cur-

rent experimental methods are unable to measure this near-field enhancement in an absolute

manner. While high resolution techniques such as near-field scanning optical microscopy

[67–69], electron energy loss spectroscopy [70], and two-photon luminescence [71] can

spatially map the relative variations in field strength near antennas, it is still very challeng-

ing to extract the absolute local field intensity with these tools. Likewise, light scattering

measurements can accurately measure far-field resonances but the results of these experi-

ments cannot directly probe the near-field properties of the antenna. In addition to exper-

imental methods, full-field electromagnetic simulations have furthered the understanding

of antenna properties, but the accuracy of these simulations is limited due to their reliance

on tabulated material properties of bulk materials. Real-world nanostructures often possess

less ideal optical properties than those tabulated for bulk (often single crystal) materials

and thus exhibit a light-concentrating ability lower than predictions. This can be due to

finite size effects, poor surface passivation, polycrystallinity, and the presence of chemical

impurities [37]. Because of the current experimental limitations and non-ideality of nanos-

tructures, it would be highly desirable to have experimental techniques that are capable of

quantifying both the absolute field concentrating ability of antennas and the real optical

properties of nano-structured antenna materials.

As good experimental techniques for quantifying optical fields near antennas are lack-

ing, their design and optimization for specific applications heavily relies on extensive full-

field simulations. The goal of the present work is to assist in the antenna design by pro-

viding a convenient experimental platform to rapidly analyze a wide variety of antenna

designs. An ideal platform would be inexpensive, easy to implement, provide an accurate


Figure 3.1: Near-field SOI detector platform architecture.(a) Schematic of the silicon-on-insulator (SOI) photodetector platform that was developed to explore near-field reso-nances of optical antennas. The platform was first evaluated by analyzing the ability of aplasmonic wedge antenna to concentrate light into the ultra-thin (40 nm) Si layer. At vari-ous resonant widths of the wedge, the antenna’s near-field produces an enhanced photocur-rent that is laterally collected via the electrical contacts. (b) Top-view scanning electronmicroscopy image of a silver wedge antenna placed onto the SOI detector platform. (c)Dark-field optical image of the same wedge shown in (b). Scale bars are 10 µm.


quantitative measurement of the near-field enhancement produced by an antenna, and allow

for rapid screening of large numbers of antennas. Here, we propose the use of a simple,

inexpensive, large-area detector platform based on silicon-on-insulator (SOI) technology

(see Fig. 3.1). SOI wafers are commercially available and detectors can be fabricated inex-

pensively by leveraging mature Si processing techniques. We focused on the development

of a metal-semiconductor-metal (MSM) detector platform in the thin Si layer of an SOI

wafer. Such detectors are well-known for their linear response, high-speed response, and

excellent signal-to-noise ratio. The placement of an antenna on top of such a detector en-

ables a direct, quantitative measurement of the local electric field enhancement near the

antenna through a simple photocurrent measurement. This follows from the fact that the

light absorption in the thin Si layer, and thus the photocurrent generation, is directly propor-

tional to the square of the local electric field in the Si layer. These fields can be enhanced

by the presence of a properly designed antenna. The Si device layer in SOI wafers can

be extremely thin (just a few tens of nanometers), allowing access to the true near-fields

of an antenna. By illuminating the antenna at different wavelengths, spectral information

can be obtained on the antenna’s resonant properties. We illustrate the usefulness of this

platform by spatially and spectrally mapping the fundamental and higher order resonances

of plasmonic as well as semiconductor antennas.

Near-field photodetector platform

The goal of the present work is to assist in the antenna design by providing a convenient

experimental platform to rapidly analyze the real performance of a wide variety of antenna

designs. An ideal platform would be inexpensive, easy to implement, provide an accurate

quantitative measurement of the near-field enhancement produced by an antenna, and allow

for rapid screening of large numbers of antennas. Here, we propose the use of a simple,

inexpensive, large-area photodetector platform based on silicon-on-insulator (SOI) technol-

ogy (see Fig. 3.1). SOI wafers are commercially available and detectors can be fabricated

inexpensively by leveraging mature Si processing techniques. We focused on the develop-

ment of a metal-semiconductor-metal (MSM) detector platform in the thin Si layer of an


SOI wafer. Such detectors are well-known for their linearity, high-speed response, and ex-

cellent signal-to-noise ratio. The placement of an antenna on top of such a detector enables

a direct, quantitative and absolute measurement of the local electric field enhancement near

the antenna through a simple optical-beam induced photocurrent [72] measurement. This

follows from the fact that the light absorption in the thin Si layer, and thus the photocurrent

generation, is directly proportional to the square of the local electric field in the Si layer.

These fields can be enhanced by the presence of a properly designed antenna. The Si device

layer in SOI wafers can be extremely thin (just a few tens of nanometers), allowing access

to the true near-fields of an antenna. By illuminating the antenna at different wavelengths,

spectral information can be obtained on the antennas resonant properties. We illustrate the

usefulness of this platform by spatially and spectrally mapping the fundamental and higher

order resonances of plasmonic as well as semiconductor antennas.

Figure 3.1a shows a fabricated thin, SOI-based photodetector with one type of antenna

that we will investigate: an adiabatically-tapered Ag wedge. At the heart of the detector is a

40 nm thick Si layer covered with a 20 nm thermally grown oxide. This oxide serves to both

electrically passivate the Si and to optically space the antennas from the absorbing Si. From

simulation studies on solar cells, optical spacers less than 10 nm in thickness were found

to cause notable damping and spectral shifts of antenna resonances [12]. Ti and Ni Schot-

tky contacts were patterned to create an asymmetric metal-semiconductor-metal (MSM)

photodiode. This configuration is known for its high-speed and low-noise operation [73].

The lateral spacing of the metallic contacts in our detector platform is larger than typical

for commercial MSM detectors to allow for placement of a large number of antennas be-

tween the contacts. The maximum useful contact spacing is limited by the minority carrier

diffusion length in the active semiconductor layer. Antennas generated with a wide vari-

ety of fabrication techniques can be tested on this platform, including those made through

chemical synthesis, electron beam lithography, and nano-imprint lithography. Focused ion

beam (FIB) techniques were found to substantially deteriorate the electrical properties of

the device platform and thus FIB-milled antennas can only be tested with thicker spacer

oxides.

Detector devices were fabricated on a commercially-available silicon-on-insulator (SOI)


wafer. The active silicon layer was thinned to 40 nm using thermal oxidation and wet etch-

ing. This left a 20 nm thick spacer oxide on top of the active silicon layer. Ti and Ni

Schottky contacts were patterned using optical lithography followed by an oxide etch and

a subsequent metal evaporation step. Excess metal was then removed by lift-off, forming

back-to-back Schottky diodes. A silver (Ag) wedge antenna was patterned by electron-

beam lithography and deposited using electron-beam evaporation followed by lift-off pro-

cessing. A 2 nm germanium wetting layer was used before metal deposition to reduce metal

roughness [74]. The Ag wedge antenna was 20 nm thick and its width varied from 50 nm

to 1 µm over a length of 100 µm. Finally, a 5 nm conformal alumina film was deposited

using atomic layer deposition to protect the Ag plasmonic structure from rapid environmen-

tal degradation. Silicon nanowire antennas were produced using the VLS growth method

using a gold catalyst on a Si substrate. Wires are sonicated off the growth substrate and

drop-cast onto the detector platform.

To spectrally analyze and spatially map the resonant behavior of the optical antennas

we constructed an optical system capable of generating photocurrent maps of antennas at

a multitude of wavelengths. Light at various wavelengths was obtained from a white-light

supercontinuum source (Fianium) that was filtered through a tunable monochromator (Ac-

ton). This light was then polarized with the electric field normal to the long wedge structure

and focused onto the sample to a 1.2 µm Gaussian spot using a 50× (NA = 0.42) objective

(Mitutoyo). The polarization direction was chosen to allow for efficient excitation of SPPs

along the width of the wedge (horizontal direction). The detector platform was mounted

on a 3-axis piezo stage to allow accurate focusing and spatial control over the location of

the excitation spot. Finally, the photocurrent maps were generated by raster-scanning the

illumination spot over the antenna and plotting the photocurrent as a function of the posi-

tion of the illumination spot. To increase the signal-to-noise ratio, the illumination beam

was chopped and the photocurrent was measured using a lock-in technique.

3.2 Photocurrent measurements of nano-strip antennas

To explore the usefulness of our detector as a general platform for mapping the resonant

properties of optical antennas, we first explored a well-studied optical antenna known and


a plasmonic resonator antenna. PRAs have recently gained significant popularity for use in

devices and light scattering applications as they feature a large ratio of the scattering and

absorption cross sections, which minimizes dissipation losses in the metal. Because these

structures have at least one dimension comparable to the wavelength of light, their reso-

nant properties are dominated by retardation effects rather than quasi-electrostatics. As a

result, PRAs exhibit strong standing wave resonances of surface plasmon-polaritons (SPPs)

[21, 45]. In fact, design rules based on radio-frequency antenna design can be applied to

such antennas [33], allowing engineers to simply adjust geometric parameters to tune the

resonance. The tapered Ag wedge shown in Figs. 3.1 a-c can locally be viewed as a strip

PRA of a specific width, allowing for study of many antenna sizes within one fabricated

structure. It was fabricated using electron-beam lithography and lift-off processing. The

wedge was 20 nm thick and its width varied adiabatically from 50 nm to 1 µm over a dis-

tance of 100 µm. The antenna dimensions were chosen to cover the size ranges that are of

high current interest to the materials, chemistry, and physics communities. They include

deep subwavelength antenna that exhibit quasi-static resonances as well as wavelength-

scale antennas that support retardation-based resonances [63].

To analyze the resonant behavior of the Ag wedge, we generated photocurrent maps at

different wavelengths. The maps were generated by raster-scanning a focused light beam

over the antenna structure and plotting the photocurrent at the different locations of the

illumination spot (see Methods). Figure 3.2a shows a photocurrent map of the wedge taken

at a fixed illumination wavelength of 700 nm. In the regions away from the antenna we ob-

served a uniform photocurrent response corresponding to the level of photoabsorption in the

bare detector platform. The map also shows regions in which the wedge structure enhanced

or suppressed the photocurrent compared to the background level. Figure 3.2b shows the

magnitude of the photocurrent enhancement along the length of the wedge, which was ex-

tracted from the photocurrent map in Fig. 3.2a. From this line-scan we clearly observe a

strong peak in photocurrent enhancement where the width of the wedge is about 95 nm.

Additionally we see a smaller peak near w = 320 nm followed by a sharp transition to

photocurrent suppression. Figures 3.2c and d show similar line-scans performed at longer

wavelengths of 750 nm and 800 nm. From these scans it becomes clear that the various

spectral features are wavelength-dependent: as the excitation wavelength increases (red


a b c d

Ja/Jo Ja/Jo Ja/Jo

Ja/Jo

Figure 3.2: Spatial and spectral photocurrent mapping of a wedge antenna. (a) Spatialmap of the photocurrent enhancement ratio measured for the wedge antenna shown inFigs. 3.1b and c by using an illumination wavelength of λo = 700 nm. The red regionsindicate photocurrent enhancements and the blue regions show suppression in photocur-rent. The scale bar is 5 µm. (b-d) Photocurrent enhancement line-scans along the lengthof the wedge taken at (b) λo = 700 nm, (c) λo = 750 nm, (d) λo = 800 nm. The horizon-tal dotted lines demarcate the narrow end of the wedge structure at w = 50 nm. Arrowsin (a) and (b) point to photocurrent enhancement resonances observed at w = 95 nm andw = 320 nm.


shifts), the resonances shift to spatial locations where the wedge is wider.

3.3 In-coupling cross-section

Before analyzing the scaling behavior of the observed resonances, it is important to note

that the measured photocurrent enhancement does not simply depend on the antenna prop-

erties alone; the measurement enhancement is also a function of the Gaussian illumination

spot size. When the spot size is chosen to be significantly larger than the antenna, much of

the light will interact with the bare detector and the measured photocurrent enhancement

is decreased. To enable a fair comparison of different antenna structures, the current en-

hancement can be quantified in terms of a spot-size independent quantity: the incoupling

cross-section σi, which is defined in terms of the measured enhancement ratio Ja/Jo:

Ja

Jo= 1+

σi

Ao. (3.1)

Here Ja and Jo are the measured photocurrents with and without the antenna, respectively;

Ao is the illumination area (spot-size). The incoupling cross-section, σi, thus quantifies the

antennas ability to couple incident free space photons into the absorbing Si layer. It can be

directly correlated to the near-field optical intensity inside the Si layer below the antenna.

According to this definition, a negative value for the cross-section results if the presence

of the antenna causes a reduction in the photocurrent (e.g. by reflecting the incident light).

Since the strip antenna is invariant in one direction, the cross-section is expressed as a

length rather than an area. Using Eq. 3.1 we can express our results in terms of σi: the

range of photocurrent enhancement ratios, Ja/Jo, from 0.75 to 1.25 in Fig. 3.2 corresponds

to a range of σi from −300 nm to +300 nm using the measured illumination spot size of

1.2 µm.


3.4 Electromagnetic simulations of nano-strip antennas

To understand the experimentally observed resonant behavior, we analyzed the field con-

centration by strip antennas into the thin Si layer with full-field, two-dimensional finite-

difference frequency-domain (FDFD) simulations. Experimental optical constants for met-

als [54] and dielectrics were used. The grid spacing was set to 1 nm and simulations were

checked for grid spacing convergence. Figure 3.3a shows the calculated PRA-mediated in-

coupling cross-section, σi, (and equivalent absorption enhancement) as a function of strip

width for an planewave illumination wavelength of λo = 700 nm. To compare to experi-

ments we assumed an illumination spot, Ao, of 1.2 µm. This cross-section and the absorp-

tion enhancement were calculated by integrating the absorption within the silicon layer and

normalizing it by the absorption with the plasmonic antenna absent. Similar to Figs. 3.2b-d,

a number of peaks in the photocurrent enhancement are observed as a function of increas-

ing strip width. These correspond to resonant widths for which the field near the antenna

is substantially enhanced. Figures 3.3b,c,d show the magnetic field distributions for strips

with a resonant widths of w = 620 nm, 350 nm, and 90 nm, respectively. The latter two

resonance widths correspond to the resonances observed experimentally in Fig. 3.2b. From

the field maps in Fig. 3.3 it is evident that the plasmonic antenna supports SPP standing

wave resonances and that the excitation of the resonant modes facilitate light concentration

into the Si detector layer. For top-illuminated strips, the excitation of resonances with an

even number of half-wavelengths is symmetry forbidden and only the resonances with an

odd number of half-wavelengths produce enhancements in the photocurrent [45].

The simulated and experimentally-observed photocurrent enhancements are in good

qualitative and reasonable quantitative agreement. The magnitude of the enhancements

observed at the resonant widths of 350 nm, and 90 nm are similar to those obtained in the

simulations. The resonance peaks are broadened, which is possibly related to imperfections

in the fabricated Ag wedge (e.g. roughness), the quality of the deposited Ag (e.g. single

crystal vs. nanocrystalline or impurity content), environmental degradation of the Ag, or

adsorption of undesired chemicals. Such differences between experiments and theory fur-

ther exemplify the need to acquire experimental data on real, fabricated structures rather

than to rely on simulations alone for antenna and device design. It is also worth noting that


b

c

d

a

strip

wid

th(n

m)

1.0 1.50.5

λo = 700 nm

600

400

600

0

– 0.6 + 0.6 0.0 σi ( µm )Ja/Jo (spot size 1.2 µm)

SiO2

Si SiO2

Ag

Figure 3.3: Analysis of the resonant behavior using 2-dimensional finite differencefrequency domain (FDFD) simulations. (a) Simulated photocurrent enhancement ratioand equivalent incoupling cross-section (x-axis) as a function of strip width at λo = 700 nm.(b-d) Cross-sectional magnetic field maps of resonant metallic strips placed on the SOIdetector. The strip widths are (b) 620 nm (c) 350 nm (d) 90 nm and the illuminationwavelength was at λo = 700 nm. Scale bars are 50 nm.

both the experimental and simulated resonances exhibit a pronounced asymmetry. This

asymmetry can be ascribed to interference effects between the incident wave and scattered

waves by the antenna. Constructive interference in the forward direction (into the detecting

layer) occurs for frequencies below resonance and destructive interference occurs above

the resonance frequency.

It is important to note that the resonance peak predicted at the larger width of w =

620 nm is missing in experimental data (Fig. 3.2). In fact, a photocurrent suppression is

observed in our experiments at this width. This mismatch can be explained based on the

choice of spot size in our experiment (1.2 µm). Our simulation assumed a plane wave

illumination and an illumination area that is substantially bigger than the antenna. This

condition is not well-satisfied for the widest area of the wedge, where the relatively small

illumination spot is incapable of efficiently exciting the antenna and the incident light is

mainly reflected. This brings up the important point that in our measurements there is

a trade-off in the ability to spatially and spectrally resolve features of optical antennas.

Depending on the goal of the experiment and the required imaging speed, a proper choice


of spot size can be made.

By performing a large set of simulations similar to Fig. 3.3a for different illumina-

tion wavelengths, it is possible to generate a two-dimensional resonance map, as shown

in Fig. 3.4a. This map quantifies the predicted photocurrent enhancements as a function

of both the illumination wavelength and the strip width. It again shows that multiple res-

onances occur at any illumination wavelength and that these resonances red-shift with in-

creasing strip width. Before we analyze the performance of our test platform by comparing

this simulated enhancement map to an experimental map, we will explain the trends in this

map.

3.5 Application of antenna model to absorption resonances

The observed resonant behavior can be understood in terms of an intuitive model that treats

each section of the wedge as a Fabry-Perot resonator for SPPs as described in Chap. 2. Be-

cause of the slow tapering of the wedge, different sections along the wedge can be viewed

as strips of more-or-less constant width. When a strip is illuminated with light polarized

normal to the strip, SPPs will be launched onto the strip from both ends. For thin strips, the

launched SPPs exhibit a high effective mode index and strong confinement. This results in

strong reflections when the SPPs reach the opposing end of the strip. At specific resonance

widths, multiple reflections give rise to a SPP standing wave that produces a high field in

the vicinity of the antenna. The high fields near the antenna intersect the thin Si layer and

cause a measurable increase in the photocurrent. For RF antennas, the resonant widths are

given by wres,m = m λo/2, where λo is the free space illumination wavelength and m is the

mode order. To find the resonant widths of an optical antenna, one needs to correct for the

shorter SPP wavelength and as well as the phase that SPPs pick up upon reflection of the

strip terminations [21, 33, 45]:

wres,m =

[m− φ

π

]λ

2 nspp. (3.2)

Here wres,m is the width of the strip where the m-th order resonance condition is satisfied,

nspp is the mode index of the SPP, and φ is the phase that is picked up when the SPP reflects


b

a

Figure 3.4: Theoretical and Experimental photocurrent enhancement maps. (a) Theo-retical and (b) experimental photocurrent enhancement maps that show the enhancement ra-tio in photocurrent produced by a wedge at different incident wavelengths and strip widthsgiven an illumination spot size of 1.2 µm. Dotted line at w = 50 nm denotes start ofthe wedge antenna. (a,b) Overlaid lines are the predictions from a Fabry-Perot resonatormodel. Solid and dashed lines correspond to different order resonances (m = 1, and m = 3,respectively).


from the strip edges. These values of nspp and φ can be determined according previously

established procedures [33] and have also been determined experimentally [53]. Physically,

the above resonance condition corresponds to a situation where the round-trip phase for

an SPP oscillating on the strip equals an integer multiple of 2π . This resonator model

predicts the appearance of multiple resonance orders. It also predicts that the resonant

wavelength of the antennas will shift to the red as the width increases. The black overlaid

lines in Figs. 3.4a and b show the predicted resonance locations according to this Fabry-

Perot model. These lines correspond to the first two odd (λ/2 (m = 1) and 3λ/2 (m = 3))

resonances of the strip. The dependence of the resonance properties on size predicted by

the Fabry-Perot model are also observed in far-field light scattering measurements (See

Section 3.7)

To compare the above simulated resonance maps to experiments, we measured the

spectral photocurrent enhancements at a large number of positions along the length of the

wedge. By taking such scans over a wide wavelength range from 500 to 900 nm we were

able to create the experimental photocurrent enhancement map shown in Fig. 3.4b. This

experimental map shows good qualitative and reasonable quantitative agreement with the

simulation results in Fig. 3.4a. The predicted photocurrent enhancements are similar to the

measured ones for those parts of the wedge where the spot size is significantly larger than

the wedge. The lowest order resonances exhibit the expected, slow red-shift with increas-

ing strip width. To further analyze the performance of the platform, we also explored light

concentration by antenna arrays. The measurements on arrays show efficient coupling to

wave-guided modes in the thin Si layer in addition to the near-field light concentration (See

section 3.7).

3.6 Measurement of the optical conductivity of the metals

used in an antenna

The silicon-on-insulator (SOI) detector platform described in this chapter is capable of

quantifying volume-averaged near-field enhancement near optical antennas. The attainable

field enhancements are a strong function of the metal’s conductivity at optical frequencies.


a

b

c

Figure 3.5: Effect of metal-loss on field intensity (|E|2) profiles. Shown is the 3λspp/2resonance (w = 350 nm) at λo = 700 nm. All figures are plotted on the same intensity scalein units of |E/Eo|2. Scale bars are 50 nm. Inset graphs represent the intensity 10 nm abovethe antenna. Each is normalized to its maximum. (a) Metal with half the bulk loss (εm =−18.35− 0.7i). (b) Metal modeled with standard bulk properties (εm = −18.35− 1.4i).(c) Metal modeled with twice the bulk loss (εm =−18.35−2.8i).


It is well known that the conductivity at optical frequencies can vary substantially in metal

nanostructures due to electrons scattering from surfaces, grain-boundaries, impurities, and

via other mechanisms that depend on the nanostructure’s geometry and deposition condi-

tions [23, 37]. Here we show how our SOI detector platform can quantify the conductivity

of the Ag in the plasmon resonator antenna described in the main text. We also show that

a near-field tip-based imaging approach would be less suited to observe such changes in

conductivity. To do this we perform full-field simulations to quantify the change to the

in-coupling cross-section of the antenna with varying degrees of metal loss (or conversely

conductivity) and compare these simulations with experimental results.

Using fits to experimental data from Rakic et al. we find that the bulk Ag dielectric

constant ε ′+ iε ′′ = −18.35− 1.4i at λo = 700 nm [54]. In Fig. 3.5 we plot the simulated

field patterns (|E|2) of the 3λspp/2 resonant structure (at λo = 700 nm) at different metal

losses. In these simulations we vary the conductivity σ of the silver by changing the imag-

inary part of epsilon, which is related to σ by ε ′′m = σ/ω . We observe that the absolute

intensity of the standing wave SPP resonance on the antenna is quite different for different

values of ε ′′m (As illustrated by the intensity differences between the subfigures of Fig. 3.5)

While the absolute intensities are quite different for these cases, we also observe that the

distribution of the electromagnetic intensity across the strip does not change significantly

as we change metal loss. To illustrate this clearly we show inset graphs in Fig. 3.5 that

plot the intensity profile 10 nm above the antenna normalized to the maximum intensity.

Each of the normalized field profiles is nearly identical despite the change in metal loss.

Thus a near-field probe measurement, which can very accurately map relative near-field

intensities but not absolute intensities, would likely produce similar maps for each of these

cases. In this sense, measurements using near-field probes and the detector platform can

nicely compliment each other.

Conversely our SOI detector platform can also quantify the optical conductivity of a

metal when used in conjunction with full-field simulations. In Fig. 3.6a we show the ex-

perimentally measured resonance in the in-coupling cross-section of the w = 90 nm strip

antenna and measure its quality factor Q as 6.1. The Q depends on the optical losses of the

material making up the antenna. By comparing the measured Q to simulated Q values for

different conductivities, the actual conductivity of the Ag in antenna can be quantified.


1.4 1.5 1.6 1.7 1.8 1.9 2.0Photon Energy (eV)

0

100

200

in-c

ouplin

g c

ross

-sect

ion (

nm

)

Q = 6.1

w = 90 nm Experiment

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0Loss Factor (LF)

0

2

4

6

8

10

Qualit

y F

act

or

(Q)

Experiment

Simulation

1.4 eV 2.0 eV

0

400

LF 0.5

LF 1.0

LF 2.0

a b

Figure 3.6: Effect of metal loss on in-coupling cross-section of a Ag plasmon resonatorantenna. (a) Experimental in-coupling cross-section spectrum for a 90 nm wide antenna.Quality factor measured at FWHM. (b) Dependence of quality factor (Q) on loss factor(LF). The solid line shows the Q determined from simulated in-coupling cross-sectionspectra with varied LF. Dashed line shows the experimentally measured Q of 6.1 and themapping of this value to a loss factor of 2.4. Shaded regions indicate ±10% error marginin the measured Q. Inset: Simulated in-coupling cross-section (in nm) spectra of a 90 nmwide silver strip antenna for several loss factors (LF).


In our simulations we assume that the conductivity is modified by a loss factor (LF)

which modifies the imaginary component of the tabulated bulk dielectric function as εm(λ )=

ε ′m,bulk(λ )+ i LF · ε ′′m,bulk(λ ). The inset to Fig. 3.6b shows simulated in-coupling cross-

section spectra of a w = 90 nm strip antenna for loss factors of 0.5, 1.0 (bulk), and 2.0.

We observe that loss decreases the in-coupling cross-section and significantly decreases

the Q of the resonance. By computing quality factors of many such simulated spectra we

map an exponential relationship between metal loss factor and resonance Q as shown in

Fig. 3.6b. We can use this plotted relationship to extract a quantitive measure of loss factor

from the experimental measurements of resonance quality factor. From experiments we

measure Q = 6.1 and this corresponds to a loss-factor of 2.4. There is some uncertainty

(up to ±10%) in our measured Q, thus we can assert that the silver in our experiments has

a metal loss between 2× and 3× larger than bulk (Rakic) values. This amount of increased

loss is within the expected range for this size (20 nm thickness) of nanostructured silver

[37].

3.7 Comparison to dark-field scattering

Light scattering experiments and photocurrent measurements using the presented SOI plat-

form provide complimentary information on the resonant properties of optical antennas.

Light scattering techniques provide information on the efficiency with which incident pho-

tons from the far-field first excite local modes of an antenna and then reradiate them to

the far-field. A photocurrent measurement provides information on the antenna’s ability to

concentrate light in the near-field of the antenna. It is well-known that the processes that

enable an antenna to concentrate light into a specific region on/near the antenna as well as

its ability to reradiate power to the far-field are inherently frequency dependent [18, 61, 75].

Larger antennas also tend to reradiate different frequencies of light into different spatial di-

rections. For these reasons, the two measurement techniques can produce distinct resonant

spectra with shifted spectral features. For metallic antennas that exhibit relatively broad,

low quality-factor (low-Q) optical resonances these shifts can be small compared to the

peak width. As the both the scattering and photocurrent resonances rely on the initial exci-

tation of charge oscillations in the antenna, the spectral features in the different experiments


600 620 640 660 680 700 720 740wavelength (nm)

0

20

40

60

80

100

120

140

160

reso

nant

wid

th (

nm

)

DF scatteringPhotocurrentFP model

Figure 3.7: Comparison of resonant widths determined from dark-field light scatter-ing experiments and near-field photocurrent mapping. The resonant width as a functionof incident wavelength is plotted. The red circles indicate the peak positions obtained fromthe near-field photocurrent scan of the wedge antenna shown in Fig. 3.4b. The blue tri-angles identify the peak position derived from the dark-field scattering spectra taken fromthe same wedge antenna. The green dotted line is the resonant width of the λ/2 (m = 1)antenna mode as predicted from the Fabry-Perot model [33].

should more-or-less track each other. To verify this we performed dark-field light scatter-

ing measurements on the same wedge antenna measured in Fig. 3.2 and Fig. 3.4b. These

measurements were performed using white light illumination through a dark-field objective

that illuminates the antenna at an incident angle of 50 off the sample normal and enables

collection of the scattered light normal to the sample with a collection numerical aperture

(NA) of 0.55. The collected light was analyzed as function of position along the wedge

using an imaging spectrometer. Figure 3.7 shows the measured dependence of the resonant

width on the illumination wavelength for the λ/2 (m = 1) mode. The figure also shows the

resonant width as determined from the photocurrent measurements with the SOI detector

platform. Here, the peak positions were extracted from the data presented in Fig. 3.4b.

We also plot the predicted resonance from the Fabry-Perot model [33] and note that both

the dark field and photocurrent data nicely track the Fabry-Perot model. This data further


validates the use of our SOI platform to explore optical resonances of antennas.

3.8 Photocurrent enhancement from a plasmonic grating

The silicon-on-insulator (SOI) detector platform described in this Chapter is generally ap-

plicable to explore the resonant properties of many antenna systems. The previous sections

illustrate how one can explore the ability of a single antenna to concentrate light. Here,

we demonstrate that the resonant properties of antenna-arrays can be explored as well.

This could find application in the design of antenna-arrays for plasmon-enhanced photo-

voltaics. We specifically investigated the photocurrent enhancement produced by an array

of silver strip-antennas on the SOI platform. Using electron beam lithography and lift-off

processing, we generated 60 nm thick × 76 nm wide silver strips of at a pitch of 400 nm.

Figure 3.8a shows a dark-field scattering image of the grating between the two electrodes

of the detector. The blue color of the grating that results under randomly polarized light is

a structural color that is intimately linked to the grating periodicity as well as the excitation

and collection angles of the dark-field microscope (incident angle of 50of the sample nor-

mal, collection NA = 0.55). Figure 3.8b shows a scanning electron micrograph illustrating

the details of the fabricated grating geometry.

Figure 3.8c and d show the photocurrent enhancement spectra of the strip array under

transverse magnetic (TM with H-field parallel to the length of the strips) and transverse

electric (TE) excitation. The sample was illuminated through a 10× (NA = 0.28) objective

to closely approximate plane wave illumination (at the loss of spatial resolution). It can be

seen that the optical response is strongly polarization dependent. The dominant feature in

the spectrum appropriate for TM polarization is related to the excitation of surface plas-

mons on the strips. Finite-difference frequency-domain (FDFD) simulations predict that

detector absorption enhancement maximum due this TM plasmonic resonance should be

located at λo = 625 nm (marked with a red vertical line), in very good agreement with the

experimental spectrum. This resonance is red-shifted from the surface plasmon resonance

of an individual strip and slightly narrower due to coupling between nearby strips [12]. The

inset to Fig. 3.8c shows a spatial map of the photocurrent enhancement when the sample

is illuminated with TM-polarized laser light using a 50× objective at λo = 625 nm. We


Figure 3.8: Spatial and spectral mapping of photocurrent enhancement from a pe-riodic plasmonic antenna array. (a) Dark-field image of the silver strip-array locatedbetween the two electrodes of the detector. The array consists of horizontal silver stripsspaced by 400 nm. The scale bar is 20 µm. (b) Scanning electron micrograph of a sectionof the fabricated array. The scale bar is 1 µm. (c-d) Photocurrent enhancement spectra ofthe silver strip array for (c) TM and (d) TE polarizations. The enhancement is obtainedby taking the ratio of the photocurrent directly on the array and adjacent to the array (baredetector). The long red vertical line denotes the location of the TM plasmon resonance ofthe coupled strips at a wavelength of 650 nm, as calculated by full-field electromagneticsimulations. The short blue vertical lines denote spectral position of the TE Si waveguidemode coupling as calculated by full-field simulations. The inset in (c) shows a photocur-rent enhancement map of the silver strip array for TM illumination at a wavelength of 650nm. The arrow indicates the direction of electric-field polarization and the scale bar for thisimage is 20 µm.


clearly see a uniform photocurrent background in the absence of the grating structure and

a uniformly enhanced photocurrent (1.75× reference) when the grating is illuminated. The

region of enhanced photocurrent nicely corresponds to the blue region in the dark-field

light scattering image (Fig. 3.8a).

The transverse electric (TE) polarization (H-field parallel to the grating elements) does

not allow for excitation of the surface plasmon resonance. However, it does allow for ef-

fective grating coupling into waveguide modes of the active Si layer. Figure 3.8d shows

the photocurrent spectrum obtained with TE polarized light. We can observe three peaks

at 555, 780 and 830 nm, which are associated with the excitation of TE waveguide modes

supported by the active Si layer. The location of the photocurrent peaks matches quite

well with the locations predicted by FDFD simulations. We note that these peaks are also

slightly visible under TM polarization (Fig. 3.8c). This is because illumination with finite

polarization contrast causes a small amount (2%) of coupling into TE waveguide modes un-

der “TM” illumination. Roughness on the silver strips is also partially responsible for the

mixing of the two orthogonal polarizations. The overall good agreement of the photocur-

rent spectra with full-field simulations, indicates that the usefulness of the SOI detector

platform in analyzing the spectral resonant properties of antenna arrays.

3.9 Dielectric Si nanowire antenna resonances

In addition to metallic (plasmonic) antennas, it has also been shown that high refractive

index nanostructures constitute a very different class of antennas that can equally well con-

centrate and redirect light [18, 65]. To illustrate that our general platform is also capable

of measuring such dielectric antennas we measured the photocurrent enhancement effects

of a Si nanowire antenna. Silicon nanowires were produced using the vapor-liquid-solid

(VLS) growth method and drop-cast onto the detector platform. Figure 3.9a shows an op-

tical micrograph of the drop-cast wires. We focus on the wire labelled “1” here. From

the AFM topography measurements we determined the wire’s diameter as 90 nm. If we

scan an 800 nm wavelength illumination beam with electric field polarized parallel to the

wires (transverse magnetic or TM illumination) across the region in Fig. 3.9a we generate


λ = 800 nm

f

SiSiO2

AirSi NW

SiO2

λ = 500 nm

e

-100 5000

a

500 600 700 800

500

300

100

-1000

300

100

-1000

c

d

Wavelength (nm)In-c

oupl

ing

cros

s-se

ctio

n [σ

i ] (nm

)

b

12

12

Figure 3.9: Spatial and spectral mapping of photocurrent enhancement from a sili-con nanowire optical antenna. (a) Optical microscope image of Si nanowires on top ofdetector platform. Scale bar is 5 µm. Two different nanowires are labelled as 1 and 2.(b) Photocurrent enhancement map at λ = 800 nm of the same region as (a). Units arenanometers of in-coupling cross-section, σi. Polarization is denoted by red arrows. Scalebar is 5 µm. (c) Experimentally measured in-coupling cross-section of Si nanowire antennaof wire 1 with an electric-field polarization parallel (TM) to the wire (45 from horizontal).(d) Simulated TM in-coupling cross-section of 90 nm Si nanowire on detector platform.Red vertical lines highlight resonant wavelengths of the nanowire. (e,f) Full field simu-lations of the TM-illuminated nanowire on the detector platform at (g) λ = 500 nm and(f) λ = 800 nm. Time-averaged longitudinal (out-of-plane) electric field is shown. Theseillustrate how wire resonances create high near-field intensities in the active detector layer.


a photocurrent enhancement map shown in Fig. 3.9b. We observed a significant photocur-

rent enhancement as compared to the surrounding bare detector, demonstrating an optical

antenna effect. We also note that other diameter wires, such as the 150 nm diameter wire 2,

do not show strong enhancement at this wavelength and polarization.

We also measured the spectral response of the nanowire antenna. Figure 3.9c shows

the spectral photocurrent enhancement quantified in terms of the in-coupling cross-section.

The peaks in this enhancement spectrum are due to leaky-mode/Mie resonances of the Si

nanowire that create high resonant fields within the silicon wire and in the surrounding near-

field [18, 65]. To illustrate this we performed full-field simulations of the wire-on-detector

geometry resulting in a simulated in-coupling cross-section spectrum in Fig. 3.9d. We

observe good peak-position and reasonable peak-height agreement between experimental

and simulated spectra. In these spectra we note a relatively sharp peak at 500 nm and a

broader feature near 800 nm wavelength. At these wavelengths we plot the magnetic field

distributions of the wire/detector system in Figs. 3.9e and 3.9f. At λ = 500 nm we observe

two lobes within the Si nanowire illustrating a dipolar (TM11) symmetry of this resonance

[65]. Similarly at λ = 800 nm we observe a single lobe in the Si nanowire corresponding

to a monopolar (TM01) resonance of the wire. In both cases the resonant scattering causes

an increased field intensity in the active Si layer below and thus produces the peaks in

photocurrent enhancement.

3.10 Conclusions

In conclusion, we have introduced a general, easily-implemented, SOI-based photodetector

platform to analyze the resonant behavior of different types of optical antennas. It com-

plements far-field light scattering techniques by enabling sensitive measurements of the

locally-enhanced fields near an individual antenna through a simple photocurrent measure-

ment. By raster-scanning a focused wavelength-tunable illumination beam over an antenna

placed onto the platform, spatial and spectral maps of antenna resonances could be created.

Its usefulness was demonstrated by showing good agreement between the calculated and

measured resonant behavior of both metallic strip antennas and dielectric Si nanowire an-

tennas. The development of techniques to quantify near-field resonances is critical to many


applications, such as thin-film photovoltaics, high-speed photodetectors, Raman scattering,

sensing, single molecule detection, and other applications where optical antennas are used

to enhance fields in deep-subwavelength volumes. This is particularly true as the real op-

tical antennas might exhibit materials or structural imperfections that may not be captured

in simulations which often assume idealized properties.

Methods

Detector devices were fabricated on a commercially-available silicon-on-insulator (SOI)

wafer. The active silicon layer was thinned to 40 nm using thermal oxidation and wet

etching. This left a 20 nm thick spacer oxide on top of the active silicon layer. Ti and Ni

Schottky contacts were patterned using optical lithography followed by an oxide etch and

a subsequent metal evaporation step. Excess metal was then removed by lift-off, forming

back-to-back Schottky diodes. A silver (Ag) wedge antenna was patterned by electron-

beam lithography and deposited using electron-beam evaporation followed by lift-off pro-

cessing. A 2 nm germanium wetting layer was used before metal deposition to reduce metal

roughness [74]. The Ag wedge antenna was 20 nm thick and its width varied from 50 nm to

1 µm over a length of 100 µm. Finally, a 5 nm conformal alumina film was deposited us-

ing atomic layer deposition to protect the Ag plasmonic structure from rapid environmental

degradation. Silicon nanowire antennas were produced using the VLS growth method using

a gold catalyst on a Si substrate. Wires are sonicated off the growth substrate and drop-cast

onto the detector platform. See Appendix D for a detailed process flow description.

To spectrally analyze and spatially map the resonant behavior of the wedge antenna

we constructed an optical system capable of generating photocurrent maps of antennas at

a multitude of wavelengths. Light at various wavelengths was obtained from a white-light

supercontinuum source (Fianium) that was filtered through a tunable monochromator (Ac-

ton). This light was then polarized with the electric field normal to the long wedge structure

and focused onto the sample to a 1.2 µm Gaussian spot using a 50× (NA = 0.42) objective

(Mitutoyo). The polarization direction was chosen to allow for efficient excitation of SPPs

along the width of the wedge (horizontal direction). The detector platform was mounted on

a 3-axis piezo stage to allow accurate focusing and spatial control over the location of the


excitation spot. Finally, the photocurrent maps were generated by raster-scanning the illu-

mination spot over the antenna and plotting the photocurrent as a function of the position

of the illumination spot. To increase the signal-to-noise ratio, the illumination beam was

chopped and the photocurrent was measured using a lock-in technique. Electromagnetic

simulations were performed using the two-dimensional finite-difference frequency domain

method. Experimental optical constants for metals [54] and dielectrics were used. The grid

spacing was set to 1 nm and simulations were checked for grid spacing convergence.

Chapter 4

Imaging the hidden emission modes ofantennas by cathodoluminescence †

The previous chapter showed that we can measure the near-field concentrating ability of

optical antennas. Antennas can not only be used as “receiving” antennas but also can be

used as “transmitting” antennas. Recent work has demonstrated that plasmonic antennas

can modify the emission properties of molecules, quantum dots and other nanoscale emit-

ters [ycjun, taminiau-nat-phot]. This modification of emission properties, such as changing

emitter lifetime and redirecting emission show that it is possible for these plasmonic anten-

nas to act as optical transmitting antennas when coupled to a nanoscale source.

This ability to increase emitter output, shorten emitter lifetime and redirect (or focus)

output is possible because antennas can change the local density of optical states (LDOS)

for an emitter in a subwavelength distance from the antenna. Because of this we would like

to be able to fully map the LDOS of this antenna system and determine optimal emitter

locations in the near-field of the antenna. Previous work has shown that cathodolumines-

cence (CL) is an effective tool to probe the LDOS of plasmonic structures with nanometer

resolution [77, 78]. Thus, in this chapter we use CL to probe the spatial and spectral depen-

dence of antenna resonances as well as the resonant mode structure of nano-strip plasmonic

resonator antennas (PRAs) that have been explored in the preceding chapters.

†This Chapter follows closely the text and results submitted to Nano Letters [76]

50

CHAPTER 4. IMAGING EMISSION MODES OF ANTENNAS BY CL 51

In this chapter we clearly show strip-width and wavelength dependent spectral reso-

nances as well as map the resonant plasmon standing wave at high spatial resolution. Sur-

prisingly we find not only the short-range surface plasmon-polariton (SR-SPP) resonance

expected from previous chapters but also a long-range (LR) SPP resonance of the antenna.

Additionally unlike in receiving mode where only odd SR-SPP resonances are observed

under normal incidence, these CL measurements reveal both even and odd resonances of

both SR and LR modes. This study thus shows the fundamental similarities and differ-

ences between the properties of a far-to-near field receiving antenna and a near-to-far field

transmitting antenna. By using the electron beam as a local excitation, this study reveals

optimal emitter positions by mapping the LDOS as function of frequency and position.

This study also clearly shows that nano-strip antennas act as resonant cavities of SPPs

and thus confirms previous theoretical studies on this geometry [33]. Additionally, to our

knowledge this is the first study to experimentally show simultaneous SR-SPP and LR-SPP

resonances in a plasmonic nano-strip antenna.

4.1 Introduction

Plasmonic antennas are extensively used to control the emission properties of molecules,

quantum dots and other nanoscale emitters [79] by modifying the local density of optical

states (LDOS) surrounding the emitter. With nanoscale control of the antennas size, shape,

and dielectric environment, the spectrum, emission rate, polarization and angular emission

profile of optical emitters can be tailored to a great extent. Maps of the LDOS near antennas

can provide valuable insights into their operation by linking their geometrical and radiation

properties. In this paper, we demonstrate this point for a metal strip antenna whose reso-

nant behavior is governed by surface plasmon polaritons (SPPs) that can propagate back

and forth between the two edges of the strip [25, 33]. These antennas have previously been

shown to resonantly scatter light [53] and effectively enhance absorption in a Si photode-

tector [59].

The most common way to study the resonant behavior of antennas is with light scat-

tering experiments. Another possibility is to operate the antenna in a receiving mode, in

which case it is used to convert incident free space photons into intense local near-fields.


In such experiments, the illumination conditions in terms of the incident beam direction

and polarization are very important. For example, symmetry dictates that only a limited set

of antenna modes can optically be excited using a normally-incident plane wave with its

electric field polarized normal to the length of the strip. One way to reveal the other hidden

modes is by changing the angle of illumination. We will follow another approach, which

is to excite the antenna modes with an electron beam and to collect the emission from the

structure in all directions. It is important to realize these hidden modes are distinct from

dark modes that exhibit a very limited coupling to free space radiation and are invisible in

CL experiments.

It is well known that very thin metal strips such as used here support two distinct types

of plasmonic modes that result from coupling between SPPs propagating on the top and

bottom surfaces of the strip. One of the coupled modes is a long-range (LR) SPP mode with

a symmetric transverse field distribution that exhibits a relatively long propagation length

because of its relatively low field overlap with the metal [32, 49, 80, 81]. Its counterpart is

the anti-symmetric, short-range (SR) SPP mode. Both the long- and short-range SPPs can

form resonant standing waves across the width of the antenna, and the antennas radiation

properties are thus determined by a combination of these modes. To control and optimize

the ultra-thin strip antenna characteristics, and to use the antenna in the transmitting mode,

detailed knowledge of the excitation of the two SPP modes and their effect on the antennas

radiation efficiency is essential.

4.2 Cathodoluminescence measurements

In this work, we use electron beam excitation to investigate the strip antenna resonances.

As we have shown before, electron beam irradiation leads to the excitation of SPPs over a

broad spectral range.[70, 77, 78, 82, 83] The antenna radiation from the electron-beam ex-

cited resonant modes can be readily detected and spectrally resolved with the use of a scan-

ning electron microscope coupled to an external spectrometer. This electron-induced op-

tical emission is termed cathodoluminescence (CL). We resolve, with deep-subwavelength


650 675 700 725 750 775 800

200

300

400

500

600

strip

wid

th (n

m)

a b

Figure 4.1: Cathodoluminescence imaging of wedge antenna. (a) Scanning electronmicroscopy image of a 20 nm thick Ag wedge on a silicon-on-insulator (SOI) substrate.The y-axis denotes the strip width at different locations along the length of the wedge.The scale bar is 1 µm. (b) Spatially-resolved cathodoluminescence scans of the Ag wedgetaken with 30 keV electrons and collected at different emission wavelengths in the rangefrom 650 nm to 800 nm. Width- and wavelength-dependent resonant bands with higher CLsignal are clearly resolved in the images.

resolution, the plasmon standing waves and find the odd-order SR-SPP resonances ob-

served earlier in optical scattering, as well as even-order resonances that are hidden in top-

illumination experiments. We also find that, in addition to the short-range SPPs [53, 59],

the long-range SPPs play a critical role in the operation of strip antennas.

Figure 4.1a shows a tapered Ag wedge that is the focus of the current study. This wedge

can locally be viewed as a nano-strip antenna of a specific width (indicated on the verti-

cal axis), allowing for study of many antenna sizes within one fabricated structure. The

20 nm thick Ag wedge antenna was fabricated on a silicon-on-insulator substrate (20 nm

SiO2 spacer on top of 40 nm of Si on a 400 nm buried oxide attached to a Si wafer), using

electron-beam lithography, Ag evaporation and lift-off, as described in Chap. 3 and Ap-

pendix D. Spectrally-resolved CL scans of the antenna were made using a 30 kV electron


beam focused to a diameter of 10 nm at a typical beam current of 1 nA. While scanning the

beam, radiation from the sample is collected by a parabolic mirror (1.46π sr. acceptance

angle) placed between the sample and the pole-piece of the microscope and then analyzed

using a spectrometer and a two-dimensional map of CL spectra is taken with a pixel pitch

of 10 nm. Measured CL spectra have contributions from both antenna resonances and back-

ground radiation from the substrate. The CL spectra shown have this background radiation

removed.

Figure 1b shows the CL signal as function of electron-beam position on the wedge for

seven equally spaced emission wavelengths in the range from 650 to 800 nm. Each image

in Fig. 1b shows regions/widths along the wedge where the CL signal is clearly enhanced.

We will argue that these signal enhancements can be attributed to the excitation of standing

wave SPP resonances. Similar bright bands have been observed and attributed to stand-

ing wave SPP resonances in nanowire antennas [77] and plasmonic Fabry-Perot cavities

fashioned into a single-crystal Au surface [84]. This interpretation is also consistent with

the fact that the brighter regions move up along the wedge (to larger widths) as the wave-

length of the collected emission is increased. The linear movement of these bright regions

with emission wavelength reflects the approximately linear dependence of the SPP resonant

wavelengths on width.

4.3 Resonance trends of nano-strip antennas

To explore the dependence of the resonant wavelengths on the strip width, we plot in

Fig. 4.2 the integrated CL intensity across the width of the strip for different strip widths

and wavelengths. This figure shows four resonant bands. We model the resonances using

a Fabry-Perot model [25, 33], in which a resonance condition is met if the antenna width

w equals an integer multiple of half SPP wavelengths including a phase advance φ upon

reflection from the sides of the wedge:

wres,m =

[m− φ

π

]λ

2 nspp. (4.1)

Here m indicates the order of the resonance, λo is the free-space wavelength and nspp


600 650 700 750 800 850wavelength (nm)

200

300

400

500

600

stri

p w

idth

(nm

)

=

=

==

0

1

Inte

gra

ted C

L in

tensi

ty (

a.u

.)

Figure 4.2: Cathodoluminescence resonance trends. Cathodoluminescence (CL) signalintegrated along the strip width, plotted as a function of strip width and emission wave-length. Four resonant bands exhibiting enhanced CL are clearly resolved. The drawn linesare calculated using Eq. (4.1) and indicate the Fabry-Perot resonances of short-range sur-face plasmon polaritons (SR-SPPs) for different mode orders m = 2−5.

the mode index. In the following, we first presuppose that the antenna behavior is domi-

nated by the anti-symmetric short-range SPP mode, with a mode index nsr−spp. The drawn

lines in Fig. 4.2 labeled by the resonance order m = 25 are calculated using Eq. (4.1) us-

ing φ = π/2 and a frequency-dependent nsr−spp ranging between 2.2 and 2.7. These values

were previously determined using numerical simulations [33, 85] and experiments [53, 59].

The solid lines in Fig. 4.2 are calculated using Eq. (4.1) and correspond well to the mea-

sured data. Unlike in normal incidence receiving mode where only odd SR-SPP resonances

are observed [59], this CL resonance map reveals both even (m = 2,4) and odd (m = 3,5)

resonances. The exciting electron beam effectively serves as a point dipole source (com-

posed of the incident point charge and its image dipole) that can couple to all of these

modes by scanning the beam over the structure. The emission from the antenna modes

could subsequently be collected with a parabolic mirror that can collect photons over a

broad angular range.


4.4 Resolving the spatial distribution of SPP resonances

Next, we focus on the fine structure in the CL signal across the width of the antenna.

Figure 4.3a shows a CL emission map taken at an emission wavelength of 700 nm. The

image shows fringes that become more pronounced near the resonant widths marked by

horizontal white lines (derived from Eq. (4.1) and Fig. 4.2). The CL intensity along these

lines is shown in Fig. 4.3b. The fringes in these line cuts are dominated by the standing

SPP wave pattern of the resonant strip, with peaks spaced by approximately λsr−spp/2. The

standing wave patterns each have a number of nodes and antinodes commensurate with

their resonance order (number of anti-nodes within the cavity equals m−1). The intensity

of the plasmonic standing wave pattern at a position x along the strip width derived from

the Fabry-Perot model is given by:

I(x) ∝

∣∣∣∣r eikx− e−ikx

1− r2 ei 2kw

(eikx− r e−ikx ei 2kw

)∣∣∣∣2 (4.2)

Here k = nsppko is the propagation constant of the relevant SPP, and r is the complex SPP

reflection coefficient that takes into account the phase advance upon reflection [33]. Figure

4.3c shows calculations of Eq. (4.2) for the resonant widths in Fig. 4.3b for short-range

asymmetric SPPs. Comparing Figs. 4.3b and 4.3c it is clear that the model correctly

predicts both the number and position of the minima and maxima in the CL scans. It does

not account for the bright peaks at the ends of the strip. However, similar peaks commonly

occur near truncations of a metallic structure [77, 84] and can be ascribed to a locally

enhanced coupling of the electron beam to SPPs. In addition to this expected discrepancy

between Figs. 4.3b and 4.3c, we note two other features in the CL data in Figs. 4.3a, b that

cannot be explained by the single-mode SR-SPP resonance model shown in Fig. 4.3c. First,

in the experiment the peak heights of the standing wave are non-uniform across the width

while in the Fabry-Perot model all of the peaks have the same height. Second, the model

shows a monotonically decreasing visibility of the standing wave pattern for increasing

width, due to increased SPP propagation losses, while in experiment the m= 4 (w= 500nm)

resonance is more intense than the m = 2 and 3 resonance.


0.0 0.5 1.0m

200

300

400

500

600

strip

wid

th (n

m)

=

=

=

=

=

=

=

=

=

=

=

=

a b c d

CL SR-SPP SR-SPP + LR-SPP

Figure 4.3: Cathodoluminescence imaging of plasmon standing waves. (a) Cathodo-luminescence image for a free-space emission wavelength of 700 nm. The scan has beenstretched 4 times in the horizontal direction to more clearly show the fine structure acrossthe width of the antenna. Horizontal lines denote widths at which resonances occur. (b)Line cuts of the CL signal taken at resonant widths from the image in (a), showing SPPstanding wave patterns. (c) Calculated intensity of SPP standing waves according to theFabry-Perot model for short-range SPP resonant modes. (d) Calculated intensity of SPPstanding Fabry-Perot model for a superposition of resonant short-range and long-rangeSPP modes.


4.5 Short- and Long-Range SPP resonances

To explain these two observations we must invoke the symmetric long-range SPP mode

as an additional relevant resonant antenna mode. For symmetry reasons, this mode is also

hidden in optical experiments where the antenna is illuminated from the top and to our

knowledge this mode has in fact remained elusive in optical scattering experiments. Figure

4.4a shows the calculated transverse magnetic field mode amplitude profiles for a free-

space wavelength of λo = 700 nm for the short-range anti-symmetric (a) and the long-range

symmetric (b) SPP mode [85]. In the calculations the layered SOI substrate was modeled by

a bulk substrate with an effective nsub = 1.87 and optical constants for Ag were taken from

Rakic [54]. We note that the LR-SPP is a leaky mode in this case, due to the high index of

the substrate. In the CL experiment, the electron beam couples to both of these SPP modes.

In Fig. 4.3d we plot the intensity of the sum of short-range and long-range SPP Fabry-

Perot standing waves calculated using Eq. (4.2). We assume their relative contributions

are equal and a reflection phase of the LR-SPP of 3π/2. The individual contributions

from long-range and short-range SPPs are plotted in green and blue, respectively. The

summed intensity shows good quantitative agreement with the experimental line plots in

Fig. 4.3b. The simulations accurately predicts the deep minimum at the center of the strip

for the largest width (w = 635 nm). The reduced intensity at the center of the CL scan

for the w = 500nm width region is also reproduced. Finally, the simulations also show

the enhanced intensity in the center of the narrowest strip (m = 2). The strong modulation

of the intensity maxima across the antenna width are the result of the large difference in

wavelength of the short-range and long-range modes, as is also evident from Fig. 4.3d.

For an antenna width w = 500 nm both SPP modes are resonant (mLR = 2 resonance for

the long-range SPP; mSR = 4 resonance for the short-range SPP), leading to a strongly

enhanced integrated intensity, as is also observed experimentally in Fig. 4.3b. In contrast,

for w = 350 nm, the short-range SPP is resonant while the long-range SPP is not, leading

to the relatively weak intensity profile for the latter.


-1 0 +1 (a.u.)

0.2

0.0

0.2

-1 0 +1 (a.u.)

300 0 300dipole

position (nm)

200

300

400

500

600

700

strip

wid

th (n

m)

300 0 300dipole

position (nm)

a b c d

()

Figure 4.4: Plasmon mode profiles and LDOS simulations. (a,b) Calculated modeprofiles (transverse magnetic field amplitude) for (a) short-range and (b) long-range SPPmodes for a 20 nm thick Ag film on an n = 1.87 substrate. (c,d) Calculated distribution ofthe local optical density of states for a point dipole placed in the substrate below the strip(c) and above the strip (d).


4.6 Calculation of LDOS near antennas

To further study the contribution of the two SPP modes to the antenna radiation, we per-

formed simulations of the local density of optical states (LDOS) near the top and bot-

tom surface of the antenna. We use two-dimensional finite-difference frequency-domain

(FDFD) [57] electromagnetic simulations on a vertically-oriented dipole placed 15 nm from

the metal surface as a source and take a substrate with an effective index of nsub = 1.87.

Figure 4.4c shows the two-dimensional LDOS distribution for dipoles placed in the sub-

strate below the antenna. The intensity distribution matches quite well with the calculated

line scans for the short-range SPP mode in Fig. 4.3c. This indicates that emitters placed

below the antenna predominantly couple to short-range SPPs. Interestingly, the LDOS

above the antenna (Fig. 4.4d) shows a very different distribution. We attribute this to the

superimposed standing wave patterns of both short-range and long-ranges SPPs. Indeed,

the calculated integrated intensity distributions in Fig. 4.3d are in good agreement with the

corresponding cuts through Fig. 4.4d. This also helps to validate our assumption of equal

relative contributions from LR and SR SPP resonances.

The difference in the two-dimensional LDOS profiles for the two dipole positions is

explained by the difference in coupling to the SPP mode profiles. A dipole placed in

the substrate below the antenna will couple most strongly to the short-range SPP due to

large mode overlap between the dipole field and the short-range SPP mode profile (see in

Fig. 4.4a). For a dipole placed above the antenna we find a comparable mode overlap with

both types of SPP modes and both modes are thus excited. As the electron beam is a direct

probe of the LDOS along its trajectory, and since it passes through both the top and bottom

interfaces, the CL measurement includes contributions from both top and bottom LDOS

patterns. This is consistent with the observation of both short-range and long-range SPP

resonances in the CL scans.


4.7 Conclusions

In conclusion, we have investigated the resonant modes of plasmonic strip antennas using

high-resolution cathodoluminescence imaging spectroscopy. From the observed CL dis-

tributions, we directly characterize the relevant resonant modes supported by the antenna.

We find that both short-range and long-range SPP modes play a critical role in the resonant

optical behavior of the antenna. The superposition of these modes gives rise to a complex

CL intensity profile across the antenna. The importance of the contributions of short-range

and long-range SPPs to the CL signal is further confirmed using calculations of the local

density of states. We find that a dipole placed in the substrate below the antenna preferen-

tially couples to the short-range SPP, while a dipole placed above the antenna excites both

types of SPP modes. This work resolves the full modal distribution of a plasmonic strip

antenna, including modes previously hidden in optical experiments. It demonstrates some

similarities and fundamental differences between resonant antenna modes excited by far

field plane-wave radiation and those excited in the near-field. The obtained results can help

guide the design of plasmonic structures as transmitting optical antennas.

Chapter 5

Applications and future directions ofoptical antennas

In the preceding chapters we have developed theoretical and experimental techniques to

understand and characterize plasmonic optical antennas. This chapter now looks at how we

can actually use the resonances of these antennas in scientific and engineering applications.

We also look forward and hopefully provide insight into where optical antenna design will

progress in the future.

5.1 Improving the efficiency of thin film solar cells∗

Recent work has shown that plasmonic antennas can be used to enhance absorption in the

active layers of thin-film photovoltaic (PV) and could potentially lead to improved effi-

ciency of such cells [1, 12]. This enhancement occurs for two reasons: 1) these antennas

can concentrate light into their near-field as shown in Chapters 2 and 3 and 2) the antennas

strongly scatter and thus can redirect light into active layers if designed correctly. These

effects are critical because thin-film PV efficiency is often limited by a length-scale mis-

match between the requirements for optical absorption and electrical current extraction as

illustrated in Fig. 5.1. From an optical absorption standpoint one would like to absorb as

much light as possible, thus a thick active layer is desired. However many lower cost cells,

∗For further details this work has been published in Advanced Materials [12]

62

CHAPTER 5. APPLICATIONS AND FUTURE DIRECTIONS 63

Figure 5.1: Photon management schemes for photovoltaics. Remedying optical andelectrical size mis-match in thin-film photovoltaics using plasmon enhanced photon man-agement. [[??? FIXME RESOLUTION]]

such as such as organic cells and amorphous silicon, have active layers with relatively poor

electric properties. In these cells carrier diffusion lengths are the limiting factor in film

thickness. In other words, if one makes the cell thick enough to absorb all the photons it

would not be possible to extract all the carriers due to limited carrier extraction properties.

Plasmonic antenna structures promise to bridge the optical and electrical length-scale gap

by redirecting and trapping light in to active layers much thinner than the optical absorption

length.

The specific structure that we investigated is an array of silver nano-strip antennas on

top of a thin crystalline silicon active layer as seen in Fig. 5.2a. This substrate layers are

the same as those described in Chap. 3. This set of antennas provides two light-trapping

mechanisms to increase the absorption: 1) individual antenna resonances and 2) collective

interactions between antennas that trap light into waveguide modes.

In the previous chapters we carefully explored the resonant properties of individual

silver nano-strip antennas and found that we can optimize the absorption in a thin active

layer by tuning the geometry of the antenna. In this case we find that thickness t = 60 nm,


Figure 5.2: Plasmon-enhanced photovoltaic scheme. a) A schematic of the proposedplasmon-enhanced cell structure. Normalized and time-averaged field intensity plots fornormal incidence, TM illumination of b) a bare Si/SiO2 structure and c) and d) the samestructure with a periodic array of metal strips spaced at p= 312 nm, a spacer layer thicknessof s= 10 nm, and an absorbing Si film thickness equal to 50 nm. The incoming wavelengths(energies) of b) and c) λ = 650 nm (1.91 eV) and d) λ = 505 nm (2.46 eV) were chosen todemonstrate the effects of strong near-field light concentration or excitation of waveguidemodes by the strips. [???FIXME RESOLUTION]]


width w = 80 nm resonators provide a large field concentration at a wavelength of 650 nm

as seen in Fig. 5.2c as compared to the bare cell shown in Fig. 5.2b.

However one antenna is not enough for a solar cell. We must place an array of such

antennas to increase absorption over a large area. When doing so the periodicity of their

placement is critical for coupling of light into waveguide modes as specific frequencies.

As illustrated in Fig. 5.2c we found that a period of p = 312 nm allows for light to be col-

lectively scattered into Si waveguide modes in the active layer, thus allowing for increased

absorption at the coupling wavelength of 505 nm. Here we see that the light is not coupled

to near-field directly beneath the antenna, but rather as part of a wave guided standing-wave

between the antennas.

By exploring and optimizing the geometric parameters of this structure we find inter-

esting interplay between localized plasmon resonances and waveguide coupling including

anti-crossing behavior. The final optimized antenna structure has a pitch of p = 295 nm

provides a 43% absorption enhancement averaged over the AM1.5 standard solar spectrum.

In addition to this theoretical work, absorption enhancement by Ag nano-strip antenna ar-

rays as been experimentally demonstrated for non-optimized structures in Section 3.8.

While this structure is not a viable commercial solar cell it nicely demonstrates the

physics of light trapping by plasmonic structures and has allowed us to extract and optimize

the effects of localized plasmon resonances and periodic placement of the antennas. Future

2D arrays of plasmonic antennas may provide substantial benefits to cells with extremely

thin active layers such as small-molecule organic PV.

5.2 Phase-coupled plasmon-induced transparency †

Another potential application for resonant optical antennas is to act as part of a modula-

tion scheme for controlling the flow of light through optical waveguides. Optical antenna

resonances are naturally sensitive to dielectric environment, so it is conceivable that their

resonances could be actively tuned by modifying its optical environment either optically

or electrically. With such tuning it is possible to create an all-optical or electro-optical

modulator. One limitation, however, is that due to both absorptive and radiative losses, the

†For further details this work has been published in Physical Review Letters [14]


quality factor Q of the antennas is not remarkably large (often less than ten). This means

that we generally need large changes in dielectric environment to see reasonable shifts in

resonances as compared with the resonance spectral width.

a

b

Figure 5.3: Phase-coupled plasmon-induced transparency schematic. (a) The lumpedstructure used for analytical modeling of the phase-coupled plasmon-induced transparency(PC-PIT) structure. (b) A plasmonic realization of the PC-PIT scheme using coupled metal-stripe antennas.

Luckily, the low Q of a single resonator antenna is not the limit on Q of coupled res-

onators. Coupling of two slightly detuned resonators has the unique property that the cou-

ple resonance of the two can have a quality factor Q much larger than the Q of the individual

resonators [cite]. Because of the fine control over resonant frequency by tuning geometry

of plasmonic nano-strip antennas we can create slightly detuned nano-strip antennas and

make use of coupling between their resonances to create a system to higher Q.

We have theoretically demonstrated a coupling scheme to observe plasmon-induced

transparency (PIT) where a sharp (large Q) transparency window is created between the

resonant frequencies of two slightly detuned plasmon resonators (or antennas). Unlike pre-

viously reported [?CITE] PIT schemes that use near-field optical coupling between two

plasmon resonators, this phase-coupled PIT (PC-PIT) scheme uses a guided far-field cou-

pling. Our PC-PIT scheme optically couples the two Ag nano-strip antennas/resonators

with a Si waveguide of a carefully tuned length (shown schematically in Fig. 5.3.) By

adjusting and optimizing the geometry of the antenna/resonators and the waveguide we

can achieve the waveguide transmission spectrum shown in Fig. 5.4b. The individual reso-

nances of these two detuned antennas (w1 = 290 nm; w2 = 320 nm) is shown in Fig. 5.4a.


760 810 860

0.2

0.4

0.0

0.1

0.2

s =

720

nmSi

ngle

ant

enna

s

Wavelength (nm)

Pow

er tr

ansm

ittan

ce

L1 L2

M

2.5

0.0

2.5

0.01.5

0.0

c

d

e

L1: 785 nm

M: 814 nm

L2: 834 nm

a

b

Figure 5.4: Phase-coupled plasmon-induced transparency results. (a,b) Power trans-mission of isolated and coupled Ag strip antennas. (a) show the resonances of the indi-vidual antennas showing their relative detuning. The dashed line is the transmittance of asingle 290 nm strip. The solid line is the transmission spectra of 320 nm wide stripe. (b)Power transmission spectra of coupled antennas with a waveguide length of s = 720 nm.The dotted lines indicate the simulated transmission and the solid lines are the analyticalfits using a Fabry-Perot model. Black triangles in (b) indicate the wavelengths used forfield-plots in (c-e). (c-e) Normalized magnetic field |H/H0| at the three wavelengths indi-cated by L1, L2, and M in (b). (c) and (e) correspond to the the individual resonances (L1and L2) of the stripes while (e) is the higher Q resonance M of the coupling region. H0is the magnetic field of an isolated waveguide at the indicated wavelengths. The incidencedirection is indicated by the white arrow.


It is clear from the coupled spectrum that a sharper Q has been achieved via waveguide-

coupling of the two detuned resonators.

5.3 Other applications

In addition to the two applications described in the previous sections plasmonic optical

antennas also hold promise for many applications that require coupling light into or out of

a deep-subwavelength (nanoscale) volume.

5.3.1 Localized heating using optical antennas

Since the metals in plasmonic optical antennas have limited conductivity at optical frequen-

cies, the antennas tend to absorb light and convert it to heat when driven at their resonant

frequency. This loss is undesirable for many applications (such as for solar cells and modu-

lators described in the preceding sections), but there are many applications where optically-

induced localized heating is advantageous. Some applications include the selective growth

of nano structures such as vapor-liquid-solid grown Si nanowires [9]or heating for growth

of nanocrystals [16].

Another exciting use for localized antenna heating is in the field of medicine. It has

been shown recently that nano antennas can be used in-vivo for localized cancer therapy

[7]. Nanoantennas coated with specific binding agents can be injected into the body and

subsequently migrate and selectively bind to cancer cells. The antennas can then be exter-

nally excited by an infra-red laser, heating only the cancer cells and causing cell death in

the tumor while leaving nearby healthy cells unharmed.

5.3.2 Nano-scale photo-detection

In the similar vein to the electrical and optical trade-offs discussed for photovoltaics in

Section 5.1, photo-detectors are limited by trade-offs imposed by the diffraction limit. To

improve the speed of photo-detectors for imaging and optical communications applications

we would like to shrink the active semiconductor in the detector as much as possible. This

is because of the improvements in carrier extraction and reduced electrical capacitance that


are achieved by reduction in active volume. However optical limitations appear when re-

ducing the size of detector smaller than the diffraction limit. At this point the it it no longer

possible to use conventional lens optics to couple the same amount of light into a smaller

volume, and thus for sub-diffraction limited detectors, we see a fall-off in responsivity.

There has been recent work [2–6] that has demonstrated that plasmonic optical antennas

can concentrate light efficiently into deep-subwavelength detectors and thus break the cur-

rent trade-off between speed and responsivity.

5.4 Conclusions and future directions

This thesis has focused on understanding and using plasmonic optical antennas. We have

developed new theoretical and experimental tools to achieve this goal. And while many

of the models and experiments have focused around a specific Ag nano-strip antenna, the

techniques and methods developed can be applied to many other optical antenna designs.

From this we now have a clear understanding and thus control over the resonances of these

structures as shown both in theory (Chap. 2) and practice (Chap. 3 and Chap. 4).

Using these modeling and measurement techniques of both antenna emission and col-

lection efficiencies, the optimization of antennas for optics becomes possible. New appli-

cations of these plasmonic antennas range from the immediately practical, such as faster

photodetectors and more efficient solar cells, to the more far-reaching goals of on-chip

optical networks and quantum optical circuits.

We have also shown in this final chapter that that there are many nascent applications

that make use of the unique ability of these antennas to bridge the gap between optics

and the nanoscale. It is important to realize that we have only just scratched the surface

of the possibilities with optical antennas. Over the past century scientists and engineers

have developed a myriad of unique radio frequency antenna designs. These antennas span

orders of magnitude of resonant frequencies and are have unique properties designed for

their equally varied uses in our everyday lives. There is much still to borrow from the

mature field and to see what is possible by shrinking these antennas to to the nano-scale to

create new optical antennas.

Appendix A

Generalized Design rules: ResonanceMaps

In Chap. 2 we saw the derivation of design rules for plasmonic nano-strip antennas. The

basic trends explored in that chapter are expanded here to give us resonance maps that allow

an optical antenna designer to build an antenna for their given application.

A.1 Resonance maps of strips in a uniform medium

Here we present resonance maps of metallic nano-strips that can allow engineers to develop

plasmonic antennas with desired properties. We show a set of design rules and parameter

maps that prescribe the optimal geometric and material parameters that give the desired

resonance properties. In Fig. A.1 we show the geometry of this nano-strip antenna. This

system that we investigate here is identical to the one in Chap. 2. Here we have a metallic

strip with width w, thickness t and metallic dielectric constant εm. We are interested in

predicting this antenna’s resonance when illuminated from the top with a TM-polarized

planewave at normal incidence.

In order to generalize the resonance conditions of this system we would like to explore

the full parameter space of the system. To do this we introduce three orthogonal, normal-

ized parameters that fully describe the geometry and material properties of the system at

a given frequency. These parameters are as follows: normalized strip thickness τ = t/λo

70

APPENDIX A. GENERALIZED DESIGN RULES: RESONANCE MAPS 71

x

y

z

Figure A.1: Geometry of a strip antenna in a uniform medium.

where λo is the free-space wavelength; normalized strip width W = w/λo; and the ratio of

optical material properties εm/εd where the metallic strip has εm and the host dielectric has

εd .

We know from the Fabry-Perot model in Chap. 2 that the resonance of such PRA can

be described in a resonance design rule. Here this design rule is rewritten in-terms of these

normalized parameters:

Wres,m =wres,m

λo=

mπ−φ(τ, εmεd)

2π

1n′spp(τ,

εmεd). (A.1)

Both φ and nspp are dependent on only the normalized thickness (τ) and dielectric

properties (εm/εd). It is also evident from Eq. (A.1) that the resulting resonance width

Wres,m is also dependent on only the other two normalized parameters. By reducing the

problem to these three properties we can create maps that predict the behavior of φ and nspp

and thus tell us which parts of geometric / materials parameter space allow for resonances.

Note, here we focus on only SR-SPP resonances as they are the dominant resonance in

such plasmon resonator antennas.

In the parameter space of all possible W ,τ,εm, resonant sets of Wres,τ,εm occupy a

small subset of this space. Of course not all of these resonant combinations can be physi-

cally accessed in the real-world. Fabrication technology limits our ability to fully explore

W and τ and the small collection of metals and alloys available for plasmonics (along with

their dispersive nature) severely limits the possible choices of εm. Even with these severe


restrictions it is possible to find resonant structures for a given wavelength and materials.

In addition to resonance position (W ) we are also interested in engineering the strength

of the resonance. One measure of the resonance strength is the end-face field Eend which

measures the field concentrating ability of the resonant antenna. This resonance strength

is determined by the losses in the antenna cavity. The resonant cavity has two loss mech-

anisms in this model: propagation losses and reflection / out-coupling losses. Propaga-

tion losses are due the lossy nature of metals and is captured in the imaginary part of the

complex kspp. Out-coupling losses at the end face are due to mode coupling between the

SR-SPP and the continuum of free-space modes at the abrupt end-face terminations. This

reflection loss is quantified in a complex reflection coefficient γ = |r|eiφ . It is important

to note that while metal losses at optical frequencies can be significant in plasmonic sys-

tems, in this geometry the out-coupling of light at the end-faces is often the dominant loss

mechanism and limits quality factor of the resonance.

In Fig. A.2 we plot the resonance maps for a loss-less metallic nano-strip in a uniform

dielectric. The components of the complex reflectivity γ = |r|eiφ are plotted as maps of R =

|r|2 and φ as a function of normalized thickness τ = t/λo and normalized dielectric constant

εm/εd . Following Eq. (A.1) we also plot maps for the resulting normalized resonant widths

Wres,m for resonance orders m = 1,3,5.

A.2 Application of resonance maps

To illustrate the use of the resonance maps in Fig. A.2 we show the optimization of two

different antennas that have the same resonant frequency. In this case we want both a Au

and a Ag antenna of the same width (120 nm) that are resonant at λo = 650 nm. Given

all these constraints, is it possible to find a resonant Au and Ag antenna, especially with

Au and Ag have different dielectric constants? It turns out that we have three tunable

parameters (width, thickness, dielectric properties) and we have only fixed two (width and

dielectric constant). This means we can optimize the third (thickness).

We first use our map of Wres,1 for the specific wavelength of λo = 650 nm. Next we

pick the desired with wres,1 = 120 nm and follow this contour on our map. Next we are

constrained by the dielectric properties of Au and Ag at λo = 650 nm. We then find the


18

16

14

12

10

8

6

ε m/εd

90%

80%

70%

60%

50% 40

%30

%

20%

10%

R

65 75 85 95

105

φ

1.5

22.

53

1.25 1.1

n ′spp

0.02 0.04 0.06 0.08 0.10 0.12 0.14

t/λo

18

16

14

12

10

8

6

ε m/εd

0.1

0.15

0.2

wres,1/λo

0.02 0.04 0.06 0.08 0.10 0.12 0.14

t/λo

1.1

1

0.9

0.8

0.7

0.6

wres,3/λo

0.02 0.04 0.06 0.08 0.10 0.12 0.14

t/λo

2.1

21.

9

1.8

1.7

wres,5/λo

Figure A.2: Resonance parameter maps for a strip antenna in a uniform medium.

intersection between the wres,1 curve for 120 nm and these appropriate metal’s dielectric

constant. From this we find that a Au antenna with a thickness of t = 13 nm will be

resonant at λo = 650 nm just like a Ag antenna with a thickness of t = 10 nm.

From our resonance map we have found two antennas made of different materials that

are resonant at the same wavelength and have the same width. To verify this overlap in res-

onant spectra we perform full-field simulations and plot in Fig. A.3 the near-field intensity

enhancement for these antennas under plane wave illumination. Here it is evident that our

optimized Au and Ag antennas do indeed share a resonance at λo = 650 nm.


W = 120 nm

Ag

Au

120nm

120nm

t =13

t =10

Ag or Au

Ei

|Eend|2

W

Hi

Figure A.3: Application of resonance maps to finding Au and Ag antennas with similarresonant properties.

Appendix B

Cavity model derivations

Here we derive the expressions that describe the field within a one-dimensional Fabry-Perot

cavity of length L. We provide two cases applicable to plasmon optical resonators acting

as receiving and transmitting antennas. As was shown in Chap. 2, we must consider the

mirrors at the ends of the cavity have special phase accumulation properties accounted for

in a complex reflectivity r = |r|eiφ . The derivations shown here involve the sum of multiple

reflections of waves that constructively or destructively interfere at a given point within the

cavity. Because of infinite sum nature of the derivation we us this sum identity

∞

∑n=0

z n =1

1− zfor z < 1. (B.1)

B.1 Normal-incidence plane-wave Fabry-Perot model

To model normal-incidence plane-wave excitation of a plasmon resonator antenna (PRA)

as described in Chap. 2 and Chap. 3 we assume excitation of a Fabry-Perot cavity from

both ends of the cavity as illustrated in Fig. B.1.

For light incident from the left we find multiple reflections contribute to field at a point

x′ within the cavity as:

E→(x′) = eikx′+ r eik(2L−x′)+ r2 eik(2L+x′)+ r3 eik(4L−x′)+ · · · (B.2)

75

APPENDIX B. CAVITY MODEL DERIVATIONS 76

n=1n=2n=3

Incident Light Incident Light

x0 Lx’

Figure B.1: Schematic of the normal-incidence plane-wave Fabry-Perot model.

Similarly for light incident from the right we find:

E←(x′) = eik(L−x′)+ r eik(L+x′)+ r2 eik(3L−x′)+ r3 eik(3L+x′)+ · · · (B.3)

We can then rewrite these as infinite sums

E→(x′) =∞

∑n=0

r2n eik(2nL+x′)+ r2n+1 eik[2(n+1)L−x′] (B.4)

E←(x′) =∞

∑n=0

r2n eik[(2n+1)L−x′]+ r2n+1 eik[(2n+1)L+x′] (B.5)

Rewriting:

E→(x′) =∞

∑n=0

r2neik2nL[e+ikx′+ r eik[2L−x′]

](B.6)

E←(x′) =∞

∑n=0

r2n eik2nL[eik[L−x′]+ r eik[L+x′]

](B.7)

Using the identity in Eq. (B.1) we can now write:

E→(x′) =e+ikx′+ r eik[2L−x′]

1− r2eik2L (B.8)

E←(x′) =eik[L−x′]+ r eik[L+x′]

1− r2 eik2L (B.9)


For odd Fabry-Perot modes the interference pattern E(x′):

E(x′) = E→(x′)−E←(x′) =e+ikx′+ r eik[2L−x′]− eik[L−x′]− r eik[L+x′]

1− r2 eik2L (B.10)

In Chap. 2 we were interested in the field at the end-face of the resonant antenna. In

this case x′ = 0 and Eend simplifies to:

Eend = E→(0)−E←(0) =1+ r eik2L− eikL− r eikL

1− r2 eik2L =

(1− r eikL)(1− eikL)

1− r2 eik2L (B.11)

B.2 Local emitter Fabry-Perot model

n=1n=2n=3

x0 Lx’a

n=1n=2n=3

Figure B.2: Schematic of the local emitter Fabry-Perot model.

In the case of local excitation by an emitter as described in Chap. 4, we must consider

the source of excitation to be within the Fabry-Perot cavity at a location x = a. From the

source two waves will emanate initially to the right (→) and to the left (←) as shown in

Fig. B.2. Here we the derive the contribution of waves at point x′ from both of these waves

starting at a. We require two sets of equations for the two cases of x′ on either side of x = a.

Case I: x′ to the left of a

| x′ ← a → |


If the point x′ is to the left of a (x′ < a) we find the following: for the initial right (→)

wave:

E→(x′) = r eik(2L−a−x′)+ r2 eik(2L−a+x′)+ r3 eik(4L−a−x′)+ · · · (B.12)

This can be express as an infinite sum:

E→(x′) =∞

∑n=0

r2n+1eik[2(n+1)L−a−x′]+ r2(n+1)eik[2(n+1)L−a+x′] (B.13)

Rearranging:

E→(x′) =∞

∑n=0

r2neik2nL[reik(2L−a−x′)+ r2eik(2L−a+x′)

](B.14)

Using the identity in Eq. (B.1) we find the right (→) contribution as

E→(x′) =reik2Le−ika

[e−ikx′+ re+ikx′

]1− r2eik2L (B.15)

Similarly for the initially left (←) propagating wave when x′ < a:

E←(x′) =∞

∑n=0

r2neik[2nL+a−x′]+ r2n+1eik[2nL+a+x′] (B.16)

E←(x′) =∞

∑n=0

r2neik2nL[eik(a−x′)+ reik(a+x′)

](B.17)

E←(x′) =eika[e−ikx′+ re+ikx′

]1− r2eik2L (B.18)

for x′ < a combine left and right:

E(x′) = E←(x′)+E→(x′) =reik2Le−ika


]+ eika


]1− r2eik2L (B.19)

Expanded


E(x′) =reik2Le−ikae−ikx′+ r2eik2Le−ikae+ikx′+ eikae−ikx′+ reikae+ikx′

1− r2eik2L (B.20)

Case II: x′ to the right of a

| ← a → x′ |

For the case of x′ to the right of a (x′ > a) we can similarly express contribution from

the initially left and right propagating waves.

For x′ > a ; right (→) propagation direction:

E→(x′) =∞

∑n=0

r2neik[2nL−a+x′]+ r2(n+1)eik[2(n+1)L−a−x′] (B.21)

E→(x′) =∞

∑n=0

r2neik2nL[eik(−a+x′)+ reik(2L−a−x′)

](B.22)

E→(x′) =e−ika

[e+ikx′+ reik(2L−x′)

]1− r2eik2L (B.23)

For x′ > a ; left (←) propagation direction:

E←(x′) =∞

∑n=0

r2n+1eik[2nL+a+x′]+ r2(n+1)eik[2(n+1)L+a−x′] (B.24)

E←(x′) =∞

∑n=0

r2neik2nLreika[e+ikx′+ re−ikx′eik2L

](B.25)

E←(x′) =re+ika

[e+ikx′+ re−ikx′eik2L

]1− r2eik2L (B.26)

for x′ > a combine left and right:


E(x′) = E←(x′)+E→(x′) =e−ika

[e+ikx′+ reik(2L−x′)

]+ re+ika

[e+ikx′+ re−ikx′eik2L

]1− r2eik2L

(B.27)

E(x′) =e−ikae+ikx′+ re2Le−ikae−ikx′+ re+ikae+ikx′+ r2eik2Le+ikae−ikx′

1− r2eik2L (B.28)

Case III: x′ = a (emitter self interference)

For the case of x′ = a the expressions simplify to:

Ex′=a(x) =1+ re2Le−ik2x + re+ik2x + r2eik2L

1− r2eik2L (B.29)

This form is used in Chap. 4 and models the self interference of a resonant mode at the

source position. Using this form where x′ = a we then can map out an a simple 1D model

of the local density of optical states (LDOS) within the cavity.

Appendix C

Electromagnetic simulation methods

C.1 Introduction

Maxwell’s equations provide a very complete description of electromagnetic response.

Faraday’s law Eq. (C.3) and Ampere’s law Eq. (C.4) form the curl equations of Maxwell’s

equations and coupled together describe the propagation of electromagnetic waves. Since

all electromagnetic phenomena derive from these laws, it is useful to use computer simu-

lation techniques to solve Maxwell’s equations in an arbitrary inhomogeneous geometry.

This appendix discusses two finite difference techniques that solve Maxwell’s equations in

an electromagnetically-inhomogeneous volume. The first technique is known as the Finite

Difference, Time Domain (FDTD) method in which the curl equations are solved directly

by using a time-stepping algorithm to calculate electromagnetic fields as a function of time

[86]. The second technique is known as the Finite Difference, Frequency-Domain (FDFD)

method in which steady-state solutions of the time-harmonic version of Maxwell’s equa-

tions are solved on an inhomogeneous dielectric grid [57]. The simulations seen in the rest

of this thesis were performed using this FDFD method.

81

APPENDIX C. ELECTROMAGNETIC SIMULATION METHODS 82

Maxwell’s Equations [87]

∇ ·D = ρv (C.1)

∇ ·B = 0 (C.2)

∇×E = −∂B∂ t

(C.3)

∇×H = Je +∂D∂ t

(C.4)

C.2 Finite Difference Schemes

Both of these techniques rely on the finite difference approximation to take these inherently

continuous equations and discretize them for calculation by computer. The derivative at a

given point xo of a function f can be approximated as the difference between f at two

points ±∆x away from xo scaled by 2∆x. This finite difference scheme is known as the

centered difference scheme and can be written as:

f ′(xo)≈f (xo +∆x)− f (xo−∆x)

2∆x. (C.5)

This is a logical approximation of the concept that a derivative is an infinitesimal change,

d f , in a field, f , over an infinitesimal change, dx, in a spatial coordinate x. Instead of an

infinitesimal change in f and x we represent these changes as small, yet finite, differences

∆ f and ∆x. As long as ∆x is not too large this is a good approximation. In fact the centered

finite difference can be derived using the Taylor-series expansion of f (xo± ∆x) around

xo. Using this expansion the finite difference scheme can be shown to be second-order

accurate, O(∆x2) [88].

It is also possible to model second derivatives using this same technique by applying

the finite difference recursively, leading to:

f ′′(xi)≈f (xi+1)−2 f (xi)+ f (xi−1)

(∆x)2 . (C.6)


C.3 Finite-difference time-domain method

The Finite Difference Time-Domain (FDTD) algorithm simply applies the finite difference

approximation to Maxwell’s curl equations on a cartesian discretization grid and in a dis-

cretized time coordinate. In cartesian coordinates the two curl equations can be written as

six scalar equations, for example:

∂Hx

∂ t=

1µ

(∂Ey

∂ z− ∂Ez

∂y

). (C.7)

Finite differences can then be applied to all derivatives in this example scalar differential

equation:

∂H∂ t

∣∣∣∣tn,xi, j,k

≈ Hn+1/2x (i, j,k)−Hn−1/2

x (i, j,k)∆t

(C.8)

∂Ey

∂ z


≈En

y (i, j,k+1/2)−Eny (i, j,k−1/2)

∆z(C.9)

∂Ez

∂y


≈En

z (i, j−1/2,k)−Enz (i, j+1/2,k)

∆y. (C.10)

These finite differences can then replace the derivatives in the original scalar equation

leading to

Hn+1/2x (i, j,k)−Hn−1/2

x (i, j,k)∆t

=

1µ

[En

y (i, j,k+1/2)−Eny (i, j,k−1/2)

∆z−

Enz (i, j−1/2,k)−En

z (i, j+1/2,k)∆y

].(C.11)

From this particular scalar field equation Hx at time to +∆t/2 can be calculated from

Hx at an earlier time (to−∆t/2) and the E fields at the earlier to. One can recognize that

the newly calculated Hx has used data from two previous half time steps. This “leapfrog”

procedure allows for this finite difference to have explicit time stepping, i.e. no information

from the current or future time steps is used to generate the result at the current step. This


FDTD Proccedure:

0 Use sources to generate initial Eand H fields

1 Process H fields (for tn+1/2) usingE fields from tn and H fields fromtn−1/2

2 Process E fields (for tn+1) usingE fields from tn and H fields fromtn+1/2

3 Repeat 1 & 2 for desired time

Figure C.1: Time Stepping in FDTD [86]

time stepping procedure is outlined in Fig. C.1.

The spacial arrangement of E and H components also exhibits a similar staggered ar-

rangement. This is done intentionally because the staggering retains the geometry of a curl

of E vectors around an H vector. In 3D this “Yee cell” consists of E and H fields staggered

so the picture of a curl is clearly visible down to a single element, as can be seen in Fig. C.2

[89].

As with any discretization solution to a continuous partial differential equation we must

be careful that are approximations are not too coarse. To ensure stability of the these finite

differences in 3D we require that

umax∆t∆x

≤ 1√3

(C.12)

where umax is the maximum phase velocity in calculation volume, ∆t and ∆x are the

time and space grid spacings, respectively [86].

Overall the FDTD method is useful for simulating the unmodified time-domain Maxwell’s

equations. There are no approximations other than discretization. Any time there is dis-

cretization, there is the possibility that certain geometries will not be represented well. For

example in the FDTD cartesian grid, spherical objects will have a jagged surface which

will lead to non-physical fields at the interface’s jagged points. FDTD is especially useful


Figure C.2: Schematic of the Yee cell [88]

for transient or short time responses where a limited number times steps required. It is

less suited for finding steady-state solutions because many time steps are required to allow

the system to reach steady-state and all intermediate time steps are required, however the

next section shows an alternative method in the frequency domain more suited to these

problems.

C.4 Finite-difference frequency-domain method

Often we are would like a steady-state solution, and the FDTD method is not best suited

for this. Finite Difference Frequency-domain (FDFD) allows for a simulation to be run

assuming steady-state conditions [57]. For the steady-state case with a harmonic source

we use the behavior of electromagnetic radiation represented by the time-harmonic form

of Maxwell’s equations. To create this representation the electric and magnetic fields are

expressed using complex phasors Ec and Hc which are defined by the relation

E(r, t) = ℜ[Ec(r)eiωt ].

We can now use this definition to rewrite the curl equations as

∇×Ec = −iωBc (C.13)

∇×Hc = iωDc (C.14)


By taking the curl of each side of these curl equations we can separate the E and Hfields from each other to make Helmholtz wave equations. For the E field wave equation

assuming no current sources the procedure is as follows:

1µ(∇×Ec) = −iωµoHc

∇× 1µ(∇×Ec) = −iωµo∇×Hc

= ω2µoDc

∇× 1µ(∇×Ec) = ω

2µoεoεEc

resulting in

∇× 1µ

∇×Ec−ω2εoµoεEc = 0 (C.15)

∇× 1ε

∇×Hc−ω2εoµoµHc = 0 . (C.16)

For two dimensions (waves propagating in the xy-plane) there are two independent po-

larization modes of these wave equations known as the transverse electric (TE) and trans-

verse magnetic (TM) modes. The TM mode has Ez, Hx, and Hy as the only non-zero fields

while the TE mode has only the Hz, Ex, and Ey fields being non-zero.

TM (aka: s or σ ):∂ 2Ez

∂x2 +∂ 2Ez

∂y2 + ε

(ω

c

)2Ez =

ω

cJz (C.17)

TE (aka: p or π):

∂

∂x1ε

∂Hz

∂x+

∂

∂y1ε

∂Hz

∂y+(

ω

c

)2Hz =

ω

cMz (C.18)

The TM mode is simplified because we make the assumption that the magnetic suscep-

tibility µ is 1. This is a good assumption for most non-magnetic materials and is a very

good assumption for all materials at optical frequencies. Because of this simplification, the

TM mode is easier to demonstrate the FDFD simulation method. If we take Eq. (C.17) and


apply the second derivative finite difference approximation from Eq. (C.6) we can write a

finite difference equation for the i , j point on the 2D grid as

Ei+1, j−2Ei, j +Ei−1, j

(∆x)2 +Ei, j+1−2Ei, j +Ei, j−1

(∆y)2 +[

ω

c

]2ε i, j Ei, j =

ω

cJi, j (C.19)

This finite difference approximation of Helmholtz’ equation is a set of coupled linear

equations of the form Eq. (C.19) for all i, j on the grid and can be expressed in the matrix

form Ax = b, shown more completely as Eq. (C.20). Unfortunately A can be a rather large

matrix and thus requires a large amount of memory to invert and solve for the field vector x.

. . . . . . . . . ...

. . . . . . . . . 1∆y2

. . . . . . . . . ... . . .. . . . . . . . . 1

∆x2. . .

· · · 1∆y2 · · · 1

∆x2

[ω2

c2 εi, j− 2∆x2 − 2

∆y2

]1

∆x2 · · · 1∆y2 · · ·

. . . 1∆x2

. . . . . . . . .. . . ... . . . . . . . . .

1∆y2

. . . . . . . . .... . . . . . . . . .

...

Ei, j−1...

Ei−1, j

Ei, j

Ei+1, j

...

Ei, j+1...

=ω

c

...

Ji, j−1...

Ji−1, j

Ji, j

Ji+1, j

...

Ji, j+1...

(C.20)

C.5 Boundary Conditions

One important consideration when using either the time domain or frequency domain finite

difference methods is what to do with the edges of the the simulation volume. A naıve


approach would be just set the fields to zero outside of the boundaries. However, by setting

the fields to zero at the edges one is effectively causing the boundaries to become perfect

electrical conductors which by definition can have no electric field. So by placing zero field

conditions around the simulation volume one is effectively placing the simulation inside a

perfect metal box and will cause strong reflections at the walls.

If the desired simulation has some periodic symmetry, periodic boundary conditions

can be used to avoid these unexpected reflections.The fields from one edge of the simu-

lation volume can be copied to the opposite side to create this effect. Additionally Bloch

periodicity can be applied by adding a complex phase to the wrapped fields.

Neither the perfect electrical conductor or periodic boundary conditions are appropriate

for the case of a plane wave propagating into the simulation volume and out the other side.

For this type of problem an absorbing layer is required. Using a dielectric model of a real

life absorber, however, would be a bad choice. Any material that has good field dampening

properties also will have a large reflection coefficient. For example, a real-life metal has

a high imaginary part of the dielectric constant but is not a good absorber because the

high conductivity also causes large reflection. To fix this problem we have to be smart

about how we enable absorption so as to avoid any reflections. Berenger has described a

“perfectly matched layer” that does this by impedance-matching the PML with the incident

wave [90]. This is done anisotropically so that only wave components directed normal to

the PML are absorbed. By impedance matching at the interface and then slowly ramping

up the absorption away from the interface, most reflection is avoided.

Appendix D

Fabrication of silicon on insulator (SOI)detectors

For fabrication of devices used in Chap. 3 we used SOI wafers (SOITEC) with a buried

oxide (BOX) thickness of 400 nm and a top Si layer of 500 nm with 0.8–1.2 Ω-cm resistiv-

ity. The steps used to fabricate SOI detectors are depicted in Figure S5. Several fabrication

steps including oxidation, wet-etching, photolithography and deposition are involved in

order to build the SOI detectors.

Preparation of SOI wafers

The final Si device layer thickness is 40 nm. Several oxidation and oxide removal steps are

followed to reach the desired thickness from 500 nm initial Si thickness. Before we start

the oxidation we carry-out a standard three step cleaning process to remove 1) any surface

organic material, 2) any trace metals that may be on the surface of the wafers and 3) the

native oxide. This leaves the wafer surface clean of any mobile ions in preparation for high

temperature processing. In each oxidation step we typically consume half of the Si starting

with wet-oxidation and using dry-oxidation in the last two steps. There is a final oxidation

step for the 20 nm passivation layer on top.

89

APPENDIX D. FABRICATION OF SOI DETECTORS 90

Fabrication of Electrical Contacts

The electrically contacts are fabricated using standard photolithography. The contacts con-

sist of 3 µm wide strips separated by 31 µm from each other. A small contact width is

chosen to minimize the dark current. Two separate lithography steps are followed for the

contacts. After the expose and develop steps an oxide removal step is followed for each

electrical contact. A Schottky contact is realized by e-beam evaporating a 20 nm Titanium

layer at a rate of 1 A/sec. An ohmic contact is formed by e-beam deposition of 20 nm of

Nickel at a rate of 0.1 A/sec on the second mask layer. It is necessary here to quickly place

the sample into the deposition chamber after the oxide removal. Depending on processing

conditions, this Ni contact can be a Schottky contact rather than Ohmic. Finally a third

photolithography layer step is taken, followed by deposition of 5 nm Titanium and 30 nm

Gold for the fabrication of the contact pads.

Process Flow

1. Standard wafer cleaning procedure:

• Removal of trace organics (Piranha clean), 4:1 H2SO4 : H2O2 (10 min) – rinse

• Removal of trace metal cations using 5:1:1 H2O : H2O2 : HCl (10 min) – rinse

• Removal of thin silicon dioxide layer using 50:1 H2O : HF (30 sec) – rinse

2. Grow thermal oxide: wet oxidation for initial large oxidation steps, more controlled

dry oxidation for final oxide growth steps

3. Measure Si and thermal oxide thickness

4. Strip oxide – use 6:1 Buffered oxide etch (BOE) (910 A/min) or 20:1 BOE (300

A/min) depending on the oxide thickness

5. Repeat steps 2 4 until the desired device thickness is reached (including the Si layer

that is turned into the top spacer oxide layer)

6. Grow thermal oxide (optical spacer) by dry oxidation


7. Hexamethyldisilazane (HMDS) prime as an adhesion promoter for photoresist

8. Spin Shipley 3612 photoresist (5.5k RPM 40 seconds – 1 µm thickness)

9. Post-bake photoresist (1 min, 90C)

10. Expose Layer 1 lithography mask to define the first metal contact layer on Si (1.2

sec). A Karl Suss MA-6 Contact Aligner operating with UV light at a wavelength of

365 nm and a power density of 15 mW/cm2.

11. Post-exposure bake photoresist (1min, 115C)

12. Develop photoresist (30 sec MF-26A, 30 sec DI water)

13. Post-bake photoresist (1 min, 110C)

14. Wet etch in 20:1 BOE (300 A/min) to strip the exposed oxide layer for Ti electrical

contact (48 sec)

15. E-beam evaporation under 5×10−7 Torr – Titanium (20 nm, 1 A/sec) [RF Sputtering

is a good alternative]

16. Lift-off of the contacts in acetone while agitating in an ultrasonic bath (5 min)

17. Rinse in isopropyl alcohol (IPA) while agitating in an ultrasonic bath (5 min)

18. Repeat 7 – 9 (spin photoresist)

19. Expose Layer 2 lithography mask to define second metal contact layer on Si – Karl

Suss (1.2 sec)

20. Repeat 11 – 14 (Develop and oxide removal)

21. E-beam evaporation – Nickel (20nm, 0.1 A/sec) quickly place in the chamber after

oxide removal

22. Repeat 16-17 (lift-off), 7 – 9 (spin photoresist)

23. Expose Layer 3 lithography mask to define large contact pads – Karl Suss (1.2 sec)


24. Repeat 11 – 13 (Develop)

25. E-beam evaporation – Titanium (5 nm, 1 A/sec) + Gold (30 nm, 1 A/sec)

26. Repeat 16 – 17 (lift-off)

27. To realize the e-beam lithographically defined Ag antenna perform the following

steps:

a. Spin e-beam resist 100 nm (PMMA in Anisole) [spin speed 1600 rpm 40 sec]

b. E-beam exposure (RAITH 150) [Dose 100 µC/cm2]

c. PMMA development (30 sec in Methyl isobutyl ketone (MIBK), 30 sec in IPA,

30 sec in DI water)

d. E-beam evaporate 2 nm Ge (sticking layer) / 20 nm Ag

e. Strip PMMA / lift-off excess Ag (Acetone)


a b c

d e f

SiO2

Si

Si

SiO2

SiO2

Si

Si

Ti

Ti Ni

AuAg

Figure D.1: Process flow for fabrication of detector platform. (a) Initial silicon-on-insulator (SOI) wafer. (b) Active Si layer thinned by oxidation and subsequent wet etching.(c) Ti Schottky contact fabrication. (d) Ni contact fabrication. (e) Gold contact pad pat-terning and lift-off. (f) Electron-beam lithography and lift-off to create Ag wedge antenna.

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Edward Simon Barnard

I certify that I have read this dissertation and that, in my opinion, it is fully

adequate in scope and quality as a dissertation for the degree of Doctor of

Philosophy.

(Mark L. Brongersma) Principal Adviser



Philosophy.

(Alberto Salleo — Materials Science & Engineering)



Philosophy.

(Shanhui Fan — Electrical Engineering)

Approved for the University Committee on Graduate Studies

plasmonic optical antennas for enhanced light detection and emission a dissertation submitted to

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