OPTICAL PROPERTIES OF METALLIC NANOSTRUCTURES A ...

OPTICAL PROPERTIES OF

METALLIC NANOSTRUCTURES

A Dissertation

Presented to the Faculty of the Graduate School

of

Yale University

in Candidacy for the Degree of

Doctor of Philosophy

By

Aric Warner Sanders

Dissertation Directors: Mark A. Reed and Eric R. Dufresne

December 2007

ABSTRACT

OPTICAL PROPERTIES OF

METALLIC NANOSTRUCTURES

by Aric Warner Sanders

Chairperson of the Supervisory Committee:

Professors Mark Reed and

Eric Dufresne

2007

Department of Physics

Surface plasmon polaritons (SPP’s) are collective oscillations of electrons

sustained at a metal dielectric interface. These oscillations confine

electromagnetic fields naturally to two dimensions. In this thesis I explore SPP’s

in one and two dimensions. Propagation shows interesting behavior including the

redirection and inter-coupling between one dimensional plasmon modes. In

addition, I explore novel far-field detection schemes and localized launching

mechanisms. These techniques are coupled with excitation polarization to

investigate the scattering mechanisms in 1-d plasmon waveguides. Finally, the

luminescent blinking of silver nanowires is presented and discussed in a statistical

manner.

Table of Contents

Abstract ................................................................................................................................ iii

List of figures ...................................................................................................................... iv

Acknowledgments............................................................................................................viii

Chapter 1..........................................................................................................................- 1 -

Introduction......................................................................................................- 1 -

Chapter 2..........................................................................................................................- 8 -

Theoretical response of the Bulk electron Gas: ................................................- 8 -

Abstract..............................................................................................................- 8 -

Metals and Electromagnetic Waves..............................................................- 8 -

Chapter 3........................................................................................................................- 26 -

Theortical treatment of Surface Plasmons on planar films:..........................- 26 -

Abstract............................................................................................................- 26 -

Surface Plasmons ...........................................................................................- 26 -

Momentum Matching to Plasmons............................................................- 44 -

Chapter 4........................................................................................................................- 53 -

Experimental Observation Plasmon Propagation on Lithographically Defined

Thin Films: .............................................................................................................- 53 -

Abstract............................................................................................................- 53 -

Experimental Results.....................................................................................- 53 -

Chapter 5........................................................................................................................- 68 -

i

Theoretical Treatment of Surface Plasmons on Cylinders : .........................- 68 -

Abstract............................................................................................................- 68 -

Theoretical Concerns of Metallic Cylinders..............................................- 68 -

Chapter 6........................................................................................................................- 77 -

Observation of Surface Plasmon Polariton Propagation, Redirection, and

Fan-out in Silver Nanowires ...............................................................................- 77 -

Abstract............................................................................................................- 77 -

Observation of Plasmon Propagation, Redirection, and Fan-out in Silver

Nanowires .......................................................................................................- 77 -

Chapter 7........................................................................................................................- 92 -

Experimental Observation of Polarization Dependent Coupling in

Nanowires...............................................................................................................- 92 -

Abstract............................................................................................................- 92 -

Polarization Dependence of SPP excitation on Metallic Nanowires...- 92 -

Chapter 8......................................................................................................................- 106 -

Conclusion............................................................................................................- 106 -

Appendix I...................................................................................................................- 111 -

Nanowire Growth and Characterization: .......................................................- 111 -

Abstract..........................................................................................................- 111 -

Introduction..................................................................................................- 111 -

Growth and Characterization ....................................................................- 112 -

ii

Appendix II .................................................................................................................- 135 -

Luminescent Blinking from Silver Nanowire Aggregates: ..........................- 135 -

Abstract..........................................................................................................- 135 -

Introduction..................................................................................................- 135 -

Luminescent Blinking from Nanowire Aggregates ...............................- 136 -

Glossary........................................................................................................................- 147 -

Bibliography .....................................................................................................................B-1

Chapter 1 Bibliography....................................................................................B-1







Appendix I Bibliography .................................................................................B-9

Appendix II Bibliography..............................................................................B-10

iii

LIST OF FIGURES AND TABLES

Number Page

Figure 2.1: Drude Model of Electron Motion. ....................................................... - 10 -

Figure 2.2: Penetration Depth of Noble Metals Using The Good Conductor

Approximation. .............................................................................................. - 15 -

Table 2.1: Drude Parameters of Noble Metals. ...................................................... - 16 -

Figure 2.3: Penetration Depth Using the Drude Model. ...................................... - 18 -

Figure 2.4: Bulk plasma wave..................................................................................... - 21 -

Figure 2.5: Comparison of Calculated Penetration Lengths. ............................... - 24 -

Figure 3.1: Surface Plasmon Polariton. .................................................................... - 30 -

Figure 3.2: Surface Plasmon Wavelength and Propagation Length. .................. - 33 -

Figure 3.3: Surface Plasmon Polariton Wavelength of Silver Experimentally and

for the Drude Model. .................................................................................... - 34 -

Figure 3.4 Electric Field Decay Length for Silver.................................................. - 35 -

Figure 3.5: Decay Lengths Perpendicular to The Propagation Direction. ........ - 36 -

Figure 3.6: Surface Plasmon Polariton Penetration Depth for Silver. ............... - 37 -

Figure 3.7: Dielectric surface plasmon penetration depth for silver air interface.- 38 -

Table 3.1: Plasmon Length Scales for Common Excitation Wavelengths at a

Silver Glass Interface..................................................................................... - 39 -

Figure 3.8: Surface Plasmon Dispersion Relationship for Silver-Air interface. - 42 -

iv

Figure 3.9: Surface Plasmon Dispersion Relationship Close to Experimental

Plasma Resonance of Silver. ........................................................................ - 43 -

Figure 3.10: Momentum Matching Techniques for Surface Plasmon Launch. - 46 -

Figure 3.12: Surface Plasmon Launching Through Scattering. ......................... - 49 -

Figure 3.13: Surface Plasmon Launching Through Scattering Experimental Setup.- 50 -

Figure 3.14: Momentum Matching Through Scattering. ...................................... - 51 -

Figure 4.1: Measured Plasmon Intensity Decay for Aluminum Microstructures

Excited at 532nm. .......................................................................................... - 56 -

Table 4.1: Plasmon Intensity Decay Lengths For Aluminum Excited at 532nm.- 57 -

Figure 4.2: Al circle with propagating plasmons launched from a defect structure

at the center..................................................................................................... - 59 -

Figure 4.3: Edge launched propagating plasmon (830nm) on a patterned Ag

surface. ............................................................................................................. - 61 -

Figure 4.4: Composite image technique................................................................... - 64 -

Figure 4.5: Comparison of Plasmon Decay Length and Scattered Light. ........ - 66 -

Table 4.2: Plasmon Decay Lengths for Silver at 830nm....................................... - 67 -

Figure 5.1: Schematic of Cross Sectional View of Penetration Depths in a

Cylinder............................................................................................................ - 73 -

Figure 5.2: Schematic View of Excitation of Surface Plasmon Polaritons on a

Cylinder............................................................................................................ - 75 -

Figure 6.1: Micrographs showing the spatial sensitivity of launching plasmons.- 81 -

v

Figure 6.2: Micrographs of plasmon propagation in silver nanowires and

emission (top), control with no laser excitation (bottom)...................... - 84 -

Figure 6.3: Plasmon Decay Length........................................................................... - 86 -

Figure 6.4: Group of overlaying nanowires that illustrates inter-wire plasmon

coupling. .......................................................................................................... - 89 -

Figure 6.5: Several wires that illustrate inter-wire plasmon coupling. ................ - 90 -

Figure 7.1: Polarization dependence of plasmon emission. ................................. - 95 -

Figure 7.2: Emission intensity of a radiating kink. ................................................. - 97 -

Figure 7.3: Kinked nanowire response to varying the polarization of excitation.- 98 -

Figure 7.4: Normalized emission intensity plotted for two wires of different

geometry. ......................................................................................................... - 99 -

Figure 7.5: Normalized emission plotted versus the excitation polarization angle

at a kink measured from the x-axis........................................................... - 101 -

Figure 7.6: Emission intensity for excitation of a small metallic particle near the

end of the nanowire..................................................................................... - 103 -

Figure 7.7: The nanowire with multiple excitation points and possible scattering

mechanisms................................................................................................... - 104 -

Figure AI.1: Structure of silver nanowires............................................................ - 114 -

Figure AI.2: UV-VIS extinction spectra of metallic nanowires......................... - 116 -

Figure AI.3A: Fluorimeter measurements of nanoscopic metallic systems.... - 119 -

Figure AI.3B: Fluorimeter measurements of nanoscopic metallic systems. ... - 120 -

vi

Figure AI.3C: Fluorimeter measurements of nanoscopic metallic systems. ... - 121 -

Figure AI.3D: Fluorimeter measurements of nanoscopic metallic systems.... - 122 -

Figure AI.4: Scanning electron micrograph of silver nanowires after evaporation

of suspension. ............................................................................................... - 124 -

Figure AI.5: Ultra high resolution field emission electron micrograph of silver

nanowires....................................................................................................... - 126 -

Figure AI.6: Electron Dispersive Spectroscopy of A nanowire on A Si/SiO2

substrate. ........................................................................................................ - 128 -

Figure AI.7: Raman Scattering spectra of Silver Nanowires............................. - 130 -

Figure AI.8: Electrical Characterization of a Silver Nanowire. ......................... - 133 -

Figure AII.1: Power Spectrum Analysis................................................................. - 138 -

Figure AII.2: Spectral Mapping of a Blinking Nanowire Aggregate. ............... - 141 -

Figure AII.3: Effect of UV exposure in the time domain. ................................. - 143 -

Figure AII.4: Spectral Mapping of a Blinking Nanowire Aggregate after UV

exposure for 30 Minutes............................................................................. - 145 -

vii

ACKNOWLEDGMENTS

It has been a long strange journey leading me to a Ph.D. in physics. I have been

blessed by the support and kindness of countless people along the way, I am

grateful to have a chance to acknowledge their gift. Being able to thank those that

have helped me gave me refuge from the scientific content of my thesis and kept

me from breaking my laptop.

First I would like to acknowledge my advisors, Mark Reed and Eric Dufresne.

Mark gave me the freedom to explore my own path in graduate school, and this

made all the difference. Despite weekend attacks of emails requiring data the next

day, I have thoroughly enjoyed working with someone so excited by the promise

of scientific discovery. His direction has guided me through graduate school. As

for Eric, he has served as an older, wiser brother that served as a role model for

what a young healthy scientist is like.

Now it is my pleasure to try acknowledge the throngs of people that I have come

to know and love. I first like to start with my fellow students, we all made it

through many years of strange torture interspersed with some of the happiest

moments of our lives. First, my fun and almost as much of a slacker as me lab

partner Betty B. (hey I only have so much room in my thesis). My roommate

Ben and his partner Alex for tolerating my well natured gay jokes (Alex is a girl,

viii

and Ben rides a motor cycle, but he likes to bake). The first to escape with a

Ph.D. Grace Chern, who along with making a great gimlet, has been a great

friend (good luck getting those lucky charms!). The Asian kid with too many

games Dale Li, who is good at everything he does. Veronica Savu, the best damn

dancing, bread-eating Romanian out there, and her always thoughtful husband

Martin(the fastest Frisbee slinging Swahili speaking white man alive). Rona

Ramos for her love of all things sheep and spiderman like climbing ability. Sevil

Salur for never being anyone but Sevil, and her … sorry I get him later. Sabas and

Tracey for there dog swapping ways that got us through the first few years. Keith

for having the bravery to leave and become himself. Adam, it is always good to

have a man in black. George Mias, the best Yale has to offer, but are you ever

going to leave?(note he apparently graduated before me) Lafe Spietz, for attacking

science in way that Royce Gracie would be proud of. Julie Wyatt (Love) for

letting me give Sean a hand where it really counts. Dave Schuster for inspiring

everyone around him to see things in a new way (over the glasses of truth).

Ettiene Boakin for showing me how they say hello in his country (happiness is

better than science). Marvin, Keith, and Allan for giving me company and a

reason to come to work at 4:00am. Vivian Smart for being always genuine (and a

lot of times scary as hell). Tanis for being so damn fun. Jayne for being a rock in

the applied physics department, I hope you enjoy your new life landscaping. Pat

for being a mother to the rowdy kids (including R.C.). Cindy for dancing up and

ix

down rocks like a dog rapped around my leg (or black rum). Phillip Kim his goal

posts showed me the way. Now as my wife is having contractions I shall

abbreviate the thanks. Jeff Caplan and Jessica Tanis for always being fun and

positive. Jeremy Draghi for his comedic ways. Of course Jermy, Jeff, Jessica,

Jason, John, Rona, and Rachael for taking my money and letting me drink the

lion’s share of the beer. Crena, Corina, Shawn for feeding me in my time of need.

Chad for being a well groomed Canadian with a healthy id. My lab mates in

Mark’s group Ryan, Eric, Elena, Guosheng, Ilona, Xinhui, Stan, Wenyong, David,

and Takhee for their help in late nights and early days with the cryostat and

JEOL. The people who helped and taught me on the fouth floor of Becton Prof.

Prober, Matthew R., Irfan, Bertrand, Konrad, Dan Jr. My co-conspritors in evil

plans in Eric D.’s lab Sara, Jason, Matt, Vincent, Sunil, Eleanor, and Cecile

(Thanks for saving my sanity). The tree-huggers for making first year fun for a

guy in a van down by the river; Confederate Jeff, Mountain Jeff, Private Stupid,

Jen, Neil, and our favorite Nurse. Professor R. Chang for teaching me about

plasmons. Norman, John, Kris, Lorelle, Paul, Kevin and Mark, for making my

first days as a postdoc great. My siblings John, Ryan, Baron, Cragg, Jenni and

Rashee for being there from the beginning to the end. For those countless others

that I have not mentioned here thank you from the bottom of my heart.

Finally, I give to my deepest gratitude and love to my family. My parents for

giving me life, and teaching me how to make the most of it. My father and

x

mother-in-law, for being there and providing support whenever we needed it.

And of course my beautiful bride Shaila, who makes everything in my life shine

brighter, and has made it all worth while. To my almost daughter, Neela, see you

soon.(after note: I have seen her and she is also beautiful)

xi

C h a p t e r 1

Introduction

This thesis is an investigation on the interaction of nanoscopic metals and light.

The research in this thesis was motivated by a simple serendipitous observation.

While exploring fluidic systems using a microscope with optical tweezers (a highly

focused laser) I found that light focused on one end of a silver nanowire

reemerged from the other end. It appeared that a solid wire of silver was acting as

a small optical fiber. In fact, this is exactly what was happening, due to confined

surface waves. Confined surface waves are by no means a new area of research,

the basic formalism was set out by Sommerfield1 and Zenneck2 close to a

hundred years ago. They were trying to study radio waves in a macroscopic

world, considering the earth and the atmosphere as large conductors. Their work

was slowly applied to metal systems, and the middle of last century saw an

explosion in research regarding surface plasma oscillations. Workers such as

Ritchie3, Stern4, and Economou5 calculated theoretical values and experimentally

observed radiating and non-radiating surface plasmons. From the late fifties to

the mid 70’s plasmon research focused on coupling to plasmons and measuring

anomalous plasmon absorption. In the mid seventies Fleischmann et al.,

discovered that roughened silver surfaces with Raman active molecules, showed

huge increases in the scattered signal6. This led to a second coming of plasmons,

- 1 -

and many complete reviews are available7-9. This effect known as surface

enhanced Raman scattering (SERS) is commonly used in biological and chemical

research. Plasmons became in vogue again close to the turn of this century with

the discovery of extraordinary transmission through sub-wavelength apertures10.

This higher than expected transmission through regular holes patterned in metal

has been linked to plasmons and is the subject of intense research. At roughly the

same time but in a separate realm, several groups became interested in the use of

surface plasma oscillations as waveguides11-16. This thesis is primarily devoted to

these waveguides. During my thesis research, I studied nanoscopic (one

dimension is smaller than an optical wavelength) waveguides in the optical

frequency range. Propagating electromagnetic modes on metallic dielectric

interfaces are today widely studied. Historically, resonances between the electron

gas and surrounding dielectrics have been exploited for millennia to create

brightly colored glass17. The interaction of light with metals is a rich field with

many unexpected results. We typically approximate a metal as a solid with a free

electron gas that responds infinitely fast to incident electric fields. In this

approximation we take the magnitude of the electric field (E) inside a metal to be

strictly zero (E=0). This leads to perfect specular reflection at the surface of a

smooth metal and any dielectric. This approximation is equivalent to the

statement that the conductivity of the metal is infinite, which from experiment

and theory, we know to be false. If instead of taking the conductivity of a metal

- 2 -

to be finite, using the well known microscopic ohms law (J=σE), we see that

inside the metal an electric field of non-zero magnitude can exist. In addition, if

we explore the frequency response of the metal to electromagnetic radiation we

find that all such waves become attenuated and have characteristic length scales

associated with them. In fact, above a certain angular frequency (known as the

plasma frequency ωp) the electron gas becomes transparent, allowing traveling

wave solutions that are relatively un-attenuated. It should not be a surprise then,

that in special conditions a propagating wave can exist at the interface of a metal

and a dielectric (even if the conductivity of the metal is infinite). This surface

confined wave is inhomogeneous, decreasing exponentially into the bulk of the

metal and dielectric. However, losses through Joule heating and radiation limit the

ultimate length scale in the direction of propagation (parallel to the interface). A

Renaissance in surface waves for the subwavelength transport of optical fields has

been generated by novel fabrication techniques allowing almost arbitrary

morphologies of metallic nanostructures to be realized18. It is the interaction of an

archetypal nanostructure, the metallic nanowire, with light that this thesis focuses

on. By fortuitous happenstance, I discovered for myself what has been known for

a long time that these surface waves on wires can propagate and radiate.

However, in the nanoscopic regime this phenomena has been neglected and

much research is needed.

- 3 -

This thesis contributes to research into the nanoscopic regime in several areas*:

1. Extension of far-field techniques for plasmon launch and detection.

The launch of SPPs has been achieved in silver nanowires by using a

focused beam13, however site specific launch on multiple points for a

single nanowire has never been realized. In addition the scattered

radiation from SPPs on lithographically defined structures have been

previously detected, yet no experiment has extended the effective

dynamic range of the detector by changing the shutter speed of the

imaging detector.

2. The first observation of SPP mode bending in metallic nanowires.

Other investigations in silver nanowires have focused on scattering

behavior and the effect of changing morphology of metallic

* The author of this thesis is responsible for the creation of all figures in this

thesis with the notable exceptions of figures AI.1 and 7.7 B (Courtesy of D.

Routenberg). In addition, all the data collection and analysis was preformed by

the author at the guidance of professors Mark Reed and Eric Dufresne with the

exception of data presented in figure AI.8 (data collection: I.Kreschtzmar,

E.Stern, R. Munden, and the author) .

- 4 -

nanowires13,19. There has not been previous research that demonstrates

the ability of chemically synthesized nanowires to redirect light.

Additionally, the extent of a nanowire to support a curved mode before it

radiates has not been addressed. In figure 6.2 both a sharply bent wire

(radius of curvature 4μm) that does not radiate, and a nanowire with even

sharper bend (radius of curvature <300nm) that does radiate are

presented.

3. The first observation of cross coupling of SPP modes in metallic

nanowires.

There has not ever been a previously reported case of SPP modes

coupling between wires in close proximity that the author is aware of.

4. The first measurement of the polarization dependence of launching SPP’s

in silver nanowires.

The polarization dependence of SPP launch has only been presumed

form the planar case or stated to be a maximum for polarizations along

the wire axis19. The measurement of the polarization dependent launch

confirms that the SPP is maximally excited when the polarization of the

incident electric field is along the axis of the nanowire. However, for

- 5 -

nanowires of more complicated launching geometry this polarization

dependency does not hold and can vary as a function of the surrounding

environment.

5. The first observation of luminescent blinking in silver nanowires.

Other structured forms of silver have been seen to show luminescence

and blink (see appendix II). However, there has not been a reported case

(that the author is aware) of silver nanowire aggregate luminescent

blinking.

This thesis is organized into 8 chapters. Chapter one, or this chapter, is an

introduction to the subject matter and the format of the thesis. In chapter two a

brief summary of electromagnetic waves interacting with metals is presented. In

addition, a discussion of the bulk plasma frequency is included. In chapter three,

confined surface waves are discussed. In chapter four I present experimental

results of propagating plasmons in lithographically defined thin films. Specifically,

I demonstrate that plasmons can be selectively launched from an edge, and

demonstrate several novel techniques used to explore the propagation and re-

emission of plasmons. In chapter 5, I extend the theoretical treatment of surface

waves to cylinders. In chapter 6, the experimental observation of plasmon

propagation, redirection and fan-out is presented. In chapter 7, I give an in depth

- 6 -

experimental description of the scattering into and out of the fundamental

propagation mode. Finally, chapter 8 acts as a conclusion to the thesis.

In addition to the central bulk of the thesis there are two appendices devoted to

important, loosely related topics. In appendix I, I discuss the growth and

characterization of nanowires used in the experiments in chapters 7-9. In

appendix II, I present a brief description of the luminescent blinking of

aggregates of silver nanowires.

- 7 -

C h a p t e r 2

THEORETICAL RESPONSE OF THE BULK ELECTRON GAS:

Abstract

This chapter is a brief introduction to the basic response of metals to

electromagnetic waves. The chapter begins with the Drude† interpretation of

conductivity. From here I move to the modified wave equation inside a metal.

The modified wave equation yields damped oscillations, and the results of several

common approximations are discussed. These approximations are compared to

the measured values for the dielectric function for some common metals. In

addition, a definition and description of bulk plasma waves are included. Finally, I

present the basic terminology and notation of plasmons.

Metals and Electromagnetic Waves

We begin developing the conductivity of a metal by taking it to be a solid of net

zero charge with electrons free to move, subject to isotropic scattering events.

The scattering events cause the momentum of the electrons to be completely

randomized, but conserve energy. We will denote the mean time between

† The paper most referenced is Drude, P., Zur Ionentheorie der Metalle. In 1900; Vol. 1, pp 161–165. However, by common practice I have adopted more modern presentations1

- 8 -

scattering events τscatter , and not worry about the physical origin of the scattering.

If we apply an electric field across the metal the electrons will feel a force (eE, e is

the charge of an electron =1.6x10-19 C) and gain a net momentum of eE τscatter

before scattering. The current density in the metal ( J) can then be deduced from

the relationship J=nq<V> were n is the density of carriers, in this case electrons,

q is the charge (-e), and <V> is the time averaged velocity. The time averaged

velocity is just the momentum gained divided by the effective mass of the

electron in the solid (m*e). Now the current density reads1:

(2.1)2

*Scatter

e

nemτ

=J E

Which is the microscopic statement of Ohm’s Law J=σE.

- 9 -

E

A

B *Scatter

e

eVmτ−

< >=E

Figure 2.1: Drude Model of Electron Motion. A) Electrons in a metal are

envisioned to diffuse randomly, scattering causing their momentum to be

randomized. B) With the application of an electric field the electrons drift,

acquiring a net velocity *e

eEVmτ−

< >= .

- 10 -

Of course this is the approximation for a static electric field. To be more

complete we can look at how the electrons respond to a time varying field. As

with many things in physics we may reduce it to a damped driven oscillator. The

equation of motion for a single electron is2:

(2.2)*

* ee

dampening

mm eτ

= −xx E where E is taken to be a periodic electric field,

inserting 0i te ω−=E E , and assuming that the response is at the same frequency

we arrive at the solution for the equation of motion

(2.3)2

( / )

dampening

e miωω

τ

−=

+0x E

Furthermore we may extend this to the multi-electron system by investigating

the current produced by this motion. For the bulk, the damping term is

characterized by the damping time ( dampeningτ ), which is very closely related to the

scattering time and it is customary to set them equal. In the interest of brevity we

will use only τ to denote the net scattering time given by 1i i

1τ τ=∑ where τi are

the characteristic scattering times associated with all scattering processes. The

current produced by the electrons with volume density n, moving back and forth

is

- 11 -

(2.4)

2

* 1( )

d nenedt m iω

τ

⎛ ⎞⎜ ⎟

= − = ⎜ ⎟⎜ ⎟−⎝ ⎠

XJ E

This gives us the AC equivalent of ohms law.

Now we see that for ω=0 we recover (2.1) or the DC statement of ohm’s law.

The frequency dependence of the current density tells us that at low frequencies

the imaginary term is negligible and the conductivity is independent of ω.

However at large frequencies, there becomes a significant phase difference

between the current density and the driving electric field2.

We may now use the microscopic statement of Ohm’s law together with

Maxwell’s equations to describe an electromagnetic wave in a metal. First we

begin by writing Maxwell’s equation in a medium of conductivity σ, and net zero

charge.

(2.5) (i) (ii) = 0∇•E = -t

∂∇×

∂BE

(iii) = 0∇•B (iv) =t

με μσ∂∇× +

∂EB E

By applying the curl operator to (2.5iii) and (2.5iv), we arrive at a modified wave

equation:

(2.6)2

22t t

με μσ∂ ∂∇ = +

∂ ∂E EE ,

22

2t tμε μσ∂ ∂

∇ = +∂ ∂

B BB

This equation has plane wave solutions with complex wave-vectors

- 12 -

( )0

i k x tE E e ω−= i

(2.7) 2 2 2 ik i ωσμεω μσω με ωε

⎛ ⎞= + = +⎜ ⎟⎝ ⎠

or damped oscillations2. The distance over which the wave drops to 1/e its

original value is known as the penetration or skin depth1,2. We find the expression

for the penetration depth by taking the square root of the expression for k2 and

reinserting it into the plane wave solution (Re[ ] ) Im[ ]0

i k x t k xE E e eω− −= i i . It follows

that the 1/e distance is 1Im[ ]pen k

δ = . This distance is usually at least an order of

magnitude smaller than the wavelength of oscillation, hence we focus on the skin

depth. In many texts2 two limits are taken

1. poor conductor σ ωε<<

2Im[ ] ~2 penk σ μ εδ

ε σ μ⇒ ⇒ = , and we have that the

penetration depth is independent of frequency.

2. good conductor σ ωε>>

2Im[ ] ~2 penk ωσμ δ

ωμσ⇒ ⇒ = , This is the penetration depth that is

most commonly used when discussing metals since the DC conductivity is on

the order of 102

11210 C

Nmε − 1810 Hzσ ω

ε>>7(Ω-m)-1 and , giving for

- 13 -

waves well into the UV range. To be fair, this is an under estimate of δpen and

later in this chapter we shall see the effects of using the frequency dependent

conductivity.

To understand what the good conductor approximation predicts for

electromagnetic penetration in a metal, the penetration depth versus free space

wavelength of EM wave for silver, gold, and copper are plotted in figure 2.2. For

the three metals shown the approximation predicts that the electric field of

optical waves falls to 1/e of its initial value in a few nm. This value is often

quoted as a first approximation.

- 14 -

Figure 2.2: Penetration Depth of Noble Metals Using The Good

Conductor Approximation. The good conductor approximation is the most

frequently used when discussing penetration depths for AC signals that are high

in frequency. It yields penetration depths of ~3nm in the optical region of the

EM spectrum.

- 15 -

Even though this is the typical penetration depth used as a first estimate, for a

more complete picture of how far the electric field penetrates a metal we can use

the frequency dependent conductivity without the good conductor

approximation.

If we insert the full expression for the conductivity from (2.4), we have

(2.8) 2 2 2

2 22 * 2

* 21 1

( )( )

ine inekc m im i

ω τω με ω ε ω ω τε ωτ

⎛ ⎞⎜ ⎟ ⎛ ⎞

= + = +⎜ ⎟ ⎜ ⎟−⎝ ⎠⎜ ⎟−⎝ ⎠

, where we have

assumed that the material in question has the property 0μ μ= .

Now we can define the penetration depth of a free electron gas as 1Im[ ]Free k

δ =

where k is defined above. We use the free electron parameters for electron

density1, scattering time3, and effective mass3 (see Table).

Table 2.1: Drude Parameters of Noble Metals. The table summarizes the

Drude parameters for the noble metals.

- 16 -

Using the dispersion relationship (k as a function of ω), with the values above we

see that the penetration depth is an order of magnitude greater than the one

predicted by the good conductor approximation (see figure 2.3). This penetration

depth is how far an electromagnetic wave would intrude into plasma made of free

electrons with isotropic scattering. When referring to the penetration or skin

depth in the Drude model, this is the value that is quoted.

- 17 -

Figure 2.3: Penetration Depth Using the Drude Model. Using the full

expression for the frequency dependent conductivity and measured values for the

bulk materials the free electron model yields a penetration depth of ~25nm in the

optical region of the EM spectrum. It also shows a large divergence in

penetration depth for lower wavelengths (see blow up).

- 18 -

This value is the most complete treatment using the Drude model. However it is

not the most popular and a more common approximation is seen widely in the

literature regarding plasmons. This approximation makes clear the connection

between the fundamental material parameters of the free electron gas and their

response to electromagnetic excitation.

If 2ω τ >>ω then we may simplify the equation to 2 2

22 *1 nek

c mω

2ε ω⎛ ⎞

= −⎜ ⎟⎝ ⎠

.

Evidently, when the quantity in the parenthesis is zero something special is

happening. In fact this is the plasma frequency.

(2.9)2

2*p

nem

ωε

⎛ ⎞= ⎜ ⎟⎝ ⎠

So that we may now write 22

22 1 pk

cωωω

⎛ ⎞⎛ ⎞⎜= − ⎜ ⎟⎜ ⎝ ⎠⎝ ⎠

⎟⎟

or that the dispersion

relationship is

(2.10)2

0 1 pk kωω

⎛ ⎞= − ⎜ ⎟

⎝ ⎠ were k0 is the wavevector in free space,

this gives rise to the commonly used form of ε for a metal4, 5,

2

1 pm

ωε

ω⎛ ⎞

= − ⎜ ⎟⎝ ⎠

. The plasma frequency for the noble metals is on the order of

- 19 -

2 28 19

* 12

6 10 (1.6 10 )8.85 10 9 10p

ne x xm x x x

ωε

−

− −

⎛ ⎞ ⎛ ⎞= =⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠

2

31 ≈ 1017Hz or a free space wavelength

of ~100nm. Roughly an order of magnitude smaller than where we would expect

that the good conductor approximation using dc conductivity breaks down. We

see that the full free electron model yields results obscured by common

approximations. The dispersion relationship using this approximation elucidates

an important physical phenomena. Below the plasma frequency k is imaginary

and waves are attenuated as they enter the metal. Above the plasma frequency k

becomes real (and smaller than k0) allowing for traveling waves. These traveling

waves are waves in the electron plasma and at the plasma frequency they are

completely longitudinal (see figure 2.4 ). The quantum of a plasma oscillation is

known as a plasmon.

- 20 -

Figure 2.4: Bulk plasma wave. At the plasma frequency a driving

electromagnetic wave sets up a electron density wave in the same direction as

propagation.

- 21 -

As stated in the introduction, the Drude model is basically a classical model that

ignores quantum mechanics except in calculation of certain parameters (the speed

that the diffusive electrons are moving is the Fermi velocity determined quantum

mechanically.) In a real metal more subtle effects are at play. In particular,

electrons in the lower lying valence band (electrons that are tightly bound to the

atomic cores) may be promoted to the conduction band, drastically changing the

optical response of the metal. This absorption from the d band electrons is what

makes gold and copper have their characteristic color. For simplicity, we can

incorporate all the material properties that affect the optical response into a single

quantity, namely the dielectric function ε of the metal. Now, without mention of

the conductivity of the metal, we may deal with metal as if were simply a

dielectric with a frequency dependent dielectric function. This type of analysis

was pioneered by Fermi6 and used extensively by Fano7. The dielectric functions

of several metals have been measured by multiple groups and it is customary to

use the tables found in Johnson and Cristy3 or Palik8. Some the values vary quite

significantly at lower wavelengths but we shall discuss theoretical results in the

context of Johnson and Cristy. The results of Johnson and Cristy are stated in

terms of the index of refraction. It is very common to find the description of the

optical properties of solids in terms of the index of refraction n. The general

relationship of n and epsilon is n ε= . This is also true for complex indices and

- 22 -

dielectric functions. The notation commonly used is n=n+ik. This is important to

keep in mind because of the dual use of k as the wavevector. Now the

penetration length is simply 1/(k0Im[n]). We can compare the measured

penetration depths with the full free electron model (see figure 2.5).

- 23 -

Figure 2.5: Comparison of Calculated Penetration Lengths. The Drude

model compared with the measured values from Johnson and Cristy3. The

penetration depth measured is slightly larger than what is computed from the free

electron model with more structure. The additional structure is attributed to band

contributions to the dielectric function. In addition, because of the band

contributions silver under goes a plasma resonance at around a wavelength of

320nm.

- 24 -

In conclusion, the basic response of electrons to electromagnetic waves can be

understood in terms of classical mechanics and Maxwell’s equations. The

penetration depth of electromagnetic waves for the noble metals is roughly 20nm

in the optical region of the electromagnetic spectrum. This penetration depth

represents the spatial scale that electromagnetic waves sample the material

properties of a metal. In addition, when the electron gas is driven at rates faster

than the plasma frequency an electromagnetic wave with a real wave vector can

be sustained. This wave includes a charge density wave that is known as a

plasmon.

- 25 -

C h a p t e r 3

THEORETICAL TREATMENT OF SURFACE PLASMONS ON

PLANAR FILMS:

Abstract

In this chapter, waves at a metal dielectric interface are discussed. A brief outline

of the solution to Maxwell’s equations using the appropriate boundary conditions

is included, along with the definition of the surface plasmon frequency. The

important length scales associated with surface waves are calculated for some

simple cases. In addition, coupling to confined surface waves is discussed. The

experimental coupling mechanism is described as an extension of the grating

coupler.. This model elucidates the general characteristics of coupling to

plasmons. The momentum of the scattered excitation must be matched to the

plasmon mode, energy must be conserved between all the processes and there

must be volumetric overlap between the scattered excitation and the plasmon

mode.

Surface Plasmons

In addition to collective oscillations inside the bulk of a metal, when a surface is

introduced new modes at the interface appear1. These modes can be as complex

as the interface itself, responding to geometric considerations2, surface

- 26 -

roughness3, 4 and the bulk properties of all the materials defining the interface.

These modes are known as surface plasmon polaritons (SPP’s), surface plasmons,

or just plasmons. These surface waves can be separated further into two

categories. Above the bulk plasma frequency they are radiative, and below what is

know as the surface plasma frequency, they are confined surface waves. The

confined surface waves are often also referred to as propagating plasmons.

Before quantum mechanics was developed, the existence of these surface waves

was predicted by Sommerfield5 and Zenneck6, however there was not a

consensus to their presence. Later both confined and radiating surface waves

became a popular subject and their existence was proven experimentally7, 8. The

solutions for surface plasmons can be found in a variety of papers and books. I

will review only the basic structure and not discuss the more complex situation of

multiple films. A similar but briefer overview is given in Raether9, and the

solutions for silver on glass are given using experimental results for the dielectric

function by Dionne et al10. In this chapter, I will also review the solution for a

planar interface and introduce the important length scales. I also follow with an in

depth discussion of how we realize plasmon excitation and detection.

Surface plasmon polaritons (SPP’s), can occur at any interface. The basic

structure of a propagating SPP is of an evanescent wave, decaying exponentially

in intensity normal to the interface, and oscillating in the direction of propagation.

Traditionally, to find the solutions that constitute confined surface waves one

- 27 -

assumes that a wave exists at the boundary and solves for the appropriate

boundary conditions. We shall follow this tradition noting that the boundary

conditions are continuity of the tangential electric field and the normal

displacement. As an archetypical example we may begin with the simplest

possible interface; a charge neutral metal of infinite extent for z>0 and a dielectric

of infinite extent for z<01, 9, 10. We also assume that the interface is smooth (see

figure 3.1). The solutions to Maxwell’s equations (2.5) in Cartesian coordinates

are known to be an infinite sum of sines and cosines. Using

ˆ( ) ˆi k tkA e ζ ω

ξ

ξ• −∑k,

E = ξ where represents the normalized Cartesian directional

vectors.

We can insert the plane wave solutions into equations (2.5 i-iv) and solve noting

that we can let the y component be zero with out loss of generality. Next using

the fact that the tangential electric field and the normal displacement is

continuous we have for planar plasmons that the electric field is in the metal is

( )0

m plasmoni k z k x txE E e ω+ −= ( )

0m plasmoni k z k x tplasmon

zm

kE E e

kω+ −= −(3.1) , , 0yE =

and outside in the dielectric it is

( )0

d plasmoni k z k x txE E e ω+ −= ( )

0d plasmoni k z k x tm plasmon

zd m

kE E e

kωε

ε+ −= −(3.2) , , 0yE =

where

- 28 -

(3.3) d mplasmon

d m

kc

ε εωε ε

=+

2d

dd m

kc

εωε ε

=+

2m

md m

kc

εωε ε

=+

, ,

where εd is the dielectric constant of the surrounding dielectric, εm is the dielectric

constant of the metal, c is the speed of light and ω is the angular frequency of the

wave.

- 29 -

Figure 3.1: Surface Plasmon Polariton. A surface plasmon polariton is a

charge density wave that travels parallel to the interface between a metal and a

dielectric. The wave is confined strongly to the interface and undergoes a

resonance when 0m dε ε+ = .

- 30 -

Now there are five length scales that come into the discussion of surface

plasmons polaritons:

1. The free space wavelength of photon 0

2ph k

πλ = , where 0kcω

=

2. The wavelength of the SPP, 2Re[ ]plasmon

plasmonkπλ = , where kplasmon is given

in (3.3)

3. The 1/e distance of the plasmon electric field in the direction of

propagation 1Im[ ]

Electricplasmon

plasmon

Lk

= , or more frequently of the 1/e

distance of the intensity of the SPP 12 Im[ ]

Intensityplasmon SPP

plasmon

L Lk

= = .

4. The 1/e distance of the electric field of SPP into the metal normal to the

direction of propagation 1m m

mkδ δ= = .

5. The 1/e distance of the electric field of SPP into the dielectric normal to

the direction of propagation 1dielectric d

dkδ δ= = .

- 31 -

Each of these important lengths is plotted below for the experimental index of

refraction data of Johnson and Cristy and for the Drude model.

- 32 -

Figure 3.2: Surface Plasmon Wavelength and Propagation Length. Taking

the electric field at the interface z=0, we see that the plasmon oscillates with a

wavelength λp which is close to the wavelength of light in the dielectric. The

surface wave continues to propagate and drops to 1/e of its original magnitude in

a characteristic distance of , which is typically 10’s to 100’s of μm in the

visible part of the electromagnetic spectrum.

ElectricplasmonL

- 33 -

Figure 3.3: Surface Plasmon Polariton Wavelength of Silver Experimentally

and for the Drude Model. The experimental values of Johnson and Cristy are

compared to the Drude model using the parameters from Table 2.1. The surface

plasmon polariton is at an air (vacuum) silver interface. The wavelength of the

plasmon is less than that of light for incident frequencies less than the surface

plasma resonance 2pair

sp

ωω = . The blow up shows that silver behaves almost

ideally in the wavelength range of 500nm-850nm. The peak around 320nm in the

experimental data is a plasma resonance caused by band contributions.

- 34 -

Figure 3.4 Electric Field Decay Length for Silver. The results of Drude

model are compared with the results of using the experimental values. The

electric field decay length ranges from μm’s to almost 1mm at longer

wavelengths. Since this model only uses the bulk dielectric function, which

contains information about conductivity but not surface morphology, radiative

losses are not considered and the energy loss that gives this length is due to

heating of the conductor.

- 35 -

Figure 3.5: Decay Lengths Perpendicular to The Propagation Direction.

For a given x value the electric field exponentially decays into the bulk of both

media. The electric field decays with a characteristic length approximately of the

penetration depth on the metal. In the dielectric, the decay is slower being closer

to the wavelength of light.

- 36 -

Figure 3.6: Surface Plasmon Polariton Penetration Depth for Silver. The

electric field of the propagating plasmon falls to 1/e of its maximum in

approximately the penetration depth of the silver. The Drude model slightly

underestimates the penetration of the electric field into the metal.

- 37 -

Figure 3.7: Dielectric surface plasmon penetration depth for silver air

interface. The surface plasmon falls to 1/e of its initial value on a length scale

comparable to the half wavelength of light in the dielectric medium. The Drude

model slightly overestimates the penetration into the dielectric. Notice the values

are in reference to the z=0 plane, so negative values indicate penetration into the

dielectric.

- 38 -

Table 3.1: Plasmon Length Scales for Common Excitation Wavelengths at

a Silver Glass Interface. The calculated plasmon length scales are extrapolated

from Johnson and Cristy data for the dielectric function for silver and a glass

interface (ε=2.25).

In addition there is a resonance when the plasmon wave vector diverges or when

m dε ε= − . This is how the surface plasma frequency is defined, or the frequency

where the dielectric function of the metal is equal to the negative dielectric

function of the dielectric. In the Drude model, and for the approximation

2

1 pm

ωε

ω⎛ ⎞

= − ⎜ ⎟⎝ ⎠

(where ωp is the bulk plasma frequency), we have that the surface

plasma frequency is 2

1p

spd

ωω

ε=

+ 2pair

sp

ωω =, or in air or a vacuum . This is

- 39 -

the common form found throughout the literature. This gives us two more length

scales important in the discussion of surface plasmons, the vacuum wavelength

corresponding to the bulk plasma frequency (ωp) and the surface plasma

frequency (ωsp).We may use these length scales to gain insight into the surface

plasmon. They are roughly in the UV, with the calculated values around 135nm

and 190nm respectively.

It should be noted sometimes a distinction is drawn between a surface plasmon

and the electric field due to a plasmon. The surface plasmon is a charge density

wave confined to the interface. It is the density of electrons being modulated as

function of distance and time. The surface plasmon is a longitudinal wave, or the

electrons are displaced in the direction of the propagation of the wave. However,

the electric field due to this charge wave has components that are both

longitudinal and transverse. It is important to understand this subtle distinction

when calculating the scattering into and out of the mode. Inside the metal the

longitudinal ( xE ) component of the electric field dominates. In the dielectric the

transverse component ( ) is larger and the electric field vector has large

components normal to the interface. Furthermore it is important to draw a

distinction between radiating and non-radiative surface plasmons. Above the bulk

plasma frequency (ω

zE

p), the charge density waves radiate strongly and the modes

are not considered confined. Below the surface plasma frequency (ωsp), the waves

are well confined and are considered non-radiative. This is the regime that is

- 40 -

explored experimentally in this thesis. Between these frequencies there is no

surface wave solution, to Maxwell’s equations at the interface, and this area is

known as the plasmon band gap. In real solids it has been proposed that quasi

bound states can exist in the plasmon band gap10. To understand the energy scale

it is common to plot the dispersion relationship of the surface plasmon.

- 41 -

Figure 3.8: Surface Plasmon Dispersion Relationship for Silver-Air

interface. The plot compares the dispersion relationship using the Drude model

and for the experimental values. At the surface plasma frequency the confined

plasmon undergoes a resonance and very localized (large k) waves are possible

(Localized Surface Plasmon Resonances). Between the surface plasma frequency

and the volume plasma frequency is known as the plasmon bandgap. Above the

volume plasma frequency, the thin film radiates. The experimental situation for

silver is complicated by band contributions.

- 42 -

Figure 3.9: Surface Plasmon Dispersion Relationship Close to

Experimental Plasma Resonance of Silver. Very similar resonant behavior to

the Drude model is seen, however due to band contributions from the silver

lattice the energy of the resonance is lowered.

- 43 -

It can be seen from the dispersion relationship that the surface plasmon has a

momentum greater than that of light. At the surface plasma frequency a

resonance occurs and allows for states of high k. These are known as localized

surface plasmon polaritons and these types of resonances are accompanied by

vary high electric fields at the interface11. As the frequency decreases the

dispersion relationship becomes closer and closer to that of light in the

surrounding dielectric. For experiments in the optical range, it can be seen that in

general the plasmon has a higher momentum than that of light, making coupling

to the plasmon mode a difficulty.

Momentum Matching to Plasmons

In studying plasmons there are several methods to add the needed momentum to

the light field in order to couple to the electron oscillations. One method utilizes

total internal reflection at an abrupt dielectric interface. A metal film is either

deposited on the prism (figure 3.10B) or brought into close proximity (figure

3.10A). When the film is deposited on the prism it is known as the Kretschmann-

Raether9,12 configuration. This configuration takes advantage of the evanescent

field associated with total internal reflection to couple photons to surface

plasmons. Also using the evanescent field associated with total internal reflection

is the historical predecessor to the Kretschmann-Raether9, 12 configuration, the

Otto configuration13. The Otto configuration relies on the coupling through an

- 44 -

air gap. Additionally, plasmons can be accessed through the use of gratings on a

metallic surface8.

- 45 -

Figure 3.10: Momentum Matching Techniques for Surface Plasmon

Launch. A. The Otto configuration13, in which a thin film is brought in close

proximity (usually through the use of a dielectric spacer) to the evanescent field of

totally internally reflected light. B. The Kretschmann-Raether9,12 configuration

where the surface plasmon on an air metal interface is launched through the thin

metallic film using the evanescent field of totally internally reflected light. C.

Coupling using a grating8, the grating momentum vector adds the need

momentum to the incident photon.

- 46 -

There exists a third method of coupling that was exploited for this thesis,

plasmon launch through scattering14, 15. In the scattering arrangement the

momentum of the incoming light and plasmon is matched when the excitation

impinges on a surface defect or an edge. The scattering from this defect or edge

causes a large amount of scattering in many directions, making this type of

coupling intrinsically less efficient then either a grating coupler or total internal

reflection scheme. However, the other types of plasmon coupling are extended in

nature and do not allow for the local excitation of nanoscale structures, in this

aspect launching through scattering is far superior. For our situation, a laser is

focused using a high numerical aperture microscope objective (NA=1.4). This

large numerical aperture is only available through the use of an oil immersion

microscope. This allows for a diffraction limited spot ( 2962

nmNAλ

= ) for

830nm (see figure 3.13). The launch of SPPs through scattering is an extension of

the grating method (see figure 3.12). Any discontinuity of dielectrics can be

related to some number of gratings. The gratings create a spatial Fourier

decomposition, which has different periodicities and amplitudes. The periodicities

that replicate any boundary determine the momentum matching thought the

grating formula 2plasmon photonk k

aπ

= ± . The amplitude of the coefficients

- 47 -

determine one aspect of how strongly the incident electromagnetic field couples

to the SPP. Another determining factor is the spatial overlap of the incident

electric fields scattered by the edge and the SPP modes found at the interface (see

figure 3.14). Finally, if conservation of energy is considered the oscillating electric

field creates a plasmon that undulates with the same frequency. It should be

noted that a third excitation such as a lattice oscillation (phonon) could cause

coupling between a photon and SPP of different frequencies, however this

coupling is expected to be smaller and is ignored hereafter.

- 48 -

Figure 3.12: Surface Plasmon Launching Through Scattering. Launching a SPP by scattering is a direct extension of the grating coupler. Any edge can be represented by a superposition of gratings, each grating matches a specific momentum of photon to the momentum of the SPP. The exact edge has many grating periodicities (Fourier components) that couple a fraction of the incident light.

- 49 -

Figure 3.13: Surface Plasmon Launching Through Scattering

Experimental Setup. Using a high NA objective a tightly focused laser beam is

scattered from the edge of a structure or a defect. A laser is focused to a

diffraction limited spot and scatters from an abrupt edge. Using this setup local

excitation of propagating plasmons has been observed in both thin films and

cylindrically symmetric nanowires of subwavelength cross section.

- 50 -

Figure 3.14: Momentum Matching Through Scattering. The incident electric

field is defined by the focusing of a laser through a high numerical aperture

objective. The incident field is then scattered by the discontinuous interface. SPPs

are driven by the overlap of their electric field with the scattered excitation.

- 51 -

In conclusion, a SPP is a surface wave at the interface of a metal and dielectric.

This chapter sketches the solution to the most basic configuration that supports a

SPP. Each of the pertinent lengths for a SPP are then defined and plotted for

silver. In addition, experimental methods for coupling light to SPPs are

presented. The method used in the experimental section is explained by the

extension of a grating coupler applied to other edge profiles. The experimental

realization of this type of coupling is presented.

- 52 -

C h a p t e r 4

EXPERIMENTAL OBSERVATION PLASMON PROPAGATION ON

LITHOGRAPHICALLY DEFINED THIN FILMS:

Abstract

Thin film plasmon waveguides are excited through scattering from an edge, using

a highly focused beam. This launching technique is seen to work regardless of

metal, frequency, or geometry of the metallic structure. This scattering technique

allows for precise spatial selection of excitation conditions. Using far-field

imaging, propagation is explored. In addition, we present a method of extending

the dynamic range of imaging by 3 orders of magnitude.

Experimental Results

In order to further investigate the coupling mechanisms of surface plasmon

polaritons, several samples were fabricated. First for maximum size and shape

variation samples were prepared using electron beam lithography1. A No. 1 ½

coverslip (Dow Corning) was spin coated with 495 k molecular weight

poly[methyl-methaccrelate] (PMMA available from Microchem, Inc). Next, a very

- 53 -

thin layer of aluminum was vacuum deposited on the coverslip. This layer

ameliorates problems stemming from the insulating nature of the substrate. The

resist was then patterned in a modified SEM (J. Nabity) at an acceleration voltage

of 40keV an approximate dose of 400 microcoulumbs/cm2. The aluminum

charge dissipation layer was then removed in a sodium hydroxide based

developer (60s in MF415), which left the PMMA layer undeveloped. The PMMA

is next developed in a methyl-iso-butyl-ketone (MIBK): isopropanol (IPA) 3:1

mixture for 45 seconds, and then rinsed in IPA for 60 seconds. Finally, a thin Al

layer (20nm) was deposited using an electron beam evaporator (Plassys, inc.). Al

was chosen because of its superior adhesion to glass and lower cost, compared to

the noble metals. The plasma resonances for aluminum have been extensively

studied2-5. Un-patterned areas were then lifted-off in a heated acetone bath (50°C

for 5 minutes). The aluminum patterns were then investigated using a focused

doubled Nd:Yag (532nm) laser. In order to focus the laser, it was coupled to a

standard inverted biological microscope (Nikon Eclipse TE2000) through an oil

immersion objective (NA=1.4) using a dichroic mirror (CVI,inc). The

polarization of the laser is linear, and was further insured to be a single state using

a polarizing beam splitter. Images were acquired using a Hitachi black and white

analog CCD with an 8 bit grabber or a Photron CMOS camera operated in an 8

bit mode.

- 54 -

Several geometries were explored, triangular, rectangular and circular are

presented. In every geometry coupling to the plasmon mode was either

accomplished through scattering from an edge or a defect. In each geometry, the

edges of the metallic film are seen to scatter the plasmon from/to a free photon.

In figure 4.1, propagating plasmons on a rectangular and triangular

microstructure (20μm) are presented. Several interesting effects are seen; first the

averaged intensity versus distance from the excitation has oscillations of a spatial

period of approximately 1μm for each excitation point. This periodic variation is

the result of the superposition of the plasmon with other ambient electric fields.

We expect the other electric fields to have three possible sources; direct

propagation of the laser in the dielectric media, the plasmon propagating at the

other surface, and plasmons originating from slightly different spatial points.

Furthermore, the magnitude is seen to be exponentially decreasing as function of

distance from the excitation point. Given that the edge is an isotropic scatterer

this exponential decrease in intensity is a direct measure of the imaginary part of

the propagation wave vector. We can compare these values with the theoretical

value using the dielectric constant of aluminum6 and glass (see table 4.1). The

experimental values for different microstructures and excitation points are in

good agreement with the theoretical value (3.65μm).

- 55 -

Figure 4.1: Measured Plasmon Intensity Decay for Aluminum

Microstructures Excited at 532nm. The color in the plot corresponds to the

averaged intensity of the boxes shown in the micrograph. Each intensity versus

position curve was fitted with a simple exponential function. The magnitude of

the amplitude was omitted for clarity.

- 56 -

Table 4.1: Plasmon Intensity Decay Lengths For Aluminum Excited at

532nm.

In order to further understand launching of the plasmon mode we can explore

launching from a defect. A circular structure, with a defect in the center provides

convenient way to probe the dynamics of launching from a defect. Since the

outer edge is a constant distance from the center it gives us insights into the

polarization dependence of launching from a defect. In figure 4.2, we present the

intensity of scattered light from a metallic edge of such a structure. The averaged

intensity of the circular edge is presented in an angular plot. This plot

demonstrates that launching of plasmons is maximal for directions coincident

with the polarization of the excitation. However, two interesting facts are evident

in figure 4.2, first the intensity is not uniform, and even for angles orthogonal to

the direction of polarization there exists scattered light. These two effects can

originate in either the incident beam or the defect structure launching the

- 57 -

plasmon. To further investigate the effects of launching, a more macroscopic set

of samples was fabricated.

- 58 -

Figure 4.2: Al circle with propagating plasmons launched from a defect

structure at the center. A laser (532nm) focused through an oil immersion

objective (NA=1.4) is used to excite a propagating surface plasmon. The edges of

the circular structure scatter the plasmon mode converting it to free photons A).

The averaged intensity of the region between the blue circles is plotted below C).

The plot of scattered intensity shows that the launch of plasmons is polarization

sensitive and increased intensity is seen for the polarization direction of the laser

(60° in this case). It is also interesting to note that the intensity at right angles to

the polarization direction is not zero, we believe this to be an effect of the defect

that the plasmon was launched. The metallic circle without excitation is shown in

B). The defect used to launch SPP’s is shown in D).

- 59 -

To gain insight into launching in more macroscopic samples, metallic stripe

structures were patterned and realized. Since the structures were larger, a metal

with longer propagation lengths (but poorer adhesion) was chosen. An 80nm

silver film was patterned using standard photolithography techniques. A standard

resist (Shipley 1813) was spin coated (3500 rpm for 45 seconds) and exposed.

The photoresist was exposed on commercial contact mask aligner to the

manufacturer recommended dose. Development was done under normal

conditions and the silver film was deposited using ebeam evaporation and lifted-

off in a room temperature bath of acetone (>30min). Because of the poor

adhesion to the substrate, and a slightly off axis source lift off of the silver

structures showed some flagging at the edges. These small pieces of silver provide

insight into the re-emission mechanism of the propagating plasmon. In figure 4.3

we see a silver stripe structure with a bend. To launch a propagating plasmon the

structure must properly scatter the incident electric field (see chapter 3). The

series demonstrates that only at edges and defects do we see a propagating

plasmon mode. In addition, figure 4.3 A and figure 4.3C are experimental proof

that points that can scatter a plasmon to a photon can do the reverse process. In

addition because of the flagging of the edge, it is no longer an isotropic scatterer,

yielding increased radiation at points were the scattering is large.

- 60 -

Figure 4.3: Edge launched propagating plasmon (830nm) on a patterned

Ag surface. A) The propagating modes are accessed at the end of the stripe,

scattering into visible radiation is evident at the edges of the plasmon wave guide.

The propagating mode scatters at points of increased roughness, evidenced in the

magnified image of A) to the right. B) Spatial selection of launch is extremely

high; the propagating mode is no longer observed for a very small motion. C)

Propagating modes can be excited at a number of locations, the image shows a

mode excited at a radiating point in A) and emitting at the excitation point in A).

Again the areas of higher roughness show higher emission intensity, the

magnified image of C) to the right emphasizes this.

- 61 -

In order to further study the nature of the scattering and propagation

mechanisms improved techniques are required. The plasmon decays

exponentially from the source and hence the points close to the excitation

saturate the detector. To ameliorate this ubiquitous problem, a simple but

powerful approach was developed. To increase the dynamic range of a standard

image sensor, we take advantage of the ability to select the shutter speed of the

camera. An image at several shutter speeds is taken, and then combined to form

an image of a larger effective bit depth. This technique has two advantages, first

for shutter speeds that overlap in bit depth we gain in averaging intensities, and

secondly huge variations in intensity are simultaneously visible. For the composite

image to be a valid representation of the intensity information it is import to

confirm the linearity of the camera as a function of shutter speed, which was

done. Additionally it is important that any modulation of the laser source is much

faster than the shutter speed, ensuring that the average power of the laser

observed by the camera is also linear in shutter speed. In our experiment, the

830nm diode laser was modulated at 10Mhz or with a characteristic time of .1μs,

much quicker than even the fastest shutter speed available with a characteristic

time of 1.6 μs. Figure 4.4, shows a graphic depiction of the composite image

process. Each image in a series is multiplied by the inverse of the shutter speed

and then added, giving a weighted mean of the stack. To further ensure the

- 62 -

maximum image quality all points that are saturated are not included in the final

summed image. So that all intensity information can be seen, the log of the

weighted image is shown.

- 63 -

Figure 4.4: Composite image technique. By acquiring images at multiple

shutter speeds, an image containing many decades of intensity information is

formed. The image to the right shows is the log of intensity.

- 64 -

This composite image technique allows for the comparison of light scattered

from the plasmon supported at the dielectric interface and light simply scattered

from the excitation. In figure 4.5 a saturated image with background illumination

is shown along with the log of a composite image. The composite image is

divided into two regions of interest, the first (black box) is light scattered in plane

during excitation. It has an exponential type behavior that is distinct from the

scattered light from the plasmon (red box). The characteristic length of the

scattered light is 1.7μm much smaller than the exponential decay of the plasmon

intensity (9 μm). The plasmon decay disagrees with the theoretical value of 84μm,

this disagreement can be the product of two effects (table 4.2). First, the surface

roughness of the deposited film causes coupling between the plasmon supported

in the film and free photons leading to radiative losses. In addition, the

conductivity of the silver film can be affected by the deposition parameters and

surface contamination. These factors can increase the imaginary part of the

dielectric function of the silver film and cause increased attenuation of the

plasmon.

- 65 -

Figure 4.5: Comparison of Plasmon Decay Length and Scattered Light. A microfabricated silver stripe (6μm x 100μm) with plasmon modes excited by the scattering technique. The images above are of the stripe with a plasmon excited. The micrograph at top right is a saturated image showing other surrounding features. The image at top right is the log intensity of a composite image showing the areas of interest. The integrated intensity for the boxed regions is plotted below the micrographs. The intensities show distinctive features over a large distance and over many orders of magnitude. The exponential decay of the light scattered from the edges is clear. The scattered excitation falls off much quicker than the light from the plasmon.

- 66 -

Table 4.2: Plasmon Decay Lengths for Silver at 830nm.

In conclusion, I have shown that SPP’s can be launched and detected using a far-

field experimental technique. This technique can further be enhanced by creating

a weighted image using variable shutter speeds on the observation camera. Using

these techniques the plasmon intensity decay length was measured to be ~3μm

for Al excited at 532nm and ~9μm for Ag excited at 830nm.

- 67 -

C h a p t e r 5

THEORETICAL TREATMENT OF SURFACE PLASMONS ON

CYLINDERS :

Abstract

This chapter is dedicated to the theoretical discussion of surface plasmons on

cylinders. In order to form a complete picture we begin with the consideration of

Maxwell’s equations in cylindrical coordinates. We move to the solution of

Maxwell’s equations with the appropriate boundary conditions writing down the

normal modes for a cylinder. This leads to dynamics similar to the thin film case,

including the same surface plasmon frequency. Next we further investigate the

dominant propagating mode, the azimuthally symmetric n=0 mode. Finally we

discuss coupling in the cylindrical case.

Theoretical Concerns of Metallic Cylinders

In chapter 3, I presented the solutions for confined surface waves in Cartesian

coordinates for the intersection of two infinite planes, in this chapter I extend the

solutions to cylindrical coordinates. The solutions to the spherical case are

covered elsewhere, and they create another set of interesting resonances and

phenomena. In the cylindrical case there are an infinite number of solutions,

- 68 -

however one propagates further than the rest. I shall start with the general

solution and move to this single mode. Finally, I will present arguments for the

coupling to this mode.

We begin where all EM problems should; Maxwell’s Equations. Inside the metal

we have the modified wave equation of chapter 2, or

22

2t tμε μσ∂ ∂

∇ = +∂ ∂

E EE2

22t t

με μσ∂ ∂∇ = +

∂ ∂B BB ,

Outside we have the version with out conductivity

22

2tμε ∂∇ =

∂EE

22

2tμε ∂∇ =

∂BB,

In order to solve these equations for a cylindrical geometry we insert the

appropriate expression for the Laplacian1

2 2 2 22 2

E E1 2E E E E Ezρ θ

ρ θ θ ρρ ρ θ θ∂⎡ ⎤∂⎡ ⎤∇ = ∇ +∇ +∇ − + + −⎢ ⎥⎣ ⎦ ∂ ∂⎣ ⎦

E

where

2 22

2 2 2

1 1z

ψ ψ ψψ ρρ ρ ρ ρ ρ

⎛ ⎞∂ ∂ ∂ ∂∇ = + +⎜ ⎟∂ ∂ ∂ ∂⎝ ⎠

we solve the wave equations using separation of variables. We assume a harmonic

time dependence that is i te ω−E = E . And further we assume each component of

the electric field vector is separable.

E E ( )E ( )E ( )zρ ρ ρ ρρ θ= E E ( )E ( )E (zθ θ θ θ, ) E E ( )E ( )E ( )z z z z z= ρ θ ρ θ= ,

- 69 -

This leads to a second order separable differential equation for each vector

component. The vector components are then constrained using the other

Maxwellian equations. Each vector component with the appropriate constraints

results in three equations, one for each coordinate dependent function.

The general solution for the electric field of the surface wave inside the wire is2, 3

(5.1) ( )02( ) ( ) plasmonin ik z i tplasmonInside Inside Inside

n m n n m nn m m

ik nE J k a J k b ek k

θ ωρ

μ ωρ ρρ

∞+ −

=−∞

⎡ ⎤′= −⎢ ⎥⎣ ⎦

∑

(5.2) ( )02 ( ) ( ) plasmonin ik z i tplasmonInside Inside Inside

n m n n m nn m m

nk iE J k a J k b ek k

θ ωθ

μ ωρ ρρ

∞+ −

=−∞

⎡ ⎤′= − +⎢ ⎥⎣ ⎦

∑

(5.3) ( )( ) plasmonin ik z i tInside Insidez n m n

nE J k a e θ ωρ

∞+ −

=−∞

⎡ ⎤= ⎣ ⎦∑

The magnetic field in the wire is

(5.4)2

( )02

0

H ( ) ( ) plasmonin ik z i tplasmonInside Inside Insidemn m n n m n

n m m

iknk J k a J k b ek k

θ ωρ

ε ρ ρμ ω ρ

∞+ −

=−∞

⎡ ⎤′= +⎢ ⎥

⎣ ⎦∑

(5.5)2

( )02

0

H ( ) ( ) plasmonin ik z i tplasmonInside Inside Insidemn m n n m n

n m m

nkik J k a J k b ek k

θ ωθ

ε ρ ρμ ω ρ

∞+ −

=−∞

⎡ ⎤′= −⎢ ⎥

⎣ ⎦∑

(5.6) ( )H ( ) plasmonin ik z i tInside Insidez n m n

nJ k b e θ ωρ

∞+ −

=−∞

⎡ ⎤= ⎣ ⎦∑

Outside in the surrounding dielectric we have

(5.7) ( )(1) (1)02( ) ( ) plasmonin ik z i tplasmonOutside Outside Outside

n d n n d nn d d

ik nE H k a H k b ek k

θ ωρ

μ ωρ ρρ

∞+ −

=−∞

⎡ ⎤′= −⎢ ⎥⎣ ⎦

∑

- 70 -

(5.8) ( )(1) (1)02 ( ) ( ) plasmonin ik z i tplasmonOutside Outside Outside

n d n n d nn d d

nk iE H k a H k b ek k

θ ωθ

μ ωρ ρρ

∞+ −

=−∞

⎡ ⎤′= −⎢ ⎥⎣ ⎦

∑

(5.9) ( )(1) ( ) plasmonin ik z i tOutside Outsidez n d n

nE H k a e θ ωρ

∞+ −

=−∞

⎡ ⎤= ⎣ ⎦∑

for the electric field and for the magnetic field

(5.10)2

( )(1) (1)02

0

H ( ) ( ) plasmonin ik z i tplasmonOutside Outside Outsidedn d n n d n

n d d

iknk H k a H k b ek k

θ ωρ

ε ρ ρμ ω ρ

∞+ −

=−∞

⎡ ⎤′= +⎢ ⎥⎣ ⎦

∑

(5.11)2

( )(1) (1)02

0

H ( ) ( ) plasmonin ik z i tplasmonOutside Outside Outsidedn d n n d n

n d d

nkik H k a H k b ek k

θ ωθ

ε ρ ρμ ω ρ

∞+ −

=−∞

⎡ ⎤′= −⎢ ⎥⎣ ⎦

∑

(5.12) ( )(1)H ( ) plasmonin ik z i tOutside Outsidez n d n

nH k b e θ ωρ

∞+ −

=−∞

⎡ ⎤= ⎣ ⎦∑

Where are Bessel functions of the first kind, and are Hankel functions.

The prime denotes differentiation with respect to the argument

nJ (1)nH

kρ .

For a long straight wire, the n=0 mode is the dominant propagating mode3. We

assume that Eθ =0, now equations (5.1) and (5.3)

Inside the wire

( )0 0 ( ) plasmoni k z tplasmonInside

mm

ikE a J k e

kω

ρ ρ −′= and

( )0 0 ( ) plasmoni k z tInside

z mE a J k e ωρ −=

outside the wire we have

( )(1)0 0 ( ) plasmoni k z tplasmonOutside

dd

ikE a H k e

kω

ρ ρ −′=

- 71 -

( )(1)0 0 ( ) plasmoni k z tOutside

z dE a H k e ωρ −=

where

d mplasmon

d m

kc

ε εωε ε

=+

,2

dd

d m

kc

εωε ε

=+

,2

mm

d m

kc

εωε ε

=+

Inside the wire the electric field dies off exponentially away from the surface

going to ~1/e of its original value in about 10-20nm, or roughly the value of its

skin depth. Outside the dielectric also is exponential from the surface and it has a

characteristic length of , larger than the skin depth but still a fraction of a

wavelength. Since the z wave vector determines the propagating mode and the

SPP resonance frequency we see that the surface plasmon frequency for a

cylinder is the same as it is for the thin film case.

mk

- 72 -

Figure 5.1: Schematic of Cross Sectional View of Penetration Depths in a

Cylinder. The lengths for cylinders of large radii correspond to the planar values

found in chapter 3.

- 73 -

In general, the electric field has both ρ and z components, however far from the

wire the ρ component tends to cancel because of its symmetry in θ. The same is

mathematically true for points along the axis of the wire. It is then reasonable for

excitations (or scattered fields) much larger than the wire, or azimuthally

symmetric about the nanowire axis, to assume that the z component of the

electric field plays the dominant role. Only in the case of scattering from objects

that are close to the side of the wire and on the same size scale as the diameter of

the wire do we expect the ρ component to contribute significantly to the coupling

of the mode. This is an important point for the difference in polarization

dependence of coupling. The basic coupling mechanism covered in chapter 3 also

applies here; the end of the wire acts as a superposition of gratings. In this case

the end makes up a very sharp discontinuity in the axial direction (see appendix I

for micrographs), which creates a large number of grating vectors to match

momentum between the incident electric field and the SPP. Mathematically, this

is equivalent to the statement that the Fourier transform of a delta function

(infinite spike) is a constant.. Figure 5.2 helps illustrate the envisioned process.

The magnitude of the overlap between the scattered field and the propagating

plasmon mode determines the ability of external fields to drive the SPP mode.

- 74 -

Figure 5.2: Schematic View of Excitation of Surface Plasmon Polaritons on

a Cylinder. The incident radiation scatters from the end and overlaps the electric

field of the plasmon. This drives the plasmon at the frequency of the excitation.

- 75 -

In retrospect, the theoretical case of a cylinder is very similar to that of a plane. In

particular the calculated parameters converge to that of a plane when the radius

of the cylinder is large. A major difference between the planar and cylindrical case

is excitation of the plasmon mode through scattering. In the planar case, an area

defined by an extended edge contributes to driving the plasmon, however in the

case of a small cylinder it is a single point, the end that drives the SPP.

- 76 -

C h a p t e r 6

OBSERVATION OF SURFACE PLASMON POLARITON

PROPAGATION, REDIRECTION, AND FAN-OUT IN SILVER

NANOWIRES

Abstract

In this chapter I report on the coupling of free space photons (vacuum

wavelength of 830nm) to surface plasmon modes of a silver nanowire. The

launch of propagating plasmons, and the subsequent emission of photons, is

selective and occurs only at ends and other discontinuities of the nanowire. In

addition, we observe that the nanowires redirect the plasmons through turns of

radii as small as 4μm. We exploit the radiating nature of discontinuities to find a

plasmon propagation length > 3±1 μm. Finally, we observe that inter-wire

plasmon coupling occurs for overlapping wires, demonstrating plasmon fan-out

at subwavelength scales.

Observation of Plasmon Propagation, Redirection, and Fan-out in Silver

Nanowires

Nanoscale waveguides and photonic circuits require sub-wavelength optical

elements1,2. Several different strategies coupling light to submicron structures

- 77 -

have been employed. For example, coupling and redirection has been achieved

through the use of semiconductor nanowires3,4, passive dielectric fibers5,6,

photonic crystals7, and coupled metallic islands8. Structures coupling free space

photons to fluctuations in the surface density of electrons (plasmons) inherently

reduce the spatial extent of propagating electromagnetic fields9. Metallic

nanowires are likely candidates for plasmonic fibers. Recent experiments have

demonstrated propagating plasmon modes in silver nanowires10,11, however,

realization of highly selective excitation, mode bending, and cross coupling has

yet to be achieved.

Here we present simple approaches for both coupling to propagating plasmon

modes and their observation in metallic nanowires. Specifically, our experiment

couples to propagating modes in a radially symmetric nanowire by using one end

as a scattering center. This scattering center creates an overlap between the

incident radiation (focused laser) and the propagating plasmon mode. Focused

laser light excites plasmons that propagate along the length of silver nanowires

and couple to free space photons, radiating at the ends. Plasmons are also

observed to couple between overlapping nanowires and fan-out from one wire

into multiple nanowires.

The wires used in this study have a mean diameter of ~100 nm and lengths that

vary from 3-20 μm. The nanowires were synthesized in a mixture of ethylene

- 78 -

glycol (EG) and poly(vinyl pyrrolidone) (PVP) as previously reported12,13 (See also

Appendix I).

Aqueous nanowire suspensions were deposited on No.1 ½ cover glasses

(Corning No. 0211 zinc titania glass) and allowed to dry in open air. Dried

nanowires were then mounted on an inverted optical microscope (Nikon Eclipse

TE-2000). A 100x oil immersion objective (N.A. = 1.4) lens was used to focus

the laser light and to collect a bright field image. The laser illumination was

coupled into the microscope via a dichroic mirror that selectively reflects 96% of

light at 830nm. The microscope objective focuses the collimated laser light to a

diffraction limited spot in its focal plane. Images were collected with either a

CCD (Hitachi, 8 bit, 480X640) or a high-speed CMOS (Photron FastCam 1024-

PCI), which both received roughly 4% of the light from the sample at the laser

frequency. To eliminate the possibility of evanescent waves propagating along

the glass surface and preferentially scattering from the tips of the silver

nanowires, we immersed all samples with index-matching oil (Nikon Type A

immersion oil, n=1.515). Even though scattering from the glass surface

disappeared, light continued to strongly radiate from the distal end of the

nanowire.

We launch plasmons by illuminating an end of a single nanowire with a

diffraction limited laser spot as shown in Figure 6.1. Plasmons can be launched

- 79 -

from either end of the nanowire (Figures 6.1A and 6.1B); thus, plasmon

propagation is reversible. In contrast, plasmon modes are not observed to be

launched when the laser is focused on the mid-section of a smooth wire (see

Figure 6.1C and 6.1D). Since the momentum of the incoming photon (kphoton) is

not matched to that of the propagating plasmon (kplasmon), there needs to be a

scattering mechanism to provide an additional wavevector (Δkscatter). At the

midsection of the wire, the nanowire is cylindrically symmetric over the extent of

the diffraction limited spot, and therefore cannot scatter in the axial direction.

However, this symmetry is broken at the tapered end of the nanowire where light

is scattered into propagating axial plasmon modes. A similar strategy has been

implemented for thin film surface plasmons utilizing gratings or dots8,14

Likewise, propagating plasmon modes incident upon a sharp discontinuity (e.g.,

the tapered end of the nanowire) can re-emit as photons.

- 80 -

Figure 6.1: Micrographs showing the spatial sensitivity of launching

plasmons. A) Nanowire with excitation at the bottom end. B) Same nanowire

when excited from top end. C) Nanowire excited at left end. D) Same nanowire

with laser positioned at the middle of the nanowire. Notice that the plasmon is

not excited in this geometry.

- 81 -

If the symmetry is gently broken over longer length scales, plasmon propagation

is unaffected. This can be seen in figures 6.1A and 6.1B, where plasmons

propagate around the bend of the nanowire with no observed radiative loss. The

smallest naturally occurring optically resolvable bend found in these nanowires is

shown in figure 6.2A. This nanowire, with a radius of curvature of 4μm, guides

plasmons with no observed radiative loss. However, extremely sharp bends in

the nanowire will behave like the end of nanowires, scattering propagating

plasmons into photons. This effect is demonstrated in figure 6.2B, where a

nanowire shows emission at two “kinks” (radius of curvature below the

diffraction limit). The kinks are spontaneous defects that form during the growth

process, and occur in a small fraction of wires. Scanning electron micrographs

reveal that typical kinks are discontinuities in the wire direction. Figure 6.2C is

representative of the structure of these kinks; i.e., sharp interior angles and flat

exterior faces, with characteristic size ~ 100nm.

Similar phenomena have recently been reported for propagation of photons

around sharp bends in semiconductor15 structures and for bends above the

diffraction limit for dielectrics6. The main difference between these and the

present approach is that photons guided by dielectrics and semiconductors can

efficiently propagate over large distances, whereas propagation in plasmon

waveguides have been demonstrated for10, and can scale to, much smaller sizes.

- 82 -

Additionally, most of the electromagnetic energy resides in the core of dielectric

fibers, as opposed to the surface for plasmonic wave guides.

- 83 -

Figure 6.2: Micrographs of plasmon propagation in silver nanowires and

emission (top), control with no laser excitation (bottom). Brightest point in

image is scattering from incident beam. A) A 7μm wire (excitation top) with a

radius of curvature of 4μm, a wire not radiating is in close proximity. Inset is a

circle of radius of 4μm for comparison. B) A 5μm wire (excitation top right) with

both the opposite end and two additional points of high curvature that radiate

(radius of curvature less than the diffraction limit.) C) An electron micrograph of

a typical wire with kinks, with insets of increased magnification.

- 84 -

A nanowire with multiple kinks can be used to estimate the plasmon propagation

length. Each kink is used dually as a plasmon launching site and photon radiating

site. We sequentially irradiate each kink and measure the radiated intensity from

all the other kinks, as illustrated in figure 6.3A. We find that the radiated intensity

is strongly correlated to the distance between points along the nanowire, as

shown in figure 6.3B. These data are well described by an exponential decay,

0( )xLI x I e

−= , with a characteristic length of L=3 ±1μm. If one makes the

assumptions that i) the photon-plasmon coupling strengths are the same at each

junction, and that ii) radiative losses (at kinks) are insignificant compared to

dissipative losses (along the nanowire length), then L represents the plasmon

propagation length. Even when these assumptions are not true, this simple far-

field measurement provides a practical lower limit for the propagation length. For

comparison, a propagation length of 2.5 μm has been reported for gold nano-

fabricated structures at 800nm 16.

- 85 -

Figure 6.3: Plasmon Decay Length. A) Micrographs of plasmon propagation

in a silver nanowire with multiple emission points (top) control with no laser

excitation (bottom). Camera shutter speed and laser intensity were varied to

increase total dynamic range. The unsaturated images of the excitation and

brightest emission points at shorter exposure times (high shutter speeds) are

overlaid for clarity. B) Semi-log plot of intensity versus distance from excitation

source. The dashed line is a fit of the data to an exponential. Six distinct points

were probed (15 unique combinations). The uncertainty is arrived at by taking the

standard deviation of all exposures with unsaturated pixels.

- 86 -

Propagating modes are also seen to couple between overlapping nanowires. In

figure 6.4, we present an image and an intensity profile from an aggregate of three

nanowires, which forms naturally during solvent evaporation. When one of these

nanowires is excited, two phenomena are observed. First, radiation is emitted at

the intersection of the overlapping nanowires, indicating that the intersection

scatters propagating plasmons into photons. Second, visible radiation is emitted

at the ends of nanowires that cross the illuminated nanowire, indicating that the

intersection couples plasmon modes in the two wires. In order for this to occur,

the plasmon modes of the two wires must overlap. In general, the electric field of

the propagating surface plasmon modes on a cylinder can be a complicated

mixture of electric (TM) and magnetic (TE) waves17. For simplicity, we choose

the n=0, or lowest order mode, which is azimuthally symmetric. Then for this

mode the field scales as ~ kE e ρ ρ− where kρ is the wavevector in the radial

direction and ρ is the distance from the surface of the nanowire17,18. Neglecting

corrections introduced by the curvature of the wire17, and taking the dielectric

constant of the surfactant to be that of the oil ( surfactant oilε ε= ), we approximate

kρ using the dispersion relations of an infinite plane9,18 where 2 2zk k kρ + = 2

22 m dz

m d

kc

ε εωε ε

⎛ ⎞= ⎜ ⎟ +⎝ ⎠, and

22

dkcω ε⎛ ⎞= ⎜ ⎟⎝ ⎠

in the dielectric. Thus,

222

2d

m d

kcρ

εωε ε

⎛ ⎞= ⎜ +⎝ ⎠

⎟ , where c = speed of light, ω = the angular frequency, dε =

- 87 -

the relative permittivity of the dielectric, and mε the relative permittivity of the

metal. Substituting material parameters for the immersion oil ( dε =2.25) and

silver ( mε =-36 extrapolated from 19 ), we find an exponential decay length of

about 340nm. Thus, wires within this distance have overlapping modes and can

couple. Inter-wire coupling has also been seen in sub-wavelength silica and

semiconductor nanowires3,6. In our system, we expect capillary stresses to drive

nearby wires into contact as solvent evaporates20. However, the surfactant

coating the wire may frustrate direct contact between the wires, maintaining a

dielectric filled gap with a maximum size of twice the surfactant thickness, about

10nm in our case (see appendix I ). Therefore even in the presence of surfactant,

the distance between the wires (d) is much less than kρ , or d kρ . The

intersections are then, in effect, plasmonic contacts capable of exchanging energy

between propagating plasmon modes, with some losses in the form of free space

photons.

In figure 6.5 similar behaviour to figure 6.4 is observed for a myriad of wires.

Figure 6.4 A) shows a wire clearly scattering radiation at the base of an

intersection with another wire.

- 88 -

Figure 6.4: Group of overlaying nanowires that illustrates inter-wire

plasmon coupling. The excitation at the far left nanowire end produces

emission at both the nanowire junctions and emission from the coupled

nanowires as well. The inset shows an intensity line cut showing the emission

intensity profile along wire.

- 89 -

Figure 6.5: Several wires that illustrate inter-wire plasmon coupling. A) Two small wires with their bases in contact with the excited wire are seen to scatter the SPP. The excitation is at the lower end of the longest wire. The image is a two layer composite of the wire (in reflection) and the excitation (no illumination besides the focused laser). B) Several small particles scatter the SPP. In addition, the SPP is seen to couple to the wire that is perpendicular to the excited wire. The wire is excited at the bottom. C) A wire system that couples at a single point and re-emits at the lower left end. The wire is excited at the top. D) Two wires, with their axis aligned. Both wires are shown to scatter SPPs to photons at their ends.

- 90 -

In conclusion, we demonstrate the selective launch and propagation of plasmons

along silver nanowires using a simple far-field excitation and detection method.

We have also observed that these propagating plasmon modes can couple

between adjacent nanowires. The phenomena are not specific to nanowire

material or excitation wavelength – we have observed similar results in gold and

copper nanowires. Technological applications require the positioning of

nanowires into a deterministic network which can be accomplished by a variety

of methods, such as flow alignment21, biologically derived templates22,

dielectrophoretic alignment23 or holographic optical tweezers 24,25 The current

study represents a new approach in the observation and manipulation of

plasmons in nanoscale structures. A report showing plasmon propagation in

similar Ag nanowires has been published26.

- 91 -

C h a p t e r 7

EXPERIMENTAL OBSERVATION OF POLARIZATION

DEPENDENT COUPLING IN NANOWIRES

Abstract

In order to understand the mechanisms by which plasmons and photons couple,

the polarization of the incident electric field was varied. In addition, nanowires

with different, spontaneously occurring geometries, were investigated. By varying

the polarization of the excitation and geometries several interesting observations

arise. First, nanowires excited at ends have a strong polarization dependence

leading to maximum reemission at the other end when the excitation polarization

is coincident with the local nanowire axis. Second, a single maximum of emission

is observed when a nanowire is excited at a bend, and it is a superposition of the

SPP modes in the wire segments. Third, special geometries can be exploited to

create polarization based routing. And finally the SPP mode on a wire can be

accessed through external scatters close to the wire.

Polarization Dependence of SPP excitation on Metallic Nanowires

- 92 -

Surface plasmonics are a promising route to subwavelength optics. Previous

experiments have shown that light may be guided with nanoscale metallic

structures(see chapter 6). In addition silver nanowires have shown great promise

in becoming plasmonic conduits. To date nanowires have shown the ability to

carry and redirect light on the nanometer scale. Experiments have shown that

metallic wires can create resonant cavities1, plasmon conduits2-5, and plasmonic

junctions5. The plasmonic dispersion relationships of metallic objects of varied

dimensions have been investigated theoretically6-8. However, a critical lack of

experimental data for cylindrical wave guides of nanometer cross section exists.

In this chapter we vary the parameters determining the coupling of plasmons and

photons in such wave guides. We investigate the polarization dependence of the

excitation of plasmon modes on the surface of silver nanowires. We demonstrate

that the emission of light from a silver nanowire waveguide is a maximum when

the excitation radiation has an in-plane polarization parallel to the local axis of the

nanowire for end excitation, regardless of geometry or dielectric surrounding. We

also discover that the dielectric surrounding of kinks and small metal particles

strongly affects the polarization dependence of the launch of plasmons.

As discussed in chapters 3 and 5 the SPP mode is driven by the overlap of the

modes electric field and the scattered excitation. For a cylindrical wire, we expect

that the only propagating surface mode that we can observe is the n=0 mode. We

can use this fact to explore in detail how surface plasmons and photons couple to

- 93 -

each other. As in chapter 6, metallic nanowires are the system of interest. The

morphology and other properties of nanowires used in this study are discussed in

appendix I. These wires are seen to have non-radiative plasmon polariton modes,

accessible by focussing a laser beam to a diffraction limited spot on the end.

In order to further understand the nature and structure of the excitation of

propagating plasmon modes the in-plane polarization of the focused laser

excitation was varied using a half wave plate. The half wave plate was used to

change the linear polarization of the laser excitation in a Fourier plane to the focal

plane. The accuracy of the plate was ±4° determined by the mechanical precision

of the physical mount. The absolute position of the electric field polarization was

±5° determined by using a cross polarizer to determine the angle of maximum

extinction. The laser used was a laser diode operated at ~15mW (140mW

maximum power) at 830nm.

When the polarization of the excitation laser is rotated the emission of light at the

“output” end varies with the input polarization angle (see figure 7.1). The spot of

emitted radiation is circular in cross section and does not change shape (except

symmetric decreases in intensity) or position as function of the excitation

polarization. Within the resolution of the experiment, the emission intensity only

exhibits a single maximum and minimum.

- 94 -

Figure 7.1: Polarization dependence of plasmon emission. This figure shows

that the maximum occurs when the excitation is polarized parallel to the local

axis of the nanowire. The inset shows the emission spot for different excitation

polarizations, clearly showing no change in shape or position, only symmetric

decreases in intensity. The image of nanowire excitation is an overlay with the

excitation and emission on the red channel. The emission intensity is integrated

over the total square pictured in the inset, normalized to one, and has the

background value subtracted (the minimum is made zero.)

- 95 -

Nanowires of more complicated geometries are also of major interest. Figure 7.2

shows a silver nanowire with several abrupt bends, formed spontaneously during

the growth process discussed in appendix I. We focus attention on a bend in the

middle of the wire that shows strong emission. The polarization dependence of

the output emission for this spot is explored in immersion oil and at a glass-air

interface. The emission shows no resolvable difference in polarization character

for either dielectric boundary condition. The reflected laser spot is seen to be

brighter because of the scattering from the dielectric discontinuity in the glass-air

case (see figure 7.3). Additional spots along the wire are seen to be bright,

possibly indicating the scattering is stronger in the glass-air case. The other spots

are seen to have the same polarization dependence regardless of their position on

the wire, indicating they are emitting from the same guide mode (see figure 7.4).

Other wires, regardless of there geometry show similar behavior when excited

from an end point (see figure 7.5). This indicates that changes in the shape of the

plasmon mode far from the excitation point do not affect excitation dynamics.

- 96 -

Figure 7.2: Emission intensity of a radiating kink. The emission shows a

maximum for an excitation polarization parallel to the local axis of the nanowire.

Additionally, the emission maximum is unaffected by a change in the local index

of refraction from n=1 (air) to 1.515 (immersion oil). This indicates that the

scattered electric couples to the plasmon mode predominately in the interior of

the end. The normalized emission intensity is plotted as a function of angular

difference from the local axis of the nanowire.

- 97 -

Figure 7.3: Kinked nanowire response to varying the polarization of

excitation. The polarization was changed in steps of 4°, the wire was at an glass-

air interface. The mean of the emission region is plotted in normalized intensity

units. The maximum of emission occurs for an in-plane polarization of the

excitation parallel to the local axis nanowire at the excitation point. Both points

of emission have the same polarization dependence, indicating they are products

of the same overlap.

- 98 -

Figure 7.4: Normalized emission intensity plotted for two wires of different

geometry. Regardless of the presence of a kink the emission is a maximum for

polarization parallel to the local axis. The images are for wires at a glass-air

interface, or for n=1.00, and the emission intensity is plotted as function of

angular separation from the local axes of the each nanowire. The shape and color

of the emphasized region in the images corresponds to the symbol in the plot of

emission intensities.

- 99 -

The regular behavior of excitation of the wire at an end is starkly contrasted by

other excitation points along the wire. Several different locations of the wire

show anomalous polarization dependencies, in particular excitation at any kink

and on a small metallic object at the end of the nanowire reveal unexpected

behavior. At an air glass-interface the tantalizing signs of a rudimentary switch are

seen, two bright emission points on the same wire are seen to have different

polarization maxima. For a single excitation position, the direction of plasmon

propagation is controlled through the polarization of the laser. Interestingly, the

maxima do not correspond to the local directions of any nearby nanowire

segments and the strongly coupled kinks are a superposition of plasmon modes,

creating a new polarization maximum, in a manner analogous to mode

scrambling in dielectric fibers at microbends9. Upon application of immersion oil,

the excitation of the two modes are seen to split into resolvable locations,

allowing for the separate excitation of each mode. By exciting the modes

separately a resolvable polarization shift of 20±10 degrees is found. This indicates

that the dielectric constant of the surrounding medium is important in the launch

of plasmons at kinks. This further implies that the electric field extending into the

surrounding dielectric plays a crucial role in the development of modes

propagating outward from the kink.

- 100 -

Figure 7.5: Normalized emission plotted versus the excitation polarization

angle at a kink measured from the x-axis. In air, a single excitation point

creates separate modes that have different maxima, forming a polarization based

switch. The angular separation between maxima is 60°±4°, for the different

modes. With the application of immersion oil there is a resolvable shift of the

maximum of emission of 20°± 10°, indicating that the local dielectric conditions

play a role in excitation at a kink. Additionally, in oil the two separate modes are

no longer excited at a single location of the laser and can be excited

independently.

- 101 -

Plasmons can also be launched from small metallic structures near the nanowire.

In figure 7.6 it can be seen that the nanowire has a small (sub resolution) metallic,

object on the upper right hand end. We postulate that this small metallic object is

a metallic particle produced simultaneously with the wires, which adheres when

the suspension of nanowires is dried on the coverslip (see figure 7.7). The

plasmon mode was excited at both a glass-air interface and in immersion oil. A

distinct phase shift of degrees is clearly seen. Both emission points have the same

polarization dependence. As in the case of the kinks this indicates that the

dielectric surrounding the wire plays an integral role in the launch of plasmons.

Indicating that coupling to the plasmon mode occurs largely in the electric field

external to the wire.

- 102 -

Figure 7.6: Emission intensity for excitation of a small metallic particle

near the end of the nanowire. The intensity shows a large polarization shift for

changes in the index of refraction. This indicates that the coupling of photons

into the propagating plasmon mode is dictated by the index of refraction, in

contrast to the excitation of the wire at an end. The normalized intensity of both

brightly radiating spots for both cases (oil and air) are plotted versus the

polarization angle relative to the local axis of the nanowire. The shapes and colors

highlighting the emission points in the images correspond to the symbols used in

the plot. The insets are increased magnification images of the particle without

excitation.

- 103 -

Figure 7.7: The nanowire with multiple excitation points and possible

scattering mechanisms. A) The wire with points that have different

polarization dependencies than ends emphasized. B) A TEM of what we believe

to be a similar structure (please note this is not the same wire). C) A SEM of a

bend similar to those seen in A), again this is not the same wire.

- 104 -

In conclusion, the launch of plasmons is seen to be highly polarization

dependent. For wires excited at an end point the axial direction is the preferential

polarization. This is contrasted by wires excited at a sharp kink or at other

features. For wires excited at points not on their ends the surrounding dielectric

environment is shown to effect the polarization dependence of the launch of

plasmons. In addition, more complicated coupling is seen to lead to a polarization

dependent switching effect.

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C h a p t e r 8

CONCLUSION

In conclusion, surface plasmon polaritons transport electromagnetic energy at the

interface of a metal and a dielectric. This electromagnetic energy travels many

microns, while being confined in one or more dimensions. The lateral

confinement is determined by the geometry and material composition of the

interface. In this thesis, I have explored the propagation of SPP’s in thin films

and silver nanowires, systems that pave the way for the manipulation of optical

information on subwavelength length scales. This exploration has lead to several

new steps forward that serve as the launching point for continuing discovery.

Experimental techniques for the launch and detection of SPPs have been

extended in this thesis. The launch of plasmons by scattering allows experiments

exciting the same structure in different locations and unique launching conditions

of SPPs. Specifically, in chapter 4 we excite structures of varied geometry, surface

roughness and composition. In figure 4.1 the propagation length of SPPs

launched from aluminum structures is measured from scattered light. The

propagation length measured is in agreement with theoretical values. This

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propagation length is seen to vary for different excitation points. Although the

variation is small, it would be impossible to detect without launch through a

localized source. In addition, by using a type of high dynamic range imaging, the

propagation of silver microstructures is measured over several decades of

intensity. Further improvements in launching could be made by creating SPPs

using different wavelengths and scanning the excitation source. This would create

profiles of the geometric dependence of launch, and the frequency response.

Detection of SPPs would be augmented by more mature theory and wavelength

sensitive detectors. By coupling the wavelength dependent probes with a mature

waveguide like theory, it should be possible to determine the index of refraction

(both real and imaginary parts) from the scattered light. This would be the first

measurement technique that would be able to determine dielectric constants of a

metal on the nanoscale.

In addition to new techniques in launching and detecting SPPs, mode bending in

SPPs supported in silver nanowires was observed. This observation is the first

steps in using silver nanowires as waveguides for on chip applications. In figure

6.2 wires with different curvature are shown to redirect SPP radiation. A wire

with radius of curvature of 4μm has no observable losses. However, a wire with

higher radius of curvature has very prominent radiative losses. This indicates that

silver nanowires could be used to redirect light on a device scale between several

hundred nanometers to microns. In order to improve on these observations, it

- 107 -

would be necessary to intentionally introduce curvature into the nanowires. This

could be done with a microprobe or by influencing the growth conditions of the

nanowires somehow to change their shape.

This thesis also presents cross coupling of SPPs in nanowires. This type of

interaction is important if SPPs are going to be used to redirect light on the

nanoscale. In figures 6.3 and 6.4 micrographs of this inter-wire coupling are

shown. These micrographs show several angles and different configurations of

nanowires that couple. In order to further extend coupling research, purposeful

nanowire manipulation is a must. The assembly of nanowire structures would

allow for a transmission measurement before and after coupling to a new

nanowire. Using this information it would be possible to determine the amount

of total energy available for coupling. This would determine if SPPs coupled to

several different wires would be intense enough to detect surface enhanced

Raman signals.

Additionally chapter 7 is the first detailed measurement of the polarization

dependence of SPP launch in silver nanowires. The data indicates that the

launching site of the SPP determines its polarization characteristics. If it is a

simple end, the polarization of maximum coupling is coincident to the axis of the

nanowire. However, if other sections of the nanowire or other objects are in close

proximity to the point of launch, then the behavior is more complicated and

- 108 -

determined by the local environment. This knowledge creates the interesting

prospective of using nanowires as polarization selective conduits. There are also

many unanswered questions about the polarization of SPPs. First, does the SPP

retain it polarization at the emission point. This can be answered by applying a

Polaroid filter to the imaging detector, to determine the polarization of the light

emitted from the end. This has been done several times and the indication is that

the polarization is along the direction of the axis for straight wires. However, due

to poor signal to noise in the all the images taken with a Polaroid filter this data is

not adequate to publish by itself. More data, with a clear polarization dependence

(or none) needs to be recorded. In addition, several different wire geometries

should be explored.

Finally, the luminescent blinking of nanowire aggregates is addressed in appendix

II. This effect resembles luminescent blinking in other silver micro and

nanostructures. In order to establish the physical mechanism causing this

phenomenon, more research is needed. First the exact location of the blinking

needs to be determined. This can be accomplished using apertures to spatially

select the observed area. Addition of an aperture in the image plane would

localize the blinking to a diffraction limited area. If further localization is needed

to determine the exact location of the blinking, an aperture in the near filed

(closer than a wavelength of light) is required. This type of aperture is commonly

used in near field scanning optical microscopy. Both of these techniques would

- 109 -

reduce the total intensity of the signal and most likely would require a more

sensitive detector than the CCD or CMOS cameras used in this thesis. A photo

multiplier tube (PMT) or avalanche photo diode (APD) would be the logical

choices. In addition to spatially selective imaging, the spectral characteristics of

the luminescent behavior need further investigation. This can be accomplished by

placing a spectrometer in the image plane, or a monochromometer before a

sensitive detector such as an APD or PMT. This type of data could determine if

the blinking effect is the cause of well define silver ion complexes or some other

defect luminescence, or a combination of the two. Finally, the time signature of

the blinking could be extended several orders of magnitude by recording longer

time sequences. This could establish if the 1/f behavior observed continues as the

frequency decreases or plateaus below a certain frequency.

To close, I would like to note that the area of optical phenomena in metallic

nanowires is wide open for new discoveries. It was my humble pleasure to make

some small ones for myself.

- 110 -

A p p e n d i x I

NANOWIRE GROWTH AND CHARACTERIZATION:

Abstract

The metallic nanowires used to investigate 1-D plasmon propagation in this

thesis were extensively characterized by a variety of methods. I present results

from imaging, absorption spectroscopy, luminescence spectroscopy, electron

dispersive spectroscopy, and resistance measurements. Where available, other

commonly available systems are also measured to help in interpreting the

characterization results. The growth protocol used by the collaborating group at

the University of Washington is also outlined.

Introduction

To extend plasmon propagation to the smallest available scales we have turned to

metallic nanowires. Metallic nanowires may be created using lithographic

techniques1, 2 , electro deposition 3, or purely chemical synthesis techniques4-8. By

creating structures of high aspect ratio, plasmon propagation can be controlled

yielding a structure that precisely determines the direction of propagation. The

metallic nanowires used in this study were synthesized by the two common

- 111 -

methods, chemical synthesis and electro-deposition. The bulk of the studies were

carried out on wires synthesized using a chemical technique at the University of

Washington. Although the exact mechanism is still unknown, I shall present the

standing interpretation given in references 4, 5 and discuss the resulting nanowires

that were used to explore 1-D plasmon transport. The discussion begins with a

description of the general synthesis technique and then specific information

concerning the wires used in this study. Once the nanowires are fabricated it is

important to quantify their behavior to certain stimuli. In particular their electro-

optical properties are import to rule out anomalous morphological and

compositional effects in the propagation of plasmons.

Growth and Characterization

The first step of the synthesis involves reducing Platinum Chloride (PtCl2) in

ethylene gylcol (EG). The PtCl2 was reduced in EG by refluxing the solution at

160˚C, creating platinum nanoparticles. This process, known as “polyol”, uses

EG as both a reducing agent and a solvent. After the formation of Pt seed

particles silver nitrate (AgNO3) and poly(vinyl pyrrodlidone) (PVP) were added

forming silver nanoparticles quickly through the reduction of AgNO3 by EG. As

the solution was refluxed for longer times nanowires began to appear and the

solution appearance changed, becoming turbid and gray in color. The reflux time

- 112 -

controls the length of nanowires present. This process seems to be nonlinear,

with particles being the main component after 10min of reflux time, small

ellipsoidal particles forming at 20min, noticeable concentrations of small

nanowires (2μm length) at 40 min, and finally long (~50μm) high aspect ratio

(100 or greater) wires are clearly present at reflux times of 60min.

The wires shipped to Yale were washed once with acetone to remove the EG,

four times with ethanol to remove the PVP and once with water. They were then

suspended in an aqueous solution that was further diluted with water to a

concentration that resulted in 10-102 wires per 100μm2 after being evaporated.

Later micrographs confirmed the presence of PVP on the surface of the

nanowires. Transmission electron micrographs showed that the wires were highly

crystalline with face centered cubic (FCC) symmetry (see figure AI.1).

- 113 -

Figure AI.1: Structure of silver nanowires. A) Transmission electron

micrograph (TEM) of the silver nanowires. B) Electron diffraction pattern of the

same nanowire, showing FCC crystalline structure. Courtesy of D. Routenberg.

- 114 -

After probing the internal structure with TEM, the nanowires were characterized

in variety of ways. To understand how sample preparation affects the nanowires

their optical absorption was measured in suspension and after deposition on a

glass coverslip. In figure AI.2 the extinction spectra for silver nanowires in

suspension, silver nanowires dispersed on a glass slide, and for gold nanowires in

suspension are presented. Since the results for silver nanowires remained

relatively unchanged gold nanowires were only investigated in solution. The

extinction spectra shows a precipitous drop at ~ 320nm showing a slight

difference for the dielectric constant differences. This corresponds to the point at

which the magnitude dielectric constant of the metal is slightly less than that of

the surrounding dielectric.

- 115 -

Figure AI.2: UV-VIS extinction spectra of metallic nanowires. The silver

wires were measured both in aqueous suspension and dried on a NO 1 ½

coverslip. The sharp dip around 320nm for the silver wires is the surface plasmon

dip. In addition, gold wires were measured and as expected showed no distinct

dip. Note the suspension of gold wires was considerably less dense.

- 116 -

In addition to absorption spectra, measurements of the luminescent properties of

the nanowires were made. The wires were suspended in aqueous solution and

placed in a standard quartz cuvette. The wires were then characterized using a

commercially available fluorimeter (Horiba Jobin Yvon) see figure AI.3. The

fluorimeter channels light from a mercury discharge lamp to a

monochromometer. The slit at the entrance to the monochromometer

determines the spectral bandwidth and the intensity of excitation. In these

measurements the slit width was always set at 5nm. The position of a grating

inside of the monochromometer determines the wavelength center of the

excitation. The excitation was set to wavelengths, 300nm, 350nm, 480nm, 532nm.

The 300nm wavelength was selected because it was smaller than the surface

plasmon resonance in silver. The other wavelengths correspond to roughly the

center of excitation from fluorescent settings on the Nikon microscope used for

propagation and blinking experiments. For a set excitation frequency the

fluorimeter scans another monochromometer detecting light emitted from the

sample at 90 degrees. A complete scan was taken in each case and the excitation

removed for improved viewing. Several samples were measured to give

comparative curves. Colloidal silver particles from Ted Pella, inc. of both 20nm

and 80nm were measured in there native solution. In addition, silver nanowires

from the University of Washington, Gold and Copper nanowires fabricated at

- 117 -

Yale, and for a standard silica particles from Dow Corning. Measurements of a

cuvette containing only de-ionized water were included as a baseline. For

excitation above the surface plasmon resonance silver particles are seen to emit

light in the lower wavelengths. In particular, the 80nm colloidal particles and

silver nanowires show very similar luminescent behavior. Both systems have a

broad resonant behavior beginning at ~350nm and extending slightly beyond

500nm. Ripples superimposed on this behavior are apparent around 480nm. The

smaller 20nm silver colloids show a sharper emission curve without any ripples.

Copper nanowires have a decaying behavior, and gold nanowires have a weak

luminescent response. In all the plots, a peak at ~320nm is visible corresponding

to the Raman scattered light from water. In figure AI.3 B the excitation

wavelength is reduced to 350nm (note color change in plots). The broad

resonance feature for the larger silver systems has been replaced with a decaying

background with two sharp peaks. The first sharp peak once again corresponds

to Raman scattering from water. The second peak corresponds to the feature

seen in AI.3 A, and its origins are unknown. All of the suspended particles show a

small broadening of the excitation. The 20nm still show a sharp resonant

emission. In figure AI.3 C we see that the emission of all of the systems has

disappeared, and only a broadening of the excitation is seen. Finally, in figure

AI.3 D similar behavior is seen, except a component is seen in the emission lower

in wavelength.

- 118 -

Figure AI.3A: Fluorimeter measurements of nanoscopic metallic systems.

Measurements were carried out on a commercially available fluorimeter, in the

emission scan mode. In the emission scan mode, a lamp excites a suspended

sample in a quartz cuvette at a specified wavelength and the emitted light is

collected at 90°. A) The results for several samples excited at 300nm. This

excitation is above the surface plasmon frequency for silver and striking response

can be seen for the samples made of silver. A large increase in luminescent

intensity for the silver samples is clear between 400nm and 500nm.

- 119 -

Figure AI.3B: Fluorimeter measurements of nanoscopic metallic systems.

B) At an excitation wavelength of 350nm (a frequency less than the surface

plasmon resonance of silver) The strong peaked behavior for the silver wires and

larger silver colloids has transformed into a decaying background behavior.

However, the 20nm silver colloids still show a resonance behavior. The other

suspended wires and silica colloids show a shelf like structure close to the

excitation point and a small peak. This small peak visible at the same wavelength

(~400nm) is the Raman shifted excitation due to water in the suspension. The

larger silver particles seem to show a second order Raman shifted peak.

- 120 -

Figure AI.3C: Fluorimeter measurements of nanoscopic metallic systems.

C) At an excitation wavelength of 480nm most features except for a broadening

of the excitation have disappeared.

- 121 -

Figure AI.3D: Fluorimeter measurements of nanoscopic metallic systems.

D) When excited even lower an anti-stokes shift appears at wavelengths smaller

than the excitation. De-ionized water and 20nm silver colloids do not show this

effect.

- 122 -

Since the silver nanowires from UW were used in the majority of experiments

they were characterized more extensively. Many micrographs of the wires

dispersed on substrates were taken. These micrographs were used in the

characterization of the wires mean diameters, lengths and the state of the

nanowires surface. In figure AI.4, four such micrographs are presented. These

micrographs show progressively more magnified views. Figure AI.4 A and AI.4 B

show the edges and center of an evaporated drop of nanowire suspension. These

SEM micrographs were taken using a JEOL 6400 with a LAB6 filament. Figure

AI.4 A and AI.4 B clearly show that the mean length of the nanowires is ~10um.

Figures AI.4 C and AI.4 D were taken using a Field Emission SEM (FEI). They

show important diameter information and highlight the structure of overlapping

nanowires. The diameters of the wires in this image are seen to be ~100nm.

Overlapping wires are seen to be in close proximity (<10nm) and some small

metallic particles are seen to remain after the evaporation of the solution.

- 123 -

A B

C D

Figure AI.4: Scanning electron micrograph of silver nanowires after

evaporation of suspension. Each image is taken at a different magnification to

emphasize different features. A. The nanowire mean length of 10um is clear. B.

The effect of fluid dynamics is evident, the edge of the drying droplet creates a

zone of high density disparity. C. A cluster of nanowires showing a metallic

object. D The wires after solution are in very close proximity (if not electrically

shorted).

- 124 -

Further micrographs using an enhanced field emission microscope reveal the

presence of surfactant on the surface of the nanowires, see figure AI.5. The

FESEM (FEI) used to acquire these micrographs was equipped with a contrast

enhancing through lens detector allow the imaging of small defects on the

surface. These defects are visible as slight halos around the nanowires in TEM

images, and are imperceptible using other standard detectors on the SEM. In

addition to the presence of surfactant it can be assumed that some of the wires in

close proximity are not electrically connected. Also, in figure AI.5 D a small silver

cube is clearly present and has been observed in other images.

- 125 -

A

C D

B

Figure AI.5: Ultra high resolution field emission electron micrograph of

silver nanowires. A) High magnification of an abrupt bend in a nanowire. The

bumps on the nanowire surface are surfactant and are only clearly visible in the

ultrahigh resolution mode. B) Micrograph that demonstrates an end of a

nanowire touching the body of another. C) A low angle nanowire crossing. D) A

cluster of nanowires, including small metallic cubes present in the solution.

- 126 -

Electrons bombarding the sample to form an image can also reveal important

information regarding the composition of the sample. The electrons impinging

on the substrate have very high energies and excite electron transitions deep

within the electronic core of the atom. These electrons are effectively knocked

lose from the sample and leave an empty shell. Other electrons decay into this

empty position and release x-rays of energies that are highly characteristic of the

sample. The spectroscopy of these x-rays is typically known as electron dispersive

spectroscopy (EDS). In figure AI.6 the results of EDS from an FESEM are

shown. The only atomic signatures seen are Ag, Si, and O. Since the sample was

prepared on a Silicon wafer both Si and O are presumed to originate from the

substrate.

- 127 -

Figure AI.6: Electron Dispersive Spectroscopy of A nanowire on A Si/SiO2

substrate. The EDS shows that only signatures of atomic Silver, Silicon, and

Oxygen are present.

- 128 -

In addition to the previous characterization methods, the silver nanowires were

characterized in a micro Raman (Horiba Jobin Yvon ). Raman scattering

experiments were carried out using a 532nm laser. The data for a single wire and

a larger aggregate of nanowires are presented in figure. Since the wires are silver

and FCC one would not expect a Raman signature. However Raman scattering

reveals a distinct broad feature at shifts between 1600cm-1-2100cm-1. The metal-

oxides have much smaller Raman shifts and are not the cause of this behavior.

The Carbon-carbon and carbon-oxygen double bond have Raman shifts in this

region, and PVP contains both. For this reason it is suspected that the Raman

scattering signature is a result of the presence of surfactant on the nanowires. In

addition, the substrate between wire positions did not show a similar signature,

indicating that the signature is mostly surface enhanced. Surface enhanced Raman

scattering is a well know effect in high surface area silver systems9.

- 129 -

Figure AI.7: Raman Scattering spectra of Silver Nanowires. The nanowires

were deposited on a glass coverslip, through the usual protocol. A single wire and

a nanowire aggregate were probed by a focused 532nm laser on a commercial

micro-Raman (Horiba Jobin Yvon) system. A broad feature is visible roughly

50nm from the pump excitation, although the exact cause of the feature is not

known, both the carbon-carbon and carbon-oxygen double bond have Raman

shifts of similar order. Both of these bonds are present in PVP. The substrate did

not show any response in this frequency range, indicating that the metallic surface

of the wire plays a role.

- 130 -

In addition to the optical and morphological properties of the silver nanowires

the electrical properties were explored. A sample was prepared by diluting the

aqueous nanowire suspension in ethanol. The nanowires were then dispersed on

a silicon\silicon dioxide surface. Leads were then patterned using standard

photolithography. The resultant sample was then characterized using in a variable

temperature continuous flow cryostat (Janis). The samples temperature is

determined by a flow of cryogen heated by a 50 ohm resistor. The electrical

resistance of the sample was determined by measuring the voltage drop of a

standard current. The wire spanned four leads and a Kelvin measurement of the

resistance made sure the contact resistance to the nanowire did not interfere. The

results of resistance measures are presented in figure AI.8. The resistance was

normalized to the resistance of the sample at 300K. For comparison, the

normalized resistance of the cryostat leads (Manganin wire) and the leads on chip

(Au leads) are also presented. The normalized resistance of the Manganin wires

from the top to bottom of the cryostat is seen to be very flat as a function of

temperature. This with the fact that Manganin is a poor thermal conductor is the

reason that the wire is used in cryogenic applications. The leads and the silver

nanowire show the characteristic behavior of a metal. At relatively high

temperatures the normalized change in resistance as a function of temperature

goes as 1T

, as the temperature is decreased the resistance goes as a power law.

Finally, the resistance plateaus as the temperature is decreased below a certain

- 131 -

point. This plateau is due to saturation of the mean free path of electrons. This

saturation can either be due to geometric restriction or impurity scattering. The

resistivity of the nanowire was calculated using the length and radius as

determined by Scanning electron micrographs. The resistivity of the measured

nanowire is measured to be 4.2x10-6 Ω-cm this is very close to the published

value for bulk silver 1.7x10-6 Ω-cm. A common measure used in thin films is the

room temperature resistivity ratio (RRR). This is in effect a measure of the

saturation of the mean free path, which in thick samples is a measure of

impurities, the RRR for the silver wire measured is 5, for comparison the RRR of

pure bulk silver can easily be in the 1000’s. This can either be an indication of

defects in the wire, or just that the mean free path is limited by the physical size

of the nanowire.

- 132 -

Figure AI.8: Electrical Characterization of a Silver Nanowire. A nanowire dispersed on a silicon oxide/Silicon substrate was contacted with Ti/Au leads. The sample formed a 4 point and the resistance of the nanowire was measured as a function of temperature from 300K to 2K. The nanowire showed the excepted response for a 3-D diffusive wire. The normalized resistance data for some of the important metals in the experiment are shown. The Cryostat wires extending from room temperature to the cryogenic temperature are made of Manganin for there thermal isolation. The Au lead resistance is also displayed using a calibration sample. The lead dependence is obviously different in slope indicating that the four point measurement is in fact a true measurement of the resistance of the wire. An image of the silver nanowire device is inset. The resistivity of the nanowire device was found to be 4.2x10-6Ω-cm using size parameters found from electron microscopy. This value is slightly larger than published value for bulk silver 1.6x10-6. In addition the temperature dependence of the resistance flattens around 50K and gives a room temperature resistance ratio of 5, which is classified as a dirty system, or the mean free path of electrons saturates at low temperatures.

- 133 -

The results of bombarding nanowires with photons and electrons are important

for a complete discussion of plasmon propagation and scattering. This chapter

provides the results of standard characterization techniques spanning several

orders of energy. The response of silver nanowires to photons shows that they

have lower absorption above the bulk plasma frequency. In addition, suspended

nanoscopic silver is shown to emit radiation when excited at 300nm. The

presence of surfactant is confirmed by imaging and Raman scattering. However,

the wires do not have any heavy impurities confirmed by EDS. Finally the DC

conductivity of the silver nanowire is seen to be close (~ 3 times greater) that of

bulk silver, and acts as a relatively dirty metal (RRR~5).

- 134 -

A p p e n d i x I I

LUMINESCENT BLINKING FROM SILVER NANOWIRE

AGGREGATES:

Abstract

Silver nanowire aggregates show bright spots of luminescence in the visible.

These spots are seen to blink on and off under constant lamp illumination. The

luminescent blinking creates a time signature that resembles flicker or 1/f noise.

The luminescence occurs for certain wavelengths and changes with the exposure

of the nanowire aggregate to UV radiation.

Introduction

Nanoscale metallic structures are full of surprising optical properties. When

illuminated with green light (510nm<λ<560nm) aggregates of nanowires are seen

to radiate light in the red (λ>590nm). Furthermore this apparent luminescence is

intermittent, that is “blinks” on and off. Similar luminescence behavior is

observed for illumination in the blue (450nm<λ<490nm) and light collection in

the green and lower (λ>510nm). For illumination in the ultraviolet (330nm-

380nm) and collection in the visible range λ>420nm only a slight constant

- 135 -

background fluorescence is visible and no obvious dynamic behavior is present.

Similar blinking has been observed in an array of silver based nanostructures1-3. In

particular, thin films of silver and silver oxide4 luminescence and have

intermittent blinking behavior. This luminescent behavior has been attributed to

clusters of molecular silver caged in silver oxide5. Here we present a statistical

description of the time series obtained from blinking nanowire aggregates. The

power spectrum of the intensity of the blinks is that of 1f α were 1<α<2. Similar

power spectra have been documented for quantum dots blinking on and off6, 7,

and are a ubiquitous feature of correlated noise found in many systems8, 9.

Luminescent Blinking from Nanowire Aggregates

Experiments were carried out on a Nikon TE 2000 inverted fluorescence

microscope. A slight level of background light was provided by a bright field

condenser. The light from a Mercury discharge lamp is wavelength filtered by

selective reflection from a dichroic mirror. The illumination light is blocked from

entering the detection camera with an absorptive low pass filter. The microscope

has a three such dichroic mirrors and low pass filters. The sample can be excited

with UV (330-380nm), blue (450-490nm), or green (510-560nm) light. A camera

(CMOS or CCD) is used to record the intensity of light of higher wavelengths

than the excitation as a function of time. The mean intensity of a series of images

for a selected area is plotted versus time in figure AII.1. From this time series a

- 136 -

power spectrum is generated by taking a fast Fourier transform (FFT) and

multiplying the conjugate of itself. In order to prevent artifacts of the transform

infiltrating the data, only half of the points are retained and plotted. In figure AII.

1 we see the power spectrum of the mean intensity of a selected area as a

function of time. The power spectrum is plotted in log-log and shows power law

behavior. A line of best fit has (black) is plotted for clarity and has a slope of ~-

1.7. The y intercept represents the zero frequency component and corresponds to

the summed intensity of the time series squared.

- 137 -

Figure AII.1: Power Spectrum Analysis. To understand the dynamics of blinking, the mean intensity versus time for a selected area is transformed into a power spectrum. The power spectrum is generated by taking a fast Fourier transform and multiplying it by its complex conjugate. To avoid aliasing effects the power spectrum has half of the original number of points as the time series.

- 138 -

The power spectrum is of the form 1f α , a ubiquitous feature of correlated noisy

systems.

- 139 -

This type of analysis can be extended to each pixel of the image. In figure AII.2, a

series of plots creates a dynamic map of a time series of images. The first row of

the matrix of plots is the summed intensity of the time sequence. It can be seen

that the aggregate of wires shows a luminescent response at every excitation.

Each pixel of the time series was transformed into a power spectrum. The log

frequency versus the log intensity of the power spectrum was then linearly fit.

The fitting parameters were then assembled into a single image. The results are in

the second and third rows. For UV illumination, the nanowire aggregate shows

little to no dynamic behavior. The total intensity of the time series exceeds those

of the blue and green excitation, yet the spectral map yields only noise. In

contrast, the spectral mapping of blue and green luminescence has pronounced

features. First α varies between -1.5 and zero, being closest to -1.5 at the brightest

and most active points. Second the blue and green excited luminescence are yield

similar luminescent intensities, blue being slightly brighter, for the summed

intensities. In addition, no points outside of the aggregate provide a significant

spectrum indicating that the 1/f behavior is independent of noise on the ccd.

- 140 -

Figure AII.2: Spectral Mapping of a Blinking Nanowire Aggregate. At each

of three fluorescent settings of the microscope data was collected for a 20 second

time period. Each of these movies was used to create a time series for each pixel,

each pixels time series was in turn transformed into a power spectra. This power

spectra was then fit to a 1/f behavior. In order to simplify the fitting process the

log of the intensity versus the log of time was fit by a line. The slope of the line

for each pixel is presented in the second row, and the constant is presented in the

third row. The top row is the time sequence summed to show the brightest areas.

When the wires are excited in the UV (>380nm) the wires have a background

luminescence, however it does not blink, this is witnessed in the spectral

mapping.

- 141 -

In similar luminescent experiments luminescence and blinking were found to be

an activated phenomena. Upon exposure to higher frequency radiation both

tended to increase. In order to better understand the nature our observed

luminescent blinking we exposed the nanowire aggregate to the UV excitation for

an extended amount of time (30 min). In figure AII.3 the effects of this exposure

in the time domain are displayed. The first and last frame of the movies that were

analyzed for dynamic behavior for green and blue are presented before and after

exposure. The integrated intensity of each frame is plotted as a function of time

for the blue excitation. We can see a strong increase in intensity that is decreasing

in time. This is characteristic of activated behavior. For the green excitation the

time series of a single pixel is plotted before and after exposure. This pixel is seen

to spend more time in the luminescent state (brighter for longer). However it

should be noted that in general there is very little spatial correlation between the

brightest points before and after exposure.

- 142 -

Figure AII.3: Effect of UV exposure in the time domain. The left (blue box)

shows the effect of UV exposure for 30 minutes on luminescence excited in the

blue. The first and last frames of the time sequence showing the nanowire

aggregate are presented. In addition, the mean of the entire image as function of

time is plotted. To the right (green box) the effect of UV exposure on

luminescence excited in the green is presented. The time signature of a single

pixel is plotted prior and after exposure.

- 143 -

It is informative to apply the spectral mapping algorithm to the data for the

nanowire aggregate after UV exposure. As in figure AII.1 a matrix of images is

provided in figure AII.4. The top row is again the summed time sequence, and

shows a noticeable increase in the luminescent intensity. The dynamic maps also

show a change in behavior for the blue and green excitation. The mean power of

the power law tends to decrease by a little less than 10%. In addition, the mean

intercept seems to increase indicating a total increasing in the time average

intensity.

- 144 -

Figure AII.4: Spectral Mapping of a Blinking Nanowire Aggregate after

UV exposure for 30 Minutes. As in the previous image, at each of three

fluorescent settings of the microscope data was collected for a 20 second time

period. Each of these movies was used to create a time series for each pixel, each

pixels time series was in turn transformed into a power spectra. This power

spectra was then fit to a 1/f behavior. The 1/f behavior for excitation in both the

green and blue is enhanced showing increased fluctuations. Also the intensity of

both has increased. Although the intensity of the UV excited luminescence has

also increased, it still shows no dynamic behavior.

- 145 -

In conclusion, aggregates of silver nanowires luminescence intermittently,

creating a dynamic light show. In this chapter, I have discussed possible

mechanisms and the dynamic time signatures produced by this blinking. We have

found that the time signature is that of 1/f noise. This type of noise is ubiquitous

in nature, and is indicative of correlated dynamics.

- 146 -

GLOSSARY

Conductivity (σ). The current density that flows for a given electric field.

D-Band. The electronic band formed by the d orbitals of the constituent atoms

of a solid.

Dielectric Function (ε(ω)). The frequency dependent dielectric constant.

Diffraction Limit. The minimum size of a focused wave given by 2NAλ where λ

is the wavelength of the wave and NA is the numeric aperture of the optic.

Electro-Deposition. The electro-chemical deposition of a metal through an

oxidation-reduction reaction.

Energy Dispersive Spectroscopy (EDS). The spectroscopy of the

characteristic x-rays emitted from a sample upon electron bombardment.

Fluorimeter. An instrument for detecting and measuring fluorescence.

Free Electron Model. A model that considers electrons independent of the

potential of their surrounding lattice.

- 147 -

Half Wave Plate. A birefringent device that rotates the polarization of light

passing through it.

Index of Refraction (n). The dielectric constant (function) squared. Typically

expressed as n=n+ik.

Nanoparticle. A particle with all dimensions (length, width and height) less than

one micron.

Nanowire. A wire with a diameter less than one micron.

Ohm’s Law. A phenomenological expression relating current density to electric

field.

Optical Tweezers. A focused laser used to exert a dielectrophoretic force on

small particles.

Penetration Depth (δ). The distance that an electric field falls to 1/e of its value

at the surface of a metal.

Phonon. A vibration of the lattice of atoms or molecules making up a solid.

Plasma Frequency (ω ).p The angular frequency defined by 2

*pnem

ωε

= were n

is the density of charge carriers, e is the charge of an electron, ε is the dielectric

- 148 -

constant of the surrounding media, and m* is the effective mass of the charge

carriers in the solid.

Plasmon. An oscillation of the plasma formed by the conduction electrons in a

solid. Also used as a synonym for surface plasmon polariton.

Polariton. A coupled charge-lattice vibration.

Polarization. The direction of the electric field of a wave.

Raman Scattering. Inelastic scattering of waves from the vibrational modes of a

molecule or group of molecules.

Resistivity(ρ). The reciprocal of conductivity.

Scattering Operator. Mathematical construct that maps one function onto

another. In the context of this thesis, the effect of an abrupt interface on an

electric field.

Scattering Time (τ ).s The mean time between scattering events for an electron.

Spectrophotometer. A machine that measures the optical transmission of a

sample as a function of wavelength.

Subwavelength. Smaller than the wavelength of light in vacuum.

- 149 -

Surface Plasma Frequency(ω ).sp The frequency at which the momentum of a

surface wave diverges.

Surface Plasmon Polariton. A confined surface wave at the interface of a metal

and dielectric.

Surface Plasmon. A synonym for Surface Plasmon Polariton

- 150 -

B i b l i o g r a p h y

Chapter 1 Bibliography

1.Sommerfeld, A., Propagation of waves in wireless telegraphy. Annalen der Physik 1909, Vol. 28, pp 665–736.

2.Zenneck, J., Uber die Fortpflanzung ebener elektromagnetischer Wellen langs einer ebenen Leiterfläche und ihre Beziehung zur drahtlosen Telegraphie. Annalen der Physik 1907; Vol. 23, p 846.

3.Ritchie, R. H., Plasma Losses by Fast Electrons in Thin Films. Physical Review 1957, 106, (5), 874.

4.Stern, E. A.; Ferrell, R. A., Surface Plasma Oscillations of a Degenerate Electron Gas. Physical Review 1960, 120, (1), 130.

5.Economou, E. N., Surface plasmons in thin films. Physical Review 1969, 182, (2), 539-54.

6.Fleischmann, M.; Hendra, P. J.; McQuillan, A. J., Raman spectra of pyridine adsorbed at a silver electrode. Chemical Physics Letters 1974; Vol. 26, pp 163-166.

7.Chang, R. K.; Furtak, T. E., Surface enhanced Raman scattering. Plenum Press New York: 1982.

8.Moskovits, M., Surface-enhanced spectroscopy. Reviews of Modern Physics 1985, 57, (3), 783.

9.Otto, A.; Mrozek, I.; Grabhorn, H.; Akemann, W., Surface-enhanced Raman scattering. In 1992; Vol. 4, pp 1143-1212.

10.Ebbesen, T. W.; Lezec, H. J.; Ghaemi, H. F.; Thio, T.; Wolff, P. A., Extraordinary optical transmission through sub-wavelength hole arrays. Nature 1998, 391, (6668), 667-669.

11.Krenn, J. R.; Weeber, J. C.; Dereux, A.; Bourillot, E.; Goudonnet, J. P.; Schider, B.; Leitner, A.; Aussenegg, F. R.; Girard, C., Direct observation of

B-1

localized surface plasmon coupling. Physical Review B (Condensed Matter) 1999, 60, (7), 5029-33.

12.Weeber, J.-C.; Dereux, A.; Girard, C.; Krenn, J. R.; Goudonnet, J.-P., Plasmon polaritons of metallic nanowires for controlling submicron propagation of light. Physical Review B (Condensed Matter) 1999, 60, (12), 9061-8.

13.Dickson, R. M.; Lyon, L. A., Unidirectional plasmon propagation in metallic nanowires. Journal of Physical Chemistry B 2000, 104, (26), 6095-8.

14.Krenn, J. R.; Salerno, M.; Felidj, N.; Lamprecht, B.; Schider, G.; Leitner, A.; Aussenegg, F. R.; Weeber, J. C.; Dereux, A.; Goudonnet, J. P., Light field propagation by metal micro- and nanostructures. Journal of Microscopy 6th International Conference on Near-Field Optics and Related Techniques, 27-31 Aug. 2000 2001, 202, (pt.1), 122-8.

15.Lamprecht, B.; Krenn, J. R.; Schider, G.; Ditlbacher, H.; Salerno, M.; Felidj, N.; Leitner, A.; Aussenegg, F. R.; Weeber, J. C., Surface plasmon propagation in microscale metal stripes. Applied Physics Letters 2001, 79, (1), 51-3.

16.Maier, S. A.; Brongersma, M. L.; Kik, P. G.; Meltzer, S.; Requicha, A. A. G.; Atwater, H. A., Plasmonics - A route to nanoscale optical devices. Advanced Materials 2001, 13, (19), 1501-1505.

17.Barber, D. J.; Freestone, I. C., Origin of the color of the Lycurgus cup by analytical transmission electron microscopy. Archaeometry 1990; Vol. 32, pp 33-46.

18.Benjamin Wiley, Y. S. B. M. Y. X., Shape-Controlled Synthesis of Metal Nanostructures: The Case of Silver. In 2005; Vol. 11, pp 454-463.

19.Ditlbacher, H.; Hohenau, A.; Wagner, D.; Kreibig, U.; Rogers, M.; Hofer, F.; Aussenegg, F. R.; Krenn, J. R., Silver nanowires as surface plasmon resonators. Physical Review Letters 2005, 95, (25), 257403-1.


1.Kittel, C., Introduction to solid state physics. 7th ed.; Wiley New York: 1996. 2.Griffiths, D. J., Introduction to Electrodynamics, 2nd Edition Prentice Hall: Englewood Cliffs, New Jersey, 1989.

B-2

3.Johnson, P. B.; Christy, R. W., Optical constants of the noble metals. Physical Review B (Solid State) 1972, 6, (12), 4370-9. 4.Economou, E. N., Surface plasmons in thin films. Physical Review 1969, 182, (2), 539-54. 5.Pfeiffer, C. A.; Economou, E. N.; Ngai, K. L., Surface polaritons in a circularly cylindrincal interface: Surface Plasmons. Physical Review B (Condensed Matter and Materials Physics) 1974, 10, (8), 3038-3051. 6.Fermi, E., The Ionization Loss of Energy in Gases and in Condensed Materials. Physical Review 1940, 57, (6), 485. 7.Fano, U., Atomic Theory of Electromagnetic Interactions in Dense Materials. Physical Review 1956, 103, (5), 1202. 8.Palik, E. D., Handbook of optical constants of solids. Academic Press Orlando: 1985.


1.Economou, E. N., Surface plasmons in thin films. Physical Review 1969, 182, (2), 539-54. 2.Maier, S. A.; Atwater, H. A., Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures. Journal of Applied Physics: 2005; Vol. 98, pp 11101-11101. 3.Maradudin, A. A.; Mills, D. L., Scattering and absorption of electromagnetic radiation by a semi-infinite medium in the presence of surface roughness. Physical Review B 1975, 11, (4), 1392. 4.Kretschmann, E.; Ferrell, T. L.; Ashley, J. C., Splitting of the Dispersion Relation of Surface Plasmons on a Rough Surface. Physical Review Letters 1979, 42, (19), 1312. 5. Sommerfeld, A., Propagation of waves in wireless telegraphy. Annalen der Physik 1909, Vol. 28, pp 665–736.

B-3

6 Zenneck, J., Uber die Fortpflanzung ebener elektromagnetischer Wellen langs einer ebenen Leiterfläche und ihre Beziehung zur drahtlosen Telegraphie. Annalen der Physik 1907; Vol. 23, p 846. 7.Ferrell, R. A., Angular Dependence of the Characteristic Energy Loss of Electrons Passing Through Metal Foils. Physical Review 1956, 101, (2), 554. 8.Teng, Y.-Y.; Stern, E. A., Plasma Radiation from Metal Grating Surfaces. Physical Review Letters 1967, 19, (9), 511. 9.Raether, H., Surface-Plasmons on Smooth and Rough Surfaces and on Gratings. Springer Tracts in Modern Physics 1988, 111, 1-133. 10.Dionne, J. A.; Sweatlock, L. A.; Atwater, H. A.; Polman, A., Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model. Physical Review B (Condensed Matter and Materials Physics) 2005, 72, (7), 075405-11. 11.Weber, W. H.; Ford, G. W., Optical electric-field enhancement at a metal surface arising from surface-plasmon excitation. Optics Letters 1981; Vol. 6, pp 122-124. 12.Raether, H., Physics of Thin Films. Academic Press, New York, 1977; Vol. 9, p 145. 13.Andreas, O., Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection. Zeitschrift für Physik A Hadrons and Nuclei 1968, V216, (4), 398-410. 14.Ditlbacher, H.; Krenn, J. R.; Hohenau, A.; Leitner, A.; Aussenegg, F. R., Efficiency of local light-plasmon coupling. Applied Physics Letters 2003, 83, (18), 3665-3667. 15.Hecht, B.; Bielefeldt, H.; Novotny, L.; Inouye, Y.; Pohl, D. W., Local Excitation, Scattering, and Interference of Surface Plasmons. Physical Review Letters 1996, 77, (9), 1889. 16.Orfinidas, S. J., Electromagnetic waves and antennas. Online at http://www.ece.rutgers.edu/~orfanidi/ewa/


B-4

http://www.ece.rutgers.edu/%7Eorfanidi/ewa/

1.McCord, M. A.; Rooks, M. J., Handbook of Microlithography Micromachining and Microfabrication vol 1. SPIE and The Institution of Electrical Engineers, Bellingham, Washington 1997. 2.Powell, C. J.; Swan, J. B., Origin of the Characteristic Electron Energy Losses in Aluminum. Physical Review 1959, 115, (4), 869. 3.Bagchi, A.; Duke, C. B., Determination of the Surface-Plasmon Dispersion Relation in Aluminum by Inelastic Electron Diffraction. Physical Review B 1972, 5, (8), 2784. 4.Duke, C. B.; Landman, U., Surface-Plasmon Dispersion in A1(111) Films. Physical Review B 1973, 8, (2), 505. 5.Porteus, J. O.; Faith, W. N., Inelastic Low-Energy-Electron Diffraction for Surface-Plasmon Studies: Extended Measurements on Epitaxial A1(111). Physical Review B 1973, 8, (2), 491. 6.Ehrenreich, H.; Philipp, H. R.; Segall, B., Optical Properties of Aluminum. Physical Review 1963, 132, (5), 1918.


1.Arfken, G. B.; Weber, H. J.; Ruby, L., Mathematical Methods for Physicists. AAPT: 1996; Vol. 64. 2.Pfeiffer, C. A.; Economou, E. N.; Ngai, K. L., Surface polaritons in a circularly cylindrincal interface: Surface Plasmons. Physical Review B (Condensed Matter and Materials Physics) 1974, 10, (8), 3038-3051. 3.Stratton, J. A., Electromagnetic theory. McGraw-Hill New York: 1941.


1.Maier, S. A.; Brongersma, M. L.; Kik, P. G.; Meltzer, S.; Requicha, A. A. G.; Atwater, H. A.,Plasmonics - A route to nanoscale optical devices. Advanced Materials 2001, 13, (19), 1501-1505.

2.Weeber, J.-C.; Dereux, A.; Girard, C.; Krenn, J. R.; Goudonnet, J.-P., Plasmon polaritons of metallic nanowires for controlling submicron propagation of light. Physical Review B (Condensed Matter) 15, 60, (12), 9061-8.

B-5

3.Sirbuly, D. J.; Law, M.; Pauzauskie, P.; Yan, H.; Maslov, A. V.; Knutsen, K.; Ning, C.-Z.;Saykally, R. J.; Yang, P., Optical routing and sensing with nanowire assemblies. Proceedings of the National Academy of Sciences of the United States of America 2005, 102, (22), 7800-5.

4.Barrelet, C. J.; Greytak, A. B.; Lieber, C. M., Nanowire photonic circuit elements. Nano Letters 2004, 4, (10), 1981-5.

5.Tong, L.; Gattass, R. R.; Ashcom, J. B.; He, S.; Lou, J.; Shen, M.; Maxwell, I.; Mazur, E., Subwavelength-diameter silica wires for low-loss optical wave guiding. Nature 2003, 426, (6968), 816-19.

6.Tong, L.; Lou, J.; Gattass, R. R.; He, S.; Chen, X.; Liu, L.; Mazur, E., Assembly of silica nanowires, on silica aerogels for microphotonic devices. Nano Letters 2005, 5, (2), 259-62.

7.Rakich, P. T.; Sotobayashi, H.; Gopinath, J. T.; Johnson, S. G.; Sickler, J. W.; Wong, C. W.; Joannopoulos, J. D.; Ippen, E. P., Nano-scale photonic crystal microcavity characterization with an all-fiber based 1.2 - 2.0 mu m supercontinuum. Optics Express 2005, 13, (3).

8.Maier, S. A.; Kik, P. G.; Brongersma, M. L.; Atwater, H. A.; Meltzer, S.; Requicha, A. A. G.; Koel, B. E. In Observation of coupled plasmon-polariton modes of plasmon waveguides for electromagnetic energy transport below the diffraction limit, Materials and Devices for Optoelectronics and Microphotonics Symposium, 1-5 April 2002, San Francisco, CA, USA, 2002//, 2002; Mater. Res. Soc: San Francisco, CA, USA, 2002; pp 431-6.

9.Raether, H., Surface-Plasmons on Smooth and Rough Surfaces and on Gratings. Springer Tracts in Modern Physics 1988, 111, 1-133.

10.Dickson, R. M.; Lyon, L. A., Unidirectional plasmon propagation in metallic nanowires. Journal of Physical Chemistry B 2000, 104, (26), 6095-8.

11.Graff, A.; Wagner, D.; Ditlbacher, H.; Kreibig, U., Silver nanowires. European Physical Journal D 2005, 34, (1-3), 263-269.

12.Sun, Y.; Gates, B.; Mayers, B.; Xia, Y., Crystalline silver nanowires by soft solution processing. Nano Letters 2002, 2, (2), 165-8.

B-6

13.Sun, Y.; Yin, Y.; Mayers, B. T.; Herricks, T.; Xia, Y., Uniform silver nanowires synthesis by reducing AgNO/sub 3/ with ethylene glycol in the presence of seeds and poly(vinyl pyrrolidone). Chemistry of Materials 2002, 14, (11), 4736-45.

14.Ditlbacher, H.; Krenn, J. R.; Schider, G.; Leitner, A.; Aussenegg, F. R., Two-dimensional optics with surface plasmon polaritons. Applied Physics Letters 2002, 81, (10), 1762.

15.Vlasov, Y. A.; McNab, S. J., Losses in single-mode silicon-on-insulator strip waveguides and bends. Optics Express 2004, 12, (8).

16.Krenn, J. R.; Weeber, J. C., Surface plasmon polaritons in metal stripes and wires. Philosophical Transactions of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences 2004, 362, (1817), 739-756.

17.Pfeiffer, C. A.; Economou, E. N.; Ngai, K. L.,Surface polaritons in a circularly cylindrincal interface: Surface Plasmons. Physical Review B (Condensed Matter and Materials Physics) 1974, 10, (8), 3038-3051.

18.Economou, E. N., Surface plasmons in thin films. Physical Review 1969, 182, (2), 539-54.

19.Johnson, P. B.; Christy, R. W., Optical constants of the noble metals. Physical Review B (Solid State) 1972, 6, (12), 4370-9.

20.Tsapis, N.; Dufresne, E. R.; Sinha, S. S.; Riera, C. S.; Hutchinson, J. W.; Mahadevan, L.;Weitz, D. A., Onset of buckling in drying droplets of colloidal suspensions. Physical Review Letters 2005, 94, (1), 018302-1.

21.Huang, Y.; Duan, X.; Wei, Q.; Lieber, C. M., Directed assembly of one-dimensional nanostructures into functional networks. Science 2001, 291, (5504), 630-3.

22.Keren, K.; Krueger, M.; Gilad, R.; Ben-Yoseph, G.; Sivan, U.; Braun, E., Sequence-specific molecular lithography on single DNA molecules. Science 2002, 297, (5578), 72-5.

23.Smith, P. A.; Nordquist, C. D.; Jackson, T. N.; Mayer, T. S.; Martin, B. R.; Mbindyo, J.; Mallouk, T. E., Electric-field assisted assembly and alignment of metallic nanowires. Applied Physics Letters 2000, 77, (9), 1399-1401.

B-7

24.Dufresne, E. R.; Grier, D. G., Optical tweezer arrays and optical substrates created with diffractive optics. Review of Scientific Instruments 1998, 69, (5), 1974-1977.

25.Agarwal, R.; Ladavac, K.; Roichman, Y.; Yu, G. H.; Lieber, C. M.; Grier, D. G., Manipulation and assembly of nanowires with holographic optical traps. Optics Express 2005, 13, (22), 8906-8912.

26.Ditlbacher, H.; Hohenau, A.; Wagner, D.; Kreibig, U.; Rogers, M.; Hofer, F.; Aussenegg, F. R.; Krenn, J. R., Silver nanowires as surface plasmon resonators. Physical Review Letters 2005, 95, (25), 257403-1.


1.Ditlbacher, H.; Hohenau, A.; Wagner, D.; Kreibig, U.; Rogers, M.; Hofer, F.; Aussenegg, F. R.; Krenn, J. R., Silver nanowires as surface plasmon resonators. Physical Review Letters 2005, 95, (25), 257403-1. 2.Weeber, J.-C.; Dereux, A.; Girard, C.; Krenn, J. R.; Goudonnet, J.-P., Plasmon polaritons of metallic nanowires for controlling submicron propagation of light. Physical Review B (Condensed Matter) 1999, 60, (12), 9061-8. 3.Dickson, R. M.; Lyon, L. A., Unidirectional plasmon propagation in metallic nanowires. Journal of Physical Chemistry B 2000, 104, (26), 6095-8. 4.Graff, A.; Wagner, D.; Ditlbacher, H.; Kreibig, U., Silver nanowires. European Physical Journal D 2005, 34, (1-3), 263-269. 5.Sanders, A. W.; Routenberg, D. A.; Wiley, B. J.; Xia, Y.; Dufresne, E. R.; Reed, M. A., Observation of Plasmon Propagation, Redirection, and Fan-Out in Silver Nanowires. In 2006; Vol. 6, pp 1822-1826. 6.Economou, E. N., Surface plasmons in thin films. Physical Review 1969, 182, (2), 539-54. 7.Pfeiffer, C. A.; Economou, E. N.; Ngai, K. L., Surface polaritons in a circularly cylindrincal interface: Surface Plasmons. Physical Review B (Condensed Matter and Materials Physics) 1974, 10, (8), 3038-3051. 8.Maier, S. A.; Atwater, H. A., Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures. In American Institute of Physics: 2005; Vol. 98, pp 11101-11101.

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9.Arya, V.; Murphy, K. A.; Wang, A.; Claus, R. O., Microbend losses in singlemode optical fibers: theoretical and experimental investigation. Lightwave Technology, Journal of 1995, 13, (10), 1998-2002.

Appendix I Bibliography

1.Kramer, N.; Birk, H.; Jorritsma, J.; Schonenberger, C., Fabrication of metallic nanowires with a scanning tunneling microscope. Applied Physics Letters 1995, 66, (11), 1325-1327. 2.Jorritsma, J.; Gijs, M. A. M.; Kerkhof, J. M.; Stienen, J. G. H., General technique for fabricating large arrays of nanowires. Nanotechnology 1996, 7, (3), 263-265. 3.Yin, A. J.; Li, J.; Jian, W.; Bennett, A. J.; Xu, J. M., Fabrication of highly ordered metallic nanowire arrays by electrodeposition. Applied Physics Letters 2001, 79, (7), 1039. 4.Sun, Y.; Gates, B.; Mayers, B.; Xia, Y., Crystalline silver nanowires by soft solution processing. Nano Letters 2002, 2, (2), 165-8. 5.Sun, Y.; Yin, Y.; Mayers, B. T.; Herricks, T.; Xia, Y., Uniform silver nanowires synthesis by reducing AgNO/sub 3/ with ethylene glycol in the presence of seeds and poly(vinyl pyrrolidone). Chemistry of Materials 2002, 14, (11), 4736-45. 6.Wiley, B., Y. S. B. M. Y. X., Shape-Controlled Synthesis of Metal Nanostructures: The Case of Silver. Chemistry - A European Journal 2005; Vol. 11, pp 454-463. 7.Keren, K.; Krueger, M.; Gilad, R.; Ben-Yoseph, G.; Sivan, U.; Braun, E., Sequence-specific molecular lithography on single DNA molecules. Science 2002, 297, (5578), 72-5. 8.Thurn-Albrecht, T.; Schotter, J.; Kastle, G. A.; Emley, N.; Shibauchi, T.; Krusin-Elbaum, L.; Guarini, K.; Black, C. T.; Tuominen, M. T.; Russell, T. P., Ultrahigh-Density Nanowire Arrays Grown in Self-Assembled Diblock Copolymer Templates. Science 2000, 290, (5499), 2126-2129. 9.Chang, R. K.; Furtak, T. E., Surface enhanced Raman scattering. Plenum Press New York: 1982.

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Appendix II Bibliography

1. Sun, Y. G.; Xia, Y. N., Gold and silver nanoparticles: A class of chromophores with colors tunable in the range from 400 to 750 nm. Analyst 2003; Vol. 128, pp 686–691. 2. Geddes, C. D.; Parfenov, A.; Lakowicz, J. R., Luminescent Blinking from Noble-Metal Nanostructures: New Probes for Localization and Imaging. Journal of Fluorescence 2003; Vol. 13, pp 297-299. 3. Chris D. Geddes, A. P. I. G. J. R. L., Luminescent Blinking from Silver Nanostructures. J. Phys. Chem. B 2003; Vol. 34. 4. Xin-Yu, P.; Hong-Bing, J.; Chun-Ling, L.; Qi-Huang, G.; Xi-Yao, Z.; Qi-Feng, Z.; Bei-Xue, X.; Jin-Lei, W., Fluorescence Microscopy of Nanoscale Silver Oxide Thin Films. Chinese Physics Letters 2003; Vol. 20, pp 133-136. 5. Capadona, L. A., Photoactivated Fluorescence from Small Silver Nanoclusters and Their Relation to Raman Spectroscopy. PhD. Thesis, Georgia Institute of Technology, USA (2004) 6. Pelton, M.; Grier, D. G.; Guyot-Sionnest, P., Characterizing quantum-dot blinking using noise power spectra. APPLIED PHYSICS LETTERS 2004, 85, (5). 7. Shimizu, K. T.; Neuhauser, R. G.; Leatherdale, C. A.; Empedocles, S. A.; Woo, W. K.; Bawendi, M. G., Blinking statistics in single semiconductor nanocrystal quantum dots. Physical Review B 2001, 63, (20), 205316. 8. Bak, P.; Tang, C.; Wiesenfeld, K., Self-organized criticality: An explanation of the 1/f noise. Physical Review Letters 1987, 59, (4), 381. 9. Mandelbrot, B. B.; Ness, J. W. V., Fractional Brownian Motions, Fractional Noises and Applications. SIAM Review 1968, 10, (4), 422-437.

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