OPTICAL PROPERTIES OF METALLIC NANOSTRUCTURES A

Transcription

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
©2007 by Aric Warner Sanders
All rights reserved.
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 -
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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
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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
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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)
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Chapter 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.
these waveguides.
This thesis is primarily devoted to
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 reemission 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-
Chapter 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) J =
ne 2 Eτ Scatter
me*
Which is the microscopic statement of Ohm’s Law J=σE.
-9-
E
A
< V >=
B
−eEτ Scatter
me*
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 < V >=
−eEτ
.
me*
- 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) me* x = e E −
me* x
τ dampening
where E is taken to be a periodic electric field,
inserting E = E0 e − iωt , and assuming that the response is at the same frequency
we arrive at the solution for the equation of motion
(2.3) x =
−(e / m)
iω
ω2 +
E0
τ dampening
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 (τ dampening ), 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
1
τ
=∑
i
1
τi
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 -
⎛
⎞
⎟
dX ⎜
ne 2
=⎜
J = −ne
⎟E
(2.4)
dt ⎜ m* ( 1 − iω ) ⎟
τ
⎝
⎠
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) ∇ • E = 0
(iii) ∇ • B = 0
(ii) ∇ × E = -
∂B
∂t
(iv) ∇ × B = με
∂E
+ μσ E
∂t
By applying the curl operator to (2.5iii) and (2.5iv), we arrive at a modified wave
equation:
(2.6) ∇ 2 E = με
∂ 2E
∂E 2
∂ 2B
∂B
+
μσ
,
∇
B
=
με
+ μσ
2
2
∂t
∂t
∂t
∂t
This equation has plane wave solutions with complex wave-vectors
- 12 -
E = E0 ei ( k i x −ωt )
iωσ ⎞
⎛
(2.7) k 2 = μεω 2 + i μσω = με ⎜ ω 2 +
ε ⎟⎠
⎝
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 E = E0 ei (Re[ k ]i x −ωt ) e − Im[ k ]i x . It follows
that the 1/e distance is δ pen =
1
. This distance is usually at least an order of
Im[k ]
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
⇒ Im[k ] ~
σ
2
μ
2
⇒ δ pen =
ε
σ
ε
,
μ
and
we
have
that
the
penetration depth is independent of frequency.
2. good conductor σ >> ωε
⇒ Im[k ] ~
ωσμ
2
⇒ δ pen =
2
ωμσ
, This is the penetration depth that is
most commonly used when discussing metals since the DC conductivity is on
the order of 107(Ω-m)-1 and ε
10−11
- 13 -
C2
σ
, giving
2
Nm
ε
1018 Hz >> ω for
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
⎜
⎟ ω2 ⎛
⎞
ine
ine 2τ
(2.8) k 2 = ω 2 με ⎜ 1 +
= 2 ⎜1 +
⎟
⎟ , where we have
*
2
c
m
i
−
(
)
ε
ω
ω
τ
* ω
2
⎝
⎠
⎜ ε m ( − iω ) ⎟
τ
⎝
⎠
assumed that the material in question has the property μ = μ0 .
Now we can define the penetration depth of a free electron gas as δ Free =
1
Im[k ]
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 ω 2τ >> ω then we may simplify the equation to k 2 =
ω2 ⎛
ne 2 ⎞
⎜1 −
⎟.
c 2 ⎝ ε m*ω 2 ⎠
Evidently, when the quantity in the parenthesis is zero something special is
happening. In fact this is the plasma frequency.
⎛ ne 2 ⎞
(2.9) ω p2 = ⎜ * ⎟
⎝ εm ⎠
2
⎛ ωp ⎞ ⎞
So that we may now write k = 2 ⎜1 − ⎜
⎟ ⎟ or that the dispersion
c ⎜ ⎝ω ⎠ ⎟
⎝
⎠
2
ω2 ⎛
relationship is
⎛ ωp ⎞
1− ⎜
⎟ were k0 is the wavevector in free space,
⎝ω ⎠
2
(2.10) k = k0
this gives rise to the commonly used form of ε for a metal4, 5,
⎛ω ⎞
ε m = 1 − ⎜ p ⎟ . The plasma frequency for the noble metals is on the order of
⎝ω ⎠
2
- 19 -
⎛ ne 2 ⎞
⎛ 6 x1028 (1.6 x10−19 ) 2 ⎞
=
=
≈ 1017Hz or a free space wavelength
ωp
⎜ *⎟
⎜
−12
−31 ⎟
⎝ εm ⎠
⎝ 8.85 x10 x9 x10 ⎠
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 -
Chapter 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
E = ∑ Ak ei ( k •ζ −ωt )ξˆ where ξˆ represents the normalized Cartesian directional
k,ξ
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
(3.1) Ex = E0 e
i ( km z + k plasmon x −ω t )
, Ez = −
k plasmon
km
E0 e
i ( km z + k plasmon x −ωt )
, Ey = 0
and outside in the dielectric it is
(3.2) Ex = E0 e
i ( kd z + k plasmon x −ωt )
, Ez = −
ε m k plasmon
i(k
E0 e
ε d km
where
- 28 -
d z + k plasmon x −ω t )
, Ey = 0
(3.3) k plasmon =
ε dε m
εd2
ε m2
ω
ω
, kd =
, km =
c εd + εm
c εd + εm
c εd + εm
ω
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 ε m + ε d = 0 .
- 30 -
Now there are five length scales that come into the discussion of surface
plasmons polaritons:
1. The free space wavelength of photon λ ph =
2. The wavelength of the SPP, λ plasmon =
2π
ω
, where k0 =
c
k0
2π
, where kplasmon is given
Re[k plasmon ]
in (3.3)
3. The 1/e distance of the plasmon electric field in the direction of
propagation LElectric
plasmon =
1
Im[k plasmon ]
, or more frequently of the 1/e
distance of the intensity of the SPP LIntensity
plasmon = LSPP =
1
.
2 Im[k plasmon ]
4. The 1/e distance of the electric field of SPP into the metal normal to the
direction of propagation δ m = δ m =
1
.
km
5. The 1/e distance of the electric field of SPP into the dielectric normal to
the direction of propagation δ dielectric = δ d =
- 31 -
1
.
kd
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 LElectric
plasmon , which is typically 10’s to 100’s of μm in the
visible part of the electromagnetic spectrum.
- 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 ωspair =
ωp
2
. 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
ε m = −ε d . 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
⎛ω ⎞
ε m = 1 − ⎜ p ⎟ (where ωp is the bulk plasma frequency), we have that the surface
⎝ω ⎠
2
ωp
ω p2
plasma frequency is ωsp =
, or in air or a vacuum ωspair =
. This is
1+ εd
2
- 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 ( Ex ) component of the electric field dominates. In the dielectric the
transverse component ( Ez ) 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 (ωp), 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 KretschmannRaether9,12 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 (
λ
2 NA
= 296nm ) 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 k plasmon = k photon ±
2π
. The amplitude of the coefficients
a
- 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 -
Chapter 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 liftedoff 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 farfield 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 -
Chapter 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
∇ E = με
2
∂ 2E
∂E 2
∂ 2B
∂B
,
B
+ μσ
∇ = με 2 + μσ
2
∂t
∂t
∂t
∂t
Outside we have the version with out conductivity
∇ 2 E = με
∂ 2E 2
∂ 2B
,
∇
B
=
με
∂t 2
∂t 2
In order to solve these equations for a cylindrical geometry we insert the
appropriate expression for the Laplacian1
∇ 2 E = ∇ 2 E ρ + ∇ 2 Eθ + ∇ 2 E z −
∂E ⎤
2 ⎡ ∂E
⎡⎣ Eθ + E ρ ⎤⎦ + 2 ⎢ ρ − θ ⎥
∂θ ⎦
ρ
ρ ⎣ ∂θ
1
2
where
1 ∂ ⎛ ∂ψ ⎞ 1 ∂ 2ψ ∂ 2ψ
ρ
∇ψ =
+
+
ρ ∂ρ ⎜⎝ ∂ρ ⎟⎠ ρ 2 ∂ρ 2 ∂z 2
2
we solve the wave equations using separation of variables. We assume a harmonic
time dependence that is E = Ee− iωt . And further we assume each component of
the electric field vector is separable.
E ρ = E ρ ( ρ )E ρ (θ )E ρ ( z ) , Eθ = Eθ ( ρ )Eθ (θ )Eθ ( z ) , E z = E z ( ρ )E z (θ )E z ( z )
- 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) EρInside =
⎡ ik plasmon
⎤ ( inθ +ik plasmon z −iωt )
μ ωn
J n ′ (km ρ )anInside − 0 2 J n (km ρ )bnInside ⎥e
km
km ρ
n =−∞ ⎣
⎦
∞
∑⎢
∞
⎡ nk
⎤ (inθ +ik plasmon z −iωt )
iμ ω
(5.2) EθInside = − ∑ ⎢ plasmon
J n (km ρ )anInside + 0 J n ′ (km ρ )bnInside ⎥e
2
km
n =−∞ ⎣ k m ρ
⎦
(5.3) EzInside =
∞
∑ ⎡⎣ J
n =−∞
n
(km ρ )anInside ⎤⎦e
( inθ + ik plasmon z − iωt )
The magnetic field in the wire is
(5.4) H Inside
=
ρ
ik
⎡ nk02ε m
J n (km ρ )anInside + plasmon J n′ (km ρ )bnInside ⎥e
∑
⎢
2
km
n =−∞ ⎣ μ 0ω k m ρ
⎦
(5.5) HθInside =
nk plasmon
⎡ ik02ε m
J n′ (km ρ )anInside −
J n (km ρ )bnInside ⎥e
∑
⎢
2
km ρ
n =−∞ ⎣ μ 0ω k m
⎦
(5.6) H Inside
=
z
∞
∞
∞
∑ ⎡⎣ J
n =−∞
n
(km ρ )bnInside ⎤⎦e
( inθ + ik plasmon z −iωt )
Outside in the surrounding dielectric we have
(5.7) EρOutside =
⎡ ik plasmon (1)
μ ωn
H n ′ (kd ρ )anOutside − 0 2 H n(1) (kd ρ )bnOutside ⎥e
kd
kd ρ
n =−∞ ⎣
⎦
∞
∑⎢
- 70 -
(5.8) EθOutside =
(5.9) EzOutside =
⎡ nk plasmon (1)
iμ ω
H n (kd ρ )anOutside − 0 H n(1)′ (kd ρ )bnOutside ⎥e
2
kd
n =−∞ ⎣ k d ρ
⎦
∞
∑⎢
∞
∑ ⎡⎣ H
n =−∞
(1)
n
(kd ρ )anOutside ⎤⎦e
for the electric field and for the magnetic field
(5.10) H Outside
=
ρ
ik plasmon (1)
⎡ nk02ε d
H n(1) (kd ρ )anOutside +
H n ′ (kd ρ )bnOutside ⎥e
∑
⎢
2
kd
n =−∞ ⎣ μ 0ω k d ρ
⎦
(5.11) HθOutside =
nk
⎡ ik02ε d
H n(1)′ (kd ρ )anOutside − plasmon
H n(1) (kd ρ )bnOutside ⎥e
∑
⎢
2
kd ρ
n =−∞ ⎣ μ 0ω k d
⎦
(5.12) H Outside
=
z
∑ ⎡⎣ H
∞
∞
∞
n =−∞
(1)
n
(kd ρ )bnOutside ⎤⎦e
Where J n are Bessel functions of the first kind, and H n(1) are Hankel functions.
The prime denotes differentiation with respect to the argument k ρ .
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
Eρ = a0Inside
ik plasmon
km
J 0′ (km ρ )e
Ez = a0Inside J 0 (km ρ )e
i ( k plasmon z −ω t )
and
i ( k plasmon z −ωt )
outside the wire we have
Eρ = a0Outside
ik plasmon
kd
H 0 (1)′ (kd ρ )e
- 71 -
Ez = a0Outside H 0 (1) (kd ρ )e
where
k plasmon =
εdε m
εd2
ε m2
ω
ω
, kd =
, km =
c εd + εm
c εd + εm
c εd + εm
ω
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 km , 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.
- 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 -
Chapter 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 1024PCI), 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,
−
x
I ( x) = I 0 e L , 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 farfield measurement provides a practical lower limit for the propagation length. For
comparison, a propagation length of 2.5 μm has been reported for gold nanofabricated 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 E ~ e
− kρ ρ
where
k ρ 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 ( ε surfactant = ε oil ), we approximate
k ρ using the dispersion relations of an infinite plane9,18 k ρ2 + k z2 = k 2
where
⎛ ω ⎞ ε mε d
k z2 = ⎜ ⎟
,
⎝ c ⎠ εm + εd
Thus,
kρ 2 =
ω2 ⎛ εd2
⎜
c2 ⎝ ε m + ε d
⎛ω ⎞
k2 = ⎜ ⎟ εd
⎝c⎠
2
2
and
in
the
dielectric.
⎞
⎟ , where c = speed of light, ω = the angular frequency, ε d =
⎠
- 87 -
the relative permittivity of the dielectric, and ε m the relative permittivity of the
metal. Substituting material parameters for the immersion oil ( ε d =2.25) and
silver ( ε m =-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 k ρ , 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 -
Chapter 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 glassair 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.
- 105 -
Chapter 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
- 106 -
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 -
Appendix 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 electrooptical 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
B
C
D
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 metaloxides 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
1
, as the temperature is decreased the resistance goes as a power law.
T
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 -
Appendix II
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 (330nm380nm) 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
1
were 1<α<2. Similar
fα
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
1
, a ubiquitous feature of correlated noisy
fα
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
λ
2 NA
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 (ωp). The angular frequency defined by ω p =
ne 2
were n
ε m*
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 (τs). 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(ωsp). 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 -
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B-9
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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OPTICAL PROPERTIES OF METALLIC NANOSTRUCTURES A

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