CHARACTERIZATION AND CONTROL OF THE NONLINEAR OPTICAL
PROPERTIES OF DENDRITIC SILVER NANOPARTICLE CLUSTERS
By
Jess M. Gunn

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Chemistry
2011

ABSTRACT
CHARACTERIZATION AND CONTROL OF THE NONLINEAR OPTICAL
PROPERTIES OF DENDRITIC SILVER NANOPARTICLE CLUSTERS
By
Jess M. Gunn

In this dissertation, the properties of the energy transport in thin films of silver
nanoparticles on dielectric surfaces are explored.

Specifically, this dissertation will

present experiments in which an ultrafast laser (~ 13 fs) centered at 800 nm is focused
at normal incidence on a thin film of polydisperse silver nanoparticles on a quartz
substrate. Upon excitation, discrete regions of polarized emission are observed as far
as 100 µm from the focal spot. The intensity of these regions of emission can be
controlled by the polarization and spectral phase of the laser used for excitation.
Studies into the properties of emission show that the emission is a two-photon
induced luminescence, enhanced by localization of the electric field by the silver
nanoparticles. The spatial distribution of the nonlinear photoluminescence is found to
have characteristics very distinct from that of normal scatter.
Further studies suggest that the excitation pulse propagates to the different
remote regions by means of surface plasmon polariton (SPP) propagation. As the SPP
propagates, it accumulates different amounts of quadratic and cubic dispersion
depending on the path taken, explaining the dependence on spectral phase.

The

quadratic and cubic dispersion for a number of such pathways is measured, and
evidence of negative dispersion is observed. Photoluminescence is observed at

locations where constructive interference and a localized resonance occurs, tens of
micrometers from the incident laser pulse.
The results presented in this dissertation regarding the nature and control of
energy transport has great implications in the field of “plasmonics,” which seeks to
bridge the realms of electronics and photonics with specially designed waveguides.
Such waveguides, which could potentially support both plasmon and electrical signals
have been designed and experimentally tested by several groups, and work has been
done to design nanoscale structures that act as mirrors and beamsplitters for SPPs.
However, these groups continue to face reduced propagation lengths, restricting
propagation to a few tens of micrometers. The approach presented here, in contrast,
shows propagation and control over a 100 µm range.

Copyright by
JESS M. GUNN
2011

In memory of Jan Gunn, who taught us that
"Girls can do anything."

v

ACKNOWLEDGMENTS
During my studies at Michigan State University, there have been many people
who have been instrumental in helping me through this process, all of whom I am
grateful for.
I first extend my thanks to my committee members, both past and present,
including Professors Gary Blanchard, Robert Cukier, Jim McCusker and Chong-Yu
Ruan. I also extend my thanks to members of the Dantus group, particularly Vadim
Lozovoy for his help with theoretical issues, and Mindi Ogden (nee Ewald) and Scott
High, two undergraduates who worked with me for more than a year each, and
performed some of the experiments presented here.
I am grateful to Professors Virginia Ayres and Martin Crimp for acquisition of
AFM and SEM/TEM images, respectively, and to CRi for loan of the SpecVis, which
permitted the acquisition of color images.
I am indebted to my family, and to all of my friends and colleagues at Michigan
State, Creighton University, and elsewhere, who cheered me on and encouraged me
through the rough times, at times believing in me more than I believed in myself.
Most of all, I am grateful to Professor Marcos Dantus, my advisor. From the
beginning, when we first observed the phenomena presented here in the course of what
was supposed to be a straightforward background experiment, he allowed me to follow
the data and observations where they led, allowing me to explore the beautiful,
fascinating world of surface plasmons.

vi

TABLE OF CONTENTS
LIST OF TABLES ............................................................................................................ ix
LIST OF FIGURES .......................................................................................................... x
KEY TO SYMBOLS AND ABBREVIATIONS ................................................................ xvi
CHAPTER 1
INTRODUCTION ............................................................................................................. 1
1.1. Introduction ................................................................................................... 1
1.2. Plasmonics ................................................................................................... 3
1.3. Conclusion .................................................................................................... 5
CHAPTER 2
SURFACE PLASMONS .................................................................................................. 6
2.1. Types of Surface Plasmons .......................................................................... 6
2.1.1. Surface Plasmon Polaritons (SPPs) ............................................... 6
2.1.2. Confinement in Strips and Wires................................................... 12
2.1.3. Launching Surface Plasmons ....................................................... 13
2.2. Localized Surface Plasmons ...................................................................... 13
2.2.1. Electromagnetic Enhancement ..................................................... 14
2.2.2. Polarizability .................................................................................. 15
2.2.3. Coupling between particles ........................................................... 17
2.2.4. Percolation .................................................................................... 18
2.3. Conclusion .................................................................................................. 18
CHAPTER 3
EXPERIMENTAL........................................................................................................... 19
3.1. Ultrafast lasers............................................................................................ 19
3.1.1. Background ................................................................................... 19
3.1.2. Phase............................................................................................ 20
3.1.3. Compensation ............................................................................... 22
3.1.4. Pulse Shaping ............................................................................... 24
3.2. Experimental Setup .................................................................................... 25
3.2.1. The laser ....................................................................................... 27
3.2.2. Pulse Shaper ................................................................................ 27
3.2.3. Microscope ................................................................................... 29
3.2.4. Detection ....................................................................................... 30
3.2.5. Integration of Systems .................................................................. 31
3.3. Multiphoton Intrapulse Interference Phase Scan (MIIPS) ........................... 31
3.3.1. MIIPS Theory ................................................................................ 31
3.3.2. Implementation of MIIPS ............................................................... 34
3.3.3. Validation of Method ..................................................................... 36
3.3.4. Use of MIIPS in a high-NA Microscope Objective ......................... 44
3.4. Conclusion .................................................................................................. 46

vii

CHAPTER 4
THE SAMPLE: PREPARATION AND CHARACTERIZATION OF LUMINESCENCE .. 48
4.1. Preparation of Sample ................................................................................ 48
4.1.1. Synthesis ...................................................................................... 48
4.1.2. Microscopy of the Sample ............................................................. 49
4.1.3. Control Experiments ..................................................................... 51
4.2. Hypothesis .................................................................................................. 52
4.3. Characterization of Solution........................................................................ 53
4.3.1. Spectrum ...................................................................................... 53
4.3.2. Multiphoton Behavior .................................................................... 56
4.4. Emission from Samples on the Substrate ................................................... 60
4.4.1. Observation .................................................................................. 60
4.4.2. Density of Particles ....................................................................... 63
4.5. Characterization of Sample on Substrate ................................................... 66
4.5.1. Multiphoton Behavior .................................................................... 66
4.5.2. Spectral Information ...................................................................... 68
4.6. Polarization ................................................................................................. 72
4.7. Conclusions on Luminescence ................................................................... 73
CHAPTER 5
CHARACTERIZATION OF ENERGY PROPAGATION................................................. 75
5.1. Further Discussion of Scattering................................................................. 75
5.2. Autocorrelation ........................................................................................... 79
5.3. Dispersion................................................................................................... 82
5.3.1. Sensitivity to Phase: Sine Function .............................................. 82
5.3.2. Quantifying Dispersion .................................................................. 89
5.4. Conclusion .................................................................................................. 92
CHAPTER 6
CONCLUSION .............................................................................................................. 94
6.1. Comment on Reported Fluorescent Enhancement ..................................... 94
6.2. Future Work ................................................................................................ 95
6.2.1. Gold .............................................................................................. 95
6.2.2. Correlation of Propagation and Emission with Structure ............... 96
6.2.3. Synthesis of Well-Defined Structures............................................ 97
6.3. Potential Applications ................................................................................. 98
6.4. Conclusion .................................................................................................. 99
REFERENCES ............................................................................................................ 102

viii

LIST OF TABLES
Table 1. Comparison of Reproducibility of MIIPS with FROG and SPIDER: Statistical
Phase Error (in rad). ...................................................................................................... 41
2

Table 2. Comparison of R Values for Linear, Quadratic, and Cubic Fits of Data in
Figure 4.11. ................................................................................................................... 68

ix

LIST OF FIGURES
Figure 1.1. Wide-field image of a silver nanoparticle film collected without scanning
either the laser or the sample. The entire image is 80 x 80 µm, and the laser was
focused near the center. Rather than observing bright emission at the focus against a
black background, discrete regions of luminescence remote from the focal spot are
observed, indicating that some mechanism for energy transport exists in the
nanoparticle network. ...................................................................................................... 3
Figure 2.1. The model surface described in this section is a smooth interface between a
metal with a dielectric function ε1(ω) for z<0 and a non-conducting dielectric with a real
dielectric constant ε2 for z>0 where the boundary plane is defined as z=0. Propagation
is defined as being in the x-direction. .............................................................................. 7
Figure 2.2. The model used in this section is a metallic sphere with a radius a and
complex dielectric constant ε1 in an environment with a constant dielectic constant ε2. 15
Figure 3.1. The effect of second-order-dispersion on pulse duration of ultrashort pulses.
2
As a reference, 1 mm of quartz introduces 36 fs GDD. High numerical-aperture
microscope objectives, such as used for the experiments reported in this dissertation,
contain as much as an inch (25.4 mm) of quartz. .......................................................... 22
Figure 3.2. Prism pair compressor used to compensate for quadratic dispersion. The
first prism disperses the beam, causing each frequency component of the pulse to travel
through different amounts of the glass in the second prism. A mirror reflects the beam
back along the same path for recombination. ................................................................ 23
Figure 3.3. A schematic of the general experimental setup.......................................... 26
Figure 3.4. Typical spectrum of the 10-fs laser pulses generated by the KM
Laboratories Ti:sapphire femtosecond laser used for the experiments presented in this
dissertation. ................................................................................................................... 27
Figure 3.5. Schematic of the pulse shaper. G = grating, CM = cylindrical mirror, M = flat
mirror, SLM = spatial light modulator. The beam enters the pulse shaper at the top-right
of the schematic, and exits at the lower right. The offset shown for the beams is for
clarity only. In the setup, a vertical offset is used, so that the incoming beam goes over
both the cylindrical and flat mirrors, strikes the grating, goes over the flat mirror again,
striking the cylindrical mirror, and finally striking the flat mirror, which directs it to the
SLM. .............................................................................................................................. 28

x

Figure 3.6. Schematic of MIIPS concept. (a) The thicker line shows the second
derivative of the unknown phase distortion, φ″(ω), the thinner line is the negative of the
second derivative of the well-known reference function, -f″(ω), and the dashed line is the
sum of the two, φ″(ω)+f″(ω). The SHG signal will have a local maximum when the sum
of φ″(ω) and f″(ω) is zero (i.e., when –f″(ω) intersects with φ″(ω)). (b) When the wellknown reference function, f(δ,ω) scans across the spectrum, SHG signals are
maximized at different frequencies, as the intersection of –f″(ω) and φ″(ω) changes. ... 33
Figure 3.7. Experimental results for MIIPS. The panels are SHG spectra as the δ
parameter of the reference function is scanned. Each vertical line corresponds to a
separate SHG spectrum obtained at a given value for δ. The black lines which separate
the MIIPS traces are used to define the region for searching δm(ω). The dots within
those boundaries show δm(ω). The panel on the left is the MIIPS trace for a typical
uncompensated pulse. After several iterations, the traces on the right, which
correspond to TL pulses, are seen. ............................................................................... 35
Figure 3.8. Experimental setup for MIIPS..................................................................... 36
Figure 3.9. Ability of MIIPS to retrieve arbitrary phase functions. (a) The result for an
applied double Gaussian function. (b) The result for an applied sine function. The dotted
curves show the retrieved phase, and the solid curves are the applied phase. ............. 37
Figure 3.10. Comparison between experimental data and theoretical simulation. The
solid curve in each panel shows the theoretical spectrum predicted for the application of
a particular binary phase (a) and (b) or a particular sine function (c) and (d). The dotted
curves correspond to the experimentally measured SHG spectrum for each case. (a)
The experimental result of the application of a binary phase mask (inset) to a pulse
compensated by MIIPS. (b) The result of the application of the same phase mask to an
uncompensated pulse. (c) and (d) The corresponding information using a sine function
(inset). ........................................................................................................................... 39
Figure 3.11. Reproducibility of MIIPS. In both panels, the solid curve shows the
average of ten independently retrieved phases, while the error bars show ±1 standard
deviation for every fifth point. The lower panel shows the full range of collected data.
The upper panel shows a closer view of the region over which MIIPS can compensate
(760–880 nm). ............................................................................................................... 40
Figure 3.12. GVD measurement of quartz using MIIPS. (a) The retrieved second
derivative of the spectral phases (from bottom to top: 0, 3.25, 4.92, 6.53, and 9.58 mm
quartz windows). (b) The GDD at 800 nm as a function of thickness. ........................... 42

xi

Figure 3.13. GVD measurement of microscope slides using MIIPS. (a) The retrieved
second derivative of the spectral phases (from bottom to top: 0, 2, 4, 6, 8, and 10 mm
microscope slides). Note that for clarity the odd number of slides (odd thicknesses)
were omitted from this graph, but not from the calculation. (b) The GDD at 800 nm as a
function of thickness. ..................................................................................................... 44
Figure 3.14. Compensation of spectral phase distortions caused by a 60x/1.45 NA
objective. The error bars indicate ±1 standard deviation. The lower panel shows the full
range of data, while the upper panel shows the same data over the FWHM of the pulse,
on a reduced scale. ....................................................................................................... 46
Figure 4.1. Panels A-C show TEM images of individual silver nanoparticles, which form
both as roughly spherical structures and as rods. Panel D shows an SEM image of the
structure of the aggregates formed. Electron microscopy images were obtained by
Professor Martin Crimp, Michigan State University. ...................................................... 50
Figure 4.2. Panel A, AFM image of typical sample, illustrating the larger features of the
sample. Panel B, AFM image of typical sample, with an emphasis on the smaller, more
connected features that lie in between the larger features. Figure 4A was obtained by
Professor Virginia Ayres, Michigan State University. .................................................... 51
Figure 4.3. Setup for acquiring the emission spectrum of the silver nanoparticle
aggregates in solution. The filter cube from the microscope is used to minimize
excitation light reaching the detector. ............................................................................ 54
Figure 4.4. Full emission spectrum of silver nanoparticles aggregated in solution after
excitation with a 13-fs Ti:sapphire laser. The spectrum is shown over the full range of
the spectrometer; note that there is no evidence of either fundamental light (800 nm) or
second-harmonic (400 nm). The observed structure is likely due to interference in the
dichroic mirror. .............................................................................................................. 55
Figure 4.5. Two-photon induced luminescence of silver nanoparticle aggregates in
solution. The emission spectra shown here were collected after a sample of aggregated
silver nanoparticles in solution were excited by a Ti:sapphire laser at varying powers:
27.5, 25.1, 11.5, 8.7, and 5.5 mW (top to bottom). ........................................................ 57
Figure 4.6. Integrated intensity of the spectra shown in Figure 4.5 plotted as a function
of excitation power. Clearly not linear, a best-fit line (in the form of a power function,
b
2.115
y=ax ) was found to be y = 14.889x
, indicating that the excitation process is, or is
largely dominated by, a two-photon process. ................................................................ 58
Figure 4.7. Integrated intensity of the spectra shown in Figure 4.5 plotted as a function
1
2
of excitation power. Data is fit to linear (y=ax , dashed line, R =0.8627), quadratic
2

2

3

2

(y=ax , solid line, R =0.9984) and cubic (y=ax , dotted line, R =0.9842) curves. From
these results, it is again clear that the relationship is quadratic, and the excitation
process two-photon. ...................................................................................................... 59

xii

Figure 4.8. Comparison of two silver samples illuminated with a femtosecond laser
under the same conditions. The sample on the left, which has a maximum intensity of
536 counts, shows distinct regions of remote emission. The sample on the right, which
has a maximum intensity of 14,568 counts (nearly saturation) shows no evidence of
remote emission. ........................................................................................................... 61
Figure 4.9. Emission that is up to 100 µm from the focal spot (denoted by cross-hairs)
is observed when a dielectric substrate with silver nanoparticles is excited by a
femtosecond laser at normal incidence. A 40x/0.60 NA objective was used in this
experiment. ................................................................................................................... 62
Figure 4.10. Effect of deposition time (and therefore particle density) on remote
emission. Exposure time was 0.5 sec, average laser power was 2.95 mW, and the gain
was set to 200. .............................................................................................................. 64
Figure 4.11. Integrated intensity of individual data points plotted as a function of
1.970
(gray squares),
excitation power. The lines of best fit were found to be y=20.4x
y=4.16x

2.054

(solid circles) and y=7.53x

1.790

(open triangles). ...................................... 67

Figure 4.12. Composite image of remote emission collected with colored filters. Signal
having wavelengths between 600 and 650 nm, wavelengths between 500 and 575 nm,
and wavelengths less than 500 nm are false colored red, green and blue, respectively.
For interpretation of the references to color in this and all other figures, the reader is
referred to the electronic version of this dissertation. .................................................... 69
Figure 4.13. Left. False color composite image of spectrally resolved silver
nanoparticle emission. Emission from 450-525 nm is colored blue, 525-600 nm green,
and 600-675 nm red. Right. Spectra from the three circled regions in the left panel are
shown. The signal from region A (red, circles) has been multiplied by 5 to make it
visible on the same set of axes as regions B (blue, crosses) and C (green, squares).
Note that there is no emission detected about 650 nm, consistent with the filters used,
nor is there emission below about 450 nm, again showing that the emission is not
second-harmonic generation. ........................................................................................ 70
Figure 4.14. False color spectrally resolved image of nanoparticle emission. Emission
from 440-510 nm was colored blue, 520-590 nm green, and 600-670 nm red. It is again
clear that different particles have distinct wavelengths of emission across at least the
entire visible spectrum................................................................................................... 71

xiii

Figure 4.15. Polarization characteristics of the silver samples. Each panel is of the
same area under different excitation and detection conditions. The top panels are
excited with 45° polarized light, and the bottom pa nels with 135° polarized light.
Horizontally polarized light was collected in the left panels, and vertically polarized light
was collected in the right panels. This figure illustrates that the observed two-photon
induced luminescence is polarized, as the area in the Ring A shows, and that emission
can be controlled by the incoming polarization, as shown by the area in Rings C and D.
...................................................................................................................................... 74
Figure 5.1. Images of a single sample under different types of illumination. Panel A
shows a sample under white-light illumination. Panel B shows the same sample excited
at the crosshairs by a 13-fs Ti:sapphire laser, while Panel C shows the sample excited
at the crosshairs by a HeNe laser. The insets in Panels B and C show the total intensity
of all pixels with signal above the noise level as a function of distance from the focal
spot. It is clear that the behavior observed upon excitation with a fs-laser is not
consistent with the behavior of scatter observed upon excitation with a HeNe laser. ... 76
Figure 5.2. Intensity profiles for a 2µm-wide section of data running horizontally (top)
and vertically (bottom) through the focal spot for a sample excited by a HeNe laser
(dashed line), and a fs-laser (solid line)......................................................................... 78
Figure 5.3. Photoluminescence from several discrete regions is shown as a pulse
shaper is used to produce a pair of pulses and scan the delay between them. The top
panel shows the optical response of a frequency doubling crystal as a function of delay
between pulses. Panels A, B, and C show the optical response from different regions.
Some regions show broadening, as shown in region C. Others show wings (visible in
panel B), or erratic behavior, likely due to melting or other irreversible change to the
sample, as shown in panel A. The behaviors are independent of distance from the
excitation point, as well as the behavior of neighboring regions (compare regions A and
B, which are only separated by approximately 1 µm). ................................................... 80
Figure 5.4. Phase control of remote emission. Each lower panel is a wide-field image of
the same region of the sample, with the focal spot at (0, 0). The phases (black line)
applied across the spectrum of the pulse are shown above each image. The circles
highlight regions of interest and are at the same position in each panel. ...................... 83
Figure 5.5. Control of emission intensity by spectral phase. The dots in panels A, B
and C show the experimental intensity of the three labeled regions as a function of δ,
when the applied phase is 1.5π sin(12(ω-ω0) - δ). The solid line shows the simulated
second-harmonic generation intensity optimized to fit the data by adjusting the secondand third-order dispersion of the pulse. ......................................................................... 84

xiv

Figure 5.6. Simulations of the intensity of SH generation as a sinusoidal phase of the
form 1.5π sin(12(ω-ω0) - δ), is applied across the spectrum of the pulse. In all panels,
the solid line shows the intensity as the phase is applied to a TL pulse with a carrier
frequency, ω0, that corresponds to the carrier frequency, λ0=800 nm. Panel A shows
how the intensity profile changes with a shift in effective carrier frequency; the dotted
line shows the intensity if the carrier frequency corresponded to λ0,eff = 825 nm. Panels
B and C show the simulations of the intensity of SH generation if the sinusoidal function
is applied to a non-TL pulse. In panel B, the broken line corresponds to a pulse with a
2
dispersion of 100 fs , while the dashed line corresponds to a pulse with a dispersion of
3

1000 fs . Note that the second order dispersion results in unequal peak spacing, while
third-order-dispersion results in unequal peak heights. In panel C, the simulations show
2
the intensity as the sinusoidal function is applied to a pulse with both 100 fs and 1000
3

fs dispersion. ............................................................................................................... 87
Figure 5.7. SHG Intensity as a function of applied phase. The maximum SHG signal
occurs when the applied phase is exactly the negative of the introduced phase. The
cross in each panel denotes the expected maximum. Panel a: results when φ'' = +200
2
3
2
3
fs and φ''' = -2000 fs . Panel b: results when φ'' = -200 fs and φ''' = -2000 fs . Panel
2

3

2

c: results when φ'' = +200 fs and φ''' = +2000 fs . Panel d: results when φ'' = -200 fs
3

and φ''' = +2000 fs . In each panel, the cross-hairs denote the expected maximum
intensity. ........................................................................................................................ 90
Figure 5.8. Measured Dispersions. A 2-dimensional histogram of measured values for
φ''w and φ'''w for over 200 regions of emission on a single sample. To the top and right
are histograms showing the distribution of φ''w and φ'''w values, respectively. .............. 91

xv

KEY TO SYMBOLS AND ABBREVIATIONS

α

in MIIPS, a parameter used to define the amplitude of the sine function

α

in the context of metals, the polarizability

AFM

atomic force microscopy

B

magnetic induction

CARS

coherent anti-Stokes Raman Scattering

δ

in MIIPS, a parameter used to define the phase of the sine function

D

dielectric displacement

ε

dielectric constant

E

electric field

EDTA

ethylenediaminetetraaceticacid

EM

electromagnetic

EMCCD

electron-multiplying charge-coupled-device

φ(ω)

phase modulation (as a function of frequency)

FROG

frequency-resolved-optical-gating

FWHM

full-width-at-half-maximum

GA

genetic algorithm

GDD

group delay dispersion

GVD

group velocity dispersion

H

magnetic field

HeNe

helium-neon

k0

propagation vector

L

propagation length

xvi

LSP

localized surface plasmon

LSPR

localized surface plasmon resonance

µ

relative permeability

MIIPS

multiphoton intrapulse interference phase scan

ñ

complex index of refraction

NA

numerical aperture

OD

optical density

PSTM

photon scanning tunneling microscopy

PVA

poly(vinyl alcohol)

QE

quantum efficiency

R-590

rhodamine-590

SE

surface-enhanced

SEM

scanning electron microscopy

SERS

surface-enhanced Raman scattering

SH

second-harmonic

SHG

second-harmonic generation

SLM

spatial light modulator

SNOM

scanning near-field optical microscopy

SPIDER

spectral phase interferometry for direct electric-field reconstruction

SPP

surface plasmon polariton

SSHG

surface second-harmonic generation

STOM

scanning tunneling optical microscopy

TE

transverse electric

xvii

TEM

tunneling electron microscopy

Ti:sapphire

titanium:sapphire

TL

transform-limited

TM

transverse magnetic

UV

ultraviolet

ω

frequency

xviii

1. INTRODUCTION
1.1. Introduction
This dissertation is, as all are, the culmination of a long journey, one with many
twists, turns and unexpected results. My first year was spent with Drs. Bingwei Xu and
Johanna dela Cruz in exploring and quantifying the capability of multiphoton intrapulse
interference phase scan (MIIPS), a method for measuring and compensating the phase
distortions of the ultrafast laser pulses used for excitation in the experiments here, as
outlined in Chapter 3 of this dissertation. As that project came to an end, it was time to
take on my own, individual, dissertation project – to explore the potential coherent
control of single molecule fluorescence.

After many false starts and struggles to

observe any fluorescence with the system that was being assembled, the decision was
made to take advantage of the fact that metal nanoparticles have been shown capable
of enhancing molecular fluorescence,

1-10

11-13

including that of single molecules.

Therefore, I prepared two films of rhodamine-590 (R590)-doped poly(vinyl alcohol)
(PVA). The first was spin-coated directly onto an unadulterated coverslip. The second
was spin-coated onto a coverslip onto which a thin layer of silver nanoparticles had
been deposited. I then prepared two controls: a blank coverslip, and a coverslip of only
the silver nanoparticles. As expected, very weak fluorescence was observed from the
unadulterated coverslip with a film of R590-doped PVA, and much, much stronger
fluorescence from the film over silver nanoparticles. The plain coverslip showed no
fluorescence.

All that was left was to show that the silvered coverslip showed no

luminescence, either. Instead, the observed emission was as strong as the R590-PVA
film over the silver nanoparticles!

1

This seemingly simple control experiment changed the entire course of my
graduate career. What began as a subsequent side project to explore the observed
emission, which is identified as two-photon-induced surface-plasmon enhanced
fluorescence from the metal nanoparticles, became the topic of this entire dissertation
when it was discovered that the emission from the nanoparticle film was not coming
only from the focal spot of the laser. Instead, emission was observed remote from the
focal spot of the laser, as shown in Figure 1.1. The 80 x 80 µm image shown in this
figure was obtained as a single wide-field image of the sample, with no scanning of the
laser or the sample. The ultrafast laser used for excitation was focused approximately
at the center of the image; this means that there is some mechanism in the system for
energy transport over a distances of tens of micrometers. Moreover, it was later found
that the intensity of various regions of emission could be controlled, both by the
polarization of the excitation beam, and by changing the spectral phase of the ultrafast
laser used for excitation.

14

This dissertation, therefore, explores in detail the nature of

the energy propagation, via surface plasmons, and its subsequent localization and
control.

2

Figure 1.1. Wide-field image of a silver nanoparticle film collected without scanning
ield
either the laser or the sample. The entire image is 80 x 80 µm and the laser was
m,
focused near the center. Rather than observing bright emission at the focus against a
black background, discrete regions of luminescence remote from the focal spot are
ackground,
observed, indicating that some mechanism for energy transport exists in the
nanoparticle network.

1.2. Plasmonics
The results presented in this dissertation are due to surface plasmons, which are
the collective oscillations of electrons in a metal. On extended metal surfaces, surface
plasmons can exist in the form of surface plasmon polaritons (SPPs), which can be
(SPPs
described as a “wave” of electrons in the “sea of electrons” model. On an infinite
electrons
surface, plasmons can propagate more than 100 µm. More control can be gained over
.
the propagation of the plasmon by reducing the surface width to micrometers or even
15-20

nanometers;

however, this reduces the propagation length of the SPP
SPP.

The ability to transport the energy over relatively long distances and localize it
has great implications in the field of “plasmonics,” which seeks to bridge the realms of

3

21

electronics and photonics

22

with specially designed waveguides.

Such waveguides,

which could potentially support both plasmon and electrical signals
22,24-26

designed and experimentally tested by several groups,

23

have been

and work has been done
26,27

to design nanoscale structures that act as mirrors and beamsplitters for SPPs.

However, these groups continue to face the reduced propagation lengths, restricting
propagation to a few tens of micrometers.
In addition to their existence as waves on extended structures, surface plasmons
can also be excited on individual nanoparticles, and are a result of the confinement of
surface plasmons to the nanoparticles, which, by definition, have dimensions from ten to
a few hundred nanometers. If the plasmon is excited by light of an appropriate
frequency, a localized surface plasmon resonance (LSPR) can be established, greatly
amplifying the electromagnetic (EM) field around the nanoparticles. It is this property
that causes the enhancement of fluorescence mentioned previously.

It is also this

property that leads to the well-studied technique of surface-enhanced-Raman-scattering
28-32

(SERS),

33-36

including at the single-molecule level.

In addition, the sensitivity of

the LSPR frequency to the index of refraction of the surrounding media has led to
37,38

applications in high-sensitivity sensing.

Similar enhancements to the electromagnetic field are also seen due to
localization of the electromagnetic field on rough surfaces in regions called ‘hot
spots.’

39-44

45,46

Extensive theoretical work,

as well as direct observation of the
47,48

localization has been made on roughened gold

4

49

and silver

films, silver colloid

fractals,

45

50

and films of nanoparticles near the percolation limit.

This localization has
45,47

been observed directly via photon scanning tunneling microscopy (PSTM)
48

scanning near-field optical microscopy (SNOM)
49

microscopy (STOM)

and scanning tunneling optical

techniques, and indirectly through the measurement of surface
51

second-harmonic generation (SSHG).

Energy can also be localized between nearly-touching pairs

52

or clusters

53

of

particles, and has behaviors distinct from that of isolated metal nanoparticles, with
54-56

shifted resonances and enhanced EM fields in the gap between particles.
57

clusters, this has been shown to enhance both linear

53

and nonlinear

In

optical

processes.
1.3. Conclusion
In this dissertation, Chapter 2 will explore the properties of surface plasmons in
far more detail than presented here, while Chapter 3, in addition to an in-depth
discussion of MIIPS, will present details on the experimental setup for the experiments
presented.

Chapter 4 will explore the properties of the emission observed, while

Chapter 5 explores methods for controlling the emission, via both polarization of the
excitation pulse, and the spectral phase of the ultrafast laser used for excitation. This
work, when taken together, is the culmination of a fascinating study at the intersection of
ultrafast optics and surface plasmons that presents an entirely new approach to the
development of plasmonic waveguides capable of sustaining the propagation of
plasmons over distances of at least 100 micrometers.

5

2. SURFACE PLASMONS
The phenomena observed and explored in this dissertation are all related to
surface plasmons, which are the collective oscillation of electrons in a metal. This
chapter will provide a framework for understanding surface plasmons; more detail can
58

be found in many other references cited throughout this chapter; books by Raether
59

and Maier

are of particularly note for their comprehensiveness.

2.1. Types of Surface Plasmons
There are two types of surface plasmons. Surface plasmon polaritons (SPPs)
are electron waves propagating at the interface between a metal and a dielectric, while
localized surface plasmons (LSPs) are confined excitations of the conduction electrons
of metal nanoparticles. Both of these will be explored in more detail in this section.

2.1.1. Surface Plasmon Polaritons (SPPs)
This section will focus on the unique behaviors of surface plasmons as they
propagate on smooth surfaces in the form of surface plasmon polaritons.

More

specifically, it will be looking at a smooth interface between a metal with a uniform
dielectic function, ε1(ω), and a non-conducting dielectric with a real dielectric constant,

ε2 as shown in Figure 2.1.

6

Figure 2.1. The model surface described in this section is a smooth interface between a
metal with a dielectric function ߳ଵ ሺ߱ሻ for z<0 and a non-conducting dielectric with a real
dielectric constant ߳ଶ , for z>0 where the boundary plane is defined as z=0. Propagation
is defined as being in the x-direction.
59, 60

By using Maxwell’s Laws:

‫ ࡰ · ׏‬ൌ ߩ௘௫௧

(2-1)

‫ ࡮·׏‬ൌ0

‫׏‬ൈࡱൌ

(2-2)

െ߲࡮
߲‫ݐ‬

‫ ׏‬ൈ ࡴ ൌ ࡶࢋ࢚࢞ ൅

߲ࡰ
߲‫ݐ‬

(2-3)

(2-4)

where D is the dielectric displacement, ρext is the external charge density, B is the
magnetic induction, E is the electric field, H is the magnetic field, and Jext is the current
density, and is equal to 0 for the systems described here, and the following relations for
linear, isotropic and nonmagnetic media:

ࡰ ൌ ߳଴ ߳ሺ߱ሻࡱ

࡮ ൌ ߤ଴ ߤሺ߱ሻࡴ

7

(2-5)
(2-6)

where ε0 is the electric permittivity, and µ0 is the magnetic permeability of a vacuum, ε
is the dielectric constant and µ is the relative permeability, and is equal to 1 for nonmagnetic substances, and assuming a uniform dielectric profile and harmonic time
dependence, the Helmholtz equation can be derived.

ଶ
‫׏‬ଶ ࡱ ൅ ݇଴ ߳ࡱ ൌ ૙

(2-7)

Given this equation, where k0 is the wave vector of the propagating wave in vacuum
and is equal to ñ(ω/c), where ñ is the complex index of refraction, and defining

ࡱሺ‫ݖ ,ݕ ,ݔ‬ሻ ൌ ࡱሺ‫ݖ‬ሻ݁ ௜௞ೣ ௫

, where kx represents the propagation constant, the wave

equation can then be expressed as

߲ ଶ ࡱሺ‫ݖ‬ሻ
ଶ
൅ ൫݇଴ ߳ െ ݇௫ ଶ ൯ࡱ ൌ 0
ଶ
߲‫ݖ‬

(2-8)

Given the complex nature of ñ, we can show that the intensity of the
electromagnetic wave, a surface plasmon, decreases as

݁ ିଶ௞ೣ ௫ ;

the propagation

length, L, defined as the distance after which the intensity decreases to a factor of 1/e,
can be defined as

58,59

‫ܮ‬ൌ

1
2‫݉ܫ‬ሾ݇௫ ሿ

(2-9)

To quantify kx, we look at eqs (2-3) and (2-4). Again assuming a harmonic time
dependence (

ࣔ

࢚ࣔ

ൌ െ࢏࣓ሻ , as well as propagation along the x-direction ሺ

ࣔ

ࣔ࢞

8

ൌ െ࢏࢑࢞ ሻ,

and homogeneity in the y-direction ሺ
can be derived.

ࣔ

ࣔ࢟

ൌ ૙ሻ, the following equations relating E and H

߲‫ܧ‬௬
ൌ െ݅߱ߤ଴ ‫ܪ‬௫
߲‫ݖ‬

߲‫ܧ‬௫
െ ݅݇௫ ‫ܧ‬௭ ൌ ݅߱ߤ଴ ‫ܪ‬௬
߲‫ݖ‬
݅݇௫ ‫ܧ‬௬ ൌ ݅߱ߤ଴ ‫ܪ‬௭
߲‫ܪ‬௬
ൌ ݅߱߳଴ ߳‫ܧ‬௫
߲‫ݖ‬

߲‫ܪ‬௫
െ ݅݇௫ ‫ܪ‬௭ ൌ െ݅߱߳଴ ߳‫ܧ‬௬
߲‫ݖ‬
݅݇௫ ‫ܪ‬௬ ൌ െ݅߱߳଴ ߳‫ܧ‬௭

(2-10)

(2-11)

(2-12)

(2-13)

(2-14)

(2-15)

If we first assume a transverse magnetic (TM) modes (Hx = 0), the equations
simplify to:

‫ܧ‬௫ ൌ െ݅
‫ܧ‬௭ ൌ െ

1 ߲‫ܪ‬௬
߱߳଴ ߳ ߲‫ݖ‬
ߚ
‫ܪ‬
߱߳଴ ߳ ௬

߲ ଶ ‫ܪ‬௬
ଶ
൅ ൫݇଴ ߳ െ ݇௫ ଶ ൯‫ܪ‬௬ ൌ 0
ଶ
߲‫ݖ‬

9

(2-16)

(2-17)

(2-18)

Solving this system for both z>0 and z<0, and considering the boundary conditions, kx
can be expressed in terms of k0 and the dielectric constants for both the metal (ε1) and
the surrounding material (ε2):

߳ଵ ߳ଶ
݇௫ ൌ ݇ ଴ ඨ
߳ଵ ൅ ߳ଶ

(2-19)

A similar analysis for can be performed for transverse electric (TE) modes (Ex = 0);
however, it turns out that the boundary conditions require Ey=0, Hx=0 and Hz=0.
Therefore, SPP modes do not exist for TE polarization.
To further understand the propagation constant, we can look at the Drude model
of the dielectric constant of a metal, from which many properties of substances can be
explained and derived, which is

ω2
p
Ԗሺωሻ=1- 2
ω +iγω

(2-20)

where γ is the characteristic collision frequency, on the order of 100 THz, and ωp is the
plasma frequency and is given by

ω2 =
p

n݁ ଶ
߳଴ m

(2-21)

where n is the number density of electrons, while m is the effective optical mass of the
electron.

10

To further examine and use the Drude model for the dielectric constant eq (2-20),
it is useful to break it into its real and imaginary parts, and express it in the form

ε(ω) = εr(ω) + iεim(ω), where
߳௥ ሺωሻ=1-

ω2 ߬ ଶ
p
1 ൅ ω2 ߬ ଶ

(2-22)

and

ω2 ߬
p
߳௜௠ ሺωሻ=
߱ሺ1 ൅ ߱ ଶ ߬ ଶ ሻ

(2-23)

From eq (2-23), it is clear that the imaginary component of the dielectric function, and
therefore the propagation constant, decrease as the frequency of the electromagnetic
field increases. As a result, the propagation length is substantially larger for lower
frequency electromagnetic pulses.

The identity of the metal will also control the

propagation length; however, this is harder to quantify, as reported values for ωp and τ
vary widely depending on the source, making reliable approximations of propagation
lengths using the Drude model difficult. Generally, however, propagation lengths are
much greater in silver than in gold, two of the most common metals used to support
surface plasmons.
Quantitatively, values for the complex dielectric constants can be calculated from
other measured optical constants. Using data experimentally obtained by Johnson and
61

Christy,

and eqs (2-9) and (2-19), propagation lengths can be calculated for various

conditions. At 397 nm, the propagation length in silver is calculated to be 1.65 µm. At
632 nm, the propagation length would be about 30 µm. At 821 nm, close to the carrier

11

frequency of the ultrafast laser used for most experiments in this dissertation, that
length is as great as 144 µm.

For comparison, the propagation length of surface

plasmons in gold are calculated to be 0.18 and 25 µm for 400 and 821 nm, respectively.
2.1.2. Confinement in Strips and Wires
The results presented in Section 2.1.1 assume an effectively infinite surface in
the y-direction.

By reducing the y-dimension to the order of microns (“stripes”) or

nanometers (“nanowires”), the direction of SPP propagation can be controlled, as
15-20

shown in a large body of work.

A brief note should be made, however, that

decreasing the width of the stripe decreases the propagation length of the SPP, as
nicely illustrated in a systematic study by Lamprecht et al,

16

which experimentally

shows that stripes with widths above 20 µm all had propagation distances approaching
60 µm after excitation with 633 nm light, while 1 µm wide stripes had propagation
distances of only a few micrometers. In nanowires, propagation distances as great as
10-15 µm

19,20

have been observed.

Several approaches have been developed to overcome this reduced propagation
length, including structured surfaces and modification of the geometries as well as using
longer wavelengths of light for excitation. In the case of silver, for example, increasing
the excitation wavelength from 633 nm to 785 nm increases the propagation length from
16

50 to 150 µm.

For wires, it has been shown that collections, or bundles, of wires can
62,63

increase the propagation distance well beyond that of individual wires.

12

2.1.3. Launching Surface Plasmons
SPPs in smooth, thin films cannot be launched by simple irradiation due to
momentum mismatch; i.e. kx>k in air. Therefore, special techniques must be used to
launch SPPs in films. One common approach is prism coupling using the Kretschmann
configuration, where the film is deposited on the hypotenuse of a prism, and attenuated
64

total internal reflection is used to excite the SPPs. However, a more recent approach

shows that high numerical objectives in contact (via index-matching oil) with the glass
substrate can overcome this, as the wide angle of the focused beam includes angles
greater than the critical angle for total internal reflection. This means that vectors are
available for coupling into the system.
This same limitation can also be overcome by rough surfaces and/or individual
nanoparticles, where the very shape of the particle or surface allows for the coupling of
light in and out of the system. The ease of exciting surface plasmons in nanoparticles,
as well as their ability to couple to adjacent structures is due to localized surface
plasmon resonance, and is the topic of the next section.
2.2. Localized Surface Plasmons
As discussed in Section 1.2, exciting a metal nanoparticle with light of an
appropriate frequency results in a localized surface plasmon resonance, greatly
amplifying the electromagnetic (EM) field around the nanoparticles. This section will
discuss the theory and implications of this amplification.

13

2.2.1. Electromagnetic Enhancement
One of the most common applications of surface plasmon resonance is in the
enhancement of electromagnetic fields. The electromagnetic enhancement factor, L(ν)
59

is given by

‫ܮ‬ሺߥሻ ൌ

|ࡱ࢒࢕ࢉ ሺߥሻ|
|ࡱ଴ |

(2-24)

where Eloc(ν) is the local field amplitude. This electromagnetic enhancement factor has
two components, and can be written as L(ν)=LSP(ν)LLR, where LSP is the enhancement
due to the resonant excitation of LSPs, and LLR is the enhancement due to what is
65,66

called the lightning-rod effect.

LLR is due to the crowding of field lines around sharp metallic features in nonspherical metal nanoparticles, while LSP is proportional to the polarizability, α, of the
particle, and is likewise frequency-dependent. Overall, the increase in luminescence,
due to both effects, scales as

ܲ௟௨௠ ‫ܮ ן‬ሺ߱௘௫ ሻଶ ‫ܮ‬ሺ߱௘௠ ሻଶ

(2-25)

where ωex and ωem are the frequency of excitation and emission, respectively. In this
section, we will focus on understanding the contribution of polarizability to, and therefore
the frequency-dependence of, the enhancement factors.

14

2.2.2. Polarizability
To explore the polarizability, we'll use an initial model of a small spherical
nanoparticle with a radius a and complex dielectric constant ε1 in an environment with a
constant dielectic constant ε2.

Figure 2.2. The model used in this section is a metallic sphere with a radius a and
complex dielectric constant ε1 in an environment with a constant dielectic constant ε2.
Assuming a<<λ, the polarizability of metal particles can be given by

ߙ ൌ 4ߨܽ ଷ

ߝଵ ሺ߱ሻ െ ߝଶ
ߝଵ ሺ߱ሻ ൅ 2ߝଶ

(2-26)

It can be easily seen from this equation that a maximum in polarizability, and therefore
in the dipole and electric fields is observed when

߱଴ ൌ ܴ݁ሾߝଵ ሺ߱ሻሿ ൌ െ2ߝଶ

which is known as the Fröhlich condition.

(2-27)

For a metal in air, with a real dielectric

coefficient given by eq (2-22), ߱଴ ൌ ߱௣ /√3.

15

An important implication of eq (2-27) is that the resonance frequency is strongly
dependent upon the nature – specifically, the dielectric constant – of the surrounding
material. This sensitivity is the source of many of the sensing applications that have
been developed using the resonance frequency of a nanoparticle to explore changes in
the local dielectric environment, due to, for example, the adsorption of a molecule to the
surface.

37,38

The approach presented so far is the “quasi-static” approach, and assumes that
a<<λ.

However, while this approach is useful to the first approximation, and in

understanding the source of the resonance properties, it fails to adequately describe all
experimental results.

Most notably, it fails to account for the shift in resonance

wavelength that occurs as particle size varies.

31,55,67,68

The most complete theory has

been that developed by Mie, and published in 1908. For larger particles, the following
69

expression, an expansion of the first mode of Mie theory, can be used.

ߙ௦௣௛௘௥௘

1
ሺ߳ ൅ ߳ଶ ሻ‫ ݔ‬ଶ ൅ ܱሺ‫ ݔ‬ସ ሻ
10ቁ ଵ
ൌ
ܸ
1
߳ଶ
1
ଶ െ ݅ 4 ߨ ଶ ߳ ଷ/ଶ ܸ ൅ ܱሺ‫ ݔ‬ସ ሻ
ቀ3 ൅ ߳ െ ߳ ቁ െ 30 ሺ߳ଵ ൅ 10߳ଶ ሻ‫ݔ‬
ଶ
3
ߣଷ
ଵ
ଶ
଴

where ‫ݔ‬

1െቀ

(2-28)

ൌ ߨܽ/ߣ଴ .

While not immediately clear, the inclusion of terms that incorporate both ε and x

has the effect of red-shifting the resonance frequency as the size of the nanoparticle
increases.

This makes sense, intuitively, as larger particles have a larger charge

separation, which weakens the restoring force and lowers the resonant frequency.

16

A final experimental observation that is not accounted for, even by the Mie theory
55,67,68,70

presented here, is the behavior of non-spherical particles.

For rod-shaped

particles, for example, there exists two resonance frequencies: a higher frequency
component corresponding to transverse resonance across the width of the rod, and a
lower-frequency resonance corresponding to longitudinal resonance along the length of
the rod. The excitation of these modes is sensitive to the polarization of the excitation
pulse.
2.2.3. Coupling between particles
In addition to coupling energy in and out of smooth surfaces, as referenced in the
previous section, the coupling between particles due to localized surface plasmon
resonance has been used as an alternate approach to plasmon waveguiding. As early
as 1998, it was predicted that such coupling could be exploited to develop waveguides
in which particles were spaced an optimal distance apart,
72

as 900 nm could be achieved.

71

such that propagation as far

Subsequent theory along the same lines supported

this idea, and extended the theory to predict waveguiding around corners and through
73,74

T-intersections,

71

as well as other geometries.

In 2003, the first waveguiding by a
75

chain of nanoparticles over ‘several hundred nanometers’ was observed.

Following

this, much work was done to refine the theoretical models used, as well as generalize
76-86

the work to spheroidal nanoparticles.

Over this time, at least one model was

developed that extended the predicted distance of waveguiding to hundreds of
micrometers.

82

17

2.2.4. Percolation
When samples are prepared in the manner discussed in Chapter 3 of this
dissertation, the density of nanoparticles begins to approach the percolation limit.
Interestingly, such an extended structure has been shown capable of supporting
SPPs,

87,88

enabling the propagation of energy in our samples. The “bumpiness,” or

roughness, of the sample means that this energy can subsequently be localized, with
the potential to manifest in many way, including promoting various surface-enhanced
51

processes, prompting surface-second-harmonic-generation,

or even exciting the

nanoparticles themselves, resulting in metal fluorescence, as it is concluded happens in
the experiments presented in this dissertation.
2.3. Conclusion
This chapter has examined the origin and applications of surface plasmons. Of
particular note for this dissertation are the results indicating that SPPs can propagate as
far as 100 µm, and that aggregates of nanoparticles can support such SPPs. As well, it
is important to note that individual nanoparticles can be used to couple energy in and
out of the system, and that the resonances of these nanoparticles are dependent not
only on the dielectric environment, but on the size, shape and orientation of the particle.
As it will be shown in later chapters, it is the combination of these properties that make
the remote observation of emission from a surface of silver nanoparticles possible.

18

3. EXPERIMENTAL
This chapter will cover all aspects of the experimental setup, from the excitation
to detection systems.

Much consideration will be given to the unique challenges

presented by the use of an ultrafast (~10 fs) laser, including the introduction of spectral
phase distortions as the laser propagates through media, and the chosen method for
compensation, MIIPS, will be discussed and evaluated in detail. That evaluation, my
first project in the Dantus group, was performed with Drs. Johanna dela Cruz and
Bingwei Xu.
3.1. Ultrafast lasers
3.1.1. Background
Ultrafast lasers, i.e. lasers with pulse durations on the order of picoseconds (ps,
-12

10

-15

s) or femtoseconds (fs, 10

s), are increasingly being used in a wide range of

applications, due to the short time duration of the pulses. Commonly, ultrafast lasers
are used in time-resolved experiments, as the short time durations allow for exploration
of molecular motions.

Other applications take advantage of the high peak power

associated with ultrashort pulses.

For reference, a 100 mW ultrafast laser with a

repetition rate of 87 MHz results in peak powers of 11.5 kW for a 100 fs pulse, and 115
kW for a 10 fs pulse. These high peak powers open the doors to nonlinear optics, with
applications in fields ranging from biological imaging to high-harmonic generation.
Other experimental work exploits the fact that femtosecond lasers are nonmonochromatic. A 30 fs pulse with a carrier frequency of 800 nm will have a ~30 nm
bandwidth, while a 10 fs pulse with a carrier frequency of 800 nm will have ~100 nm

19

bandwidth.

As will be discussed more in the pulse shaping section, this provides

avenues for selective excitation.
3.1.2. Phase
One of the critical aspects to optimally using ultrashort pulse lasers is controlling
spectral-phase distortions introduced by the interaction of the pulses with an optical
surface such as a dielectric mirror, or their transmission through a lens, an optical fiber,
or a microscope objective.

These distortions, which stem from the frequency-

dependent index of refraction of materials, have a significant effect on the nonlinear
properties of the pulse, leading to increased pulse duration, loss of peak intensity and,
in some cases, loss of information.

Acquired dispersion can not only result in

discrepancies in laser properties between setups, but different lasers, with slightly
different properties, traveling through the same setup may also end up with different
properties.
The phase modulation as a function of frequency, φ(ω), produced by all physical
processes is typically a continuous function, and can therefore be written as a Taylor
expansion:

1
߶ሺ߱ሻ ൌ ሺ߱଴ ሻ߶ ൅ ሺ߱ െ ߱଴ ሻ߶ ᇱ ൅ ൬ ൰ ሺ߱ െ ߱଴ ሻଶ ߶ ᇱᇱ
2
1
൅ ൬ ൰ ሺ߱ െ ߱଴ ሻଷ ߶ ᇱᇱᇱ ൅ …
6

(3-1)

where ω0 is the carrier frequency of the pulse.
The linear term, ሺ߱ െ ߱଴ ሻ߶Ԣ, serves only to shift the pulse in time; it does not
affect the components of the pulse relative to one another.

20

The quadratic term,

ቀଶቁ ሺ߱ െ ߱଴ ሻଶ ߶ԢԢ contributes to broadening of the pulse, and is known as group delay
ଵ

dispersion (GDD). The shorter the initial pulses, the more significant the broadening
becomes, as shown in Figure 3.1. A substantial amount of GDD can be introduced by
the optical setup, as quartz has a group velocity dispersion (GVD; a measure of GDD
2

per unit length) of 36 fs /mm. In the experiments that form the basis for the results
presented in this dissertation, the high-numerical aperture objective alone contains up to
2

an inch of glass, contributing nearly 1000 fs . For a 10 fs pulse, such as used in the
experiments presented here, this results in a pulse more than 100 fs in duration, clearly
having the potential to severely hinder the optimal use of the laser. Finally, the cubic
term, ቀ଺ቁ ሺ߱ െ ߱଴ ሻଷ ߶ ᇱᇱᇱ , results in pulse trains.
ଵ

These, and even higher order-

dispersions, lead to unwanted and/or inexplicable results when nonlinear processes are
studied. Moreover, they lead to a lack of reproducibility between experimental systems.
It is therefore necessary to measure and then compensate for these dispersions in
order to both understand what is happening in a measured nonlinear process as well as
to enable reproducibility of experimental results.
Compensation of dispersion becomes even more critical when pulse shaping, or
controlling the time-domain characteristics of a pulse, is a part of the experiment.
Without a defined and attainable “zero-phase,” or transform-limited (TL) pulse, the
applied phase is meaningless, as it will be applied over unknown and potentially
variable values. The actual spectral phase of the pulse will therefore be unknown and
interpretation of results nearly impossible.

21

Figure 3.1. The effect of second-order-dispersion on pulse duration of ultrashort pulses.
2
As a reference, 1 mm of quartz introduces 36 fs GDD. High numerical-aperture
microscope objectives, such as used for the experiments reported in this dissertation,
contain as much as an inch (25.4 mm) of quartz.

3.1.3. Compensation
One approach to compensating for the dispersion experienced by a pulse as it travels
through media is the use of a prism pair compressor, as shown in Figure 3.2. This
approach has the advantage of simplicity; however, it is limited to compensation of
quadratic dispersion only.

While this is, indeed, the most significant dispersion

component experienced by ultrashort pulses propagating through media, the higher
order dispersions, including the cubic dispersion introduced by the glass of the prisms
themselves, may still cause deleterious effects.

22

Figure 3.2. Prism pair compressor used to compensate for quadratic dispersion. The
first prism disperses the beam, causing each frequency component of the pulse to travel
through different amounts of the glass in the second prism. A mirror reflects the beam
back along the same path for recombination.
Other disadvantages to the prism pair compressor approach are the facts that
dispersions are not actually measured and that it is not possible to apply phases to the
pulse. These limit the applications of such compression, when used alone. However,
for setups in which high quadratic dispersion is present, such as when a high numericalaperture objective is used, a prism pair compressor can be successfully used in
conjunction with other measurement/compensation methods to optimize results.
In the early 2000's, the established phase measurement methods included
89-95

frequency resolved optical gating (FROG)

direct electric-field reconstruction (SPIDER).

and spectral phase interferometry for

96-99

These methods, and their variants,

depend upon the measurement of autocorrelations or cross correlations between two
pulses to characterize the spectral phase of a pulse. In FROG, the frequency and timeresolved signals are used to retrieve the spectral phase of the pulses. SPIDER requires
that the laser pulse be split into two beams that are then upconverted by a heavily
chirped pulse. The interference of the upconverted pulses in the spectral domain is
used to reconstruct the spectral phase in the original pulse.

23

3.1.4. Pulse Shaping
The full power of ultrafast lasers can be exploited by the use of pulse shaping, or
controlling the phase of each frequency of the pulse. In the spectral domain, this can be
used for the selection of specific frequencies for selective multi-photon excitation. In
this case, constructive interference between different components of the pulse is used
to optimize the desired frequency, and destructive interference between other
components to minimize the background. In the time domain, phase can be used to
chirp the pulse, where red frequencies arrive before blue or vice versa, or to create
pulse trains with very specific timing between pulses, a technique that has been shown
100-105

106

to optimize CARS.
control

of

chemical

semiconductors,
113

applications.

110

Other applications include optical communications,
107,108

reactions,
111

quantum

nonlinear

102,109

optical

processes,
112

and nonlinear optical computation,

and biomedical

Ideally, characterization and pulse shaping can be used together to

produce pulses with a precisely determined phase function, such as a TL pulse.
Combining the characterization and shaping of pulses has been attempted through
intricate methods that either utilize a genetic algorithm (GA)-controlled shaper to
114-138

optimize a nonlinear optical signal,

an acousto-optic programmable filter.

139

or implement time-domain interferometry with

These indirect methods are limited by the lack

of sensitivity of the total nonlinear optical signal to phase deformations outside the
FWHM of the spectrum.

24

The method presented in Section 3.3, MIIPS, takes advantage of the influence
that phase modulation has on the probability of nonlinear optical processes at specific
frequencies.

140-143

It is a single beam method that not only characterizes spectral

phase but also compensates for unwanted phase distortions and can deliver accurate
user-specified phase functions at the location of a sample. It does not require beam
splitters, interferometry, autocorrelation, or global optimization, and is capable of
analytically retrieving the spectral phase across the pulse. Consequently, this method
has proven to be extremely powerful for the accurate and reproducible demonstration of
144

selective microenvironment probing,
148,149

imaging,

145-147

multiphoton microscopy
150

chemical agent identification,

functional

and encoding of information using

151

ultrashort phase-shaped pulses.
3.2. Experimental Setup

A schematic of the general experimental setup used for the experiments shown
in the next two chapters is shown in Figure 3.3.
described in the sections below.

Details of each component are

Briefly, an ultrashort (~10 fs) laser pulse was

generated by a Ti:sapphire oscillator. The laser was then passed through a spatial light
modulator (SLM)-based pulse shaper, which compensates for spectral phase distortions
in a pulse, compressing it to its transform-limited pulse duration with MIIPS. Known
phase functions can also be applied to the pulse as required for particular experiments.
The beam was then passed into the rear port of an inverted microscope and focused
onto the sample. A wide-field image of emitted light was collected by an electron-

25

multiplier charge-coupled-device (EMCCD) camera and passed to a computer for data
processing.

Figure 3.3. A schematic of the general experimental setup.

26

3.2.1. The laser
The excitation source used in all the experiments in this dissertation was a KM
Laboratories Ti:sapphire femtosecond laser, pumped by a Spectra-Physics Millennia V
solid state diode-pumped laser, which has a wavelength of 532 nm. The fs-laser is
capable of producing sub-10 fs pulses (110 nm FWHM) centered around 800 nm. The
average output power of the oscillator was 250 mW, with a repetition rate of 97 MHz. A
typical spectrum of the laser pulses is shown in Figure 3.4.

Figure 3.4. Typical spectrum of the 10-fs laser pulses generated by the KM
Laboratories Ti:sapphire femtosecond laser used for the experiments presented in this
dissertation.
3.2.2. Pulse Shaper
The pulse shaper is the means by which the phase of each spectral component
of the laser pulse is controlled, and is an integral part of the experimental setup for both
compensation purposes and for future experiments on surface plasmon polariton
152

propagation. The design used here, based on the general 4-f design of Weiner,

is

shown in Figure 3.5. It consists of two 600 grooves/mm gratings, two 200-mm focal

27

length cylindrical mirrors and a dual-mask SLM (CRi, Inc., SLM-256). In this design, the
laser entering the pulse shaper first strikes the grating, which disperses the frequency
components of the broadband laser pulse, while the cylindrical mirror focuses the
spread beam onto the SLM. The beam is then recombined by a parallel set of optics.
The SLM used in these experiments is dual-mask, with 128 liquid crystal pixels.
Changing the potential applied to each pixel changes the index of refraction, retarding
the light traveling through that pixel. As the spectrum is dispersed across the pixels,
this allows the relative phase of individual frequency components to be independently
controlled. To achieve accurate phase delays, each pixel of the SLM was carefully
calibrated by measuring the polarization-dependent transmission of light through each
pixel; pixel-by-pixel calibration is necessary because of the frequency dependence of
index of refraction values.

.
Figure 3.5. Schematic of the pulse shaper. G = grating, CM = cylindrical mirror, M = flat
mirror, SLM = spatial light modulator. The beam enters the pulse shaper at the top-right
of the schematic, and exits at the lower right. The offset shown for the beams is for
clarity only. In the setup, a vertical offset is used, so that the incoming beam goes over
both the cylindrical and flat mirrors, strikes the grating, goes over the flat mirror again,
striking the cylindrical mirror, and finally striking the flat mirror, which directs it to the
SLM.

28

3.2.3. Microscope
After leaving the pulse shaper, the beam was then steered towards the rear port
of a Nikon TE-2000U inverted microscope. Neutral density filters were placed in the
beam path after the shaper but before the microscope in order to moderate its power.
Typically, a low optical density filter was used during compensation with MIIPS, and
then a higher optical density filter of the same thickness was used during the
experiments. This allowed for proper compensation of the dispersion introduced by the
filter.
The beam out of the pulse shaper was smaller than the entrance aperture of the
60x/1.45 NA objective.

Therefore, when this objective was used, a Galilean beam

expander was used to expand the beam to overfill the microscope objective, and ensure
the tightest focusing. While this did result in the loss of power, most of the experiments
discussed in the next chapters of the dissertation required considerable reduction of
power to the sample to prevent damage, and so this loss was not a problem.
Inside the microscope, a 650 nm shortpass dichroic mirror was used to direct the
excitation beam up to the sample, where a Nikon 60x/1.45 NA objective tightly focused
the beam at normal incidence onto the sample with a focal spot of ~1 µm. Emission
was collected back through the same objective; however, the dichroic mirror allowed
emitted light <650 nm to pass through, where it was then directed to the Andor iXon
EMCCD camera for detection. A cover was used over the sample during experiments
to eliminate the inadvertent collection of ambient light, not only substantially reducing
the background but also preventing fluctuations due to shadows falling over the sample
and collection optics.

29

The primary microscope objective used for the experiments reported in this
dissertation was a Nikon Plan Apo TIRF oil immersion 60x/1.45 NA objective (Type NF
immersion oil was used.) For some experiments, in which a wider field of view was
desired, or in which the use of immersion oil would not be appropriate, a Nikon Plan
Fluor ELWD 40x/0.60 NA objective, which will be referred to simply by its power and
numerical aperture (40x/0.60 NA) was used. The resulting focal spot size for both of
these objectives is less than 1 µm.
3.2.4. Detection
The detector used to image the emission is an Andor iXon back-illuminated
EMCCD camera, thermoelectrically cooled to -64°
C.

This camera is highly sensitive,

with a quantum efficiency (QE) >80% over the visible spectrum, from 450-750 nm, and
90% from 500-650 nm. It contains an array of 512x512 pixels, each 16x16 µm in size.
With the 60x/1.45 NA objective typically used, this results in a field of view of
approximately 135 µm in each dimension. For the 40x/0.60 NA objective occasionally
used, imaging capabilities expand to 205 µm in both dimensions.
The sensitivity of the camera is a significant part of what makes the experiments
presented in the next two chapters possible, as the excitation beam power must be kept
low to prevent photodamage. Therefore, optimizing gain and integration time settings
were important issues.

A typical integration time was 200 ms, while gain settings

between 100-150 were found to be ideal. Longer integration times increased the length
of the experiments, therefore increasing the risk of photodamage to the sample, while
shorter integration times did not appreciably shorten the duration of the experiment, due
to data transfer times. Under these integration times, gain settings above 150 generally

30

led to an unsatisfactory amplification of noise, while the system was better served by
reducing the power instead of reducing the gain below 100.
3.2.5. Integration of Systems
An essential component of the work presented in the next two chapters was the
development of a program to coordinate the behavior of the computer controlled
devices used. Specifically, the SLM and the camera had to be under full control of the
user to ensure processes happened in the appropriate sequence. National Instruments’
LabVIEW program was used to coordinate the instrumentation described here. Using
drivers, and, in some cases, sub-routines, provided by the companies, as well as
utilizing portions of programs for control over the SLM previously written by other
members of the Dantus group, a program was written to permit full control over the
various capabilities and to ensure the timing of various processes.
3.3. Multiphoton Intrapulse Interference Phase Scan (MIIPS)
The following section is adapted from Ref. 153, on which I am the 2

nd

author.

It is reproduced in part with permission from Xu, B.; Gunn, J.M.; Cruz, J.M.; Lozovoy,
V.V.; Dantus, M., Quantitative investigation of the multiphoton intrapulse interference
phase scan method for simultaneous phase measurement and compensation of
femtosecond laser pulses. Journal of the Optical Society of America B 2006, 23, (4),
750-759. Copyright 2006. Optical Society of America.
3.3.1. MIIPS Theory
MIIPS is an analytical method for retrieving and compensating the phase across
the spectrum of the laser pulse. Unlike other approaches, it is a single-beam method
and is capable of not only characterizing the spectral phase of the pulses, but

31

compensating for the measured distortions, and, when desired, using the same setup to
apply user-defined phase functions.
In MIIPS, a known reference function, f(ω), is introduced by a pulse shaper to
cancel, at least locally, distortions by the unknown spectral phase φ(ω) of the pulse. The
sum of the unknown phase and the reference phase is given by ϕ(ω)= φ(ω)+f(ω). The
second-harmonic-generation (SHG) spectrum resulting from the total phase ϕ(ω) can be
used to retrieve φ(ω) accurately.
Assuming the use of a thin nonlinear crystal with a pulse that is a few optical
154, 155

cycles long,

the SHG intensity S

(2)

at frequency 2ω can be written as an integral

over the spectral amplitude |E(ω)| and phase ϕ(ω) of the pulse:

ܵ

ሺଶሻ

ሺ2߱ሻ ‫ ן‬ฬන|‫ܧ‬ሺ߱ ൅ Ωሻ||‫ܧ‬ሺ߱ െ Ωሻ|݁

ሼ௜ሾఝሺఠାΩሻାఝሺఠିΩሻሿሽ

݀ Ωฬ

ଶ

(3-2)

According to this equation, the signal is proportional to the integral of the product
of a real positive kernel, |E(ω+Ω)||E(ω−Ω)|, with the complex exponent of phase

ϕ(ω+Ω)+ϕ(ω−Ω). TL pulses (ϕ = 0) generate the maximum intensity for a SHG spectrum
because the oscillatory component of the integral is zero.
According to eq (3-2), the SHG spectrum is maximized when ϕ(ω+Ω)+ϕ(ω−Ω) is
zero. Based on the Taylor expansion of this expression:

φሺω ൅ Ωሻ ൅ φሺω െ Ωሻ

ൌ 2φሺωሻ ൅ φᇱᇱ ሺωሻΩଶ ൅ ‫ ڮ‬൅ ൬

32

2
ᇲ
൰ φଶ୬ ሺωሻΩଶ୬
ሺ2nሻ!

(3-3)

where ߮ ௡ ሺ߱ ሻ ‫ ݀ ؠ‬௡ ߮ሺ߱ሻ/݀߱௡ , the SHG spectrum has a local maximum, to first
ᇲ

approximation, at ω when the quadratic phase term, ϕ’’(ω) equals zero, i.e., when

߮ ᇱᇱ ሺ߱ሻ ൌ ߶ ᇱᇱ ሺ߱ሻ ൅ ݂ ᇱᇱ ሺ߱ሻ ՜ 0.

(3-4)

At this frequency, f’’’(ω) compensates φ’’(ω), and the unknown function φ’’(ω) can be
retrieved; this concept is illustrated in Figure 3.6(a).

Figure 3.6. Schematic of MIIPS concept. (a) The thicker line shows the second
derivative of the unknown phase distortion, φ″(ω), the thinner line is the negative of the
second derivative of the well-known reference function, -f″(ω), and the dashed line is the
sum of the two, φ″(ω)+f″(ω). The SHG signal will have a local maximum when the sum
of φ″(ω) and f″(ω) is zero (i.e., when –f″(ω) intersects with φ″(ω)). (b) When the wellknown reference function, f(δ,ω) scans across the spectrum, SHG signals are
maximized at different frequencies, as the intersection of –f″(ω) and φ″(ω) changes.
To measure the phase distortion across the spectrum, the reference function,
f(ω), is parameterized as f(δ,ω), where δ is a parameter that is scanned, so that the

33

reference function samples all frequencies in the bandwidth. The resulting SHG
spectrum, SHG(δ,2ω), reaches a maximum when

߮ ᇱᇱ ሺߜ௠ ሺ߱ሻ, ߱ሻ ൌ ߶ ᇱᇱ ሺ߱ሻ ൅ ݂ ᇱᇱ ሺߜ௠ ሺ߱ሻ, ߱ሻ ՜ 0

(3-5)

where δm(ω) denotes the δ value of the SHG maximum for each frequency. Graphically
(see Figure 3.6(b)), this condition can be represented as an intersection of the second
derivative of the unknown, and the negative of the calibrated scanned function, i.e.

φ ′′ (ω ) = − f ′′ (δ m (ω ) , ω )

.

Based on eq (2)(3-4), the resulting SHG spectrum, SHG(δ,2ω) reaches a
maximum when ϕ’’[δm(ω),ω]=φ’’(ω)+f’’(δm(ω),ω]→ 0 or φ’’(ω)=−f’’[δm(ω),ω], where δm(ω)
denotes the δ value of the SHG maximum for each frequency. The phase of the pulse
across the whole spectrum φ(ω) can be analytically retrieved by double integration of

φ’’(ω) in the frequency domain. SHG and MIIPS are not affected by the choice of
0

integration constants, the relative phase φ and linear term φ’.
3.3.2. Implementation of MIIPS
For the MIIPS measurements made in this dissertation, a sine function was
utilized as the reference:

݂ሺߜ, ߱ሻ ൌ ߙ sin ሺߛ߱ െ ߜሻ

(3-6)

where α and γ are fixed parameters with values equal to 1.5π and the duration of the
pulse, respectively; the phase shift, δ, is a parameter typically scanned from zero to 4π,
as shown in Figure 3.6(b). By acquiring an SHG spectrum for each step over this
range, two replicas of the MIIPS trace are obtained, as shown in Figure 3.7. The value

34

of δm(ω) for each frequency is found, and from these values, the second derivative of
the unknown phase is calculated by

߶ ᇱᇱ ሺ߱ሻ ൌ ߙߛ ଶ sin ሺߛ߱ െ ߜ௠ ሺ߱ሻሻ

(3-7)

By substituting φ″ = 0 into the above equation, it can be shown that, for TL pulses,
௡
ߜ௠ ሺ߱ሻ ൌ ߛሺ߱ െ ߱଴ ሻ ൅ ݊ߨ, ݊ ൌ 0, േ1, േ2 …

(3-8)

In a MIIPS trace, this results in TL pulses having parallel lines separated by π.
The phase of non-TL pulses are measured by finding the values for δm(ω) for
each of two regions, as shown in Figure 3.7, and the average is used to calculate the
second derivative of the unknown phase distortions:

1
ଵ
ଶ
߶ ᇱᇱ ሺ߱ሻ ൌ െ ߙߛ ଶ ሾsin൫ߛ߱ െ ߜ௠ ሺ߱ሻ൯ ൅ sin൫ߛ߱ െ ߜ௠ ሺ߱ሻ൯ሿ
2

(3-9)

Figure 3.7. Experimental results for MIIPS. The panels are SHG spectra as the δ
parameter of the reference function is scanned. Each vertical line corresponds to a
separate SHG spectrum obtained at a given value for δ. The black lines which separate
the MIIPS traces are used to define the region for searching δm(ω). The dots within
those boundaries show δm(ω). The panel on the left is the MIIPS trace for a typical
uncompensated pulse. After several iterations, the traces on the right, which
correspond to TL pulses, are seen.

35

To optimize the accuracy of MIIPS, an iterative procedure of measurement and
compensation is used. The experiment begins as described above, and the phase is
I

retrieved. To compensate this distortion, the measured phase of the first iteration, -φ (ω)
is added to the applied phase using the pulse shaper, the process is repeated, and the
II

I

II

next order of phase correction, φ (ω) is measured. The sum -(φ (ω)+φ (ω)) is used as
the correction function. The convergence towards an accurate result is exponentially
fast. By using this iterative approach, large dispersions, e.g., dispersions larger than
the range of the shaper, can be quantified and compensated.
3.3.3. Validation of Method
The basic experimental setup for MIIPS necessitates only a thin SHG crystal, a
spectrometer, and a pulse shaper capable of accurately introducing spectral phase
modulation (Figure 3.8). It is worth noting that there are no beams to overlap in space
and time, and there are no moving parts. Using this setup, a series of experiments
were performed to quantify the capabilities, as well as validate the accuracy and
precision of MIIPS as it compares to other methods of compensating the phase
distortions in pulses.

Figure 3.8. Experimental setup for MIIPS

36

The ability of MIIPS to accurately retrieve the spectral phase of a pulse was
tested by first compensating the pulse to make it TL, and then applying known phases
and using several iterations of MIIPS to retrieve those phases. Two phase functions
were applied: a double Gaussian function and four periods of a sinusoidal function.
These functions are shown by the solid lines in Figure 3.9. The phase retrieved by
MIIPS is shown by the dots. It can be seen that MIIPS is capable of retrieving these
synthetic phases quite accurately.

Figure 3.9. Ability of MIIPS to retrieve arbitrary phase functions. (a) The result for an
applied double Gaussian function. (b) The result for an applied sine function. The dotted
curves show the retrieved phase, and the solid curves are the applied phase.
Another test was performed to ensure that MIIPS is capable of not just retrieving
the phase, but accurately compensating for the phase measured. To do this, MIIPS
was used to compensate for the dispersion of the pulse. Two known phases, a square
wave and a sinusoidal wave, were then applied to the pulse, and the resulting SHG
spectrum compared to that predicted by theory. The results are shown in Figure 3.10,
with the spectrum and applied phases shown above each of the results. In panels (a)
and (c), it is seen that theory (solid lines) and experiment (dots) agree well, indicating
that the use of MIIPS results in well-behaved TL pulses. As a comparison, the bottom

37

panels show the SHG spectra obtained when the phases are applied, but the laser is
not compensated. It is clear that without compensation, the dispersions in the system
have significant deleterious effects on nonlinear processes. This reiterates both the
necessity for a method such as MIIPS as well as the effectiveness of MIIPS in
compensating for these dispersions.
Another test of MIIPS’ performance was the reproducibility. For this experiment,
several iterations of MIIPS were run to acquire a compensation mask (the negative of
the measured phase). This compensation mask was applied, and a single iteration of
MIIPS was run ten times successively (each time starting from the compensation mask).
The results for the retrieved phase are shown in Figure 3.11. The lower panel shows
the average retrieved phase across the entire spectrum of the pulse, with error bars
denoting ± 1 standard deviation for every fifth point. The upper panel shows the same
results, focused in on the portion of the spectrum over which MIIPS can compensate.
As the figure shows, MIIPS is highly reproducible over a very broad portion of the
spectrum (essentially the portion where the red spectrum is more than 10% of the
maximum value).

38

Figure 3.10. Comparison between experimental data and theoretical simulation. The
solid curve in each panel shows the theoretical spectrum predicted for the application of
a particular binary phase (a) and (b) or a particular sine function (c) and (d). The dotted
curves correspond to the experimentally measured SHG spectrum for each case. (a)
The experimental result of the application of a binary phase mask (inset) to a pulse
compensated by MIIPS. (b) The result of the application of the same phase mask to an
uncompensated pulse. (c) and (d) The corresponding information using a sine function
(inset).

39

.
Figure 3.11. Reproducibility of MIIPS. In both panels, the solid curve shows the
average of ten independently retrieved phases, while the error bars show ±1 standard
deviation for every fifth point. The lower panel shows the full range of collected data.
The upper panel shows a closer view of the region over which MIIPS can compensate
(760–880 nm).
To quantify the reproducibility, and compare MIIPS to other, published, methods
of compensation, the statistical phase error was calculated by averaging the standard
deviation at each point, using the power spectrum as a weighting function. Over the
entire range of the spectrum, analyzing the full set of data, the statistical phase error
was calculated to be 0.013. Using a reduced set of the first five scans, the statistical
phase error is reduced to 0.011. These results, as well as a comparison with FROG
and SPIDER, are shown in Table 1, below. Also of interest is the great reduction of the
statistical phase error when the range of data analyzed was reduced to that in which the
retrieved phase was flat (i.e. MIIPS had successfully compensated). For this range, the

40

statistical phase error was reduced to just 0.004 rad. Over the FWHM of the pulse, the
statistical phase error is further reduced to 0.0028 rad.
Table 1. Comparison of Reproducibility of MIIPS with FROG and SPIDER: Statistical
Phase Error (in rad)
Method
MIIPS
156
FROG
156

SPIDER

Full Data Set
0.013
0.122

Reduced Data
Set
0.011
0.048

0.044

Full Data Set (FWHM)

0.017

0.0028

157

A different study, performed by Schlup and Bartels,

compared how robust these

methods are to noise in the retrieved spectral phase of the pulse; MIIPS was shown to
perform substantially better than FROG.
To further quantitatively test the accuracy of the phases retrieved by MIIPS, the
GVD of quartz, a well-characterized material, was determined.

In this experiment,

MIIPS was used to measure the phase of the setup alone (0 mm quartz) and when
quartz windows with thicknesses of 3.25, 4.92, 6.53 and 9.58 mm were placed in the
path of the beam prior to its incidence on the SHG crystal. MIIPS was used to retrieve
the second derivatives of the spectral phases of those pulses, and the spectral phase
was quantified, with the results from MIIPS performed on the setup alone as a
reference.
The second derivative of the phase for the different thicknesses of quartz. are
shown in the top panel of Figure 3.12, and the GDD at 800 nm for each window is
shown in the lower panel. It is important to note that the curves are both parallel and
spaced proportionally to the thickness of the quartz. The GVD (GDD per unit length)
2

introduced by the quartz windows was measured to be 36.2 ± 0.5 fs /mm at 800 nm.

41

For comparison, the “gold standard” experimental method of determining GVD is white
2

158

light interferometry, which has determined the GVD of quartz to be 35.92 fs /mm.

For further comparison, the GVD of quartz at 800 nm was calculated using the Sellmeir
159

formula and the constants found from Maltison

2

and was found to be 36.162 fs /mm,

which is in excellent agreement with these measured results.

Figure 3.12. GVD measurement of quartz using MIIPS. (a) The retrieved second
derivative of the spectral phases (from bottom to top: 0, 3.25, 4.92, 6.53, and 9.58 mm
quartz windows). (b) The GDD at 800 nm as a function of thickness.

42

The measurement was then repeated with increasing numbers of glass
microscope slides (crown glass, Fisher Scientific, 1 mm thick) sandwiched with Nujol oil,
an index-matching fluid.

As the thickness of the slides is uniform, reliable

measurements will show a linear plot of GDD versus the number of slides used. The
results are shown in Figure 3.13. The top panel shows the retrieved second derivatives
of the spectra phase for every other slide addition, while the lower panels shows the
GDD as a function of thickness, which can be successfully fitted by a line. The GVD
2

introduced by the microscope slides was measured to be 50.7±0.5 fs /mm at 800 nm.
Assuming the crown glass used in the microscope slides corresponds to Ohara glass SNSL 5 (equivalent to Schott glass K5), the measured GVD can be compared with the
160

value calculated using the Sellmeier formula with constants available from Ohara.
2

The GVD was calculated to be 50.13 fs /mm at 800 nm, which is in good agreement
with the experiment.

43

Figure 3.13. GVD measurement of microscope slides using MIIPS. (a) The retrieved
second derivative of the spectral phases (from bottom to top: 0, 2, 4, 6, 8, and 10 mm
microscope slides). Note that for clarity the odd number of slides (odd thicknesses)
were omitted from this graph, but not from the calculation. (b) The GDD at 800 nm as a
function of thickness.
3.3.4. Use of MIIPS in a high-NA Microscope Objective
Before MIIPS, the characterization of the spectral phase distortions of sub-10 fs
161

pulses was limited to objectives with a NA up to 0.85.
with an NA up to 1.30 could be compensated.

162-165

For longer pulses, objectives
This limitation to the most

effective use of high-NA microscope objectives was one of the greatest obstacles to
fully developing the potential of multiphoton imaging and other techniques that utilize

44

high focusing of ultrashort pulses, such as the results presented in this dissertation. It
was therefore critical to demonstrate that MIIPS could compensate for these objectives.
As the MIIPS method requires that second-harmonic (SH) be measured at the location
of the sample, the same microscope setup discussed in Figure 3.3 was used, with
detection optics mounted on a tower above the microscope objective for forward
collection.
The three objectives that have specifically been tested were a Nikon Plan Fluor
ELWD 20x/0.45 NA objective, a Nikon Plan Fluor ELWD 40x/0.60 NA objective, and a
Nikon Plan Apo TIRF oil immersion 60x/1.45 NA objective. MIIPS alone compensated
for the phase distortions introduced by the 20x/0.45 NA and 40x/0.60 NA microscope
objectives (results not shown). To best compensate for all orders of phase distortion in
the 60x/1.45 NA objective, however, a prism pair compressor utilizing SF10 prisms, was
used to pre-compensate the quadratic phase contributions, which were on the order of
4

2

10 fs ).
Figure 3.14 shows the residual phase after MIIPS is used to compensate for the
dispersions in a typical microscopy setup utilizing the 60x/1.45 NA objective. The solid
line, in both panels, shows the average phase residue from five independent
measurements, while the error bars show ±1 standard deviation for every fifth point.
The lower panel shows the full data set across the entire spectrum (shown by the
dashed line), while the upper panel shows the data over the FWHM of the pulse. Note
that the distortions are reduced to 0.1 rad over that range, indicating that MIIPS is
compensating well. It is also important to note the extremely small standard deviations
over this range, showing that MIIPS can very reproducibly compensate for the

45

distortions of even highly dispersive materials.

The statistical phase error was

calculated to be just 0.026 over the full range of data, where the uncompensated phase
distortion was ~100 rad.

Figure 3.14. Compensation of spectral phase distortions caused by a 60x/1.45 NA
objective. The error bars indicate ±1 standard deviation. The lower panel shows the full
range of data, while the upper panel shows the same data over the FWHM of the pulse,
on a reduced scale.
3.4. Conclusion
This chapter has presented the experimental setup used for the experiments
presented in this dissertation. To summarize, the experimental setup is based around a
~12 fs laser coupled into an inverted microscope via a 650 nm short-pass filter and
focused down to ~1 micrometer onto the sample. Wide-field emission is collected back
through the objective and allowed to pass through the short-pass filter and to the highlysensitive EMCCD camera.
To compensate for the phase distortions introduced by the propagation of the
ultrafast laser through media, including the 60x/1.45 NA microscope objective used to

46

focus the beam, a prism pair compressor and 4-f pulse shaper were used in conjunction
with MIIPS.

A detailed documentation of MIIPS’ accuracy and reproducibility is

presented, confirming that the results presented in Chapter 5, in which information
about the mechanisms of energy transfer in the system is obtained via studies of the
effect of applied phases on emission intensity, are reliable and reproducible.

47

4. THE SAMPLE: PREPARATION AND CHARACTERIZATION OF LUMINESCENCE
This chapter and the following outline the results of the experiments performed to
explore and understand the propagation of energy through the silver nanoparticle films.
These chapters are adapted from Refs. 14 and 166, both articles on which I am the first
author. They are reproduced in part with permission from Gunn, J. M.; Ewald, M.;
Dantus, M., Polarization and phase control of remote surface-plasmon-mediated twophoton-induced emission and waveguiding. Nano Letters 2006, 6, (12), 2804-2809.
Copyright 2006, American Chemical Society, and from Gunn, J. M.; High, S. H.;
Lozovoy, V. V.; Dantus, M., Measurement and Control of Ultrashort Optical Pulse
Propagation in Metal Nanoparticle-Covered Dielectric Surfaces. Journal of Physical
Chemistry C 2010, 114, (29), 12375-12381.

Copyright 2010, American Chemical

Society.
4.1. Preparation of Sample
4.1.1. Synthesis
Silver nanoparticles were synthesized using the method utilized by Wensellers,
3

41,167,168

et al. In this method, a citrate synthesis,

90 mg of AgNO3 is dissolved in 500

mL of H2O. The solution is brought to a boil, and 10 mL of 1% sodium citrate is added.
The solution is boiled for an hour, resulting in a green-gray suspension. After cooling to
room temperature, cluster formation is induced by adding 15 mL of 0.026 M fumaric
169

acid,

and the solution is allowed to precipitate onto the substrates, typically for 48 to

72 hours.

The effect of different precipitation times is discussed in more detail in

Section 4.4.2. In this reaction, the citrate plays two roles, acting as both a reducing

48

agent, promoting the growth of the silver nanoparticles, and a capping agent which
stabilizes the nanoparticles. While citrate is the most commonly used reducing agent
168

for the synthesis of silver nanoparticles,
171

and Eriochrome Black T.
been shown to

affect

170

others can be used,

including EDTA

42

The choice of reducing agent and its concentration has

the size, shape and

dispersity of

the synthesized

42,168

nanoparticles.

The primary substrates used were 0.15 mm-thick quartz coverslips, although a
few experiments were performed using atomically flat mica as a control.

As no

differences in the optical behavior were observed, quartz was used for all optical
experiments presented in this dissertation due to ease of use.
4.1.2. Microscopy of the Sample
Electron microscopy images were obtained in order to characterize the
nanoparticle samples. Panels A-C of Figure 3 show transmission electron microscopy
(TEM) images obtained of the samples, while panel D shows a scanning electron
microscopy (SEM) image obtained. The TEM images indicate that the nanoparticles
form primarily as roughly spherical structures (Figure 3A), with a small quantity as rods
(Figure 3B), with dimensions on the order of 50 nm, while the SEM image shows the
dendritic nature of the nanoparticle aggregate film.

49

Figure 4.1. Panels A-C show TEM images of individual silver nanoparticles, which form
both as roughly spherical structures and as rods. Panel D shows an SEM image of the
structure of the aggregates formed. Electron microscopy images were obtained by
Professor Martin Crimp, Michigan State University.

Further characterization of the samples was done via atomic force microscopy
(AFM). Images of a typical sample are shown in Figure 4.2. As shown in Figure 4.2A
and B, the dielectric surface is only partially covered. There are a few large
(micrometer-sized) agglomerations of nanoparticles (seen prominently in Figure 4.2A),
as well as interconnections among islands, observed in the form of regions with
nanoparticles at distances shorter than the incident laser wavelength, shown in Figure
4.2B.

50

Figure 4.2. Panel A, AFM image of typical sample, illustrating the larger features of the
sample. Panel B, AFM image of typical sample, with an emphasis on the smaller, more
connected features that lie in between the larger features. Figure 4A was obtained by
Professor Virginia Ayres, Michigan State University.

4.1.3. Control Experiments
Several control experiments were performed to determine if ambient oxygen or
humidity affected the optical properties of the samples. In one set of experiments,
samples were prepared with either nitrogen or air continuously bubbling through the
solution during synthesis, and over it during precipitation. In another, samples spincoated with a protective polymer layer were compared to those left exposed. In each of
these experiments, there was no difference observed in the optical properties.
Another consideration is that irradiation has been shown to change the shape
172-178

(and therefore the optical properties) of metallic nanoparticles.

To assure that

ambient radiation was not altering the samples, a final control experiment was
performed in which every stage of the process, from the synthesis to the experiments
themselves, were performed in complete darkness. Some of the samples were then
irradiated with light from a mercury lamp for eight hours.

51

No difference in optical

properties was observed between the samples synthesized and used under normal,
ambient conditions and those produced under darkness, with or without subsequent UV
irradiation.
Due to these results, all subsequent synthesis was performed under ambient
conditions. While samples were typically stored in a dark cabinet, and experiments
performed in the dark (to minimize background), no special care was taken to protect
the samples from ambient light during transfer and preparation of the experiment.
However, there was no visible degradation of the samples, and they could be used
regularly over a period of months with no change in their optical properties.
4.2. Hypothesis
As briefly mentioned in Chapter 1, emission is observed from these samples
when excited with the laser system discussed in Chapter 3. The rest of this chapter will
seek to characterize and identify the nature of this emission, while the following chapter
will investigate the energy transport leading to emission so remote from the focal spot.
There are several possible sources of emission from metallic nanoparticles
structures. One initial hypothesis is that the detected photons are from scattered laser
light (~800 nm). However, a compelling case for the absence of simple scatter can be
made by an examination of the experimental setup. As explained in detail in Section
3.2.3, there is a short-pass dichroic mirror (cut-off=650 nm) in the microscope setup to
separate the excitation and emission signals. When a Schott glass BG39 filter, which
has essentially zero transmittance above 750 nm, was placed in the emission beam
path, there was no change in the intensity. If the detected light were trace remnants of

52

the fundamental pulse, a reduction or complete elimination of the signal would have
been observed.
In addition to scattering of the fundamental excitation beam, rough surfaces can
179-183

result in SHG

which could then also be scattered. Another possible source of

emission is luminescent emission after two-photon excitation.

This luminescence
184,185

process is from the excitation of electrons from the d to the sp conduction band,

resulting in a broad, visible emission. Luminescence was first observed in bulk gold and
186

copper in 1969, although with an extremely low quantum efficiency,

and has since

been observed with several orders of magnitude higher efficiency in gold
187-190

nanoclusters,

nanoparticles

185,191,192

and

luminescence has been observed in nanoclusters,
195-198

of Ag nanocrystals),
202

patterned

films.

199

island

194

colloid

In

silver,

silver oxide films (via production

199-201

and colloid

193

films.

films, as well as fractal

199

and

This substantial increase in efficiency is possible due to the

amplified local electromagnetic fields, as discussed in Section 2.2.1, which has been
shown to readily provide an enhancement in the two-photon excitation or hyper-Raman
5,33,39,180,203-208

excitation of molecules.

4.3. Characterization of Solution
4.3.1. Spectrum
Initial characterization of the spectral properties of the silver nanoparticles was
done by studying the properties of the solution after aggregation, but before
precipitation. Most significantly, we were interested in the emission spectrum of the

53

aqueous sample upon excitation with an ultrafast laser. To most closely mimic the
microscope setup that was to be used in future experiments, collection of emission was
done along the z-axis, with the filter cube used in the microscope used to separate the
excitation and emission beams, as shown in Figure 4.3.

The resulting spectrum,

collected with an excitation power of 25.1 mW and shown over the entire range of the
spectrometer, is shown in Figure 4.4.

Figure 4.3. Setup for acquiring the emission spectrum of the silver nanoparticle
aggregates in solution. The filter cube from the microscope is used to minimize
excitation light reaching the detector.
The structure observed in the spectrum is most likely due to interference in the
filter, possibly from the dichroic mirror used to separate the excitation and emission
beams. The exact position of the structure can be shifted a small amount by slightly
adjusting the position of the filter. The sharp cut-off at 650 nm is due to the cut-off filter
in the cube. It can be seen that this filter has an extremely sharp cut-off, and is capable
of suppressing the detection of light with wavelengths higher than 650 nm. Significantly,
there is no evidence that any of the fundamental light (750-850 nm) passes through.
This is further evidence that the light detected in future experiments on the microscope
is not scattered fundamental. It is also significant that there is no emission centered
around 400 nm, indicating that the detected light is also not the result of second179, 180

harmonic generation from the surface.

54

Figure 4.4. Full emission spectrum of silver nanoparticles aggregated in solution after
excitation with a 13-fs Ti:sapphire laser. The spectrum is shown over the full range of
the spectrometer; note that there is no evidence of either fundamental light (800 nm) or
second-harmonic (400 nm). The observed structure is likely due to interference in the
dichroic mirror.

55

4.3.2. Multiphoton Behavior
As discussed in detail previously, ultrafast lasers are capable of inducing
nonlinear optical processes due to their high peak intensities. This has been observed
in metallic nanoparticles: luminescence via a nonlinear absorption process was first
noted in 1981, as a broad background beneath a strong surface-enhanced second180

harmonic generation signal,
209

and was explored in more detail by Boyd, et al. in

It has since been observed and studied as third-harmonic generation in Au

1986.

210

nanoparticles,

211

aggregates,

as two-photon-induced luminescence in gold nanoparticle colloids and
179

nanostructured films,

212-218

as well as nanoparticles.
219

recently, the two-photon-induced luminescence of Ag films
have been studied, as well.

More
220

and nanoparticles,

The efficiency of two-photon excitation on metallic

nanoparticles is high enough that it has been detected for continuous wave laser
221

excitation.

As excitation of the silver solution shown above takes place in the IR regime, but
emission is in the visible, a multiphoton absorption process is immediately suspected.
To test this hypothesis, the emission spectrum was collected at a series of excitation
powers, in which neutral density filters of known optical densities (OD) (0, 0.04, 0.38,
0.50 and 0.70 OD, resulting in excitation powers of 27.5, 25.1, 11.5, 8.7 and 5.5 mW,
respectively) were placed in the excitation beam path. The resulting emission spectra
are shown in Figure 4.5. It is clear that there is a non-linear decrease in intensity as the
excitation power is decreased. To quantify this trend, the integrated intensity over the

56

entire spectrum was plotted against excitation power. OriginPro was used to obtain a
b

best fit line of the form ax . The data and best fit line (y = 14.889x

2.115

) are shown in

Figure 4.6. With an exponent (b) of 2.115 (±0.096), it is clear that the excitation process
is two-photon in nature.

Figure 4.5. Two-photon induced luminescence of silver nanoparticle aggregates in
solution. The emission spectra shown here were collected after a sample of aggregated
silver nanoparticles in solution were excited by a Ti:sapphire laser at varying powers:
27.5, 25.1, 11.5, 8.7, and 5.5 mW (top to bottom).

57

Figure 4.6. Integrated intensity of the spectra shown in Figure 4.5 plotted as a
function of excitation power. Clearly not linear, a best-fit line (in the form of a power
b
2.115
function, y=ax ) was found to be y = 14.889x
, indicating that the excitation
process is, or is largely dominated by, a two-photon process.
1

To confirm this analysis, the data was then fit to a linear (y=ax , dashed line),
2

3

quadratic (y=ax , solid line) and cubic (y=ax , dotted line) curves. The results are
2

shown in Figure 4.7. With R values of 0.8627, 0.9984, and 0.9842 for the linear,
quadratic, and cubic fits, respectively, it is again clear that the relationship is quadratic,
and the excitation process two-photon.

58

Figure 4.7. Integrated intensity of the spectra shown in Figure 4.5 plotted as a
1
2
function of excitation power. Data is fit to linear (y=ax , dashed line, R =0.8627),
2

2

3

2

quadratic (y=ax , solid line, R =0.9984) and cubic (y=ax , dotted line, R =0.9842)
curves. From these results, it is again clear that the relationship is quadratic, and the
excitation process two-photon.

59

4.4. Emission from Samples on the Substrate
4.4.1. Observation
When the Ti:sapphire laser discussed in Section 3.2.1 is focused at normal
incidence onto the sample, emission from the nanoparticles at the focal spot is
observed. This emission, which is solely from the focal spot, is referred to as "local
emission." On certain samples, or regions of a sample, focusing of the Ti:sapphire laser
results in minimal emission at or near the focal spot, but significant emission from a
number of regions tens of micrometers away from the focal spot. It is this emission that
is referred to as “remote” emission, and is the focus of the studies in this dissertation. A
comparison of these two phenomena is shown in Figure 4.8.
In this figure, two samples were illuminated with a femtosecond laser under
identical conditions.

The panel on the right shows intense local emission with no

remote emission, while the panel on the left shows emission about 30 times less
intense, with visible regions of remote emission.

60

Discrete regions of emission have been observed and recorded as far as 99 µm
from the focal spot, as shown in Figure 4.9. Under typical excitation conditions, stable,
remote emission is routinely observed up to 20-40 µm from the focal spot. Under higher
excitation powers, distances that are estimated to be greater can be observed by eye
through the microscope objective, but are not stable, and cannot be documented due to
the limited field of view of the collection camera.

Figure 4.8. Comparison of two silver samples illuminated with a femtosecond laser
under the same conditions. The sample on the left, which has a maximum intensity of
536 counts, shows distinct regions of remote emission. The sample on the right, which
has a maximum intensity of 14,568 counts (nearly saturation) shows no evidence of
remote emission.

61

Figure 4.9. Emission that is up to 100 µm from the focal spot (denoted by cross-hairs)
is observed when a dielectric substrate with silver nanoparticles is excited by a
femtosecond laser at normal incidence. A 40x/0.60 NA objective was used in this
experiment.
When excited at sufficiently low powers, the observed emission is stable for tens
of minutes, allowing time to study its various properties as well as methods of control,
as discussed in the following chapter. The definition of “sufficiently low” varies from
sample to sample, but is typically ~1 mW. Focused down to a 1 µm spot size, typical for
the 60x/1.45 NA objective, this results in a power of 11 pJ/pulse and peak intensities of

62

11

1.12 x 10

2

W/cm . At lower powers, the signal to noise ratio significantly deteriorates,

while at higher powers, the emission tends to be unstable.
4.4.2. Density of Particles
While the effect has not been quantified, a correlation between distance of
remote emission and what defines a “sufficiently low power” for a sample, or section of
a sample, has been observed. That is to say, a sample that shows extensive emission
far from the focal spot will be more stable at higher powers than a sample that emits
only in the region at the focal spot; in fact, it is nearly impossible to study emission that
is confined to the focal spot due to the instability of the intense emission observed, even
at very low (µW) excitation powers. This observation can be readily explained by the
hypothesis that at least some of the instability is due to melting, or other permanent
changes to the structure of the particle that affect its ability to resonate with the given
172-174,176-178

frequency of excitation.

Samples that show remote emission have an

additional mechanism to dissipate energy, and are therefore less likely to experience
structural changes due to melting from high heat deposition.
When looking at samples, it is possible to visually gauge which sample, or
regions on a sample, are more likely to show strong local or strong remote emission.
Empirically, “darker,” or more opaque samples or regions, in which there is heavier
deposition of nanoparticles, tend to show localized emission, while “lighter,” more
transparent samples or regions are more likely to have extended regions of remote
emission that are stable over long periods of time.
To systematically explore this phenomenon, a study was performed in which the
amount of time a substrate remained in the precipitation chamber was varied, from a

63

quick dip (1 sec) to 48 hours. This allowed a more developed determination of the
conditions under which different types of emission are observed. The results are shown
in Figure 4.10.

It should be noted that for this experiment, as for all experiments

reported in this dissertation, the sample position must be fine-tuned using the stage to
minimize local emission, even in a region of good “remote” emission.

Figure 4.10. Effect of deposition time (and therefore particle density) on remote
emission. Exposure time was 0.5 sec, average laser power was 2.95 mW, and the gain
was set to 200.
At the highest deposition times (and presumably the highest particle density), the
remote emission was relatively limited. At lower deposition times, the scope of the
remote emission increases. At 1 hr, optimal remote emission is observed, although it is
overshadowed in this image by emission near the focal spot. After just dipping the
sample into the sample (1 sec), the most remote emission was observed. However, this

64

emission was less consistent; excitation of many areas of the sample did not result in
emission strong enough to capture on the camera.
To explain these results, we have to consider that increasing density will result in
an increased number of paths for energy to transfer through.

After a very short

deposition time, there will be very few nanoparticles on the surface, and therefore few
paths for the energy to transfer through. As the density of nanoparticles increases with
increased deposition time, there will be more connectivity within the sample, and
therefore a greater likelihood of remote emission taking place. As the density continues
to increase, the paths will become less distinct. The entire surface will more closely
resemble a rough surface, with the energy localizing at the focal spot.
It should be noted that this study is limited only to identifying the deposition times
leading to the best emission for this “batch” of samples. In general, batch-to-batch
comparisons lead to as wide of range as results as shown within this batch, a
42

phenomenon that has been seen elsewhere, as well.

This is likely due to the wide

range of environmental factors that affect nucleation and aggregation in the growth of
the nanoparticles.

A retrospective view of the data suggests that better remote

emission tends to come from samples prepared in the summer, when the laboratories
are cooler and much more humid, versus the winter, when the laboratories are warmer
and much more dry.

Other factors, such as the amount of water evaporated during

boiling, rate of cooling, etc. make the effect of humidity and temperature difficult to
isolate, however.

65

4.5. Characterization of Sample on Substrate
4.5.1. Multiphoton Behavior
To confirm that the luminescence observed on the substrate is due to a
multiphoton absorption, as was shown in solution, a variable filter with a linear optical
density gradient was placed in the laser beam path after it was collimated but before it
was expanded. The experiment was performed by moving the variable filter along the
gradient, collecting an image and then collecting the spectrum of the laser. This was
repeated 100 times, with every tenth data point (5, 15, 25, etc.) an image collected with
the beam blocked to check for drift in the background, and every tenth data point on the
tens (0, 10, 20, etc.) collected at full laser power. While this did increase the possibility
of damaging the sample, it also allowed for a check of drift in laser intensity, as well as
in response of the sample. The results presented here are for a sample that showed no
evidence of damage or drift of either sort.

66

To aid in analysis, both the laser spectrum and the power were collected at
several different laser intensities, and the linear relationship between the integrated
intensity of the spectrum and the laser power quantified. This relationship was then
used to transform the integrated intensity of the collected spectra to the power of the
excitation beam.

Figure 4.11. Integrated intensity of individual data points plotted as a function of
1.970
excitation power. The lines of best fit were found to be y=20.4x
(gray squares),
y=4.16x

2.054

(solid circles) and y=7.53x

1.790

(open triangles).

After discarding images collected with a fully blocked beam, or in which any pixel
was saturated, the remaining data was used to analyze the power dependence of
individual points of emission. The intensity of individual regions of emission was plotted
versus the excitation power, and the data fit to a power function, as it was for the

67

solution data. A plot of the power dependency of three representative data points is
shown in Figure 4.11. Using OriginPro for data fitting, exponents of 1.970±0.085 (gray
squares), 2.054±0.344 (solid circles) and 1.790±0.340 (open triangles) were found,
indicating that, as with the solution, the emission process is due to a two-photon
absorption.
To further confirm these results, particularly given the noisiness inherent to the
data, an analysis similar to that presented in Section 4.3.2 (and Figure 4.7, in particular)
was performed, and the data from each region of emission was fit to linear, quadratic
2

and cubic curves. The R values for each of these fits is shown in the table below.
2

Table 2. Comparison of R Values for Linear, Quadratic, and Cubic Fits of Data in
Figure 4.11.
Data Set
gray squares
solid circles
open triangles

Linear
0.8132
0.7777
0.8911

Quadratic
0.9250
0.8892
0.9783

Cubic
0.8919
0.8667
0.9330

4.5.2. Spectral Information
To further characterize the emission from the particles when on the substrate,
red, green and blue-pass (>600 nm, 500-575 nm, and <500 nm) filters were placed
between the microscope and the detector. A composite image is shown in Figure 4.12.
It can be seen that a substantial component of the emission is in the 500-575 nm range,
with some emission >600 nm, and virtually no emission below 500 nm.
consistent with the aggregate solution spectra shown in Figure 4.5.

68

This is

5 µm
Figure 4.12. Composite image of remote emission collected with colored filters. Signal
having wavelengths between 600 and 650 nm, wavelengths between 500 and 575 nm,
and wavelengths less than 500 nm are false colored red, green and blue, respectively.
For interpretation of the references to color in this and all other figures, the reader is
referred to the electronic version of this dissertation.
More refined insight into the spectral properties of the sample was gained by
placing an electronically controlled variable color filter (VariSpec Filter 51010, CRi)
immediately before the camera. This device allows only a narrow band of wavelengths
(10 nm FWHM) to pass. By scanning the transmission wavelength, a spectrum of the
emission can be acquired. A false color composite image is shown in Figure 4.13, left.
Emission from 450-525 nm is colored blue, 525-600 nm green, and 600-675 nm red. It
is clear that different regions have distinct wavelengths of emission. Figure 4.13, right,
shows the spectra of the three circled regions of emission. From these spectra, several
properties of the emission can be determined. First, there is no emission below 450
nm, so the observed emission cannot be second-harmonic generation of the
fundamental excitation beam. Second, there is no emission above 650 nm, showing

69

that the dichroic mirror used to separate the excitation from the emission is effective,
and that the observed emission cannot be attributed to direct scatter of the fundamental
of the excitation laser beam.

Third, the spectra illustrate that the particles have

emissions with different line shapes and line widths. Region A (red, circles) has a
narrow band of emission around 610 nm, region B (blue, crosses), has a strong, slightly
broader emission around 510 nm, while region C (green, squares) has a very broad
emission. The spectrum of region A has been multiplied by 5 to make it clearly visible
on the same axes as B and C. Figure 4.14 is another false color spectrally resolved
image of nanoparticle emission, over a wider field of view. Emission from 440-510 nm
was colored blue, 520-590 nm green, and 600-670 nm red.

It is again clear that

different regions of emission have distinct wavelengths of emission across the entire
visible spectrum.

Figure 4.13. Left. False color composite image of spectrally resolved silver
nanoparticle emission. Emission from 450-525 nm is colored blue, 525-600 nm green,
and 600-675 nm red. Right. Spectra from the three circled regions in the left panel are
shown. The signal from region A (red, circles) has been multiplied by 5 to make it
visible on the same set of axes as regions B (blue, crosses) and C (green, squares).
Note that there is no emission detected about 650 nm, consistent with the filters used,
nor is there emission below about 450 nm, again showing that the emission is not
second-harmonic generation.
70

Figure 4.14. False color spectrally resolved image of nanoparticle emission. Emission
from 440-510 nm was colored blue, 520-590 nm green, and 600-670 nm red. It is again
clear that different particles have distinct wavelengths of emission across at least the
entire visible spectrum.

71

4.6. Polarization
The propagation of electromagnetic fields as SPPs is known to be polarizationdependent, and the resulting localized and amplified electromagnetic field polarized,
both on rough surfaces

51,222

215

and on individual non-spherical nanoparticles.

Additionally, the intensity of luminescence and second-harmonic generation from
52,213,223-225

irregular surfaces

is sensitive to the polarization of excitation. Therefore,

we examined both the polarization of emitted light, as well as the ability to change which
regions emit based on the polarization of the excitation beam.
To control the polarization of the excitation beam, a Berek compensator,
configured to act as a half-wave plate, was placed in the laser beam path after the
shaper, but before the telescope. A thin linear polarizer was placed immediately before
the camera so that only light of a particular polarization is recorded.
The results of this experiment are shown in Figure 4.15. Each panel of Figure
4.15 is a wide-field image of the same area under different polarization conditions for
excitation and emission. The top panels were excited with a beam of 45º polarized light,
while the bottom panels were excited with a beam of 135º polarized light. Horizontally
polarized emission was detected in the left panels, and vertically polarized emission
was detected in the right panels. It can be seen from this figure that the emission is
polarized, with the regions not all having the same emission polarization. For example,
the area in region A emits distinctly vertically polarized light for both excitation
polarizations, while the area in region C only emits horizontally polarized light.
Additionally, polarization of the excitation beam can be used to control the presence or
absence of emission in certain spots. This is clearly illustrated by the areas in regions D

72

and E, which only emit upon excitation with 135º polarized light, but not under excitation
with 45º polarized light.

Region C clearly shows that the excitation and emission

polarizations are separated, as emission is only seen upon excitation with 135º
polarized light, but that emission is clearly vertically polarized, with no horizontally
polarized emission seen.

Were the emission polarization to match the excitation

polarization, we would expect to see approximately equal intensities for detected
vertical and horizontal polarization.
4.7. Conclusions on Luminescence
The luminescent phenomena observed in this chapter is consistent with twophoton-induced luminescence of the silver nanoparticles, enhanced by the LSPR effect.
Based on spectral information, the emission is clearly not scattered fundamental or
second-harmonic generation, as no 800 nm or 400 nm emission is observed.
Additionally, it is observed that regions of emission as close as 1 µm can display
different spectral and polarization properties, suggesting that energy transfer to each
region of emission, which will be discussed in the next chapter, is an independent
process.

73

Figure 4.15. Polarization characteristics of the silver samples. Each panel is of the
same area under different excitation and detection conditions. The top panels are
excited with 45° polarized light, and the bottom pa nels with 135° polarized light.
Horizontally polarized light was collected in the left panels, and vertically polarized light
was collected in the right panels. This figure illustrates that the observed two-photon
induced luminescence is polarized, as the area in the Ring A shows, and that emission
can be controlled by the incoming polarization, as shown by the area in Rings C and D.

74

5. CHARACTERIZATION OF ENERGY PROPAGATION
While the previous chapter discussed the characteristics of the emission
observed, this chapter takes the observation a step further and seeks to understand the
nature of the propagation of energy, as well as how the intensity of the luminescence
can be controlled. This information serves two purposes. First, it provides further
insight into the physics behind the observed phenomena.

Secondly, being able to

control the propagation and subsequent enhancement of the electromagnetic field is
critical for the development of future applications.
5.1. Further Discussion of Scattering
In the previous chapter, it was discussed that the spectral properties of the
samples were consistent with two-photon-induced luminescence, and not scattered
fundamental or SHG. Here, the comparison with scatter is explored further detail, with
an emphasis on the transport, as opposed to the emissive, properties.
In this experiment, a sample was alternately illuminated by the femtosecond
laser and a HeNe laser at 632 nm, which was configured to propagate collinearly
through the same optics, and thus focus at the same point. This wavelength is short
enough (<650 nm) that it is not blocked by the dichroic mirrors and filters that prevent
the observation of scattered light from the fs-laser, and allows characterization of the
behavior of such light in this sample.

75

Figure 5.1. Images of a single sample under different types of illumination. Panel A
shows a sample under white-light illumination. Panel B shows the same sample excited
at the crosshairs by a 13-fs Ti:sapphire laser, while Panel C shows the sample excited
at the crosshairs by a HeNe laser. The insets in Panels B and C show the total intensity
of all pixels with signal above the noise level as a function of distance from the focal
spot. It is clear that the behavior observed upon excitation with a fs-laser is not
consistent with the behavior of scatter observed upon excitation with a HeNe laser.
An image of the sample collected under white light illumination is shown in Figure
5.1A. The image shown in Figure 5.1B corresponds to the same sample shown in Panel
A when it is excited by ultrashort laser pulses focused down to 1 µm spot size located at
the cross-hairs, while the image shown in Panel C shows the sample when excited with
the 632 nm HeNe laser. The inset in each shows the total luminescence from the
sample as a function of distance from the excitation point, in 2 µm increments. It is
clear that the remote regions of luminescence observed upon excitation by the fs-laser
(B) are not consistent with the scattering behavior observed upon excitation with the
HeNe laser (C).
To further characterize the behavior of the emitted light, and compare what is
observed upon excitation with a fs-laser to the scatter observed upon excitation with a
HeNe laser, the intensity of 2 µm-wide cross-sections running horizontally and vertically
through the focal spot are plotted in Figure 5.2. From this figure, it is strikingly clear that

76

the behavior observed upon excitation with the fs-laser is not scatter.

The overall

spatial profile of the photoluminescence is much broader, with clearly discrete regions of
emission (shown by sharp spikes). When scatter is detected, no such discrete regions
are observed. Another significant observation is that the maximum intensity for the fslaser excited sample is not found immediately at the focal spot. This is consistent with
numerous observations, in which very strong emission at the focal spot correlated with a
lack of discrete regions of remote luminescence; i.e., strong emission at the focal spot is
indicative of poor energy transport, a phenomenon discussed in detail in Section 4.4.

77

Figure 5.2. Intensity profiles for a 2µm-wide section of data running horizontally (top)
and vertically (bottom) through the focal spot for a sample excited by a HeNe laser
(dashed line), and a fs-laser (solid line).

78

5.2. Autocorrelation
In order to investigate the nature of energy transport in these samples, the pulse
shaper (described in detail in Section 3.2.2) was programmed to produce a pair of
pulses and to scan the delay between them.

226,227

228-232

experiments have been reported in the literature,

Although similar types of
the experiments presented

here are different from those, as our excitation is in the near-IR, which then propagates,
and

the

measured

signal

corresponds

to

localized

two-photon-induced

photoluminescence and not to photoelectrons, as, for example, in Ref. 233.
Figure 5.3 shows the intensity of photoluminescence from individual regions of
the thin film as a function of time delay between the two pulses. Because the two
pulses are collinear, they interfere with each other. The top panel shows the signal
obtained from a frequency doubling crystal for reference.

The 2.67 fs oscillations

correspond to the optical period of the fundamental laser wavelength. A representative
image is shown at left, and the intensities of the three circled points, as a function of the
delay between pulses, are shown to the right.

79

Figure 5.3. Photoluminescence from several discrete regions is shown as a pulse
shaper is used to produce a pair of pulses and scan the delay between them. The top
panel shows the optical response of a frequency doubling crystal as a function of delay
between pulses. Panels A, B, and C show the optical response from different regions.
Some regions show broadening, as shown in region C. Others show wings (visible in
panel B), or erratic behavior, likely due to melting or other irreversible change to the
sample, as shown in panel A. The behaviors are independent of distance from the
excitation point, as well as the behavior of neighboring regions (compare regions A and
B, which are only separated by approximately 1 µm).
Of first note is that the period and overall shape of the photoluminescence from
the various regions, particularly region B, correspond well with the second-harmonic
signal, which is further evidence that the behavior observed is two-photon in nature.
Further insight can be gained by examining the behavior of each individual region. Over
the course of the autocorrelation, it has been observed that some regions will
spontaneously stop emitting. Of these, some will later be observed to emit with the
same properties observed before, in a blinking phenomenon. Others will remain “off.”
The behavior of those regions, and others that exhibit an irreversible change in
behavior, such as region A, are attributed to structural changes to the sample upon

80

174,177,178

irradiation, with melting of the sample

a likely cause. It is also significant to

note that adjacent regions, such as A and B, which are separated by approximately 1
µm, can exhibit very different behaviors.

In this case, region A exhibits an abrupt

change in intensity, while region B exhibits no such change. This indicates that the
regions respond independently to the laser used for illumination, and further indicate
that no sequential scattering is taking place.
Other behaviors are also observed in the optical response, including broadening
(region C) of the pulse, which indicates that quadratic dispersion has been acquired as
the SPP propagates.

Side-peaks, visible in the signal from region B and more

pronounced in other regions, suggest that cubic dispersion is also acquired by the
excitation pulse as it propagates to the regions where localized two-photon-induced
luminescence occurs.
Clearly, there are significant differences in the luminescent properties of different
regions of the sample while an autocorrelation is performed at the focus. While the
implications of some of these observations are not immediately clear, the observed
broadening and presence of side-peaks in the traces are consistent with the behavior
expected if the pulse experienced dispersion as it propagated through the sample. As
each region of photoluminescence results from energy traveling along a different path, it
would be expected to find evidence for pulse broadening due to dispersion (chirp).
Pulse broadening in our measurements indicate that the propagating SPP experiences
different amounts of dispersion as it travels to the region where it induces two-photon
photoluminescence, a concept we explore further below.

81

5.3. Dispersion
As a control strategy, a series of measurements using shaped laser pulses were
performed.
nonlinear
pulses.

The Dantus group has developed a number of strategies to control
optical

excitation

141,142,144,234,235

based

on

phase-shaped

femtosecond

laser

Here we explore the influence of phase-shaped pulses on

the intensity of the two-photon-induced luminescence from the silver.
5.3.1. Sensitivity to Phase: Sine Function
Figure 5.4 shows three wide-field images of a region (bottom panels) obtained
using different sinusoidal phase functions of the form 1.5π sin (12ω − δ) (top panels)
applied across the spectrum of a laser pulse that has been compensated for previously
-1

existing phase distortions by MIIPS. The frequency, ω, is in fs . In these images, only
the value of δ (in rad) is varied from panel to panel. It can be seen by the bottom
images that the intensity of emission of different regions is, indeed, sensitive to the
spectral phase applied to the pulse; see, for example, the three circled regions of
emission, each of which exhibit a maximum intensity under different phase conditions.

82

Figure 5.4. Phase control of remote emission. Each lower panel is a wide-field image of
the same region of the sample, with the focal spot at (0, 0). The phases (black line)
applied across the spectrum of the pulse are shown above each image. The circles
highlight regions of interest and are at the same position in each panel.
To further explore the spectral phase dependence of emission, the intensity of
individual regions of emission were plotted as a function of δ as it was scanned from 0
to 4π. The results for three different regions of emission are shown in Figure 5.5. As
suggested by Figure 5.4, the dependence of the intensity of emission on applied
spectral phase is different for different regions. However, not only do the locations of
the intensity maxima vary, but the overall profile of the intensity dependence on phase
varies as well.

83

Figure 5.5. Control of emission intensity by spectral phase. The dots in panels A, B
and C show the experimental intensity of the three labeled regions as a function of δ,
when the applied phase is 1.5π sin(12(ω-ω0) - δ). The solid line shows the simulated
second-harmonic generation intensity optimized to fit the data by adjusting the secondand third-order dispersion of the pulse.
Given the use of a sinusoidal phase function of the same form utilized in MIIPS, it
is not surprising to note that the intensity profiles resemble the integrated intensity of
MIIPS traces of uncompensated pulses, and further suggesting that the profiles could
be due to dispersion acquired by the SPP as it propagates through the sample. In order
to explore this idea, simulations of the integrated intensity of second-harmonic
generation as a function of sinusoidal phases of the form 1.5π sin(12(ω-ω0) - δ) were
performed, and shown in Figure 5.6. For an ideal pulse with no phase dispersion, the
SHG intensity results in four evenly spaced peaks of equal height, located at δ = π/2,
3π/2, etc. as the value of δ is scanned from 0 to 4π, very similar to the behavior shown
in region A in Figure 5.5.
The first hypothesis as to the source of the alternate behaviors of regions B and
C was that the effective carrier frequency, ω0, had changed, either by loss of the red or

84

blue component of the spectrum during propagation, or by varying absorption spectra in
the regions of emission. However, simulations show that a shift in ω0 results only in a
shift of the intensity profiles, with no change in spacing or relative peak heights, as
shown in Figure 5.6, top, in which the dotted line shows a simulation in which λ0 = 825
nm, instead of 800 nm. This is not consistent with the observed behaviors. A second
hypothesis is that the SPP acquires dispersions as it propagates, and that this
dispersion affects the phase-dependent behavior of the luminescence. As each region
of emission results from energy traveling along a different path, it would be expected
that different regions would reflect the acquisition of different dispersion (chirp). Panel B
2

shows the integrated intensity of simulated SHG spectra with 100 fs

of quadratic

3

dispersion (broken line) and 1000 fs of cubic dispersion (dashed line). It can be seen
that quadratic dispersion affects the spacing of the peaks, while cubic dispersion affects
the relative peak heights, and, less noticeably, peak spacing. If both quadratic and
cubic dispersions are present, arbitrary profiles of spacing and peak height are seen, as
shown in Panel C.
With this in mind, simulations of SH generated by a pulse with a sinusoidal phase
function and quadratic and cubic dispersion were fit to the raw data in Figure 5.5, and
2

the best-fits are shown as solid lines. It is found that region A experiences -70 fs
quadratic dispersion and -150 fs

3

2

cubic dispersion, region B experiences -150 fs

3

2

quadratic dispersion and +3500 fs cubic dispersion, and region C experiences +20 fs
3

quadratic dispersion and -3500 fs cubic dispersion.

85

The data shown in Figure 5.5 was collected over a period of several minutes,
necessitating low excitation powers to ensure the sample is not damaged. This low
excitation power, while permitting longer-term data collection, reduces the signal of the
2

detected emission, resulting in noisy data and introducing error, estimated at ±50 fs
3

and ±1000 fs for the data with the lowest signal-to-noise ratio, into the fits. However, it
is important to consider that there is no ambiguity as to the sign of the quadratic and
cubic dispersion.

That is, there is a clear difference in the shape of curves when
2

2

3

comparing, for example, +100 fs and -100 fs of quadratic dispersion and/or +5000 fs
3

and -5000 fs .

86

Figure 5.6. Simulations of the intensity of SH generation as a sinusoidal phase of the
form 1.5π sin(12(ω-ω0) - δ), is applied across the spectrum of the pulse.

87

Figure 5.6, con't.
In all panels, the solid line shows the intensity as the phase is applied to a TL pulse
with a carrier frequency, ω0, that corresponds to the carrier frequency, λ0=800 nm.
Panel A shows how the intensity profile changes with a shift in effective carrier
frequency; the dotted line shows the intensity if the carrier frequency corresponded to
λ0,eff = 825 nm. Panels B and C show the simulations of the intensity of SH generation
if the sinusoidal function is applied to a non-TL pulse. In panel B, the broken line
2
corresponds to a pulse with a dispersion of 100 fs , while the dashed line corresponds
3

to a pulse with a dispersion of 1000 fs . Note that the second order dispersion results
in unequal peak spacing, while third-order-dispersion results in unequal peak heights.
In panel C, the simulations show the intensity as the sinusoidal function is applied to a
2
3
pulse with both 100 fs and 1000 fs dispersion.

88

5.3.2. Quantifying Dispersion
To directly quantify the amount of quadratic and cubic dispersion acquired by the
pulse as it propagates, a grid of phase functions of the form

ϕ (φ'', φ''')=

½[ φ''(ω−ω0)2] + 1/6[φ'''(ω−ω0)3], where φ'' and φ''' are the quadratic and cubic
dispersions, is applied, and intensity of two-photon induced emission from discrete
regions on the sample recorded. Assuming that maximum emission from a particular
region occurs when the pulse is transform-limited (φ''=φ'''=0), the chirp introduced by the
waveguide can be directly determined: φ''w = -φ''max and φ'''w = -φ'''max.
To demonstrate and validate this approach, a control experiment was run in
which frequency integrated SHG emission spectra were collected as a function of
phase. First, the signal was collected as a function of phases applied to an otherwise
transform-limited pulse, and the integrated intensity plotted as a function of φ'' and φ'''.
As expected, the maximum intensity occurred when φ'' = 0 and φ''' = 0 (results not
shown).

This experiment was then repeated, with additional quadratic and cubic

dispersion (φ''add and φ'''add) values introduced to mimic the acquisition of chirp during
SPP propagation. Results are shown in Figure 5.7. In each case, as expected, the
maximum integrated intensity occurs when the applied phase is the negative of the
additional introduced phase, which is denoted by the cross in each panel.

89

Figure 5.7. SHG Intensity as a function of applied phase. The maximum SHG signal
occurs when the applied phase is exactly the negative of the introduced phase. The
cross in each panel denotes the expected maximum. Panel a: results when φ'' = +200
2
3
2
3
fs and φ''' = -2000 fs . Panel b: results when φ'' = -200 fs and φ''' = -2000 fs . Panel
2

3

c: results when φ'' = +200 fs and φ''' = +2000 fs . Panel d: results when φ'' = -200 fs

2

3

and φ''' = +2000 fs . In each panel, the cross-hairs denote the expected maximum
intensity.
Having validated the measurement method, similar experiments were then run on the
silver nanoparticle sample.

For each experiment, a collection of 441 images were

acquired, each one with values for φ'' and φ''' defined by the grid discussed above.

90

Figure 5.8 summarizes the results for these measurements, after tracking the phase
dependence of ~200 individual regions of localized emission, plotted as a 2-dimensional
histogram of the number of discrete regions of emission for which a given φ''w and φ'''w
value are determined.

91

To the top and right are histograms reflecting the total number of points with a given φ''w
2

3

and φ'''w, respectively. The bins correspond to the step size used (50 fs and 1000 fs ,
respectively), which was chosen based on the estimated experimental error. It is clear
that there is a wide range of both quadratic and cubic dispersions introduced by the
various surface plasmon waveguides, and that this range encompasses both positive
and negative values for each. The magnitude and sign of φ''w and φ'''w for any given
regions does not exhibit any dependence on the position of the region in the sample.
5.4. Conclusion
In this chapter, the properties of the energy transport in the silver samples was
explored. The two-photon-induced emission, which is observed over 40 µm from the
focal spot, is consistent with the reports of tens of micrometers range of propagation of
16,236

surface plasmons in metals on dielectric surfaces.

This supports the idea,

discussed in Section 2.2.4, that a surface covered by silver nanoparticles can behave
as a continuous thin metallic surface under certain conditions. The dynamics of SPP
transport on a dielectric surface partially covered by a very thin layer of
nanoparticles

87,237,238

and “islandized” metals

239-243

are extensively discussed in

literature, and there is also evidence that the presence of relatively large, irregular
clusters of nanoparticles is favorable for transition from a delocalized SPP mode to a
48,238,244

localized surface plasmon.

While the energy can be transported as either a

near-IR wave (~800 nm), or as a second-harmonic wave (~400 nm), the IR SPP wave

92

has been shown (as in Section 2.1.1) to have less attenuation than its corresponding
SH wave.

16,23,208,245,246

Therefore, it is proposed that silver nanoparticles with dimensions ~20-100 nm,
randomly arranged, with numerous interconnections and interparticle distances shorter
than the optical wavelength, deposited on a dielectric surface provide a medium for long
range surface plasmon propagation. Femtosecond laser pulses with a central
wavelength near 800 nm excite a surface plasmon resonance and launch a surface
plasmon polariton on the very thin but interconnected layer of nanoparticles. The SPP,
with a very long attenuation length, propagates from the excitation spot. The
combination of constructive interference and localized surface plasmon resonance
induces localized photoluminescence in the visible spectral range at distinct locations,
which are observed as bright spots at distances of several tens of microns from the
excitation point.

93

6. CONCLUSION
6.1. Comment on Reported Fluorescent Enhancement
As mentioned briefly in the introduction, this project began with an effort to use
thin films of silver nanoparticles to amplify the fluorescence from a dye-doped polymer
film. The enhancement of the intensity of emission by one to five orders of magnitude
1

1,5

has been reported for a variety of dyes, including Nile Blue,
2,4

Rhodamine 6G,

and others.

5-10

Rhodamine B,

This enhancement in signal has also been reported
4-7

for both solutions of dye with silver aggregates in the solution,
3

10

polymers, dye-doped polymers,

chromophoric

and neat dye deposited on non-continuous metallic

1,2,8-10

films.

However, when Melinda Ewald, an undergraduate in the research group, and I
performed an experiment to look for enhancement of fluorescence from a rhodamine
590-doped thin film of poly(vinyl alcohol) on a thin film of silver nanoparticles, we found
that the amplification observed for rhodamine-590 emission could be attributed directly
to the luminescence of the silver nanoparticle clusters themselves. That is, through
comparison of average peak intensity of a film of rhodamine-590, a film of silver
nanoparticle clusters, and a film of the two together, a simple addition of the signal from
the two former leads to the signal of the latter. Corresponding experiments done in
solution, where signal from silver nanoparticles, rhodamine 590, and a solution of both
was analyzed, yielded similar results: any increase in signal when comparing rhodamine
and rhodamine with silver nanoparticles could be attributed to luminescence directly
from the silver nanoparticles. Moreover, simply adding the emission spectra of the

94

individual rhodamine and silver nanoparticles together, with no scaling, results in a
spectrum more similar to that of the combined solution (of the same concentrations)
than simply scaling the R590 emission.
This suggests that literature in the field of metal-enhanced fluorescence (MEF)
needs to be viewed with a particularly critical eye, considering the substantial spectral
overlap between the emission spectra of commonly studied dyes, such as rhodamine
590 and rhodamine 6G, and the luminescence of silver. A survey of the literature
indicates many papers reporting metal-enhanced fluorescence fail to report a control
experiment in which it is shown that the luminescence of the silver nanoparticles is
negligible compared to the reported fluorescent enhancement. However, it is worth
noting the results of Lakowicz, et al.

199

who reported that metal-enhanced-

fluorescence is observed at powers ~1000 times lower than those that generate
luminescence from nanoparticles. This indicates that it is possible to strictly study MEF,
but that care must be taken to ensure that luminescence from the nanoparticles does
not affect the interpretation of the results.
6.2. Future Work
6.2.1. Gold
The surface plasmon properties of gold have been much more extensively
studied than those of silver, due to the relative ease of synthesizing monodisperse
solutions of nanoparticles of a well-defined size. Therefore, it may be interesting to
explore the phenomena associated with surface plasmons on silver structures
presented in this dissertation on gold.

95

In fact, preliminary studies (results not shown) were performed by Scott High, an
undergraduate in the research group, using gold nanoparticles synthesized by a citrate
41

reduction,

analogous to the synthesis of the silver nanoparticles that made up the bulk

of the work presented in this dissertation. However, while intense, local emission was
observed, remote emission was not.
There are several possible reasons for the lack of observed remote emission.
First, as mentioned in Section 2.1.1, the propagation length of surface plasmons in gold
is significantly smaller than that of silver.

However, with 800 nm excitation, the

propagation length is still potentially a detectable 10 µm. Another explanation is that the
density of particles on the substrate appeared to be much higher than most of the silver
samples; samples were nearly opaque. As discussed in Section 4.4.2, a correlation
between the observed density of particles and lack of remote emission has been
observed for silver. Other work has shown that the EM enhancement of two-photoninduced luminescence from rough gold surfaces is significantly lower than that of
184

silver,

193

and that colloid samples of Au

199

and Ag

show significant differences in

both the conditions required to observe luminescence and the luminescence, itself, as
well.

Any one, or a combination of these factors could explain the lack of remote

emission observed here. However, were the right synthetic approach and found and
matched to the right excitation conditions, it remains possible that similar results could
be observed.
6.2.2. Correlation of Propagation and Emission with Structure
The interpretation of the results presented in this dissertation has one very
significant limitation: the prepared structures were random in nature. Moreover, there

96

was not a way to map, at the nanoparticle level, the exact sample being irradiated. All
images, whether of laser-induced emission, AFM, SEM or TEM, are “typical” samples,
as far as the researchers know. However, to be able to map a sample, immediately
irradiate the same area, and then map it again would allow much insight into the physics
behind the behaviors observed. Changes in emission could be correlated with melting
or other changes in sample, and the conditions under which maximum remote emission
is observed could be further explored. A set-up that includes an AFM/NSOM coupled to
an inverted microscope could potentially be used for such explorations.
A related issue is that of monitoring the actual paths of plasmon propagation. A
247

potentially useful technique would be that presented by Ditlbacher et al.

In this

work, 1/100th of a monolayer of Rhodamine 6G is deposited over silver structures. The
metal-enhanced fluorescence from the dyes allows for optical imaging of the surface
plasmon fields.

A similar experiment performed on the samples here would allow

insight into the paths of propagation. However, it would be most useful in conjunction
with the inverted AFM/NSOM setup mentioned above, to observe what structural
features optimize propagation.
6.2.3. Synthesis of Well-Defined Structures
After studying the structural conditions that lead to the observations made here, it
would then be interesting to construct well-defined samples to explore how plasmon
propagation could be optimized. By working with well-defined samples, it could be
determined even more precisely what characteristics of the sample lead to the distant
propagation and subsequent localization. This would open up doors to being able to

97

design waveguides to allow control over which path the energy will take as it
propagates.
6.3. Potential Applications
2

This dissertation has shown results indicating that a laser focused to a 1 µm
4

2

region can cause controllable emission in localized regions around a 10 µm area.
This four orders-of-magnitude control achieved with phase-shaped and polarized pulses
may have great significance in the field of electronics, in which miniaturization of chips
is limited by the size of (and subsequent heat loss due to) the wires used to transport
electronic information.
One of the greatest potential applications of the work presented here is in the
development of plasmonic waveguides designed to bridge the realms of electronics and
photonics. The development of such waveguides will allow for controlled transport of
optical information in such a way that lowers the size barrier currently faced. While
work has been done to develop waveguides to control plasmon propagation, there has
been a consistent trade-off between control of the propagation (confinement) and the
distance over which propagation can occur. At one end of the spectrum is surface
plasmon propagation on infinite smooth surfaces, in which the propagation length of
surface plasmons on silver can be as great as 100 µm. However, the ability to localize
the energy is limited. At the other end of the spectrum are metal stripe waveguides,
with very short propagation lengths, but control over the localization.

Metal stripe

waveguides are also limited to a linear path. Chains of nanoparticles also allow for
control over the direction of propagation, and have been used to guide energy around

98

74

corners and split energy down two paths in a “tee” shape,

but are still limited by the

distance over which propagation can take place.
The work presented in this dissertation shows that structures exist that combine
the long propagation length of infinite surfaces with the localization existing for stripes
and nanoparticle chains. Moreover, it has been shown here that the localization can be
controlled via polarization and/or phase of the excitation laser. Particularly if extensive
characterization work were performed, it seems reasonable that structures could be
constructed, either though tightly controlled synthesis or more rigorous, artificial means,
that would allow for multiple, controlled paths to be mapped onto a single substrate. If
this were to be coupled with the work that has been done using metallic nanostructures
27

as beam splitters,

and mirrors,

27, 248

a truly all-optical chip could be produced.

6.4. Conclusion
This dissertation has presented studies on the nonlinear optical properties of
surface plasmons in films of silver nanoparticles. After presenting an overview of the
field in Chapter 1, Chapter 2 focused on the theoretical background behind surface
plasmons and their propagation as waves, as well as their ability, as a localized
resonance, to enhance the electromagnetic field and contribute to surface-enhanced
spectroscopies, while Chapter 3 outlined the experimental approach used in this
dissertation, with a detailed discussion of the MIIPS method for compensating for the
phase distortions inherent in ultrashort pulses.
After setting up the appropriate background, Chapters 4 and 5 outlined the
results obtained over the past several years, in which emission from a thin film of silver
nanoparticles is shown to exhibit discrete regions of localized emission more than 100

99

µm from the focal spot of an ultrafast laser. Chapter 4 focused on the characterization
of the observed emission, identifying it as two-photon-induced fluorescence from the
silver nanoparticles, with a broad, visible emission spectrum. Chapter 5 proceeded to
explore both the nature of the propagation of the surface plasmons, and how the
emission could be controlled. It was shown that polarization and spectral phase could
be used to modulate the relative intensities of regions of emission. This chapter has
concluded by discussing both future work that could extend from that presented in the
dissertation, as well as discuss the potential applications of the observations here in
plasmonics, where metallic structures capable of sustaining surface plasmons are used
to create waveguides, with the hope of further miniaturizing electronics.
The results reported in this dissertation are the result of work at the intersection
of multiple fields – most notably that of ultrafast lasers and surface plasmons -- where
little other experimental work has been done. These results are particularly intriguing as
the

literature

indicates

that

propagation,

luminescence from silver structures

194-202

15-20,62,63

45,47-51

localization,

and

have each been observed, but not

simultaneously, as reported here. It is interesting, therefore, to explore the reasons this
might be the case.
One reason these observations may not have been previously made is that little
research is being done using ultrafast lasers to study surface plasmons. Of the more
than 18,000 results returned by a search for “surface plasmon” on the Web of Science
database, only 316 included “ultrafast OR femtosecond,” and only a third of those
involved silver. Furthermore, many of those papers were concerned with the study of
individual nanoparticles, rather than films and extended structures. Of these systems, it

100

is unlikely that many would be using detection modalities that would capture wide-field
images. It is only once all the components are brought together that such fascinating
observations can be made.

101

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102

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