# Time-Resolved 2PPE and Time-Resolved PEEM as a Probe of LSP's in Silver Nanoparticles

Authors: D. Bayer; C. Wiemann; O. Gaier; M. Bauer; M. Aeschlimann
Journal: Journal of Nanomaterials
 (2008)

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## Abstract

The time-resolved two-photon photoemission technique (TR-2PPE) has been applied to study static and dynamic properties of localized surface plasmons (LSP) in silver nanoparticles. Laterally, integrated measurements show the difference between LSP excitation and nonresonant single electron-hole pair creation. Studies below the optical diffraction limit were performed with the detection method of time-resolved photoemission electron microscopy (TR-PEEM). This microscopy technique with a resolution down to 40 nm enables a systematic study of retardation effects across single nanoparticles. In addition, as will be shown in this paper, it is a highly sensitive sensor for coupling effects between nanoparticles.


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## Body

## 1. Introduction

The interaction of light with metal
nanoparticles has attracted considerable attention for many centuries. One of
the most impressive examples of their magic colourful properties is the
artistic adoption of the light scattering and absorption by small noble metal
particles in the church windows of Marc Chagall. In modern science, the optical
properties of nanostructures have raised to a topic of high interest for
fundamental physics as well as for technical applications. Silver and gold
nanoparticles with typical sizes of 5 nm to 150 nm can exhibit particularly
strong optical extinction in the visible spectral range due to resonantly
driven electron plasma oscillations, termed as localized surface plasmons
(LSP). The resonance energy of the LSP depends critically on the size and the shape
as well as on the material of particle and embedding environment [1–3]. This enables spectral tuning of the resonance, an
ability which is of considerable interest in the context of future electronic
and optical device applications. Due to the rapid advances in the fabrication
of small particles [4] and nanowires [5], their optical properties are now used in a wide
range of applications, including biosensors [6, 7], near field microscopy [8], and new optical devices [9–11]. Furthermore, since plasmons are associated with
large electromagnetic fields near the particle surface, they play an important
role in surface-enhanced Raman scattering (SERS) [12], second harmonic generation [13, 14], and multiphoton photoemission [15–19]. The limiting factor for applications is the energy
loss of the collective electron oscillation due to the damping of the LSP,
which is manifested in the plasmon decay time τp1 [20].The fundamental microscopic
mechanisms of collective electron excitations in small particles as well as
their decay are still far from being completely understood. As a pioneer in
this field, Gustav Mie developed a first theory based on Maxwell’s equations to
explain the optical properties of spherical nanoparticles. Mie’s theory easily
describes red shifts and the lifetime broadening of the dipole plasmon
resonance as the particle size is increased. It also explains the appearance of
resonance contributions of higher multipolar order [1]. However, this theory is strictly valid only for single
particles with a spherical geometry. Therefore, during the last decades, lots
of theoretical studies focused on the properties of LSP in nanostructures of different
shapes in order to gain insight, for example, into their optical response, the field
distribution of the resonant modes as well as relevant decay channels, and the coupling
between neighbouring particles [21–23].A simple oscillator model
describing the interaction of a light field and a nanoparticle can be discussed
as follows [24]. The light field couples occupied and unoccupied single
electron states which are separated by the photon energy hυ. The induced polarizations
of these different, coherently coupled transitions superpose to a macroscopic
polarization which represents the collective response of the electronic system.
This induced polarization field adds to the incident light field and causes a
modification of the particle internal field (Figure 1). The relation between
internal field and light field is described by the frequency-dependent field enhancement
factor f(ω) [15]. Figure 2 displays the phase shift ϕ(ω) of the induced polarization field with respect to the light field and
the amplitude of the field enhancement factor f(ω). For frequencies below the evident
resonance peak, the internal field is small because the π-shifted polarization field adds destructively to the light field. While
passing the resonance frequency, the polarization response undergoes a phase
shift by π. The extraordinary field enhancement at λp1 (corresponding
to the LSP resonance) is determined by the resonant response of the electron
collective to the light field adding up to an extremely large polarization
field. Finally, in the short wavelength regime, the amplitude of the
polarization field decreases as now the electron collective is too inert to
follow the oscillating light field.Figure 1
Influence of a LSP
resonance on the amplitude and duration of the laser pulse.Figure 2
The solid line shows the
field enhancementf(ω) of a silver nanoparticle in respect to the wavelength of
the exciting light; the dashed line represents the phase relation Φ(ω) of the
polarization field in respect to the exciting light.The damping of the plasmon
excitation is basically governed by two different decay channels (see Figure3).
First, the plasmon energy can be returned coherently to the external radiation
field (radiation damping), as the oscillating polarization field must emit
electromagnetic radiation. Within the optical far field theory, this decay
channel corresponds to the elastic scattering of the incident exciting light. The
signals exploited by pure optical far field detection techniques, such as
second harmonic generation [13, 14] and extinction spectroscopy [25], are due to the coupling to this radiation damping channel.Figure 3
Damping mechanisms of a
localised surface plasmon [26].Furthermore, the decay of
a plasmon is possible by the creation of electron-hole pairs and a subsequent transfer
of energy to the internal degrees of freedom inside the particles (internal
damping). This process results in a complete loss of coherence to the exciting
light field. In the far field, this damping channel is recognized as absorption.
The involvement of single electron excitations in this process suggests that
also electron emission techniques such as photoemission may be useful as probes
for plasmonic properties. In this paper, we demonstrate that particularly two-photon
photoemission (2PPE) is highly sensitive to plasmon excitations in metallic
nanoparticles. A striking example is the study of particle shape
characteristics of the plasmon damping in elliptical nanoparticles as probed by
means of the time-resolved 2PPE. Furthermore, we show that 2PPE in combination
with the photoemission electron microscopy technique (PEEM) allows to map local
near field variations associated with plasmonic excitations with subdiffraction
(<40 nm) resolution. In contrast to Cinchetti et al. [27] who first
investigated LSP excitation in special moon-like tapered silver nanoparticles
(around 400 nm) on silicon, we concentrate on arrays of smaller particles of different
shape. Observed effects that will be discussed are the field retardation in
large nanoparticles and the plasmon-governed coupling of neighbouring
nanoparticles.


## 2. Experimental

Figure4 shows the basic scheme of
the time-resolved two-photon photoemission technique applied to a metal surface
[28]. A first ultrashort laser pulse (pump) in interaction with the electronic
subsystem at a given time t0 populates an intermediate excited electron
state EI below the vacuum level. A second laser pulse (probe) incident
at the time t1 couples this excited state population to a detection
state above the vacuum level, where it is addressed by an electron-sensitive detector
such as an electron energy analyzer or a photoemission electron microscope. A
successive and controlled increment of the time delay between both pulses
enable to record the time-evolution of the depopulation of the intermediate
state. For the electron gas of a metal, the depopulation is governed by inelastic
electron-electron scattering processes and is characterized by the inelastic
lifetime τee.Figure 4
Scheme of a 2PPE excitation
process.A
typical experimental time-resolved 2PPE trace as a function of the time delay
between cross-polarized pump and probe pulses is shown in Figure5. The shape
of this cross-correlation trace is a convolution of the two laser pulses and the
exponential decay of the probed intermediate state EI determined by
the inelastic lifetime τee. A deconvolution of τee can be
performed by a fit of simulated correlation traces to this data set. For bulk
electron excitations, these simulations are performed within a rate equation
model which corresponds to the solution of the Liouville-von Neumann equations
of a three level system within the density matrix formalism in the limit of
rapid dephasing [29–31]. For qualitative statements on τee and
for comparing studies, it is, however, often sufficient to analyse the
broadening (Δ FWHM) of the cross-correlation trace, which increases linearly
with the life times of the intermediate state τee (Δ FWHM ≈a*τee;a∼1.13).Figure 5
Typical 2PPE
cross-correlation trace.So far, only single
electron states have been considered for the description of the 2PPE process.
In the following, we will discuss to what extent the 2PPE process is also
sensitive to the collective electron excitations in nanoparticles (LSP).2PPE is a second-order process and,
therefore, the measured electron yield is proportional to the fourth power of
the electric field (j2PPE(r→)∝|E→int4|) acting on the electrons. In the case of plasmon resonant
excitation of a nanosized particle, this (particle internal) field is
determined by the local field enhancement f(ω) as governed by the properties of
the LSP. It is this relation which makes the two-photon photoemission a
versatile tool in the investigation of plasmonic excitations. Later, we will
see that besides a high field enhancement, an efficient transfer of energy from
the LSP resonance to the single electron excitation spectrum is a necessary
condition to generate a high-photoemission signal.The participation of the plasmon
excitation in the 2PPE process has also direct consequences for the shape of
the cross-correlation trace obtained from the time-resolved experiments. Next
toτee, the
inelastic lifetime of single electron excitation, also the LSP-lifetime τLSP has to
be considered for a correct deconvolution. A correct quantitative deconvolution
of these two quantities from the cross-correlation trace is a rather complex
task as has been shown, for instance, in reference [24]. However, as we will see in the following, a clever
use of the different experimental degrees of freedom will already enable
interesting qualitative statements about LSP and single electron dynamics, again
by considering the FWHM of the cross-correlation only.The
setup of the time-resolved 2PPE experiments used for our studies is shown in Figure6. Pump and probe laser pulses are delivered from the frequency-doubled output (photon
energy of 3.1 eV) of a femtosecond Ti: Sapphire laser system (repetition
frequency 80 MHz, temporal pulse width 20 femtoseconds). A Mach-Zehnder
interferometer allows to adjust the difference in optical pathway between pump and
probe pulse with an accuracy of better than 100 nm corresponding to a timing
accuracy of <0.3 femtosecond. The collinear pulse pair is then focussed onto
the sample surface and excites the electrons in a 2PPE process which are
subsequently detected by a suitable detection unit.Figure 6
Setup for the time-resolved 2PPE
experiment: a femtosecond laser system and a UHV-chamber equipped with a
photoemission electron microscope.For our studies, two different types
of electron detectors have been used. Spectroscopic measurements have been
performed with a
cylindrical sector electron energy analyzer (Focus
CSA 200) with an energy resolution of better than 100 meV. For the plasmonic
systems under consideration, it enables us to investigate the energy dependence
of electron-hole pair excitation subsequent to a LSP decay. However, this
detector does not provide any spatial resolution.The second detector used for our
studies is an electrostatic photoemission electron microscope (Focus IS-PEEM),
which is described in detail elsewhere [32, 33]. The lateral resolution of this
instrument is better than 40 nm and enables us to focus even on a single nanoparticle. For this experiment, a mercury vapour UV
source (high energy cutoff 4.9 eV) is available in addition to the femtosecond
laser. It allows imaging of the surface by linear photoemission near the work function
threshold which is located at about 4.5 eV photon energy for silver.The investigated samples
have been prepared by electron beam lithography in a lift-off process. This
technique enables a controlled and flexible design of metal nanoparticles. The
shape and size of the particles used in our studies were tuned such that their LSP
resonance frequencies match the experimental setup conditions of the laser
system. Figure7 shows SEM images of the different silver nanostructures
deposited on ITO-covered glass substrates as they are used in this study. The dimensions
of the elliptical-shaped silver nanoparticles in Figure 7(a) are 140 nm (long
axis), 60 nm (short axis), and 50 nm (height). They constitute a versatile sample
for the investigation of the dependence of the LSP lifetime in respect to
resonant or off-resonant excitation. The silver nanodot array (Figure 7(b) diameter:
200 nm, height: 50 nm) as well as the silver nanowire array (Figure
7(c) length: 1.6 μm, width: 60 nm, and height: 50 nm) will be used in the time-resolved
PEEM experiments to map retardation effects associated with a plasmon
excitation at a nanometer resolution. Studies of the plasmon-induced
particle-particle coupling are possible with nanodot pairs of varying centre-to-centre
spacing. Figure 7(d) shows an example of 50 nm dimers (height: 40 nm) at an
interparticle spacing of 130 nm (grating constant: 740 nm).Scanning electon microscope
image of the used nanoparicle arrays: (a) elliptical silver nanoparticles (long
axis: 140 nm, short axis: 60 nm, and height: 50 nm), (b) silver nanodots
(diameter: 200 nm, height: 50 nm), (c) silver nanowires (length: 1.6μm, width:
60 nm, and height: 50 nm), and (d) silver nanodot pairs (diameter: 50 nm,
height: 40 nm, interparticle spacing: 130 nm, and grating constant: 740 nm).
(a)(b)(c)(d)


## 3. Results and Discussion

Figure8 shows measured (black line)
and calculated extinction spectra of the array of elliptically-shaped silver
nanoparticles (Figure 7(a)). The experiments were performed at normal light
incidence using unpolarized light. The calculations are based on a numerical
model described in [34]. We identify three different resonances at 431 nm, 450 nm,
and 795 nm corresponding to plasmon excitations along the z-axis, the in-plane
short axis, and the in-plane long axis, respectively (see Figure 8 for
details). However, the experimental configuration (perpendicular light
incidence) allows a coupling to the in-plane resonances, only. The resonance
energies of these two modes are almost perfectly reproduced by the
calculations, whereas the broadening of the resonances is somewhat underestimated.
This indicates the presence of damping mechanisms in the nanoparticles which
are not taken into account in the simulation, for example, the interaction between
particle and substrate and an enhanced internal damping due to a finite defect
density in the particle itself [16].Measured and
calculated extinction spectra of the investigated array of elliptical
nanoparticles (see Figure7).
(a)(b)The 400 nm laser-light used for the TR-2PPE
experiment couples almost resonantly to the in-plane short-axis mode of the
particle. In contrast, far off-resonant conditions are given for the case of an
excitation of the long-axis mode. At perpendicular incidence of the laser light,
a rotation of the polarization vector of the light enables to switch between this
resonant and off-resonant excitation conditions. An off-resonant excitation is possible
for a polarization vector (electric field) oriented along the long axis since
the resonance is at 795 nm, resonant excitation is possible for an orientation
along the in-plane short axis.The difference between off-resonant
and resonant excitation becomes evident from the polarization dependence of the
photoemission current which is a sensitive probe of the field enhancement as
discussed above. The black line in Figure9 shows the measured 2PPE yield as a
function of the polarization angle of the incident laser light. We observe a
clear variation in the yield, where the yield maxima and minima correspond to
orientations of the electric field vector along the short and long axis,
respectively. The same periodicity is observed if time-resolved 2PPE data are
considered. The red line in Figure 9 displays the variation of the FWHM of the
cross-correlation traces as obtained from sech2 fits as function of
polarization angle. As discussed above, differences in the FWHM of the
correlation trace are an indirect measure for the lifetime of the LSP. For resonant
(short-axis) excitation, we measure a maximum in the LSP lifetime, for complete
off-resonant excitation, the LSP lifetime is minimum. Interestingly, the
variations of yield and FWHM with polarization angle show a fixed phase shift
of about 30°. This observation indicates that the excitation conditions
resulting in the highest photoemission yield do not coincide with conditions resulting
in the maximum LSP lifetimes. The reason for this unexpected mismatch is not
clear, yet.Figure 9
TR-2PPE measurement of the 2D
nanoparticle array with perpendicular light incidence showing the 2PPE count
rate and the FWHM of the corresponding cross-correlation trace with respect to
the polarization angle (in respect to the direction of the long axis).TR-2PPE experiments at varying
intermediate state energiesE‐EF of the single electron excitations allow
to highlight the different origins of τee and τLSP. For
metals, τee exhibits a characteristic energy dependence as has been shown in the past in
several theoretical and experimental works [24, 35–37]. As an example, Figure 10(b) shows lifetime results
obtained in the TR-2PPE of single electron excitations in a polycrystalline
silver sample. τee increases monotonously as the intermediate state energy decreases. In contrast,
the lifetime of the plasmon τLSP should
be independent of (E‐EF). Figure 10(a) shows the FWHM of the cross-correlation
curves at varying intermediate state energies (E‐EF) measured for the
elliptical nanoparticles under resonant and off-resonant conditions. Both
curves exhibit an energy dependence characteristic for the single electron
decay τee in
silver. At the same time, the resonant
and off-resonant curves keep a constant displacement along the abscissa (time
axis) representing the energy-independent broadening caused by the LSP decay.
The offset is about 3 femtoseconds and is of the same order of magnitude as the
plasmon decay time determined from line width analysis of the optical extinction
spectrum (1/Γ≈2 femtoseconds).(a) Measured FWHM on a 2D
silver nanoparticle array of elliptically-shaped particles (right); (b) inelastic
lifetimeτee of excited electrons measured on a polycrystalline
silver. bulk crystal.
(a)(b)In order to study local
variations in the electron dynamics on nanometer scales, a technique capable of
a high lateral resolution is required, such as photoemission electron
microscopy. In combining the high temporal resolution of the time-resolved 2PPE
technique and the high lateral resolution of the PEEM, we succeeded to map
local variations in the LSP dynamics even within a single nanoparticle. Figures11(a) and 11(b) show PEEM images of a 2D array of silver nanodots (diameter:
200 nm, height: 50 nm, and grating constant: 650 nm) recorded with a mercury
vapour lamp in 1PPE and the second harmonic of the laser in 2PPE, respectively.PEEM images of the investigated silver
nanodot array (diameter: 200 nm, height: 50 nm, and grating constant: 650 nm): (a)
the PEEM image is taken with the mercury vapour lamp (4.9 eV); (b) 2P-PEEM image
of the same sample excited with a photon energy of 3.1 eV; (c) corresponding
lifetime map.
(a)(b)(c)The homogeneous response of the
nanoparticle array to the UV excitation as visible in Figure11(a) is a clear evidence for the
accurate lithography process. In contrast, the 2P-PEEM image (Figure 11(b)) exhibits
a distinct brightness variation among the particles pointing in the first
instance to considerable variations in the LSP excitation conditions. However, a
detailed analysis of the data and the comparison of images taken at different
excitation wavelengths show that these inhomogeneities are caused by the internal
defect structure of the different particles rather then differences in the
collective electron response [16]. For further information about the fundamental behaviour
of the LSP, we plan to perform energy resolved measurements as, for example,
done by Cinchetti et al. by combining the time of flight technique with PEEM [38].Figure11(c) shows the result from a
time-resolved PEEM scan of the identical area of the sample. In this depiction,
the colour-coded FWHM-value of the cross-correlation trace of every image pixel
is plotted as a measure for the local femtosecond dynamics. This lifetime map
allows in an intuitive way for the identification of local variations in the
ultrafast response between the particles as well as within a single particle
itself. The quantitative analysis of a selected particle out of the array is
displayed in Figure 12.(a) 2PPE yield and FWHM
(calculated with asech2 fit) across a single particle; (b) correlation traces at three different points at the
right edge of the particle with a time constant fitted to the exponential
decay.
(a)(b)The open squares correspond to the measured
FWHM of the TR-2PPE correlation curve along a section through the centre of the
particle. As a guide to the eye, the corresponding 2PPE yield is plotted, roughly
reproducing the particle profile. Surprisingly, FWHM-trace and profile do not
match each other; the FWHM-trace is shifted to the left in respect to the 2PPE yield
trace. It seems as if the LSP lifetime varies considerably across the particle.
This view is confirmed by the data plotted in Figure12(b). Here, sections of
three cross-correlation traces from the particle are displayed together with an
exponential fit on a logarithmic scale. For reference, the corresponding
locations within the particle are shown in the inset. Quantitatively, we find
in this area a systematic local variation in the ultrafast electron dynamics of
more than 10 femtoseconds. This observation is against the intuition that the LSP
as a collective excitation of the electron gas is a global and characteristic property
of the entire nanoparticle. In locally probing, the LSP excitation with the
external field, however, we create a situation of laterally varying
interference conditions between external an internal fields, quite similar to
the explanation given by Meyer zu Heringdorf et al. [39] for the observation of
stationary emission maxima along self-assembled nanowires. In their study, they
image silver wires of varying length by 2PPE induced by the second harmonic of
a Ti : Sa oscillator in PEEM using a setup very similar to our experiment. In the
PEEM images, emission maxima occur along the wire whose positions do not change
with wire length. The authors explain the occurrence as well as the position of
the emission maxima by taking into account interference between a surface
plasmon wave inside the wire with the external light field which is incident at
an oblique angle of 74° with respect to the surface normal. Since the surface
plasmon wave inside the wire propagates at a lower velocity than the light
field, the phase between the two fields changes along the wire, forming a
stationary beating pattern of alternating constructive and destructive
interference. In our case, the situation is similar to that extent that we
observe photoemission from local fields which result from the superposition of
the external light field and the polarization field within the nanoparticle.
Since the particles are much smaller than the wires discussed above, we do not
see a considerable variation in the photoemission yield, since the second
emission maximum occurs only about 2.5 μm away, which is already far outside the
particle. What we do observe, however, are traces of a locally varying phase
between light and plasmon fields. At very high temporal resolution, one finds a
lateral variation of the fringe patterns in phase-resolved 2PPE correlation traces
which clearly show the varying phase difference between the two fields across
the particle [17]. The data presented here was collected with a less elaborate
setup which is not capable of resolving the fringe patterns. However, the
overall shape of the phase-averaged correlation traces is influenced by the
varying phase between light and plasmon field and changes systematically across
the particle, which in turn results in a systematic variation of the best-fit
sech2 FWHM parameter.
The colour-coded display of the FWHM in the rightmost image of Figure 11 shows
that it is indeed a systematic effect, since each of the imaged nanoparticles
shows a distinct red-blue contrast from left to right. To put it differently,
what we observe here is a result of electromagnetic retardation. Since the
particles are not far smaller than the wavelength of the exciting light (in
fact, they are about half a wavelength wide), not every position inside the
particle is excited with the same phase.Such retardation effects are
expected to be even more pronounced for structures elongated along the
direction of incidence of the laser light, as was already shown in the
abovementioned study by Meyer zu Heringdorf. [39]. Figure 13 shows 1P-PEEM
and a 2P-PEEM images and a corresponding lifetime map of the nanowire array introduced
in Figure 13(c).Figure 13
PEEM images
of the investigated silver nanowires with a length of 1.6μm: (a) 1P-PEEM image
taken with the mercury vapour lamp; (b) 2P-PEEM image excited with a
femtosecond laser; and (c) corresponding TR-PEEM lifetime map.The nanowires as mapped in the 1P-PEEM
image show clear internal intensity variations indicating a structural inhomogeneity
of the nanowires. Also, the 2PPE image shows distinct brightness variations
along the wires. Note that for the 2PPE measurements, the nanowires have been
aligned perpendicular to the direction of incidence of the exciting light. Strikingly,
the endings of the wires always exhibit the highest photoemission yield. In
addition, most of the wires show three further emission maxima. Local
variations are also reproduced by the lifetime map of the nanowire array (Figure13(c)). The FWHMs of the cross-correlation traces vary along the wire on a scale
of about 100 nm, a value which corresponds roughly to the width of the wires. Perpendicular
to the long wire axis, the FWHM variations are very similar to those observed for
the nanodot array in Figure 11. We conclude that the present sample does not actually
consist of homogeneous nanowires. Instead, during the preparation process, the
wires obviously decomposed into conglomerates of small silver particles. The
brightness variations originate from LSP excitations in the individual small
islands as well as variations in the defect density along the wire. This result
is in good agreement with the findings in Kubo et al. [40] and Chelaru et al. [41].
In this context, the observed FWHM characteristics can be interpreted in terms
of the model introduced before. These findings are corroborated by SNOM measurements
of Ditlbacher et al. [42], who could show that propagating modes leading to
standing waves patterns are only supported in single crystalline nanowires.Finally, we would like
to discuss the coherent coupling of LSP modes excited in two neighbouring
particles by the same external laser field. The local interference conditions determining
this coupling depend on the relative phase of the contributing LSP fields and,
hence, on the interparticle distance and the angle of light incidence. Here, we
investigate how secondary fields from neighbouring particles in an array of
particle dimers modulate the local 2PPE signal. Figure14 shows 1P-PEEM (Figure 14(a)) and 2P-PEEM (Figure 14(b)) images of silver
particle pairs (diameter: 50 nm, height: 40 nm, and grating constant: 740 nm)
with a centre-to-centre distance of 130 nm. The 2PPE data were collected under
resonance conditions with respect to the particle LSP at a photon energy of
3.1 eV (400 nm, p-polarized light along the dimer axis).PEEM images of a silver particle pair array (diameter: 50 nm, height:
40 nm,  and grating constant: 740 nm)
with a centre-to-centre distance of 130 nm: (a) 1P-PEEM image taken at a photon
energy of 4.9 eV; (b) 2P-PEEM image taken at a photon energy of 3.1 eV
(p-polarised light, light coming from the right).
(a)(b)In the 1P-PEEM image, the individual
particles are clearly resolved. For the 2P-PEEM image, we observe again a
random local variation of the photoemission signal as observed before for the
nanodot sample. We assign these inhomogeneities to particle variations in the defect
density (Figure11(b)). To be still able to deduce the systematic local
variations arising from the particle-particle coupling, we performed a
statistical analysis of the photoemission yield from the particle dimers. The average
brightness values in a 7×7 pixel region of interest centred on the left and on
the right particle within each pair is extracted from the image. In a further
step, we calculate the relative count rate difference between left and right particle ΔIrel=(I¯r−I¯l)/I¯l.
Figure 15(a) shows the frequency distribution of ΔIrel as of the sample
area.(a) Distribution of the relative
count rate difference between two neighbouring particles with a distance of 130 nm (left); (b) dependence of the relative count rate difference with respect to
the distance in between the particle pair.
(a)(b)A positive value ofΔIrel corresponds to the situation that the right particle is
brighter than the left particle. The histogram gives evidence that in average,
the right particle which is located towards the direction of light incidence shows
a 28% yield enhancement in comparison to the left particle. Calculations based
on a dipole model can qualitatively reproduce this observation. Further, measurements
have been conducted for particle dimers at varying intrapair distances between 100 nm and 140 nm (Figure 15). For all particle pairs, we observe an asymmetry in
the photoemission yield exhibiting a positive ΔI value. However, as function of
the particle distance, we also observe a monotonous variation in ΔI with a
local flat maximum at about 120 nm. In general, for excitation at a fixed
wavelength (λ=400 nm), a periodic distance dependence is expected, since the
conditions for constructive and destructive interference of the particle fields
at the location of the right particle will change alternately  with increasing distance. The periodicity
should be of the order of the wavelength. At sufficient large distances, the differences
in the particle yields should disappear due to the decrease of the particle field
strength with distance. The experimental data shown in Figure 15(b) display a
section out of the periodic coupling modulation close to an oscillation
maximum. It is noteworthy that this coupling effect could be mapped on the
basis of a statistical analysis of the particle array. This approach delivers
obviously very reproducible and significant results, even though the photoemission
signal is considerably blurred by sample inhomogeneities. The 2PPE yield
analysis gives direct evidence for the dipole-induced coupling between
neighbouring particles.


## 4. Conclusions

Time-resolved 2PPE is a
well-established method to investigate the relaxation dynamics of optically
excited electrons. In contrast to pure optical methods, the 2PPE directly
addresses the electronic system and is therefore well suited to investigate the
complex interplay between collective and single electron excitations on a
microscopic level. Using special elliptically-shaped nanoparticles switching
between resonant and off-resonant excitation conditions is possible by rotating
the polarization vector of the perpendicular incident light. The presented laterally
integrated time-resolved 2PPE results allow extracting the lifetime of
collective electron oscillation. The results presented in this context confirm the
model developed by Merschdorf et al. [24], which treats the plasmon resonance as a
modification of the internal electric field with respect to amplitude, phase,
and temporal structure.The combination of TR-2PPE and a
photoemission electron microscope permits a spatial resolution much below the
optical diffraction limit as well as a femtosecond time-resolution. The direct
imaging gives access to the spatiotemporal dynamics of the plasmon resonance-enhanced
electric fields in and around metal nanostructures. In comparison to other
microscopy techniques such as SNOM, the PEEM lacks the need to scan the sample
surface, enabling a parallel data acquisition. The presented data underlines the
possibilities of TR-PEEM in visualising the ultrafast dynamics of energy flow
through nanoscopic devices. Investigations of the near fields around single
particles, nanowires, and particle pairs were discussed. In the case of large
single particles, direct observation of the phase propagation of a plasmon mode
through an extended nanoparticle was demonstrated. In polycrystalline
nanowires, the method was used to identify the observed patterning caused by
structural defects. Finally, a LSP field energy distribution influenced by the
coupling in particle pair structures with a centre-to-centre distance of 130 nm
was demonstrated. This shows the possibilities of channelling light through
resonant metallic nanostructures into areas well below the diffraction limit.
In conclusion, we would like to stress that TR-PEEM as characterization tool
for the metal nanostructures shows the potential to become a key technique in
the field of nano-optics.



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*Source: 249514-2008-09-28.xml*