Linear and nonlinear optical response of silver nanoprisms: Local electric fields of dipole and quadrupole plasmon resonances

Article abstract of DOI:10.1021/jp048193q

By means of femtosecond pump and probe spectroscopy, linear and nonlinear optical properties of silver nanoprisms have been investigated, focusing on enhancement of local electric fields due to dipole and quadrupole surface plasmons. Ag nanoprsims were prepared by direct reduction of AgNO₃ by the solvent N,N-dimetnylformamide in the presence of poly(vinylpyrrolidone). The average edge length and thickness of the nanoprisms (triangles and truncated triangles) were 67 and 35 nm, respectively. In the absorption spectra, dipole and quadrupole plasmon resonance bands have been observed. The values of the imaginary part of nonlinear susceptibility Im??⁽³⁾ measured at the dipole and quadrupole plasmon bands are -5.7 ?? 10^-15 and -3.0 ?? 10^-15 esu, respectively. The local electric field factors f_Q and f_D of quadrupole and dipole plasmon resonances were obtained from the observed dispersion curve of Im??⁽³⁾ and absorption spectra, yielding a ratio f_Q/f_D of a??0.7. The nonlinear response times of both resonances were found to be a??2 ps, which is close to the value for spherical nanoparticles, indicating that the relaxation process via electron-phonon interaction is governed by bulk crystal properties.

Full text of DOI:10.1021/jp048193q

© Copyright 2004 by the American Chemical Society
VOLUME 108, NUMBER 26, JULY 1, 2004
LETTERS
Linear and Nonlinear Optical Response of Silver Nanoprisms: Local Electric Fields of
Dipole and Quadrupole Plasmon Resonances
Noriyuki Okada,† Yasushi Hamanaka,†,‡ Arao Nakamura,*,†,‡ Isabel Pastoriza-Santos,§ and
Luis M. Liz-Marza´n*,§
Department of Applied Physics, Nagoya UniVersity, Chikusa-ku, Nagoya 464-8603, Japan, Core Research for
EVolutional Science and Technology (CREST), Japan Science and Technology Agency, Shibuya-ku,
Tokyo 150-0002, Japan, and Departamento de Qu´ımica F´ısica, UniVersidade de Vigo, 36200 Vigo, Spain
ReceiVed: April 26, 2004; In Final Form: May 20, 2004
By means of femtosecond pump and probe spectroscopy, linear and nonlinear optical properties of silver
nanoprisms have been investigated, focusing on enhancement of local electric fields due to dipole and
quadrupole surface plasmons. Ag nanoprsims were prepared by direct reduction of AgNO3 by the solvent
N,N-dimethylformamide in the presence of poly(vinylpyrrolidone). The average edge length and thickness of
the nanoprisms (triangles and truncated triangles) were 67 and 35 nm, respectively. In the absorption spectra,
dipole and quadrupole plasmon resonance bands have been observed. The values of the imaginary part of
nonlinear susceptibility Imø(3) measured at the dipole and quadrupole plasmon bands are -5.7 × 10-15 and
-3.0 × 10-15 esu, respectively. The local electric field factors fQ and fD of quadrupole and dipole plasmon
resonances were obtained from the observed dispersion curve of Imø(3) and absorption spectra, yielding a
ratio fQ /fD of ∼0.7. The nonlinear response times of both resonances were found to be ∼2 ps, which is close
to the value for spherical nanoparticles, indicating that the relaxation process via electron-phonon interaction
is governed by bulk crystal properties.
Introduction
have developed a photoinduced method for converting large
quantities of silver nanospheres into nanoprisms, showing a
change in color during progression of the conversion process.14
Recently, we have reported a novel procedure for the synthesis
of anisotropic Ag nanoparticles based on the use of N,N-
dimethylformamide (DMF) as a solvent and as a reducing
agent, in the presence of the polymer poly(vinylpyrrolidone)
(PVP).12,15
In the case of spherical nanoparticles embedded in dielectric
materials, the Mie scattering theory has succeeded to describe
extinction spectra in the visible region, including the surface
plasmon resonance of dipole modes, which result in strong
attenuation of incident light.21 The linear optical properties of
nanospheres in a nonabsorbing medium can be quantitatively
predicted by effective medium theories. In particular, the
Optical properties of metal nanoparticles have been of great
interest for a long time, not only because of the beautiful colors
of stained glass1 but also because of other aspects as materials
properties with applications for instance in photocatalysis2 and
in linear and nonlinear optical devices.3-7 Recent technologies
as diverse as e-beam lithography and wet chemistry have
enabled the fabrication of nanoparticles with controlled shape
and size, but particularly rods8-13 and triangles,14-17 as well as
spherical nanoparticles18-20 with well-defined sizes. Jin et al.
* Corresponding authors.
† Nagoya University.
‡ CREST, Japan Science and Technology Agency.
§ Universidade de Vigo.
10.1021/jp048193q CCC: $27.50 © 2004 American Chemical Society
Published on Web 06/02/2004

8752 J. Phys. Chem. B, Vol. 108, No. 26, 2004
Letters
Maxwell-Garnett theory has been successfully applied to the
calculation of nonlinear optical properties as well as the linear
optical properties.3,5,22,23 The surface plasmon resonance leads
to large local electric fields, and such local fields result in
enhancement of absorption coefficients and third-order nonlinear
susceptibilities ø(3) at the resonance frequency. The observed
enhancement of ø(3) as large as 10-7 esu around the surface
plasmon resonance is well interpreted in terms of the local field
effect.5,6,24,25
Recently, a considerable effort has been devoted to derive a
theoretical interpretation of the linear optical response of
nonspherical nanoparticles in which higher surface plasmon
modes such as a quadrupole mode appear. Extinction spectra
of perfect or truncated triangular Ag nanoprisms were numeri-
cally calculated using a discrete dipole approximation.14,26 The
extinction spectra show dipole and quadrupole plasmon reso-
nances for both in-plane and out-of-plane polarizations. Surface
plasmon resonances of Ag nanowires with a nonregular cross
section have also been calculated by Kottmann et al.27 Theoreti-
cal studies showed a dramatic localized enhancement of local
electric fields at surface plasmon resonances in nonspherical
nanoparticles. These local fields play a key role in nonlinear
optical response, as well as surface enhanced Raman scattering.
Experimentally, however, enhancement of ø(3) due to the
quadrupole plasmon resonance and a local field factor of this
resonance have not yet been reported.
In this paper, we report on third-order nonlinear susceptibili-
ties due to both the dipole and quadrupole plasmon resonances
of Ag nanoprisms. We have measured linear and nonlinear
absorption spectra using femtosecond pump-probe spectros-
copy. Local field factors fD and fQ of dipole and quadrupole
plasmon resonances were obtained from the observed absorption
spectra and dispersion curve of ø(3), yielding a ratio fQ/fD of
0.7. The characteristic times for the nonlinear optical response
of both plasmon modes were also measured in the subpicosec-
ond time region.
Figure 1. (a,b) SEM images of Ag nanoparticles in two different scales.
(c) Histogram of edge length of Ag nanoprisms.
frequency of ωprobe (ωpump ) ωprobe or ωpump * ωprobe) were
deduced from differential absorption spectra measured with
pump peak powers of 3-13 GW/cm2.
Results and Discussion
Experimental Section
In Figure 1 (a and b) we show SEM images of the
nanoparticles used in this study. The SEM image of Figure 1a
shows nanoparticles with various shapes: triangles, rods, and
polygonal shapes. However, statistically we have found that
most of the nanoparticles are either perfect triangles or triangles
truncated at each tip (Figure 1b). The presence of nanorods in
the sample used for this study was found to be about 12% from
the statistics of several SEM images. Figure 1c shows a
histogram of the edge length of the triangles obtained from the
measurement of about 100 particles. The edge length ranges
between 40 and 90 nm, and assuming a Gaussian distribution
the average and the standard deviation obtained are 67 and 11
nm, respectively. The average thickness measured by AFM is
about 35 nm for the triangles. The average length and diameter
of nanorods are 180 and 40 nm, respectively, and the aspect
ratio is about 4.5.
Figure 2 shows the absorption spectrum of the same nano-
prism sample characterized with SEM (see Figure 1). Three
bands can be clearly identified within the photon energy region
below the band-to-band transition energy (∼4.3 eV). A calcula-
tion performed by Jin et al.14 for perfectly triangular prisms
and triangular prisms truncated at each tip has shown surface
plasmon bands corresponding to dipole and quadrupole plasmon
excitations. Comparing the observed spectrum to the calculation,
we can attribute the lowest energy band (2.50 eV) to the in-
plane dipole resonance, the band at 3.15 eV to the in-plane
quadrupole resonance and the highest energy band (3.50 eV)
Silver nanoprisms were prepared using a modification of a
recently developed procedure15 based on the use of N,N-
dimethylformamide (DMF) as both a solvent and a reducing
agent, in the presence of poly(vinylpyrrolidone) (PVP). Briefly,
15 µL of a 0.4 M aqueous solution of AgClO4 (Aldrich) was
added to 13 mL of DMF (Fluka) containing 0.2 g of PVP (MW
40 000, Fluka) at 175 °C, to form small Ag nanoparticles. Once
these Ag nuclei were formed (8 min at 175 °C), 0.57 mL of an
aqueous solution of AgNO3 (Aldrich) 0.12 M was added in steps
(30 µL every 3 min) and then the reaction was stopped by
cooling and removing excess PVP by centrifugation. Finally,
the particles were redispersed in ethanol.
Scanning electron microscopy (SEM) was carried out with a
Hitachi S-4300 cold field emission SEM, and particle shape
and size distributions were measured from several SEM images.
Thickness and lateral size of triangles and particles with other
polygonal shapes were also measured by using atomic force
microscopy in contact mode (TMX2100 Explorer). Transient
absorption spectra were measured by a femtosecond pump and
probe method with a 150 fs pulse from an amplified Ti:sapphire
laser system.23 The pump pulse energy was set to 3.12 eV
(ωpump) corresponding to the in-plane quadrupole plasmon
resonance. The probe pulse was a white-continuum generated
by self-phase modulation of a part of the output pulse.
Degenerate and nondegenerate components Imø(3)(-ωprobe
-ωpump, ωpump, ωprobe) of the imaginary part of ø(3) at the probe
:

Letters
J. Phys. Chem. B, Vol. 108, No. 26, 2004 8753
Figure 2. Absorption spectrum of Ag nanoprisms at room temperature.
A: in-plane dipole resonance, B: in-plane quadrupole resonance, C:
out-of-plane dipole resonance, D: out-of-plane quadrupole resonance.
to the out-of-plane quadrupole resonance. The out-of-plane
dipole resonance is only observed as a shoulder in the calcula-
tion, and indeed this resonance is not observed as a clear band
around 3.2 eV.
Although nanorods coexist with triangular prisms in the
sample, the effect of the nanorods on the absorption spectrum
is negligible. We calculated surface plasmon energies of
nanorods with aspect ratios between 3 and 6 using the theory
derived by Gans.28 The resonance bands in the long axis and
short axis directions appear at about 1.5 and 3.4 eV, respectively,
for the nanorod with the aspect ratio of 4.5. The stronger
resonance band in the long axis direction cannot be observed
in the experimental absorption spectrum, and thus we can
conclude that the contribution of nanorods to the absorption
spectrum can be neglected.
Figure 3. Absorption spectrum (a) and differential absorption spectra
(b) for different delay times between pump and probe pulses shone
through a dispersion of Ag nanoprisms at room temperature.
the linear absorption spectrum and the differential absorption
spectra (∆R) measured in the spectral range between 1.55 and
3.05 eV with a pump photon energy of 3.12 eV. The pump
photon energy corresponds to the in-plane quadrupole resonance.
∆R shows a decrease at the high-energy side of the in-plane
dipole resonance band and an increase at the low-energy side.
The observed features of the differential spectra suggest a red-
shift of the dipole resonance band. An increase in absorption
observed above 2.95 eV is related to the in-plane quadrupole
resonance, though the signal above 3.05 eV corresponding to
the resonance band cannot be detected because of the leakage
of the pump pulse light. Shown in Figure 3b are the differential
absorption spectra with various delay times between pump and
probe pulses. As the delay time is increased, ∆R decreases, but
the spectral features remain constant.
Within the framework of the Maxwell-Garnett theory the
electric field El, which the metal nanoparticles in the composite
(the dispersion, in this case) see is related to the incident electric
field Eo by
El ) fl Eo
(1)
where fl is the local field factor.3,5 We extend this relation to
the case of the quadrupole plasmon resonance. Using an
imaginary part ꢀm′′ of the dielectric function ꢀm of the metal
nanoparticles and a volume fraction of nanoparticles p, the
absorption coefficient RD (RQ) at the dipole resonance frequency
ωD (quadrupole resonance frequency ωQ) is given by
Using the Maxwell-Garnett theory for the dielectric function
of the composite system, the nondegenerate component of ø(3)
of metal nanoparticle composites can be represented by the third-
(3)
order susceptibility øm of the bulk metal:3,5
2
ø(3)(ωprobe) ) pfl2(ωprobe)|fl(ωpump)| øm(3)(ωprobe
)
(4)
ωi
2
Ri ) p |fi| ꢀm′′
(2)
nc
Under our experimental conditions of ωpump ) 3.12 eV,
|fl(ωpump)| is equal to the local field factor |fQ| at the in-plane
quadrupole resonance frequency ωQ. For moderate laser intensi-
ties, I, the change in the absorption coefficient is described by
∆R ) âI, where â is a nonlinear absorption coefficient. â is
related to Imø(3) by
where i ) D or Q, c is the speed of light, fD (fQ) is the local
field factor at the dipole resonance frequency (quadrupole
resonance frequency), and n is the refractive index of the
composite. In the case of Ag nanoparticles, the band-to-band
transition energy (∼4.3 eV) is well above the surface plasmon
resonance energies. Consequently, ꢀm′′ is approximately con-
stant in the vicinity of the surface plasmon resonance and n is
also constant at the photon energy (or frequency) concerned.
Therefore, the ratio RQ/RD is given by the following equation,
Imø(3)(-ωprobe: -ωpump, ωpump, ωprobe) )
n2c2
â (5)
240π2ωprobe
2
RQ ωQ |fQ|
Therefore, we can estimate Imø(3) values from the dependence
of ∆R on I.29 In Figure 4a, ∆R values measured at 2.30 eV and
0.1 ps are plotted as a function of the intensity of the pump
pulse I. ∆R increases linearly with I. From the linear least-
squares fit, a value for â is obtained of (6.1 ( 0.8) × 10-13
m/W which yields Imø(3) of (1.2 ( 0.2) × 10-14 esu. Here, we
used n ) 1.36 which is the refractive index of ethanol, because
the concentration of nanoparticles in ethanol is low. For the
negative peak at 2.65 eV in the differential absorption spectra,
)
(3)
2
RD
ω
D |fD|
From this relation we can estimate a ratio fQ/fD between the
local field factor at the quadrupole resonance frequency and
that at the dipole resonance frequency. Taking the measured
ratio RQ/RD as 0.57, we obtained an fQ/fD ratio of 0.67.
Nonlinear absorption spectra and values of Imø(3) were
measured using the pump and probe technique. Figure 3 shows

8754 J. Phys. Chem. B, Vol. 108, No. 26, 2004
Letters
Figure 4. (a) Change in absorpion coefficient ∆R measured at 2.30
eV and 0.1 ps as a function of the pump pulse intensity. The dotted
line is a linear fit to the data. (b) Absorption spectrum and dispersion
curve of Imø(3) in Ag nanoprisms at room temperature. The arrow
indicates the photon energy of the pump pulse for the measurements
of Imø(3). Arrows labeled with ωD and ωQ point to the dipole and
quadrupole resonance peak frequencies, respectively.
Figure 5. Time evolutions of the differential absorption ∆R measured
at 2.65 eV (a) and 3.12 eV (b). The dashed lines are exponential fits to
the data.
Imø(3) is -(1.6 ( 0.2) × 10-14 esu, which is the maximum
value in the vicinity of the dipole resonance frequency. For the
in-plane quadrupole resonance we measured ∆R using a probe
pulse with the same photon energy (3.12 eV) as that of the pump
pulse. The Imø(3) value obtained at ωQ is -(3.0 ( 0.6) × 10-15
esu.
prisms. The time evolutions measured at 2.65 and 3.12 eV with
a pump fluence of about 2 mJ/cm2 are shown in Figure 5. ∆R
exhibits exponential decay behavior; an exponential fit to the
data yields for 2.65 and 3.12 eV relaxation times of 2.1 ( 0.4
and 1.7 ( 0.2 ps, respectively. The observed relaxation times
for both cases are the same within the experimental error and
are comparable to the values for spherical particles measured
with a similar pump fluence.30 The relaxation time of spherical
particle-insulator composites can be successfully analyzed by
means of the two-temperature model, which indicates the strong
dependence of the relaxation time on the pump fluence. With a
lower pump fluence the relaxation time becomes less than 1 ps
because the initial temperature of the electron system heated
by the pump pulse excitation is relatively low.6,31 Using the
two-temperature model,6,30 an estimation of electron and lattice
temperatures in triangular prisms for the pump fluence of 2 mJ/
cm2 yields about 1000 and 310 K, respectively. Consequently,
the agreement between the relaxation times measured for
triangular prisms and those for spherical particles is reasonably
understood, taking into account that the relaxation time is
determined by the cooling dynamics of hot electrons into the
lattice system via the electron-phonon interaction in the
particles. The electron-phonon coupling constant is a bulk
crystal property and is independent of the nanoparticle shapes
and the local electric field.
The Imø(3) values obtained are summarized together with the
absorption spectrum in Figure 4b. The Imø(3) value is positive
at the low-energy side and negative at the high-energy side of
the dipole resonance band (2.50 eV). At the dipole resonance
peak frequency, ωD (2.50 eV), Imø(3) is negative, with a value
of -5.7 × 10-15 esu. A similar feature is observed for the
quadrupole resonance: the Imø(3) value is positive at the low-
energy side and negative at the high energy side of the band.
The Imø(3) values at the dipole (Imø(D3)) and quadrupole (Im
ø(Q3)) resonance peak frequencies are thus -5.7 × 10-15 esu
and -3.0 × 10-15 esu, respectively. The ratio ImøQ(3)/Imø(D3) is
also related to the local field factors fQ and fD. Under our
experimental conditions, ø(Q3) at ωQ and ø(D3) at ωD can be
expressed through the following expressions:
2
2
ø(Q3) ) pfQ |fQ| ø(m3)
(6)
2
2
ø(D3) ) pfD |fQ| ø(m3)
Taking into account that the real part of ø(3) is extremely small
compared to Imø(3) at resonance,23 the ratio ImøQ(3)/Imø(D3) is
given by
Conclusions
2
2
ImøQ(3)/Im ø(D3) ≈ fQ /fD
(7)
We have investigated linear and nonlinear optical properties
of Ag nanoprisms by means of femtosecond pump and probe
spectroscopy. For Ag nanoprisms prepared by direct reduction
of AgNO3 by solvent DMF in the presence of PVP, over 85%
of the nanoparticles were either triangles or truncated triangles
with lateral sizes between 40 and 90 nm. In the absorption
spectra, dipole and quadrupole plasmon resonance bands were
observed, and from the ratio of absorption coefficients at both
bands, a value of 0.67 was obtained for the ratio of the local
field factor fQ/fD. The values of Imø(3) at the dipole and
quadrupole plasmon resonance frequencies are -5.7 × 10-15
and -3.0 × 10-15 esu, respectively, which yields a fQ/fD ratio
of 0.73. Therefore, we have found that the local field enhance-
ment of the quadrupole plasmon resonance is 0.7 times that of
the dipole resonance. The nonlinear response times of both
resonances were ∼2 ps, which is close to the value for spherical
nanoparticles, indicating that the relaxation process via electron-
phonon interaction is governed by bulk crystal properties.
Using the measured value of the ratio Imø(Q3)/ImøD(3) (0.53), the
ratio fQ/fD obtained is 0.73. This value is in good agreement
with the value obtained from the ratio of the absorption
coefficients within the experimental error. Therefore, the local
field factor of the quadrupole plasmon resonance is 0.7 times
that of the dipole plasmon resonance for Ag nanoprisms
consisting of a mixture of perfect triangles and triangles
truncated at each tip. In this enhancement of the local field, the
contribution of band-to-band transition is not included, because
the transition energy (∼4.3 eV) is situated far away from the
surface plasmon resonances. To investigate surface plasmon
related phenomena,23,29 this is actually an advantage of Ag over
Au and Cu nanoparticles, in which the band-to-band transition
(∼2 eV) appears close to the surface plasmon resonance.
We now discuss the response time of optical nonlinearities
due to the dipole and quadrupole resonances in Ag triangular

Letters
Acknowledgment. The authors are grateful to I. Yamakawa
for his assistance in SEM experiments. L.M.L.M. acknowledges
financial support from the Spanish Ministerio de Ciencia y
Tecnolog´ıa (Project no. BQU2001-3799) and Xunta de Galicia
(Project no. PGIDIT03TMT30101PR).
J. Phys. Chem. B, Vol. 108, No. 26, 2004 8755
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