Synthesis and second-harmonic generation studies of noncentrosymmetric gold nanostructures

Article abstract of DOI:10.1021/jp9845874

Noncentrosymmetric gold nanoparticle structures were prepared in porous anodic aluminum oxide films via a modified template synthesis procedure. The noncentrosymmetric structures are defined by two gold particles in close proximity (ca. 22±8 nm end to end) within a single host oxide pore, one having average dimensions of a = 37±6 nm and b = 26±3, and the other having dimensions of a = 27±5 nm and b = 26±3 nm, where a is the axial length and b is the diameter of the quasi-cylindrical structures. Linear UV/vis polarization spectra of the gold particle/porous alumina film composites show plasmon resonance bands whose λ_max incidence angle dependence is similar to composites containing centrosymmetric gold structures, where the incidence angle is defined with respect to the surface normal. Second harmonic generation (SHG) studies using an incident wavelength of 780 nm indicate that SHG intensities under s-polarization are low and independent of incidence angle (θ) for composites containing centrosymmetric and noncentrosymmetric gold nanostructures. However, in p-polarization, both composites show an increase in SHG counts with θ, with the noncentrosymmetric structures showing a higher SHG signal than their centrosymmetric counterparts. These results are consistent with local-field enhancements arising from long particle axis dipolar plasmon resonances.

Full text of DOI:10.1021/jp9845874

2668
J. Phys. Chem. B 1999, 103, 2668-2673
Synthesis and Second-Harmonic Generation Studies of Noncentrosymmetric Gold
Nanostructures
Marie L. Sandrock, Charles D. Pibel,† Franz M. Geiger,‡ and Colby A. Foss, Jr.*
Department of Chemistry, Georgetown UniVersity, Washington, District of Columbia 20057
ReceiVed: December 2, 1998; In Final Form: February 12, 1999
Noncentrosymmetric gold nanoparticle structures were prepared in porous anodic aluminum oxide films via
a modified template synthesis procedure. The noncentrosymmetric structures are defined by two gold particles
in close proximity (ca. 22 ( 8 nm end to end) within a single host oxide pore, one having average dimensions
of a ) 37 ( 6 nm and b ) 26 ( 3, and the other having dimensions of a ) 27 ( 5 nm and b ) 26 ( 3 nm,
where a is the axial length and b is the diameter of the quasi-cylindrical structures. Linear UV/vis polarization
spectra of the gold particle/porous alumina film composites show plasmon resonance bands whose λmax
incidence angle dependence is similar to composites containing centrosymmetric gold structures, where the
incidence angle is defined with respect to the surface normal. Second harmonic generation (SHG) studies
using an incident wavelength of 780 nm indicate that SHG intensities under s-polarization are low and
independent of incidence angle (θ) for composites containing centrosymmetric and noncentrosymmetric gold
nanostructures. However, in p-polarization, both composites show an increase in SHG counts with θ, with
the noncentrosymmetric structures showing a higher SHG signal than their centrosymmetric counterparts.
These results are consistent with local-field enhancements arising from long particle axis dipolar plasmon
resonances.
Introduction
Our interest in composites containing noncentrosymmetric
nanostructures arises in part because they represent nanoscale
analogues to molecular structure-based second-order nonlinear
optical materials. It is well-known that within the dipole
approximation,36 materials possessing inversion symmetry will
not exhibit second-order nonlinear optical effects. Indeed, many
studies of the nonlinear optical properties of nanometal com-
posite systems have focused on third-order effects.21-23 Studies
of second-order processes have been limited to metal nano-
structures at interfaces, which necessarily remove inversion
symmetry.37-43 An interesting exception is the study by Leitner,
who employed a two-stage vacuum deposition procedure to
prepare silver particles of low symmetry on glass substrates.44
However, the significant second harmonic generation (SHG)
intensities observed under normal incidence excitation could
not be specifically attributed to particle asymmetry, and may
have been the result of local field enhanced magnetic dipole
and quadrupole modes.44
Metal particles of nanoscopic dimensions have played an
interesting role in materials technology ever since the first gold-
laden “ruby glass” was manufactured over three centuries ago.1
Many metals in nanoscopic form strongly absorb and scatter
visible light, and therefore give rise to a rich variety of colors.
They have thus been used as pigments in the fine arts,1-3
photographic development, and in industrial metal colorizing
processes.5,6 Over the past two decades, interest in nanoscopic
metal particles has grown well beyond aesthetic considerations,
as they find application in selective solar materials,7-9 cytology10
and molecular biology,11 surface-enhanced spectroscopy,12-20
and nonlinear optics.
It is well-known that the wavelength of maximum optical
extinction, as well as the wavelength of optimal local electric
field enhancement, depends on such factors as the size, shape,
and orientation of the particle, as well as spacing between
particles.16-18 Thus, the improved application of nanoscopic
metal structures in the aforementioned areas, as well as the
prospect of their application in new areas of research and
technology, depends on our ability to control these features.
There are many methods for preparing nanoscopic particles
of nominally spherical geometry.23-28 Methods for preparing
uniformly nonspherical metal particles are less numerous, but
include the grazing incidence vacuum deposition methods of
Liao,29 and the template synthesis methods developed by
Moskovitz30,31 and Martin.32,33 We recently discussed extensions
of the template synthesis method, whereby noncentrosymmetric
metal pairs34 and metal-semiconductor35 structures are prepared
in the pores of anodic aluminum oxide films.
In this paper, we describe the details of the synthesis of
noncentrosymmetric gold particle pair structures. We also
discuss the UV/vis/near-IR linear polarization spectra of non-
centrosymmetric gold particle/porous aluminum oxide film
composites, and their symmetric gold particle analogues. Finally,
we present the first results of a study of SHG from these
composite materials.
Experimental Section
Porous Anodic Alumina Film Preparation. Aluminum
plates (Aldrich 99.999%, 10 cm × 10 cm × 1 mm) were first
electropolished in a cell containing 2 L of 2:3 (v/v) mixture of
sulfuric acid (96% Mallinckrodt) and phosphoric acid (85%
Mallinckrodt). The cathode consisted of a lead plate (6 cm ×
15 cm × 2 mm). The aluminum anode was masked with
* Corresponding author.
† Current address: Department of Chemistry, American University,
Washington, DC 20016.
‡ Current address: Department of Chemistry, Massachusetts Institute of
Technology, Cambridge, MA 02139.
10.1021/jp9845874 CCC: $18.00 © 1999 American Chemical Society
Published on Web 03/18/1999

Noncentrosymmetric Gold Nanostructures
J. Phys. Chem. B, Vol. 103, No. 14, 1999 2669
adhesive tape (3M mailing tape no. 23-8043) such that only
ca. 100 cm2 of aluminum remained exposed. The temperature
of the electropolishing solution was 75 °C, and 10 A was
delivered to the cell for ca. 3 min using a Sorenson DCR300-
9B power supply. The polished aluminum plate was then
immersed in deionized water to rinse.
The electrochemical preparation of the nanoporous alumina
films utilized a two-electrode temperature-controlled anodization
cell. Within the cell, stainless steel coils connected to an external
circulation refrigerator bath (1:1 ethylene glycol/water mixture)
maintained a constant temperature of the acid bath at 0 °C. Lead
foil (6.5 cm × 14 cm × 2 mm) served as the cathode and the
polished plate (100 cm2 of exposed aluminum) was the anode.
The supporting electrolyte was 6% sulfuric acid (prepared from
96% Mallinckrodt). The anodization cell was constantly stirred
and a programmable power supply (Kepco ABC 25-4DM)
provided a potential of 20 V. The anodic aluminum oxide film
was grown (through the oxidation of aluminum) for a period
of 14 h to produce pores with a 32 nm diameter and a film
thickness of 40-60 µm.
Separation of the alumina film from the anode was achieved
using a voltage reduction procedure which creates small
branched pores45 in the barrier layer of the oxide film, which
makes this layer vulnerable to acid dissolution. The reduction
occurred in gradual 5% decrements from 20 to 2 V and lasted
approximately 1.5 h. After each reduction step, the current was
allowed to rise to at least 85% of its previous value. After the
reduction, the alumina films were placed in a 25% (V/V) sulfuric
acid bath (96% Mallinckrodt) for oxide detachment, which lasted
ca. 3 h. The films were then rinsed with deionized water,
ethanol, and acetone, and air-dried. The thickness of the alumina
nanoporous film was determined by a micrometer (Mitutoyo).
Nanoparticle Preparation. The porous alumina membranes
were used as a template to synthesize gold particles of different
symmetries.46 The barrier side of the film was sputtered with
ca. 45 nm of silver using an Anatech Hummer 10.2 plasma
deposition device. The silver-coated oxide film was then
attached to a three-electrode cell equipped with an Ag/AgCl
reference electrode and a platinum mesh counter electrode. The
power source was an EG&G Princeton Applied Research Model
273A potentiostat. Nitrogen was purged into the system for
mixing.
A 0.80-1.27 C/cm2 foundation of silver was potentiostatically
deposited over a 3.14 cm2 area of porous oxide from a silver
thiocyanate plating solution47 at -0.6 V vs Ag/AgCl. This
foundation ensured that the subsequent gold deposition would
fill the 32 nm porous region of the film. After rinsing with
deionized water, gold nanoparticles were formed potentiostati-
cally at -0.9 V vs Ag/AgCl reference from Au(I) (Technic Inc.,
Orotemp 24 gold plating solution). 0.3 C of Au was deposited
over the 3.14 cm2 area for centrosymmetric particles. Addition-
ally, for noncentrosymmetric particles, 0.1 C of Au was first
deposited over the area, followed by another layer of Ag (0.1
C) and finally another layer of Au (0.2 C).
All of the composites were immersed in nitric acid (69-
71% EM), to dissolve any silver, leaving only gold in the pores.
The composite films were rinsed with deionized water, ethanol,
and acetone and air-dried. The procedure for preparing both
types of particle composites is summarized in Figure 1.
Figure 1. Schematic of nanoparticle synthesis: (1) porous anodic
alumina film after detachment from Al substrate; (2) one face of alumina
film coated with silver using plasma deposition; (3) electrodeposit silver
foundation into pores; (4c) electrodeposit gold onto silver foundation
to form centrosymmetric gold particles; (4n) electrodeposit layers of
gold, silver, and then a second gold layer to form noncentrosymmetric
gold particles; (5c and 5n) immerse film in nitric acid to remove silver
foundation and silver spacing segments.
embedded in a resin and heated at 70 °C for 12 h. A 70 µm
section was cut using a diamond knife (SPI Inc.) and placed on
a Formvar-coated Cu grid (200 mesh, EM Sciences). The
samples were then examined with a JEOL 1200 EX transmission
electron microscope.
Linear Optical Analysis. Linear polarization spectra were
collected with a Hitachi U3501 UV/vis/near-IR spectrometer
equipped with a 210-2130 polarizer accessory. Sample extinction
(measured as sample absorbance) was measured at 1 nm
increments between 350 and 800 nm, at a bandwidth of 2 nm.
In this spectral range, the U3501 employed a tungsten lamp
source and photomultiplier tube detector. Spectra were obtained
with the incident propagation vector normal to the composite
film surfaces (incidence angle θ ) 0), and at incidence angles
of 20°, 30°, and 45° under p-polarization. These four incidence
angles correspond to an incident electric field which is
perpendicular, 70°, 60°, and 45°, respectively, to the particles’
rotation axis. The configuration of the linear optical experiment
is shown schematically in Figure 2.
Second Harmonic Generation Studies. The SHG studies
employed a high repetition rate femtosecond titanium-sapphire
laser system, which was constructed following the design of
Murnane48 and pumped by an argon ion laser (Spectra Physics
2060). The Ti:sapphire laser has a tunable output range of 710-
900 nm. We restricted our initial studies to an output of 780
nm. The pulse widths employed were ca. 150 fs at an 80 MHz
repetition rate. The average power was 100-300 mW, corre-
sponding to an energy of ca. 3 nJ per pulse.
Figure 3 shows a schematic of the optical bench used in the
SHG studies. The 780 nm source line was split and directed to
a sample and reference line. A slide-mounted mirror allowed
for the alternate detection of sample and reference signals using
a single monochromator and detection system. The reference
material consisted of a slurry of potassium dihydrogen phosphate
(KDP, Fisher Scientific) in decahydronaphthalene (Aldrich
99%).
Nanoparticle Characterization. Transmission electron mi-
croscopy was used to characterize the dimensions of the template
synthesized gold nanoparticles. Additional sample preparation
was required in order to obtain TEM (transmission electron
microscope) images. The gold particle composite films were

2670 J. Phys. Chem. B, Vol. 103, No. 14, 1999
Sandrock et al.
trosymmetric gold structures. The noncentrosymmetric structures
consist of two segments of gold, one roughly spherical and the
other rodlike in geometry. The longer segments show an average
length a ) 37 ( 6 nm, and the smaller segments have an
average length a ) 27 ( 5 nm. The diameter of the particles is
ca. 26 ( 3 nm. The separation distance between the two
segments is 22 ( 8 nm. The centrosymmetric particles have an
axial length a ) 54 ( 7 nm and diameter b ) 30 ( 4 nm.49
In Figure 5 we show the polarization spectra for the two types
of gold particle composites. The numbers on the curves pertain
to the angle of incidence under p-polarization. The spectra for
centro- and noncentrosymmetric particle composites are gener-
ally similar in the following respects: At normal incidence (θ
) 0), the spectra are characterized by a plasmon resonance band
centered at ca. 530-540 nm. As the angle of incidence increases,
and a correspondingly greater component of the incident electric
field is coincident with the long axes of the particles, a broad
plasmon resonance band grows in at longer wavelengths. For
the centrosymmetric structures, the long axis resonance is
centered at ca. 640 nm. For the noncentrosymmetric pair
particles, the long axis resonance is centered at ca. 650 nm.
The observed dichroic properties of the composite films at
nonnormal incidence under p-polarization are consistent with
the results of earlier studies on nanoscopic gold rods oriented
in polyethylene films,50 and can be understood in terms of the
quasi-static limit expression for particle polarizability (R):
Figure 2. Schematic of polarization spectroscopy setup. The sample
film is rotated about an axis perpendicular to the page. The angle of
incidence is indicated by θ. p-Polarization corresponds to an incident
electric field polarized in the plane on the page. s-Polarization
corresponds to an electric field oscillating perpendicular to the page.
4πab2
ꢀ˜m - ꢀ˜o
Lx ꢀ˜m + κꢀ˜o
R )
(1)
(
)
where a and b are the semimajor and semiminor axes,
respectively, of an ellipsoid of revolution. The complex dielectric
functions of the metal and host medium are ꢀ˜m and ꢀ˜o,
respectively. The screening factor κ is related to the depolar-
Figure 3. Schematic of second harmonic generation optics bench.
Meaning of symbols: BS, beam splitter; M, stationary mirror; R,
retarder; P, polarizer; L, lens; MM, moving mirror to select sample or
reference beam for measurement.
-1
ization factor Lx via κ ) Lx - 1, which in turn can be
calculated from a and b.51 For free-electron metals, the real part
of the complex dielectric constant is generally negative, and
monotonically decreasing with wavelength in the visible spec-
trum. Thus, as the screening factor κ increases, the plasmon
resonance maximum is expected to shift to longer wavelengths.51
For the spectra shown in Figure 5, the emergence of a long-
wavelength resonance with increasing incidence angle under
p-polarization is consistent with a long-axis screening factor
(κ|) greater than 2 (the value for spherical particles). The 0.096
C cm-2 of Au(I) deposited in the centrosymmetric particle
synthesis results in rodlike particles of aspect ratio a/b ≈ 1.8;
this corresponds to a screening factor κ| ) 3.6. On the other
hand, in the noncentrosymmetric particle synthesis, the distribu-
tion of 0.096 C cm-2 into two segments results in one particle
being roughly spherical (a/b ≈ 1, κ ) 2), and one being
moderately rodlike (a/b ≈ 1.4, κ| ) 2.8). The rodlike segment
alone should give rise to spectral dichroism, but with a long
axis λmax at a shorter wavelength than exhibited by the
centrosymmetric particles. An isolated spherelike segment
should show no dichroism. Apparently, the similarity of the long
axis λmax values for the centrosymmetric and noncentrosym-
metric particle pair composites arises from the close proximity
of the rod- and spherelike segments in the latter system. We
will discuss particle spacing effects on linear polarization spectra
in a later publication.52
For the gold particle/porous alumina sample line, the source
polarization was controlled by a variable retarder (Meadowlark
Optics) and a Glan laser polarizer (Zeta International). A second
polarizer was incorporated to attenuate the beam to an average
power of 24 mW, which results in a fluence well below each
sample’s measured optical damage threshold (ca. 40 mW). The
SHG signal was measured for polarizations at 0° (p) and 90°
(s) with respect to the plane of incidence. The incidence angle,
θ, was varied by rotating the composite film along an axis
perpendicular to the tabletop. Three trials were performed for
both composite materials, each focusing on a different portion
of the film. This step is necessary, as the composite films are
not isotropic materials.
The SHG signal (from sample and reference lines) was
focused into a monochromator (Oriel 77298) which contained
a grating (1200 lines/mm) blazed at 350 nm, and a filter placed
before monochromator (transmitted range 353-462 nm). The
monochromator output was set at 390 nm (band-pass ) 10.0
nm) and the SHG photons were detected using a Hamamatsu
R5858 PMT with a discriminator (F-100T Advanced Research
Instruments). The pulses due to single SHG photons were
counted using an I/O board (Computer Boards Inc. Model CIO-
DIO24) over a 1 s collection interval.
In the SHG studies, we examined the same centro- and
noncentrosymmetric Au particle alumina composite samples
considered in the polarization spectroscopic measurements. For
both sample types, we measured SHG intensities at normal
Results and Discussion
Figure 4 shows TEM images of cross-sections of porous
anodic alumina films containing centrosymmetric and noncen-

Noncentrosymmetric Gold Nanostructures
J. Phys. Chem. B, Vol. 103, No. 14, 1999 2671
Figure 4. Transmission electron microscope images: (A) 0.1 C cm-2 Au centrosymmetric Au particles in alumina host; (B) 0.10 C cm-2
noncentrosymmetric Au particles in alumina host (0.06 C cm-2 Au(I) deposited for larger segment, 0.03 C cm-2 Au(I) deposited for smaller
segment). Scale bar in both cases corresponds to 50 nm.
Figure 6. Second harmonic generation (SHG) intensity as a function
of the angle of incidence. Open circles correspond to p-polarized
incident light. Boxes correspond to s-polarized excitation. (A) Cen-
trosymmetric Au particle/alumina composite. (B) Noncentrosymmetric
pair particle/alumina composite.
alumina samples are normalized against the counts from the
KDP reference. The error bars are based on the results of
measurements on three different locations of the composite
films. We should also note that SHG studies on porous oxide
films containing no gold were also performed, and showed
negligible signals for all incidence angles and polarizations.
With our laser system, SHG yields range from 4 to 210
counts. For the centrosymmetric particle composite (Figure 6A),
the SHG counts are small for both s-polarization (ca. 8 counts),
and p-polarization (ca. 8-30 counts). The SHG signal for
p-polarized excitation shows a small increase with incidence
angle θ. In s-polarization, the SHG signal is constant within
Figure 5. UV/visible p-polarization spectra: (A) centrosymmetric Au
particle/alumina composite; (B) noncentrosymmetric Au pair/alumina
composite. Incidence angles indicated next to curves. “Extinction”
abscissa is unitless and corresponds to spectrometer “absorbance”
output. However, the measured extinction includes losses due to
absorption, scattering and reflectance. All measurements were made
in double-beam mode, with no material in the reference beam.
incidence and at incidence angles of 20°, 30°, and 40° under s-
and p-polarization. Figure 6 summarizes the results of these
studies. In all cases, the SHG counts from the Au particle/

2672 J. Phys. Chem. B, Vol. 103, No. 14, 1999
Sandrock et al.
limit treatment based on eq 2, where the gold particle dimensions
are assumed to be negligibly small relative to λ. According to
this treatment, local field enhancement R becomes significant
only for particles with aspect ratios greater than ca. 2.5.
However, if particle size is incorporated into Lx and κ,17,54
R
becomes significant at smaller aspect ratios (see solid curve in
Figure 7).
The local field model also explains in part the observed SHG
in the centrosymmetric particle composites. From the dipole
approximation treatment of nonlinear optical processes, we
would not expect to observe SHG from small centrosymmetric
particles.36,55 However, metal spheres a few nanometers in
diameter or larger can support quadrupolar electric and magnetic
induction modes, which in theory can give rise to SHG.56-58
Since the dimensions of the Au particles in this study are such
that quadrupole modes would necessarily be quite weak (we
do not observe quadrupole bands in the linear spectra), local
field enhancements must play an important role in the SHG
from the centrosymmetric particles. The observation that SHG
counts increase for p-polarized excitation (Figure 6A) is
consistent with a local field enhanced process.
Finally, it is significant to note that in the comparison of
centro- and noncentrosymmetric particle composites, the latter
system shows higher SHG counts in s-polarization even at
normal incidence (θ ) 0). In an ideal composite structure where
the cylindrical pores (and therefore the template-synthesized
particles) are uniformly aligned perpendicular to the film surface,
we would expect the SHG counts from centro- and noncen-
trosymmetric composites to be very similar. In fact, the pores
are not perfectly aligned and the film surfaces are not perfectly
flat. Thus, in s-polarization, there will be some fraction of
particles which experience a nonzero component of the incident
electric field along their asymmetry axis. While we have not
yet quantified the distribution of the particle orientation within
the composites, it should be emphasized that the net deviation
from perpendicular orientation (relative to the average film
surface plane) must be small, as we do not detect long-axis
plasmon resonance bands in the normal incidence linear spectra
(Figure 5).
Figure 7. Calculated SHG local field enhancement factors (based on
eq 2) as a function of particle aspect ratio for gold particles where
incident wavelength is 780 nm, and second harmonic output wavelength
is 390 nm. Dashed curve corresponds to quasistatic limit where particle
dimensions are assumed to be negligibly small relative to λ. Solid
curve: SHG local field enhancement calculation taking into account
dynamic depolarization and radiation damping in rodlike particles of
radius 15 nm.
experimental error. In the noncentrosymmetric particle com-
posite (Figure 6B), the SHG counts under s-polarization are,
within experimental error, constant with θ (ca. 30 counts).
However, in p-polarization, the SHG counts increase dramati-
cally with incidence angle (ca. 30-200 counts). At θ ) 40°,
the normalized SHG counts are about 6 times higher than the
corresponding signal for the centrosymmetric particle composite.
The observed dependence of the SHG signal on incidence
angle for the noncentrosymmetric particles under p-polarization
is reasonable in two respects. First, as the incidence angle
increases, the component of the incident electric field directed
along the asymmetry axis (the axis perpendicular to the rotation
axis of the rod) of the gold pair-particle structure increases.
Second, enhancement effects associated with the long-axis
dipolar plasmon resonance are increased with θ. For the
s-polarization case, the electric field is always perpendicular to
the asymmetry axis, and consequently, there is no dependence
of SHG on θ.
The connection between the linear spectra and the local field
enhancement factor R for SHG can be seen in the approximate
expression37,39
Conclusions
R ) |L2(ω)L(2ω)|
(2a)
We have prepared centro- and noncentrosymmetric Au
particle structures in porous anodic alumina hosts using an
electrochemical template synthesis method. The linear polariza-
tion spectra of the Au particle/anodic alumina composites reveal
that both types of composites are dichroic under p-polarization
for incidence angles θ > 0. In the case of the noncentrosym-
metric Au particle pair structures, the strong linear dichroism
arises in part because of the close proximity of the spherical
and rodlike segments in the porous host.
where the function L is given by
2
ꢀo(ω)
L(ω) )
(2b)
(
)
Lx(ꢀm(ω) + κꢀo(ω))
Thus, the local field and R are large when either the fundamental
frequency (ω) or the second harmonic (2ω) is close to a plasmon
resonance.
Second harmonic generation studies of the centro- and
noncentrosymmetric particle composites reveal that the latter
system gives rise to stronger SHG signals, and that the SHG
intensity under p-polarized excitation increases with incidence
angle (i.e., as the component of the incident electric field parallel
to the asymmetry axis increases). These observations are
consistent with local field enhancements arising from long-axis
dipolar plasmon resonances. The weak SHG observed in the
centrosymmetric particle system may arise from quadrupole
induction modes.
We calculated the local field enhancement factors for gold
rods of various aspect ratios in a nonabsorbing host (refractive
index no ) 1.33 at both λ ) 780 nm and λ ) 390 nm). The
optical constants of gold were taken from Johnson and Christy.53
The enhancement factor curves shown in Figure 7 pertain
specifically to the case where the incident electric field is parallel
to the long (rotation) axis of the gold particle. In our SHG
studies, normal incidence (θ ) 0) corresponds to the case where
the electric field component along the long axis is zero; however,
as the incidence angle increases under p-polarization, the electric
field component along the long axis also increases. The influence
of long-axis local field enhancements increases accordingly.
Figure 7 shows local field enhancements based on two
theoretical treatments. The dashed curve shows the quasi-static
Quasistatic theory calculations of the local field enhancement
factors for SHG from gold particles suggest that enhancements
become appreciable for particle aspect ratios greater than ca. 3,
which is larger than the value associated with the particles

Noncentrosymmetric Gold Nanostructures
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The average length, diameter, and standard deviations were determined from
measurements of fifteen to twenty individual structures.
(50) Al-Rawashdeh, N. R.; Sandrock, M. L.; Seugling, C. J.; Foss, C.
A., Jr. J. Phys. Chem. B 1998, 102, 361.
Acknowledgment. The authors are grateful to the National
Science Foundation for its support of this work (Grant DMR
9625151). M.L.S. also acknowledges the support of the ARCS
Foundation. F.M.G. thanks the National Aeronautics and Space
Administration for a Global Change Graduate Student Fellow-
ship in Earth Science Systems. Electron microscopy support
was provided by the Lombardi Cancer Center Microscopy and
Imaging Shared Resource (U.S. Public Health Services Grant
2P30-CA-51008).
References and Notes
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-1
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