We present third-order optical nonlinearities of Ag nanoparticles fabricated using a two-step ion exchange method. The
nonlinearities are studied using the well-known Z-scan technique. In our experiments, we use a Ti-Sapphire laser source
operating at 800 nm, which is far from the resonance of the Ag nanoparticles. The nonlinear refraction of these
nanoparticles is studied using the closed aperture configuration of the Z-scan method. Contrary to expectations from
previous studies for similar-sized nanoparticles, our nanoparticles possess positive nonlinear refractive index. The
estimated nonlinear refractive indices are in the range of 10-12 cm2/W.
Second-order nonlinear optical effects are electric-dipole-forbidden in centrosymmetric materials, but become allowed
through magnetic-dipole and electric-quadrupole effects. Furthermore, such higher multipole effects can play a role also
in the response of non-centrosymmetric materials, as demonstrated for second-harmonic generation (SHG) from chiral
thin films of organic molecules and from metal nanostructures. For nanostructured materials, higher multipole effects can
occur due to elementary light-matter interactions or due to field retardation across nanoparticles. For SHG from metal
nanostructures, the latter mechanism was operative and associated with nanoscale defects, which attract strong local
fields. The evidence of multipolar SHG emission was obtained from the different radiative properties of the various
multipolar sources. The goal of the present work is to perform a more comprehensive multipolar analysis of SHG from
arrays of L-shaped metal nanoparticles. In particular, we seek evidence of the presence of multipole interactions also at
the fundamental frequency by performing detailed polarization measurements of the SHG response and relying on the
different transformation properties of the various multipolar interactions for SHG emitted in the transmitted and reflected
directions and for the fundamental beam incident on the metal or substrate side of the sample.
We show that local fields associated both with overall structural features and with unintended defects can be important in
the second-order nonlinear response of metal nanostructures. We first consider noncentrosymmetric T-shaped gold
nanodimers with nanogaps of varying size. The reflection symmetry of the T-shape is broken by a small slant in the
mutual orientations of the horizontal and vertical bars, which makes the sample chiral and gives rise to a different
nonlinear response for left- and right-hand circularly-polarized fundamental light. Measurements of achiral and chiral
second-harmonic signals as well as the circular-difference response exhibit a nontrivial dependence on the gap size. All
results are explained by considering the distribution of the resonant fundamental field in the structure and its interaction
with the surface nonlinearity of the metal. We also prepared arrays of ideally centrosymmetric circular nanodots.
Second- and third-harmonic generation microscopies at normal incidence were used to address polarization-dependent
responses of individual dots. Both signals exhibit large differences between individual dots. This is expected for second-harmonic
generation, which must arise from symmetry-breaking defects. However, similar results for third-harmonic
generation suggest that both nonlinear responses are dominated by strongly localized fields at defects.
We present a comprehensive multipolar tensor analysis to investigate the roles of dipolar and higher-order
multipoles to second-harmonic radiation from a regular array of noncentrosymmetric L-shaped gold nanoparticles.
We find the nonlinear response to be dominated by a tensor component which is associated with chiral symmetry
breaking and has strong multipolar character. These findings substantiate our interpretation that one of the
major contributors to the optical response of the present sample are structural defects, which break the symmetry
and make multipolar contributions to the SH response important.
Nanoscale variations in the local fields and material properties can enable higher-multipole (magnetic-dipole and
electric-quadrupole) contributions to the nonlinear response in addition to electric-dipole contributions. Moreover,
the local-field distribution in the structure is important to achieve favorable interaction with the locally varying
nonlinearity. Local-field enhancement is particularly important for nonlinear optical effects. Extremely
small features of a few nm, such as nanogaps between two particles, are expected to be particularly beneficial
for field localization and enhancement. Here, we provide evidence of multipole interference in polarized secondharmonic
generation from arrays of L-shaped gold nanoparticles. We also prepare T-shaped gold nanodimers
and vary the size of the nanogap between their vertical and horizontal bars. Surprisingly, the second-harmonic
signals do not decrease trivially with increasing gap size, because the gap region is nearly centrosymmetric,
thereby forbidding second-order effects. Instead, asymmetric local fundamental field distributions along the
dimer perimeter are favorable, in accordance with the symmetry rule.
Great progress has been achieved in fabricating arbitrary metal nanoparticle shapes and geometries in order to control their linear optical properties. However, their nonlinear optical properties, particularly their second-order response, are frequently overlooked. Exploiting the nonlinear responses of metal nanoparticles opens another exciting avenue for developing nanoscale photonics applications. Second-harmonic generation (SHG) from metal nanoparticles is typically attributed to electric dipole excitations at their surfaces, but nonlinearities involving higher multipole effects, such as magnetic dipole interactions, electric quadrupoles, etc., may also be significant due to strong nanoscale gradients in the local material properties and fields. The nanoscale nonlinear optical processes in metal nanoparticles are not well-understood at present, and determining the sources of the SHG response can be arduous. In order to study the role of higher multipoles in the second-order response of gold nanoparticle arrays, we propose SHG measurements employed in both transmission and reflection geometries. Due to different radiative properties of the various multipoles in the forward and backward directions, the presence of multipoles should lead to opposing interference effects in the two directions. Strong polarization dependence of the response can modify the relative strengths of the interfering terms, thereby allowing electric-dipole and higher-multipole contributions to the overall SHG response to be distinguished. Analysis of the measured polarization dependencies would thus provide further knowledge of the mechanisms underlying the nanoscale SHG process in gold nanoparticles.
The physical processes underlying the complex nanoscale optical responses of metal nanoparticles must be understood
both experimentally and theoretically if they are to be developed for use in photonic devices. While
many linear optical measurements have been performed on gold nanoparticle arrays, only a handful of nonlinear
measurements have been reported. Here, we discuss a collection of experiments of both types on arrays of gold
nanoparticles. However, on nanoscale-rough metal surfaces, such as nanoparticles with small-scale defects, local
electric fields may vary rapidly and strong field gradients can induce significant multipolar contributions, making
a theoretical description of second-harmonic generation (SHG) from nanoparticle arrays infeasible at present.
A macroscopic nonlinear response tensor approach based on the input and output fields to the system avoids
with these complications. Contributions from higher multipoles are implicitly included, and electric-dipole-type
selection rules can be applied to address symmetry issues. While the experimental geometry constrains the
formalism, additional insight into the underlying physical processes is expected from experimental variations.
Good agreement with direct SHG tensor measurements validates the formalism, providing the framework for a
deeper understanding of the nanoscale optical responses of metal nanoparticles.
Considerable attention is devoted to determining and refining the optical properties of metal nanoparticle arrays. The evolution of nanofabrication techniques towards miniaturizing optoelectronic devices naturally suggests the possibility of using such arrays in nanoscale optical components. However, small-scale defects (tens of nanometers or less) in individual particles themselves may exert a significant influence on the overall optical responses of the array, especially when the particles (and/or arrays) appear symmetric on the scale of the particle (and/or array). We have observed strong linear and nonlinear chiral responses from regular arrays of lithographically-designed, low-symmetry, L-shaped gold nanoparticles (~ 200 nm arm lengths) through polarization azimuth rotation and circular difference measurements. Second-harmonic generation measurements exhibit much larger circular difference responses, being more sensitive to symmetry. Comparisons between arrays of symmetric and asymmetric particles imply that the small defects may be the primary source of broken symmetry and hence chirality.
Recent interest in the study of metal nanoparticles and related structures has greatly increased. Technologies such as electron beam lithography facilitate the fabrication of such subwavelength structures. Much research has focused on the linear optical properties of high-symmetry particles, such as ellipsoids and spheroids. However, we focus on both the linear and nonlinear optical responses of low-symmetry L-shaped nanoparticles. We show that these nanoparticle arrays are exceptionally sensitive to polarization. Small asymmetries in the particle shapes lead to large deviations in the primary extinction directions from expected locations. The structural asymmetries may also induce optical activity. We present results of detailed polarization analysis through second-harmonic generation experiments that are based on symmetry arguments regarding the second-order susceptibility tensor. The results confirm that the structural deviations from the ideal shape lead to further breakdown in the symmetry properties of the arrays.