208
M. Kauranen et al.
6.1 Introduction
The optical response of metal nanoparticles is dominated by particle plasmons, which
are collective oscillations of the metallic conduction electrons in the particles [1, 2].
The resonance wavelengths of the particle plasmons depend on the size and shape
of the particles as well as their dielectric environment [3]. When the particles are
arranged in an array, as is often the case for metamaterials [4, 5], near-field or longrange coupling between the individual particles can further modify the resonances,
giving rise to sharp spectral features [6–12]. All these mechanisms provide several
degrees of freedom for tuning the resonances and optical properties of metal nanostructures over broad wavelength ranges [13–16].
The plasmon resonances are associated with strong local electromagnetic fields
near the particles [17, 18]. Such “hot spots” can be used to enhance optical interactions, allowing for example surface-enhanced Raman scattering from individual
molecules [19, 20]. The local-field enhancement is of particular interest for nonlinear
optical effects, which scale with a high power of the local field. The nonlinear effects
are therefore expected to be locally enhanced at the hot spots and, with judicious
design, even when the response is averaged over the whole sample volume.
In this Chapter, we focus on second-order nonlinear optical properties of plasmonic nanostructures. Relatively strict symmetry rules constrain second-order effects
to non-centrosymmetric material systems [21]. Such effects are therefore sensitive
probes of symmetry breaking in the material structure. A well-known example of this
is the fact that the symmetry of bulk materials is necessarily broken at surfaces, which
justifies second-order techniques as probes of surfaces, interfaces, and molecular order in thin films [21–24]. Such responses can only be accessed when the optical fields
couple with the direction of the sample normal. In the plane wave limit and planar
samples, the experiments therefore need to be performed at oblique angle of incidence. In the context of metal nanostructures, possible sources of symmetry breaking
are deviations of the overall features of the sample from design and nanoscale defects
that can support their own highly-localized plasmonic modes [18, 25].
In our work, we have studied second-harmonic generation (SHG) from arrays
of metal nano-objects on a dielectric substrate. SHG is the most common secondorder process, which is easy to implement experimentally. In order to break their
centrosymmetry, our objects have consisted of L-shaped nanoparticles and T-shaped
nanodimers. More specifically, such objects look non-centrosymmetric even when
investigated at normal incidence to avoid the coupling of the optical beams with
the traditional surface nonlinearity with the out-of-plane character. Our work therefore addresses the nonlinear response arising from the shape of the particles, rather
than uses the nanoparticles to enhance the coupling with the traditional surface
nonlinearity.
The role of various multipole effects in the optical responses is an important
aspect that needs to be considered when nanostructures are discussed. In addition to
the traditional electric-dipole interaction, higher-multipole interactions, magneticdipole and electric-quadrupole interactions in particular, can become important in
M. Kauranen et al.
6.1 Introduction
The optical response of metal nanoparticles is dominated by particle plasmons, which
are collective oscillations of the metallic conduction electrons in the particles [1, 2].
The resonance wavelengths of the particle plasmons depend on the size and shape
of the particles as well as their dielectric environment [3]. When the particles are
arranged in an array, as is often the case for metamaterials [4, 5], near-field or longrange coupling between the individual particles can further modify the resonances,
giving rise to sharp spectral features [6–12]. All these mechanisms provide several
degrees of freedom for tuning the resonances and optical properties of metal nanostructures over broad wavelength ranges [13–16].
The plasmon resonances are associated with strong local electromagnetic fields
near the particles [17, 18]. Such “hot spots” can be used to enhance optical interactions, allowing for example surface-enhanced Raman scattering from individual
molecules [19, 20]. The local-field enhancement is of particular interest for nonlinear
optical effects, which scale with a high power of the local field. The nonlinear effects
are therefore expected to be locally enhanced at the hot spots and, with judicious
design, even when the response is averaged over the whole sample volume.
In this Chapter, we focus on second-order nonlinear optical properties of plasmonic nanostructures. Relatively strict symmetry rules constrain second-order effects
to non-centrosymmetric material systems [21]. Such effects are therefore sensitive
probes of symmetry breaking in the material structure. A well-known example of this
is the fact that the symmetry of bulk materials is necessarily broken at surfaces, which
justifies second-order techniques as probes of surfaces, interfaces, and molecular order in thin films [21–24]. Such responses can only be accessed when the optical fields
couple with the direction of the sample normal. In the plane wave limit and planar
samples, the experiments therefore need to be performed at oblique angle of incidence. In the context of metal nanostructures, possible sources of symmetry breaking
are deviations of the overall features of the sample from design and nanoscale defects
that can support their own highly-localized plasmonic modes [18, 25].
In our work, we have studied second-harmonic generation (SHG) from arrays
of metal nano-objects on a dielectric substrate. SHG is the most common secondorder process, which is easy to implement experimentally. In order to break their
centrosymmetry, our objects have consisted of L-shaped nanoparticles and T-shaped
nanodimers. More specifically, such objects look non-centrosymmetric even when
investigated at normal incidence to avoid the coupling of the optical beams with
the traditional surface nonlinearity with the out-of-plane character. Our work therefore addresses the nonlinear response arising from the shape of the particles, rather
than uses the nanoparticles to enhance the coupling with the traditional surface
nonlinearity.
The role of various multipole effects in the optical responses is an important
aspect that needs to be considered when nanostructures are discussed. In addition to
the traditional electric-dipole interaction, higher-multipole interactions, magneticdipole and electric-quadrupole interactions in particular, can become important in