266
M. B. Raschke et al.
The general principles of surface- and plasmon-enhanced nonlinear optical effects
are well understood. However, details in terms of the relative surface and bulk modifications to the susceptibility, the interband and intraband transitions, finite size effects
on band structure, plasmon mediated effects in the nanostructure, and interactions
with the substrate are not yet well understood. Furthermore, the spectral dependence
and magnitude of the field enhancement varies critically depending on the surface
morphology, which is difficult to model. Grating structures can be useful for the treatment of surface-enhanced nonlinear processes, since they provide a model system
for rough surfaces. Experimentally, the enhancement of nonlinear optical effects has
been demonstrated on various samples, with roughness controlled to a certain extent
through film thickness and growth conditions [47], and SHG enhancement of 10 4 on
a roughened Ag surface was observed early on [48], in addition to surface-enhanced
higher order processes [49]. However, just as for a planar geometry, the surface and
bulk contributions to the SHG are difficult to separate, and both may be modified by
the roughness [50].
7.3.5 Nonlinear Light Scattering
One of the complications of surface-enhanced nonlinear interactions is that the
roughness can lead to extrinsic dephasing and depolarization. Similarly, nonlinear
processes in particle systems, e.g. in gas and liquid phase, where there is a substantial
spatial inhomogeneity in local fields and nonlinear susceptibilities, will be accompanied by scattering. For the small particle limit, where the particles can be treated
as dipole sources (i.e. 5–10 nm for visible light), nonlinear light scattering is known
as hyper-Rayleigh scattering, in analogy to Rayleigh scattering [11]. Some confusion in terminology exists in the literature, but according to the strict definition, the
nonlinear response in particles larger than 10 nm arises from coherent effects, even
when the contributions from the particles add incoherently, and so hyper-Rayleigh
scattering can be a misleading term [51].
The change in momentum conservation rules in scattering processes compared
to bulk media produces new and additional symmetry selection rules, which are
described in the context of nonlinear Mie and Rayleigh scattering with an effective
surface susceptibility χ
(n)
s [52–54]. In particular, the lack of translational invariance
and k ◦ 1/r for a single nanoscopic system lifts the phase matching condition, so that
the projection of the nonlinear k-vectors to the far field is not restricted to a particular
direction. Of the different nonlinear interactions in individual nanoparticles, thirdorder processes such as THG behave similarly to linear scattering, while secondorder processes such as SHG have additional sensitivity to the particle surface and
geometric details. Furthermore, the susceptibilities for nanoparticles can be very
strongly affected by grain size and crystallinity. Analogous to the linear case, if the
particles are large enough to allow for retardation effects over the particle diameter,
higher order multipolar contributions to the nonlinear polarization occur.
M. B. Raschke et al.
The general principles of surface- and plasmon-enhanced nonlinear optical effects
are well understood. However, details in terms of the relative surface and bulk modifications to the susceptibility, the interband and intraband transitions, finite size effects
on band structure, plasmon mediated effects in the nanostructure, and interactions
with the substrate are not yet well understood. Furthermore, the spectral dependence
and magnitude of the field enhancement varies critically depending on the surface
morphology, which is difficult to model. Grating structures can be useful for the treatment of surface-enhanced nonlinear processes, since they provide a model system
for rough surfaces. Experimentally, the enhancement of nonlinear optical effects has
been demonstrated on various samples, with roughness controlled to a certain extent
through film thickness and growth conditions [47], and SHG enhancement of 10 4 on
a roughened Ag surface was observed early on [48], in addition to surface-enhanced
higher order processes [49]. However, just as for a planar geometry, the surface and
bulk contributions to the SHG are difficult to separate, and both may be modified by
the roughness [50].
7.3.5 Nonlinear Light Scattering
One of the complications of surface-enhanced nonlinear interactions is that the
roughness can lead to extrinsic dephasing and depolarization. Similarly, nonlinear
processes in particle systems, e.g. in gas and liquid phase, where there is a substantial
spatial inhomogeneity in local fields and nonlinear susceptibilities, will be accompanied by scattering. For the small particle limit, where the particles can be treated
as dipole sources (i.e. 5–10 nm for visible light), nonlinear light scattering is known
as hyper-Rayleigh scattering, in analogy to Rayleigh scattering [11]. Some confusion in terminology exists in the literature, but according to the strict definition, the
nonlinear response in particles larger than 10 nm arises from coherent effects, even
when the contributions from the particles add incoherently, and so hyper-Rayleigh
scattering can be a misleading term [51].
The change in momentum conservation rules in scattering processes compared
to bulk media produces new and additional symmetry selection rules, which are
described in the context of nonlinear Mie and Rayleigh scattering with an effective
surface susceptibility χ
(n)
s [52–54]. In particular, the lack of translational invariance
and k ◦ 1/r for a single nanoscopic system lifts the phase matching condition, so that
the projection of the nonlinear k-vectors to the far field is not restricted to a particular
direction. Of the different nonlinear interactions in individual nanoparticles, thirdorder processes such as THG behave similarly to linear scattering, while secondorder processes such as SHG have additional sensitivity to the particle surface and
geometric details. Furthermore, the susceptibilities for nanoparticles can be very
strongly affected by grain size and crystallinity. Analogous to the linear case, if the
particles are large enough to allow for retardation effects over the particle diameter,
higher order multipolar contributions to the nonlinear polarization occur.