216
M. Kauranen et al.
A large body of work also exists for arrays of nanoparticles and nanoapertures.
Arrays of split-ring resonators (SRRs) were found to give rise to particularly strong
SHG when the fundamental wavelength matched the magnetic resonance of the SRR
[56–58]. However, more recent results suggested that the excitation of the magnetic
resonance is not a prerequisite for a strong response [59]. These results have been
interpreted by models based on free-electron approaches to the optical response of
metals [60]. Finally, the role of resonance enhancement in SHG from SRRs has
been addressed [61]. The interpretation was that a resonance at the fundamental
frequency is advantageous, whereas a resonance at the harmonic frequency is just a
loss mechanism, reabsorbing the generated SHG light.
Nanoapertures are interesting, because they can enhance light transmitted through
them [62]. SHG has been used to investigate holes with high [63, 64] and low
symmetry [65] as well as dimers consisting of two holes [66]. Careful inspection of
these results on apertures and particles as well as other work [67, 68] reveals that the
expected symmetry rules of SHG are only approximately fulfilled, suggesting that the
results have also been influenced by defects and imperfections of the nanostructures.
Beyond results regarding nonlinear effects in coherent SHG, incoherent
Hyper-Rayleigh scattering (HRS) has been used to characterize nanoparticles, including their multipolar nonlinear responses. For small (diameter below 50 nm)
spherical gold and silver nanoparticles, imperfections in the particle shape give
rise to a dominant dipolar contribution in HRS. For larger particles, the response
has strong quadrupolar contribution due to retardation effects in the interaction of
the electromagnetic fields with the particles [30, 69, 70]. These results were supported by theoretical calculations, using finite element method, for particles with
noncentrosymmetric shape [31]. By using long acquisition times and signal statistics, single nanoparticle sensitivity has also been achieved [71, 72]. The technique
has also been used for the discrimination of single particles from their aggregates
[73]. Furthermore, the octupolar contribution to HRS has recently been observed
[32], which can also be used to separate the surface and bulk contributions to the
signal [74]. Recently, polarization resolved SH intensity measurements on arrays
of gold nanocylinders showed that the incoherent SHG response arises from small
defects present at the surface of nanocylinders [75, 76].
6.5 Local-Field Issues
6.5.1 Gap Dependence
The optical response of individual metal nanoparticles can be significantly modified
by bringing the particles close to each other. Due to charge accumulation close
to surfaces within each particle, a very strong local field can exist within the gap
between the particles [77–80]. The consequences of this for nonlinear responses
were first tested using a dimer consisting of two gold nanospheres and four-wave
M. Kauranen et al.
A large body of work also exists for arrays of nanoparticles and nanoapertures.
Arrays of split-ring resonators (SRRs) were found to give rise to particularly strong
SHG when the fundamental wavelength matched the magnetic resonance of the SRR
[56–58]. However, more recent results suggested that the excitation of the magnetic
resonance is not a prerequisite for a strong response [59]. These results have been
interpreted by models based on free-electron approaches to the optical response of
metals [60]. Finally, the role of resonance enhancement in SHG from SRRs has
been addressed [61]. The interpretation was that a resonance at the fundamental
frequency is advantageous, whereas a resonance at the harmonic frequency is just a
loss mechanism, reabsorbing the generated SHG light.
Nanoapertures are interesting, because they can enhance light transmitted through
them [62]. SHG has been used to investigate holes with high [63, 64] and low
symmetry [65] as well as dimers consisting of two holes [66]. Careful inspection of
these results on apertures and particles as well as other work [67, 68] reveals that the
expected symmetry rules of SHG are only approximately fulfilled, suggesting that the
results have also been influenced by defects and imperfections of the nanostructures.
Beyond results regarding nonlinear effects in coherent SHG, incoherent
Hyper-Rayleigh scattering (HRS) has been used to characterize nanoparticles, including their multipolar nonlinear responses. For small (diameter below 50 nm)
spherical gold and silver nanoparticles, imperfections in the particle shape give
rise to a dominant dipolar contribution in HRS. For larger particles, the response
has strong quadrupolar contribution due to retardation effects in the interaction of
the electromagnetic fields with the particles [30, 69, 70]. These results were supported by theoretical calculations, using finite element method, for particles with
noncentrosymmetric shape [31]. By using long acquisition times and signal statistics, single nanoparticle sensitivity has also been achieved [71, 72]. The technique
has also been used for the discrimination of single particles from their aggregates
[73]. Furthermore, the octupolar contribution to HRS has recently been observed
[32], which can also be used to separate the surface and bulk contributions to the
signal [74]. Recently, polarization resolved SH intensity measurements on arrays
of gold nanocylinders showed that the incoherent SHG response arises from small
defects present at the surface of nanocylinders [75, 76].
6.5 Local-Field Issues
6.5.1 Gap Dependence
The optical response of individual metal nanoparticles can be significantly modified
by bringing the particles close to each other. Due to charge accumulation close
to surfaces within each particle, a very strong local field can exist within the gap
between the particles [77–80]. The consequences of this for nonlinear responses
were first tested using a dimer consisting of two gold nanospheres and four-wave