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M. Kauranen et al.
opens the path towards metamaterials with truly tailorable nonlinear properties. We
have also presented the first example of this possibility by modifying the nonlinear
response by the detailed arrangement of the particles in the array.
In spite of this experimental progress, there are still several theoretical challenges
in the understanding of the nonlinear properties of plasmonic metal nanostructures.
For a proper approach, one would have to account for the locally varying fields,
nonlinear responses, and nonlinear sources. However, it is not clear at present as
to what the relative importance of the surface and bulk effects in the local secondorder response are. Our experiments on planar metal films suggest that surface terms
dominate [130]. Some theoretical approaches, on the other hand, have emphasized
bulk terms [59, 131], whereas others indicate that the weight of surface and bulk
effects depends on the experiment [117]. It is not even clear whether the various
approaches are mutually compatible, representing different limiting cases of the
same underlying approach.
The role of surface and bulk effects in the local nonlinear response may have
significant implications for the optimization of the local-field distribution in the metal
structure. The plasmonic resonances typically confine the strongest fields into small
volumes at the ends of the nanoparticles. If the local response mainly arises from the
local surface response, the present approaches poorly utilize the total surface area
of the metal particles. It will be interesting to see whether completely new sample
designs can be conceived, where the strong fields are spread over larger surface areas.
The role of resonance enhancement as such is better understood. As usual, a nonlinear response is enhanced when any combination of the interacting frequencies is
resonant with the nonlinear material. In contrast to traditional atomic, molecular, and
crystal systems, where resonant transition between the energy levels of the system
play a role, the resonances of plasmonic systems arise mainly from the local-field factors [132]. It has recently been suggested that, for harmonic generation, a resonance
at the fundamental frequency is beneficial, whereas a resonance at the harmonic frequency is just a loss mechanism [61]. However, this may also be due to fact that the
strong local fields at the fundamental and second-harmonic frequency do not overlap
spatially. In principle, a resonance at the harmonic output frequency should also be
beneficial, as is the case for other cases where plasmonic systems are used to enhance
radiation. It therefore remains to be seen whether the nonlinear responses could be
further enhanced by simultaneous resonances at multiple wavelengths.
Losses are nevertheless a significant challenge for plasmonic systems. For now,
the strongest nonlinear responses have been obtained at resonances with high losses.
One approach to mitigate this may be to utilize diffractive coupling between the
particles. It can lead to sharper resonances, which may allow optimizing the losses
and resonance enhancement in an attractive way. Another possibility is to use the
higher-order plasmon resonances, which can also enhance the nonlinear response
without significantly increasing the losses.
Additional routes for optimizing the nonlinear optical properties of metal nanostructures can be found by combining several particles into more complex structures.
We have demonstrated this by the T-nanodimers, where the coupling between the
bars significantly affected the nonlinear response. In the future, the dimensions of
M. Kauranen et al.
opens the path towards metamaterials with truly tailorable nonlinear properties. We
have also presented the first example of this possibility by modifying the nonlinear
response by the detailed arrangement of the particles in the array.
In spite of this experimental progress, there are still several theoretical challenges
in the understanding of the nonlinear properties of plasmonic metal nanostructures.
For a proper approach, one would have to account for the locally varying fields,
nonlinear responses, and nonlinear sources. However, it is not clear at present as
to what the relative importance of the surface and bulk effects in the local secondorder response are. Our experiments on planar metal films suggest that surface terms
dominate [130]. Some theoretical approaches, on the other hand, have emphasized
bulk terms [59, 131], whereas others indicate that the weight of surface and bulk
effects depends on the experiment [117]. It is not even clear whether the various
approaches are mutually compatible, representing different limiting cases of the
same underlying approach.
The role of surface and bulk effects in the local nonlinear response may have
significant implications for the optimization of the local-field distribution in the metal
structure. The plasmonic resonances typically confine the strongest fields into small
volumes at the ends of the nanoparticles. If the local response mainly arises from the
local surface response, the present approaches poorly utilize the total surface area
of the metal particles. It will be interesting to see whether completely new sample
designs can be conceived, where the strong fields are spread over larger surface areas.
The role of resonance enhancement as such is better understood. As usual, a nonlinear response is enhanced when any combination of the interacting frequencies is
resonant with the nonlinear material. In contrast to traditional atomic, molecular, and
crystal systems, where resonant transition between the energy levels of the system
play a role, the resonances of plasmonic systems arise mainly from the local-field factors [132]. It has recently been suggested that, for harmonic generation, a resonance
at the fundamental frequency is beneficial, whereas a resonance at the harmonic frequency is just a loss mechanism [61]. However, this may also be due to fact that the
strong local fields at the fundamental and second-harmonic frequency do not overlap
spatially. In principle, a resonance at the harmonic output frequency should also be
beneficial, as is the case for other cases where plasmonic systems are used to enhance
radiation. It therefore remains to be seen whether the nonlinear responses could be
further enhanced by simultaneous resonances at multiple wavelengths.
Losses are nevertheless a significant challenge for plasmonic systems. For now,
the strongest nonlinear responses have been obtained at resonances with high losses.
One approach to mitigate this may be to utilize diffractive coupling between the
particles. It can lead to sharper resonances, which may allow optimizing the losses
and resonance enhancement in an attractive way. Another possibility is to use the
higher-order plasmon resonances, which can also enhance the nonlinear response
without significantly increasing the losses.
Additional routes for optimizing the nonlinear optical properties of metal nanostructures can be found by combining several particles into more complex structures.
We have demonstrated this by the T-nanodimers, where the coupling between the
bars significantly affected the nonlinear response. In the future, the dimensions of