Nonlinear optics of random metal-dielectric films

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Abstract
Surface-enhanced optical nonlinearities are studied in a semicontinuous film consisting of metal granules randomly distributed on an insulating substrate. The local fields are very inhomogeneous in such films and consist of strongly localized sharp peaks. In peaks (“hot” spots), the local fields exceed the applied field by several orders of magnitudes resulting in giant enhancements of the optical nonlinearities. Because of such a pattern for the local field distributions, the nonlinear signals are mostly generated from small nanometer-size areas. The corresponding spatial distributions for the generated fields form, in turn, a set of very sharp peaks on a homogeneous, on average, semicontinuous film. It is shown that the spatial positions of the localized hot spots at the fundamental and generated frequencies are located, in general, in different parts of a film. The local enhancements in the hot spots exceed the average enhancement by several orders of magnitude. The predicted giant local enhancements open fascinating possibilities in nonlinear spectroscopy of single molecules on a semicontinuous metal film. A number of surface-enhanced optical nonlinearities are studied, namely, those that are responsible for the Kerr-effect, four-wave mixing, second-, and third-harmonic generation. The enhancement for nonlinear optical processes is shown to strongly increase toward the long-wavelength part of the spectrum. Spatial distributions of the local fields are calculated in our broad-scale numerical simulations. A scaling theory for the high-order field moments is developed. It predicts that the moments of the local fields are very large and independent of the frequency in a wide spectral range. The theory predicts anomalous field fluctuations and giant enhancements for the nonlinear optical processes, from the visible to the far-infrared spectral range.