Theory of enhanced second-harmonic generation from randomly rough metal surfaces

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Abstract
We present a Green's-function theory of enhanced second-harmonic generation from a randomly rough metal surface. The enhancement is due to an increase in the incident field because of the excitation of the localized surface polaritons (SP's) at the fundamental frequency. Additional enhancements are found when these SP's generate another SP at the second-harmonic frequency due to the nonlinear interaction at the metal surface which decays into a radiative photon in the presence of surface roughness. Multiple scattering of SP's is included by the solution of the previously derived Bethe-Salpeter equation for the averaged two-SP Green's function. The calculated enhancements for Ag and Au rough surfaces are found to be in good agreement with the experiments.