Enhanced second harmonic generation by nanorough surfaces: Nanoscale depolarization, dephasing, correlations, and giant fluctuations

On the basis of spectral-expansion Green's function theory, we theoretically describe the topography, polarization, and spatial-coherence properties of the second-harmonic (SH) local fields at rough metal surfaces. The spatial distributions of the fundamental-frequency and SH local fields are very different, with highly-enhanced hot spots of the SH. The spatial correlation functions of the amplitude, phase, and direction of the SH polarization all show spatial decay on the nanoscale in the wide range of the metal fill factors. This implies that SH radiation collected from even nanometer-scale areas is strongly depolarized and dephased, i.e., has the nature of hyper-Rayleigh scattering, in agreement with recent experiments. The present theory is applicable to nanometer-scale nonlinear-optical illumination, probing, and modification.