Size dependence of second-harmonic generation at the surface of microspheres

The resonance-enhanced surface second-harmonic generation (SHG) from a suspension of polystyrene microspheres was investigated as a function of particle size in a range of the order of the fundamental wavelength for two different second-harmonic-enhancing dyes--malachite green and pyridine 1. The two dyes gave the same strongly modulated pattern of the forward second-harmonic scattering efficiency. Direct comparison to the nonlinear Rayleigh-Gans-Debye (NLRGD) and nonlinear Wentzel-Kramers-Brillouin (NLWKB) model predictions showed that the NLWKB model reproduces the overall trend in the size dependence but fails with respect to the strong modulations. The standard NLRGD model was found to fail altogether in the present particle size range, which was well beyond the observed upper particle size for which the NLRGD and NLWKB models give comparable results. A generalization of the NLRGD model to allow for dispersion and to use the particle refractive indices instead of those of the surrounding medium extended its applicability range by almost an order of magnitude in particle size. There is a pronounced maximal SHG efficiency for particles with a radius that is close to the fundamental wavelength inside the particle. The optically soft particle approximation is inadequate to describe the SHG in this particle size range, as refraction and reflection of the waves at the particle surface have a decisive influence. Dispersion of the media plays a negligible role for particle sizes up to about twice the optimal one for SHG.