Theory of surface-emitting second-harmonic generation from optically trapped microspheres

Abstract

Using a Debye-potential approach we present a theoretical formulation of surface-emitting second-harmonic generation (SESHG) from an optically trapped microsphere with Mie size. A useful analytical expression for evaluating the conversion efficiency is derived. With the surface-emitting scheme where nonlinear interactions among the whispering-gallery cavity modes (fundamental waves) and the scattering mode (second-harmonic wave) are considered, problems that would arise in the phase matching among discrete cavity modes are avoidable. Through numerical calculations for the SESHG from a ${\mathrm{LiNbO}}_3$ microsphere in water, we predict drastic enhancement of the process for certain sizes of the sphere.