Whispering-gallery-mode phase matching for surface second-order nonlinear optical processes in spherical microresonators

Abstract

The theory of surface-second-harmonic generation in a dielectric microsphere using whispering-gallery modes (WGMs) is developed. The second-order nonlinearity is restricted to the surface of the sphere. The coupling coefficients for a coupled-mode theory are derived and conditions for double resonance and phase matching are discussed for TE and TM polarizations. We demonstrate that phase matching of WGMs amounts to conservation of the angular momentum of the electromagnetic mode while at the same time we obtain an analytical expression for the coherence length.