Quasi-resonant and quasi-phase-matched nonlinear second-order phenomena in whispering-gallery resonators

Recently achieved radial poling of whispering-gallery resonators (WGRs) strongly extends the capabilities of tailoring the second-order nonlinear phenomena, such as second-harmonic generation and optical parametric oscillation, and transferring them to the range of low-power continuous-wave light sources. Owing to discreteness of the frequency spectrum, the resonance and phase-matching conditions for interacting waves cannot be fulfilled simultaneously in WGRs in the general case. Using Yariv’s generic approach to the description of WGR phenomena, we analyze two closely related issues: the possibilities to achieve the resonant and phase-matching conditions using the temperature tuning and the impact of detunings and phase mismatches on the nonlinear transformation efficiencies. It is shown that the radial poling provides important necessary conditions for the subsequent fine tuning to the nonlinear resonances. The requirements to the temperature tuning, as exemplified by the case of lithium niobate, are substantially dependent on the nonlinear process in question, the actual wavelength range, and the pump intensity.