Domain patterns for quasi-phase matching in whispering-gallery modes

Quasi-phase matching conditions for second-harmonic generation are analyzed for whispering-gallery modes. Several domain patterns, particularly those useful for resonators made of lithium niobate, are compared in terms of their effective nonlinear optical coefficients and spectral bandwidths. Only if the grating period at the circular surface of the resonator is monotonically increasing will the effective nonlinearity be independent of small variations of the properties of the resonator, such as the radius, and the offset between the domain pattern and the center of the resonator.