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

Abstract

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.

Three‐wave mixing in whispering gallery resonators

“…In order to obtain a compromise between simple fabrication and high nonlinearity, patterns comprising six regions with parallel domains aligned along the y-axes have been proposed [54].…”

Nonlinear optics in spheres: from second harmonic scattering to quasi‐phase matched generation in whispering gallery modes

“…3. Recently, more complicated poling patterns were considered in relation to a toroidal cavity both theoretically [54] and experimentally [55] with the aim of a broader tunability. Finally, in [24] and [41], it was recognized that the effective nonlinear susceptibility could vary along the azimuthal coordinate for an AlGaAs crystal.…”

Continuous-wave ultraviolet emission through fourth-harmonic generation in a whispering-gallery resonator

“…We compensate for the deviation from momentum conservation by quasi phase-matching, as shown below. Quasi phase-matching to conserve momentum for the harmonics and pump is achieved by periodic poling of lithium niobate [30,33] and facilitated by a combination of high order transverse resonance modes [24]. For momentum conservation, the optimum poling period for each three-photon interaction harmonic generation process is given by ( )…”

“…Further, our millimeter-scale emitter is simple, as the polished lithium niobate resonator comprises both the nonlinear medium and the mode-confining resonator. Finally, a non-uniform poling of lithium niobate [30] and existence of higher order transverse modes [24] provides the required quasi phase-matching between the infrared pump and the corresponding near-infrared, visible, and ultraviolet harmonics.…”