Generalization of Second-Order Quasi-Phase Matching in Whispering Gallery Mode Resonators Using Berry Phase

TL;DR

This paper explores how Berry phase effects influence second-order nonlinear interactions in whispering gallery mode resonators, expanding the understanding of phase matching conditions across different crystal symmetries.

Contribution

It generalizes the quasi-phase matching theory in whispering gallery mode resonators by incorporating Berry phase effects, applicable to various crystal symmetries.

Findings

Berry phase causes additional quanta in azimuthal selection rules.

The theory is detailed for Zinc-blende materials and generalized to other symmetries.

Enhanced understanding of nonlinear processes in integrated photonics.

Abstract

Second order nonlinearities in whispering gallery mode resonators are highly investigated for their many applications such as wavelength converters, entangled photon sources and generation of frequency combs. In such systems, depending on the material under scrutiny, the derivation of quasi-phase matching equations can lead to the appearance of additional quanta in the selection rule on the azimuthal confinement order. Here, we demonstrate that these additional quanta show up due to the Berry phase experienced by the transverse spin angular momentum components of the whispering gallery modes during their circulation within the resonator. We first detail the case of Zinc-blende materials and then generalize this theory to other crystal symmetries relevant for integrated photonics.