Nonlinear mode coupling in whispering-gallery-mode resonators

TL;DR

This paper derives coupled nonlinear Schrödinger equations for mode interactions in whispering-gallery-mode resonators, revealing modulational instability and bright soliton trains in various dispersion regimes.

Contribution

It provides the first principle derivation of mode coupling equations in whispering-gallery resonators, advancing understanding of their nonlinear dynamics.

Findings

Identification of modulational instability regions

Existence of bright soliton trains in normal and anomalous dispersion regimes

Development of a theoretical framework for mode interactions

Abstract

We present a first principle derivation of the coupled nonlinear Schr\"{o}dinger equations that govern the interaction between two families of modes with different transverse profiles in a generic whispering-gallery-mode resonator. We find regions of modulational instability and the existence of trains of bright solitons both in the normal and in the anomalous dispersion regime.