Spatiotemporal Model for Kerr Comb Generation in Whispering Gallery Mode Resonators

TL;DR

This paper introduces a new spatio-temporal PDE model for Kerr comb generation in whispering gallery mode resonators, enabling better understanding and simulation of wide-span combs and pulse formation.

Contribution

It develops an exact PDE variant of the Lugiato-Lefever equation including higher-order effects, improving theoretical and numerical analysis of Kerr combs.

Findings

Kerr combs can be modeled as dissipative cavity solitons in anomalous dispersion regimes.

The model captures pulse formation with multiple interacting modes.

Wide-span combs can be generated with low pump power.

Abstract

We establish an exact partial differential equation to model Kerr comb generation in whispering-gallery mode resonators. This equation is a variant of the Lugiato-Lefever equation that includes higher-order dispersion and nonlinearity. This spatio-temporal model, whose main variable is the total intracavity field, is significantly more suitable than the modal expansion approach for the theoretical understanding and the numerical simulation of wide-span combs. It allows us to explore pulse formation in which a large number of modes interact cooperatively. This versatile approach can be straightforwardly extended to include higher-order dispersion, as well as other phenomena like Raman, Brillouin and Rayleigh scattering. We demonstrate for the first time that when the dispersion is anomalous, Kerr comb generation can arise as the spectral signature of dissipative cavity solitons, leading to wide-span combs with low pumping.