Numerical simulation of Lugiato-Lefever equation for Kerr combs generation in Fabry-Perot resonators

TL;DR

This paper develops and compares numerical methods for solving the Lugiato-Lefever equation in both dynamic and steady states, aiding the understanding of Kerr combs in Fabry-Perot resonators.

Contribution

It introduces numerical techniques tailored for the LLE in Fabry-Perot resonators and discusses mathematical properties to interpret simulation outcomes.

Findings

Numerical methods effectively solve the LLE in various regimes.

Mathematical properties assist in understanding simulation results.

Enhanced modeling of Kerr combs in Fabry-Perot resonators.

Abstract

Lugiato-Lefever equation (LLE) is a nonlinear Schr\"odinger equation with damping, detuning and driving terms, introduced as a model for Kerr combs generation in ring-shape resonators and more recently, in the form of a variant, in Fabry-Perot (FP) resonators. The aim of this paper is to present some numerical methods that complement each other to solve the LLE in its general form both in the dynamic and in the steady state regimes. We also provide some mathematical properties of the LLE likely to help the understanding and interpretation of the numerical simulation results.