A normal form for frequency combs and localized states in Kerr-Gires-Tournois interferometers

TL;DR

This paper develops a simplified mathematical model to explain how frequency combs and localized states form in Kerr-Gires-Tournois interferometers, linking physical setup parameters to pattern formation.

Contribution

It introduces a normal form reduction from complex delay equations to a cubic Ginzburg-Landau equation with high-order effects, clarifying the formation mechanisms of localized states.

Findings

Normal form accurately predicts localized states near bistability onset.

High-order effects like third order dispersion are crucial for localized state formation.

Model parameters relate directly to optical setup configurations.

Abstract

We elucidate the mechanisms that underly the formation of temporal localized states and frequency combs in vertical external-cavity Kerr-Gires-Tournois interferometers. We reduce our first principle model based upon delay algebraic equations to a minimal pattern formation scenario. It consists in a real cubic Ginzburg-Landau equation modified by high-order effects such as third order dispersion and nonlinear drift. The latter are responsible for generating localized states via the locking of domain walls connecting the high and low intensity levels of the injected micro-cavity. We interpret the effective parameters of the normal form in relation with the configuration of the optical setup. Comparing the two models, we observe an excellent agreement close to the onset of bistability.