Self-synchronization Phenomena in the Lugiato-Lefever Equation

TL;DR

This paper investigates self-synchronization phenomena in the Lugiato-Lefever equation, revealing how stable cavity solitons and patterns emerge through a new reduced oscillator model that links mode synchronization with pattern formation.

Contribution

It introduces a novel reduced nonlinear oscillator model for the Lugiato-Lefever equation, elucidating the connection between self-synchronization and spatiotemporal pattern formation in optical resonators.

Findings

Identification of stable cavity solitons and Turing patterns

Development of a reduced oscillator model capturing synchronization

Insight into energy and momentum conservation governing coupling

Abstract

The damped driven nonlinear Schr\"odinger equation (NLSE) has been used to understand a range of physical phenomena in diverse systems. Studying this equation in the context of optical hyper-parametric oscillators in anomalous-dispersion dissipative cavities, where NLSE is usually referred to as the Lugiato-Lefever equation (LLE), we are led to a new, reduced nonlinear oscillator model which uncovers the essence of the spontaneous creation of sharply peaked pulses in optical resonators. We identify attracting solutions for this model which correspond to stable cavity solitons and Turing patterns, and study their degree of stability. The reduced model embodies the fundamental connection between mode synchronization and spatiotemporal pattern formation, and represents a novel class of self-synchronization processes in which coupling between nonlinear oscillators is governed by energy and momentum conservation.