Bifurcation structure of localized states in the Lugiato-Lefever equation with anomalous dispersion

TL;DR

This paper investigates the bifurcation structures of localized bright states in the Lugiato-Lefever equation with anomalous dispersion, revealing how these structures evolve with system parameters in fiber cavities and microresonators.

Contribution

It characterizes the bifurcation structures of localized states in the Lugiato-Lefever equation, including the transition from homoclinic snaking to foliated snaking as detuning varies.

Findings

Bright localized states form homoclinic snaking bifurcation structures at low detuning.

Increasing detuning destroys the snaking structure and leads to foliated snaking bifurcation.

The bifurcation transition depends on the intracavity phase detuning value.

Abstract

The origin, stability and bifurcation structure of different types of bright localized structures described by the Lugiato-Lefever equation is studied. This mean field model describes the nonlinear dynamics of light circulating in fiber cavities and microresonators. In the case of anomalous group velocity dispersion and low values of the intracavity phase detuning these bright states are organized in a homoclinic snaking bifurcation structure. We describe how this bifurcation structure is destroyed when the detuning is increased across a critical value, and determine how a new bifurcation structure known as foliated snaking emerges.