Origin, bifurcation structure and stability of localized states in Kerr dispersive optical cavities

TL;DR

This paper reviews the formation, stability, and bifurcation structures of localized states in Kerr dispersive optical cavities modeled by the Lugiato-Lefever equation, focusing on anomalous and normal dispersion regimes.

Contribution

It provides a comprehensive analysis of localized structures' bifurcation scenarios in different dispersion regimes within the Lugiato-Lefever framework.

Findings

Localized structures exhibit homoclinic snaking in anomalous dispersion.

Foliated snaking occurs when homoclinic snaking is destroyed.

Collapsed snaking characterizes bifurcations in the normal dispersion regime.

Abstract

Localized coherent structures can form in externally-driven dispersive optical cavities with a Kerr-type nonlinearity. Such systems are described by the Lugiato-Lefever equation, which supports a large variety of dynamical solutions. Here, we review our current knowledge on the formation, stability and bifurcation structure of localized structures in the one-dimensional Lugiato-Lefever equation. We do so by focusing on two main regimes of operation: anomalous and normal second-order dispersion. In the anomalous regime, localized patterns are organized in a homoclinic snaking scenario, which is eventually destroyed, leading to a foliated snaking bifurcation structure. In the normal regime, however, localized structures undergo a different type of bifurcation structure, known as collapsed snaking.