Dissipative localized states and breathers in phase mismatched singly resonant optical parametric oscillators: Bifurcation structure and stability

TL;DR

This paper investigates the formation, bifurcation structures, and stability of dissipative localized states and breathers in phase mismatched singly resonant optical parametric oscillators, revealing complex bifurcation patterns and oscillatory behaviors.

Contribution

It provides a detailed bifurcation analysis of localized states in optical parametric oscillators, highlighting new bifurcation structures and stability properties in different bistable regimes.

Findings

Localized states form in collapsed and homoclinic snaking bifurcation structures.

Localized states can undergo oscillatory instabilities leading to breathing dynamics.

The study characterizes how control parameters influence bifurcation structures and stability.

Abstract

We study the emergence of dissipative localized states in phase mismatched singly resonant optical parametric oscillators. These states arise in two different bistable configurations due to the locking of fronts waves connecting the two coexisting states. In one of these configurations the bistabiity is mediated by the coexistence of two uniform states. Here the localized states are organized in a collapsed snaking bifurcation structure. Moreover, these states undergo oscillatory instabilities which lead to a breathing behavior. When the the bistability is related with the coexistence of an uniform state and a spatially periodic pattern, localized states are organized in a bifurcation structure similar to the standard homoclinic snaking. Performing an exhaustive bifurcation analysis, we characterize in detail the previous structures, their linear stability and the modification of their dynamics as a function of the control parameters of the system.