Dark quadratic localized states and collapsed snaking in doubly resonant dispersive cavity enhanced second harmonic generation

TL;DR

This paper theoretically explores the formation, bifurcation, and stability of dark localized states in a nonlinear optical cavity, revealing complex behaviors like collapsed snaking and oscillations in second harmonic generation.

Contribution

It introduces a detailed analysis of dark localized dissipative states in doubly resonant cavities, highlighting their bifurcation structure and dynamic behaviors, which were not previously characterized.

Findings

Dark localized states undergo collapsed homoclinic snaking.

States can exhibit oscillatory dynamics.

Bifurcation structure influences stability and dynamics.

Abstract

We theoretically investigate the dynamics, bifurcation structure and stability of quadratic dark localized dissipative states arising in cavity enhanced second-harmonic generation. These states, formed through the locking of plane front waves, undergo collapsed homoclinic snaking and may exhibit oscillatory dynamics.