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

正常色散Kerr谐振腔中多模共振向塌缩蛇形分岔结构的转变：亮孤子与暗孤子

Multimode resonance transition to collapsed snaking in normal dispersion Kerr resonators: Bright versus dark solitons

本文研究正常色散Kerr腔中相位调制诱导的多模共振如何促进高阶亮孤子形成，并揭示随势强度减小亮孤子向暗孤子转变对应于多模共振向塌缩蛇形分岔结构的演化，为访问多稳态提供新途径。

具有四次-二次色散的塌陷蛇形相关暗和亮Kerr耗孤子的涌现

Emergence of collapsed snaking related dark and bright Kerr dissipative solitons with quartic-quadratic dispersion

该研究理论探究了含二阶、四阶色散的Kerr腔中暗局域态的特性，揭示其由畴壁锁定形成、呈塌陷同宿蛇形分岔结构，还发现增大四阶色散可稳定亮局域态。

Experimental observations of bright dissipative Kerr cavity solitons and their collapsed snaking in a driven resonator with normal dispersion

Driven Kerr nonlinear optical resonators can sustain localized structures known as dissipative Kerr cavity solitons, which have recently attracted significant attention as the temporal counterparts of microresonator optical frequency combs. Whilst conventional wisdom asserts that bright cavity solitons can only exist in the region of anomalous dispersion, recent theoretical studies have predicted that higher-order dispersion can fundamentally alter the situation, enabling bright localized structures even under conditions of normal dispersion driving. Here we demonstrate a flexible optical fibr…

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

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…

Parametric localized patterns and breathers in dispersive quadratic cavities

We study the formation of localized patterns arising in doubly resonant dispersive optical parametric oscillators. They form through the locking of fronts connecting a continuous-wave and a Turing pattern state. This type of localized pattern can be seen as a slug of the pattern embedded in a homogeneous surrounding. They are organized in terms of a homoclinic snaking bifurcation structure, which is preserved under the modification of the control parameter of the system. We show that, in the presence of phase mismatch, localized patterns can undergo oscillatory instabilities which make them br…

Localized structures formed through domain wall locking in cavity-enhanced second-harmonic generation

We analyze the formation of localized structures in cavity-enhanced second-harmonic generation. We focus on the phase-matched limit, and consider that fundamental and generated waves have opposite sign of group velocity dispersion. We show that these states form due to the locking of domain walls connecting two stable homogeneous states of the system, and undergo collapsed snaking. We study the impact of temporal walk-off on the stability and dynamics of these localized states.