Origin, bifurcation structure and stability of localized states in Kerr dispersive optical cavities. (English) Zbl 1479.78019

Summary: Localized coherent structures can form in externally driven dispersive optical cavities with a Kerr-type non-linearity. Such systems are described by the Lugiato-Lefever (LL) equation, which supports a large variety of dynamical states. Here, we review our current knowledge of the formation, stability and bifurcation structure of localized structures in the one-dimensional LL 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, localized structures undergo a different type of bifurcation structure, known as collapsed snaking. The effects of third-order dispersion and various dynamical regimes are also described.


78A60 Lasers, masers, optical bistability, nonlinear optics
35B32 Bifurcations in context of PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
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