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

Abstract 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...

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Bibliographic Details
Published inIMA journal of applied mathematics Vol. 86; no. 5; pp. 856 - 895
Main Authors Parra-Rivas, P, Knobloch, E, Gelens, L, Gomila, D
Format Journal Article
LanguageEnglish
Published Oxford University Press 01.10.2021
Subjects
non-linear optics
bifurcation structure
homoclinic snaking
collapsed snaking
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Summary:Abstract 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.
ISSN:0272-4960
1464-3634
DOI:10.1093/imamat/hxab031