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arXiv · 2010.03375

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

P. Parra-Rivas·E. Knobloch·L. Gelens·D. Gomila
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Abstract

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 eventually destroyed, leading to a foliated snaking bifurcation structure. In the normal regime, however, localized structures undergo a different type of bifurcation structure, known as collapsed snaking.

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P. Parra-Rivas, E. Knobloch, L. Gelens, D. Gomila. 2020-10-07. Origin, bifurcation structure and stability of localized states in Kerr dispersive optical cavities. https://arxiv.org/abs/2010.03375

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