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Title: 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, 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.  more » « less
Award ID(s):
1908891
NSF-PAR ID:
10333629
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
IMA Journal of Applied Mathematics
Volume:
86
Issue:
5
ISSN:
0272-4960
Page Range / eLocation ID:
856 to 895
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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