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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| Published in | IMA journal of applied mathematics Vol. 86; no. 5; pp. 856 - 895 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Oxford University Press
01.10.2021
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| Abstract | 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. |
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| AbstractList | 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. 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. |
| Author | Gomila, D Parra-Rivas, P Gelens, L Knobloch, E |
| Author_xml | – sequence: 1 givenname: P surname: Parra-Rivas fullname: Parra-Rivas, P email: pparrari@ulb.ac.be – sequence: 2 givenname: E surname: Knobloch fullname: Knobloch, E – sequence: 3 givenname: L surname: Gelens fullname: Gelens, L – sequence: 4 givenname: D surname: Gomila fullname: Gomila, D |
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| CitedBy_id | crossref_primary_10_1063_5_0143923 crossref_primary_10_1103_PhysRevA_109_033524 crossref_primary_10_1137_24M1644328 crossref_primary_10_1364_OPTICA_460175 crossref_primary_10_1063_5_0133576 crossref_primary_10_1063_5_0249873 crossref_primary_10_1016_j_chaos_2023_114064 crossref_primary_10_1038_s41467_023_38412_w crossref_primary_10_1103_PhysRevE_108_014203 crossref_primary_10_1103_PhysRevE_110_054409 crossref_primary_10_1038_s41377_023_01076_8 crossref_primary_10_1109_JPHOT_2024_3370179 crossref_primary_10_1016_j_chaos_2024_115201 crossref_primary_10_1103_PhysRevFluids_10_034402 crossref_primary_10_1038_s42005_023_01176_2 crossref_primary_10_1364_OL_472900 crossref_primary_10_1364_AOP_438025 crossref_primary_10_1140_epjp_s13360_023_04803_7 crossref_primary_10_1016_j_chaos_2023_113808 |
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| Keywords | non-linear optics bifurcation structure homoclinic snaking collapsed snaking |
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Localized coherent structures can form in externally driven dispersive optical cavities with a Kerr-type non-linearity. Such systems are described by... Localized coherent structures can form in externally driven dispersive optical cavities with a Kerr-type non-linearity. Such systems are described by the... |
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| Title | Origin, bifurcation structure and stability of localized states in Kerr dispersive optical cavities |
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