A ring resonator made of a silica-based optical fiber is a paradigmatic system for the generation of dissipative localized structures or dissipative solitons. We analyze the effect of the non-instantaneous nonlinear response of the fused silica or the Raman response on the formation of localized structures. After reducing the generalized Lugiato–Lefever to a simple and generic bistable model with a nonlocal Raman effect, we investigate analytically the formation of moving temporal localized structures. This reduction is valid close to the nascent bistability regime, where the system undergoes a second-order critical point marking the onset of a hysteresis loop. The interaction between fronts allows for the stabilization of temporal localized structures. Without the Raman effect, moving temporal localized structures do not exist, as shown in M. G. Clerc, S. Coulibaly, and M. Tlidi, Phys. Rev. Res. 2, 013024 (2020). The detailed derivation of the speed and the width associated with these structures is presented. We characterize numerically in detail the bifurcation structure and stability associated with the moving temporal localized states. The numerical results of the governing equations are in close agreement with analytical predictions.
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August 2020
Research Article|
August 03 2020
Nonlocal Raman response in Kerr resonators: Moving temporal localized structures and bifurcation structure
Special Collection:
Instabilities and Nonequilibrium Structures
M. G. Clerc
;
M. G. Clerc
1
Departamento de Física and Millennium Institute for Research in Optics, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile
, Casilla 487-3, Santiago, Chile
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S. Coulibaly
;
S. Coulibaly
a)
2
Univ. Lille, CNRS, UMR 8523 - PhLAM - Physique des Lasers Atomes et Molécules
, F-59000 Lille, France
a)Author to whom correspondence should be addressed: saliya.coulibaly@univ-lille.fr
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P. Parra-Rivas
;
P. Parra-Rivas
3
OPERA-photonique, Université libre de Bruxelles
, 50 Avenue F. D. Roosevelt, CP 194/5, B-1050 Bruxelles, Belgium
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M. Tlidi
M. Tlidi
4
Faculté des Sciences, Université Libre de Bruxelles (U.L.B)
, CP 231, Campus Plaine, B-1050 Bruxelles, Belgium
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a)Author to whom correspondence should be addressed: saliya.coulibaly@univ-lille.fr
Note: This article is part of the Focus Issue, Instabilities and Nonequilibrium Structures.
Chaos 30, 083111 (2020)
Article history
Received:
March 26 2020
Accepted:
July 13 2020
Citation
M. G. Clerc, S. Coulibaly, P. Parra-Rivas, M. Tlidi; Nonlocal Raman response in Kerr resonators: Moving temporal localized structures and bifurcation structure. Chaos 1 August 2020; 30 (8): 083111. https://doi.org/10.1063/5.0007350
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