Math. Model. Nat. Phenom.
Volume 15, 2020
Systems with Hysteresis and Switching
|Number of page(s)||18|
|Published online||24 September 2020|
2 Lobachevsky State University of Nizhni Novgorod, pr. Gagarina 23, Nizhni Novgorod 603950, Russia.
*** Corresponding author: email@example.com
Accepted: 21 November 2019
Nonlinear localised structures appear as solitary states in systems with multistability and hysteresis. In particular, localised structures of light known as temporal cavity solitons were observed recently experimentally in driven Kerr-cavities operating in the anomalous dispersion regime when one of the two bistable spatially homogeneous steady states exhibits a modulational instability. We use a distributed delay system to study theoretically the formation of temporal cavity solitons in an optically injected ring semiconductor-based fiber laser, and propose an approach to derive reduced delay-differential equation models taking into account the dispersion of the intracavity fiber delay line. Using these equations we perform the stability and bifurcation analysis of injection-locked continuous wave states and temporal cavity solitons.
Mathematics Subject Classification: 78A60 / 70K50 / 34K13 / 37G15
Key words: Temporal cavity solitons / semiconductor laser / chromatic dispersion / time-delay model / large delay
© The authors. Published by EDP Sciences, 2020
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