Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes

By Cyril Godey, I. Balakireva, Aurelien Coillet, Yanne K. Chembo. 2013

379 citations recorded by the source corpus.

We present a stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs in whispering gallery mode resonators pumped in the anomalous dispersion regime. This article is the second part of a research work whose rst part was devoted to the regime of normal dispersion, and was presented in ref. [1]. The case of anomalous dispersion is indeed the most interesting from the theoretical point of view, because of the considerable variety of dynamical behaviors that can be observed. From a technological point of view, it is also the most relevant because it corresponds to the regime where Kerr combs are predominantly generated, studied, and used for dierent applications. In this article, we analyze the connection between the spatial patterns and the bifurcation structure of the eigenvalues associated to the various equilibria of the system. The bifurcation map evidences a considerable richness from a dynamical standpoint. We study in detail the emergence of superand sub-critical Turing patterns in the system. We determine the areas were bright isolated cavity solitons emerge, and we show that soliton molecules can emerge as well. Very complex temporal patterns can actually be observed in the system, where solitons (or soliton complexes) co-exist with or without mutual interactions. Our investigations also unveil the mechanism leading to the phenomenon of breathing solitons. Two routes to chaos in the system are identied, namely a route via the so called secondary combs, and another via soliton breathers. The Kerr combs corresponding to all these temporal patterns are analyzed in detail, and a discussion is led about the possibility to gain synthetic comprehension of the observed spectra out of the dynamical complexity of the system.

Subfields: Atomic and Molecular Physics, and Optics, Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d0140d3fa78e39a167bb5391313338f4ff0ee7ab

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In Atomic and Molecular Physics, and Optics

In Computer Networks and Communications

Yanne K. Chembo

In Statistical and Nonlinear Physics

Citations in the corpus

Micro-combs: A novel generation of optical sources (2017, background): “In-depth analyses of the characteristics of LLE solutions have been reported by a number of groups [184,192,216] and Fig.”
Mode-locked dark pulse Kerr combs in normal-dispersion microresonators (2014, methodology): “2 / 32 theory and simulation [27]-[28], investigating dark solitons experimentally is extremely difficult and no time-domain characterization has ever been reported.”
RF Photonics: An Optical Microcombs’ Perspective (2018, background): “occurs in the regime of anomalous dispersion, but it can also be sustained in the presence of normal dispersion, although under very marginal conditions [114], [119].”
Nonlinear photonics with high-Q whispering-gallery-mode resonators (2017, methodology): “It is interesting to note that the stability analysis of the LLE was first performed in the context of mathematical physics [145,146], and then in the context of Kerr combs [139,147].”
Kerr optical frequency combs: theory, applications and perspectives (2016, background): “Bright solitons are by essence subcritical, because they correspond to a pulse that has been isolated from a subcritical roll pattern in the anomalous dispersion regime [18].”
Integrated turnkey soliton microcombs (2019, background): “[36] C.”