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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 first part was devoted to the regime of normal dispersion, and was presented in ref. cite{Part_I}. 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 different 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 super- and 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 identified, 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.
We raise a detuning-dependent loss mechanism to describe the soliton formation dynamics when the lumped filtering operation is manipulated in anomalous group velocity dispersion regime, using stability analysis of generalized Lugiato-Lefever equation.
The regions of existence and stability of dark solitons in the Lugiato-Lefever model with normal chromatic dispersion are described. These localized states are shown to be organized in a bifurcation structure known as collapsed snaking implying the p
The model, that is usually called Lugiato-Lefever equation (LLE), was introduced in 1987 with the aim of providing a paradigm for dissipative structure and pattern formation in nonlinear optics. This model, describing a driven, detuned and damped non
A generalized Lugiato-Lefever equation is numerically solved with a Newton-Raphson method to model Kerr frequency combs. We obtain excellent agreement with past experiments, even for an octave-spanning comb. Simulations are much faster than with any
We analyze dark pulse Kerr frequency combs in optical resonators with normal group-velocity dispersion using the Lugiato-Lefever model. We show that in the time domain these correspond to interlocked switching waves between the upper and lower homoge