Related papers: Origin, bifurcation structure and stability of loc…
The origin, stability and bifurcation structure of different types of bright localized structures described by the Lugiato-Lefever equation is studied. This mean field model describes the nonlinear dynamics of light circulating in fiber…
We study the stability and bifurcation structure of spatially extended patterns arising in nonlin- ear optical resonators with a Kerr-type nonlinearity and anomalous group velocity dispersion, as described by the 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…
We theoretically investigate the dynamics, bifurcation structure and stability of dark localized states emerging in Kerr cavities in the presence of second- and fourth-order dispersion. These states form through the locking of uniform wave…
We investigate the formation of dark vector localized structures in the presence of nonlinear polarization mode coupling in optical resonators subject to a coherent optical injection in the normal dispersion regime. This simple device is…
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…
It has been recently uncovered that coherent structures in microresonators such as cavity solitons and patterns are intimately related to Kerr frequency combs. In this work, we present a general analysis of the regions of existence and…
In this work we characterize the dynamical instabilities of localized structures exhibited by a recently introduced Gelens et al., Phys. Rev. A 75, 063812 2007 generalization of the Lugiato-Lefever model that includes a weakly nonlocal…
The Lugiato-Lefever equation is a cubic nonlinear Schr\"odinger equation, including damping, detuning and driving, which arises as a model in nonlinear optics. We study the existence of stationary waves which are found as solutions of a…
We consider the formation of temporal localized structures or Kerr comb generation in a microresonator with inhomogeneities. We show that the introduction of even a small inhomogeneity in the injected beam widens the stability region of…
We investigate time-independent solutions of a discrete optical cavity model featuring saturable Kerr nonlinearity, a discrete version of the Lugiato-Lefever equation. This model supports continuous wave (uniform) and localized (discrete…
We study temporally localized structures in doubly resonant degenerate optical parametric oscillators in the absence of temporal walk-off. We focus on states formed through the locking of domain walls between the zero and a non-zero…
We study the formation of localized patterns arising in doubly resonant dispersive optical parametric oscillators. They form through the locking of fronts connecting a continuous-wave and a Turing pattern state. This type of localized…
We study the emergence of dissipative localized states in phase mismatched singly resonant optical parametric oscillators. These states arise in two different bistable configurations due to the locking of fronts waves connecting the two…
We theoretically investigate the dynamics, bifurcation structure and stability of localized states in Kerr cavities driven at the pure fourth-order dispersion point. Both the normal and anomalous group velocity dispersion regimes are…
Many engineering structures are composed of weakly coupled sectors assembled in a cyclic and ideally symmetric configuration, which can be simplified as forced Duffing oscillators. In this paper, we study the emergence of localized states…
Two-dimensional spatially localized structures in the complex Ginzburg-Landau equation with 1:1 resonance are studied near the simultaneous occurrence of a steady front between two spatially homogeneous equilibria and a supercritical Turing…
Localized planar patterns in spatially extended bistable systems are known to exist along intricate bifurcation diagrams, which are commonly referred to as snaking curves. Their analysis is challenging as techniques such as spatial dynamics…
Lugiato-Lefever (LL) equations in one and two dimensions (1D and 2D) accurately describe the dynamics of optical fields in pumped lossy cavities with the intrinsic Kerr nonlinearity. The external pump is usually assumed to be uniform, but…
We study the stabilization of localized structures by discreteness in one-dimensional lattices of diffusively coupled nonlinear sites. We find that in an external driving field these structures may lose their stability by either relaxing to…