Origin, bifurcation structure and stability of localized states in Kerr dispersive optical cavities
arXiv:2010.03375
Abstract
Localized coherent structures can form in externally-driven dispersive optical cavities with a Kerr-type nonlinearity. Such systems are described by the Lugiato-Lefever equation, which supports a large variety of dynamical solutions. Here, we review our current knowledge on the formation, stability and bifurcation structure of localized structures in the one-dimensional Lugiato-Lefever equation. We do so by focusing on two main regimes of operation: anomalous and normal second-order dispersion. In the anomalous regime, localized patterns are organized in a homoclinic snaking scenario, which is eventually destroyed, leading to a foliated snaking bifurcation structure. In the normal regime, however, localized structures undergo a different type of bifurcation structure, known as collapsed snaking.
References in corpus (34)
- Optical frequency comb generation from a monolithic microresonator
- Temporal solitons in optical microresonators
- Mode interaction aided excitation of dark solitons in microresonators constructed of normal dispersion waveguides
- Spatiotemporal Model for Kerr Comb Generation in Whispering Gallery Mode Resonators
- Stability Analysis of the Lugiato-Lefever Model for Kerr Optical Frequency Combs. Part I: Case of Normal Dispersion
- Frequency combs and platicons in optical microresonators with normal GVD
- Breather soliton dynamics in microresonators
- Dark solitons in the Lugiato-Lefever equation with normal dispersion
- Dynamics of localized and patterned structures in the Lugiato-Lefever equation determine the stability and shape of optical frequency combs
- Origin and stability of dark pulse Kerr combs in normal dispersion resonators
- Solitons and frequency combs in silica microring resonators: Interplay of the Raman and higher-order dispersion effects
- Observations of spatiotemporal instabilities in the strong-driving regime of an AC-driven nonlinear Schrödinger system
- Stable dark and bright soliton Kerr combs can coexist in normal dispersion resonators
- Bifurcation structure of localized states in the Lugiato-Lefever equation with anomalous dispersion
- Stimulated Raman Scattering Imposes Fundamental Limits to the Duration and Bandwidth of Temporal Cavity Solitons
- Excitability mediated by localized structures
- Dissipative Light Bullets in Passively Mode-Locked Semiconductor Lasers
- On localized vegetation patterns, fairy circles and localized patches in arid landscapes
- Switching dynamics of dark-pulse Kerr comb states in optical microresonators
- Effect of Cherenkov radiation on localized states interaction
- Interaction of solitons and the formation of bound states in the generalized Lugiato-Lefever equation
- Characterization of spatiotemporal chaos in Kerr optical frequency {comb generators} and in fiber cavity
- Turbulence-induced rogue waves in Kerr resonators
- Influence of Stimulated Raman Scattering on Kerr domain walls and localized structures
- Dynamical instabilities of dissipative solitons in nonlinear optical cavities with nonlocal materials
- Dark breathers in a normal dispersion optical microresonator
- Phase-space structure of two-dimensional excitable localized structures
- Time-delayed nonlocal response induces traveling localized structures
- Existence and Switching Behavior of Bright and Dark Kerr Solitons in Whispering-Gallery Mode Resonators with Zero Group-Velocity Dispersion
- Theory of quantum fluctuations of optical dissipative structures and its application to the squeezing properties of bright cavity solitons
- Parametric localized patterns and breathers in dispersive quadratic cavities
- Bifurcation structure of periodic patterns in the Lugiato-Lefever equation with anomalous dispersion
- Stability and variational analysis of cavity solitons under various perturbations
- Dissecting the snake: the transition from localized patterns to isolated spikes in pattern formation systems