Dark solitons in the Lugiato-Lefever equation with normal dispersion

Abstract

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 presence of a region in parameter space with a finite multiplicity of dark solitons. For some parameter values dynamical instabilities are responsible for the appearance of oscillations and temporal chaos. The importance of the results for understanding frequency comb generation in microresonators is emphasized.

18 pages, 22 figures

References in corpus (20)

• Optical frequency comb generation from a monolithic microresonator
• Complex Patterns in a Simple System
• Mode interaction aided excitation of dark solitons in microresonators constructed of normal dispersion waveguides
• Universal Dynamics of Kerr Frequency Comb Formation in Microresonators
• Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model
• Octave-spanning frequency comb generation in a silicon nitride chip
• Spectral Line-by-Line Pulse Shaping of an On-Chip Microresonator Frequency Comb
• 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
• Universal scaling laws of Kerr frequency combs
• Frequency combs and platicons in optical microresonators with normal GVD
• 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
• Excitability mediated by localized structures
• Bistability and instability of dark-antidark solitons in the cubic-quintic nonlinear Schroedinger equation
• Phase-space structure of two-dimensional excitable localized structures
• Formation of localized structures in bistable systems through nonlocal spatial coupling I: General framework
• Effects of inhomogeneities and drift on the dynamics of temporal solitons in fiber cavities and microresonators
• Formation of localized structures in bistable systems through nonlocal spatial coupling II: The nonlocal Ginzburg Landau Equation
• Dissipative soliton excitability induced by spatial inhomogeneities and drift

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• Localized structures formed through domain wall locking in cavity-enhanced second-harmonic generation
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• Generation of Vector Platicons and Hybrid Soliton-Platicon Complexes in Optical Microresonators via Modulated Pump
• Stationary peaks in a multivariable reaction--diffusion system: Foliated snaking due to subcritical Turing instability
• Dark quadratic localized states and collapsed snaking in doubly resonant dispersive cavity enhanced second harmonic generation
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• Bandwidth and Conversion-Efficiency Analysis of Kerr Soliton Combs in Dual-Pumped Resonators with Anomalous Dispersion
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• Two-color flat-top solitons in microresonator-based optical parametric oscillators
• A Korteweg-de Vries description of dark solitons in polariton superfluids
• Temporal localized states and square-waves in semiconductor micro-resonators with strong time-delayed feedback
• Stochastic and deterministic switches in a bistable polariton micropillar under short optical pulses
• Platicon Stability in Hot Cavities
• Emergence of collapsed snaking related dark and bright Kerr dissipative solitons with quartic-quadratic dispersion
• Stationary States and Instabilities of a Mobius Fibre Resonator
• Bistability of travelling waves and wave-pinning states in a mass-conserved reaction-diffusion system: From bifurcations to implications for actin waves
• Hybrid patterns and solitonic frequency combs in non-Hermitian Kerr Cavities
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• Metamorphoses of the flow past an obstacle of a resonantly-driven bistable polariton fluid
• Global search for localised modes in scalar and vector nonlinear Schrödinger-type equations
• Observation of the Eckhaus Instability in Whispering-Gallery Mode Resonators
• Origin, bifurcation structure and stability of localized states in Kerr dispersive optical cavities
• Experimental and numerical investigations of switching wave dynamics in a normally dispersive fiber ring resonator
• Impact of phase modulation on the dynamics of temporal localized structures in injected Kerr microcavities
• Effects of source and loss terms on the wave-pinning description of cell polarisation