Origin, bifurcation structure and stability of localized states in Kerr dispersive optical cavities

2020/10/07 by Pedro Parra‐Rivas, E. Knobloch, Parra-Rivas, P. +8 · 1 citation
Computer Science · Physics and Astronomy · #Advanced Fiber Laser Technologies #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Laser-Matter Interactions and Applications #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Optics (physics.optics) #Pattern Formation and Solitons (nlin.PS)

paper · pdf · doi:10.48550/arxiv.2010.03375

openalex publication_date 2020/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Dynamics of interacting cavity solitons

Related

• Stability Analysis of the Lugiato-Lefever Model for Kerr Optical Frequency Combs. Part II: Case of Anomalous Dispersion
• Dissipative structures in one- and two-dimensional Kerr cavities with a spatially periodic pump
• Existence and stability of soliton-based frequency combs in the Lugiato-Lefever equation
• The Lugiato-Lefever equation driven by a double tightly focused pump
• Nonlinear dynamics of dissipative structures in coherently-driven Kerr cavities with a parabolic potential