Swift-Hohenberg equation with third order dispersion for optical fiber cavity

Abstract

We investigate the dynamics of a ring cavity made of photonic crystal fiber and driven by a coherent beam working near the resonant frequency of the cavity. By means of a multiple-scale reduction of the Lugiato-Lefever equation with high order dispersion, we show that the dynamics of this optical device, when operating close to the critical point associated with bistability, is captured by a real order parameter equation in the form of a generalized Swift-Hohenberg equation. A Swift-Hohenberg equation has been derived for several areas of nonlinear science such as chemistry, biology, ecology, optics, and laser physics. However, the peculiarity of the obtained generalized Swift-Hohenberg equation for photonic crystal fiber resonators is that it possesses a third-order dispersion. Based on a weakly nonlinear analysis in the vicinity of the modulational instability threshold, we characterize the motion of dissipative structures by estimating their propagation speed. Finally, we numerically investigate the formation of moving temporal localized structures often called cavity solitons.

arXiv comment8 pages, ) figures

References in corpus (10)

• Spectral Line-by-Line Pulse Shaping of an On-Chip Microresonator Frequency Comb
• Spatiotemporal Model for Kerr Comb Generation in Whispering Gallery Mode Resonators
• Hybrid photonic-crystal fiber
• Introduction: Localized Structures in Dissipative Media: From Optics to Plant Ecology
• Stable dark and bright soliton Kerr combs can coexist in normal dispersion resonators
• Bouncing localized structures in a liquid-crystal light-valve experiment
• Effect of Cherenkov radiation on localized states interaction
• Dissipative soliton excitability induced by spatial inhomogeneities and drift
• Existence and Switching Behavior of Bright and Dark Kerr Solitons in Whispering-Gallery Mode Resonators with Zero Group-Velocity Dispersion
• Spontaneous motion of localized structures induced by parity symmetry transition

Cited by in corpus (6)

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• Modulating traveling fronts in a dispersive Swift-Hohenberg equation coupled to an additional conservation law
• Spatially Extended Dislocations Produced by the Dispersive Swift-Hohenberg Equation
• Dynamic Transitions of the Swift-Hohenberg Equation with Third-Order Dispersion