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

Abstract

We investigate the dynamics of a ring cavity made of photonic crystal fiber and driven by a coherent beam working near to 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.

Localized states in passive and active phase-field-crystal models

“…The influence of various nonvariational modifications of Eq. (1.1) through additional terms that break its gradient structure has also been discussed [Kubstrup et al, 1996;Burke et al, 2009;Houghton & Knobloch, 2011;Kozyreff & Tlidi, 2007;Burke & Dawes, 2012;Lejeune et al, 2004;Bordeu et al, 2016;Hariz et al, 2019].…”

Oscillatory motion of dissipative solitons induced by delay-feedback in inhomogeneous Kerr resonators

“…05 , the two folds collide, i.e., for lower values of A , no DS pinned on the center of the inhomogeneity exists. persion effect have been reported [33][34][35][36][37] . Nonlinear gradient convection term in the cubic complex Ginzburg-Landau can lead to the drift of dissipative solitons [38,39] .…”

Dynamic transitions of the Swift-Hohenberg equation with third-order dispersion

“…Of particular interest to us is when a ring cavity made of optical fibers is driven by a beam. When the beam is operating near the resonant frequency of the cavity, the dynamics exhibited by the the cavity is modelled by the Swift-Hohenberg equation with a third-order dispersion term [2].…”