International audienceWe consider a photonic crystal fiber resonator pumped by a coherent injected beam. We show that temporal cavity solitons exhibit a motion with a constant velocity. This regular drift is induced by a broken reflection symmetry mediated by a third-order dispersion. We focus the analysis on dark temporal cavity solitons. They consist of asymmetric moving dips in a uniform background of the intensity profile. The number of the moving dips and their temporal distribution are determined solely by the initial conditions. We characterize this motion by computing the velocity of the dark temporal cavity soliton. Without fourth-order dispersion, dark cavity solitons do not exist

We investigate analytically and numerically the formation of temporal localized structures (TLSs) in an all photonic crystal fibre resonator. These dissipative structures consist of isolated or randomly distributed peaks in a uniform background of the intensity profile. The number of peaks and their temporal distribution are determined solely by the initial conditions. They exhibit multistability behaviour for a finite range of parameters. A weakly nonlinear analysis is performed in the neighbourhood of the first threshold associated with the modulational instability. We consider the regime where the instability is not degenerate. We show that fourth-order dispersion affects the threshold associated with the formation of bright TLSs. We estimate both analytically and numerically the linear and nonlinear corrections to the velocity of moving temporal structures induced by spontaneous broken reflection symmetry mediated by third-order dispersion. Finally, we show that thirdorder dispersion affects the threshold associated with the moving TLSs.

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.

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