Drift of dark cavity solitons in a photonic-crystal fiber resonator

We 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.

Figure 1

Schematic setup of cavity filled with photonic crystal fiber (PCF) and driven by a coherent input beam $S$ amplitude. BS denotes a beam splitter.

Figure 2

Single moving (a1) bright and (b1) dark temporal cavity solitons obtained by numerical simulations of Eq. (1). The parameters are $B_2=0.75$, $B_3=0.12$, $B_4=0.2$, and $\Delta =3$. For (a1, a2) $S=2;$ (b1, b2) $S=2.4$; and (a2, b2) are $\tau -t$ maps showing the time evolution of bright and dark cavity solitons, respectively. Maxima are plain white and mesh number integration is 512.

Figure 3

Bifurcation diagram associated with a moving single dark temporal cavity soliton. Parameters are $B_2=0.75$, $B_3=0.12$, $B_4=0.2$, and $\Delta =3$. The full (broken) curve indicates stable (unstable) solutions. The open circle indicates the minimum numerical values of the real part associated with moving DTCS.

Figure 4

$\tau -t$ maps showing the time evolution dark cavity solitons obtained for the same parameters as in Fig. 2b, the real part of the intracavity field presenting (a) two and (b) three moving dark temporal solitons obtained by numerical simulations of Eq. (1).