Curvilinear Motion of Multivortex Laser-Soliton Complexes with Strong and Weak Coupling

We reveal the existence of stable dissipative soliton complexes with curvilinear motion of their center of mass. This type of motion results from the field distribution asymmetry and is well pronounced for asymmetric complexes of laser solitons with strong coupling. We present results of numerical simulations of such complexes in a model of wide-aperture lasers or laser amplifiers with saturable gain and absorption. The complex consists of a pair of strongly coupled vortex solitons weakly coupled with a number of other vortex solitons. Similar complexes are expected to exist in different spatially distributed nonlinear dissipative systems, including schemes with discrete dissipative solitons.

Figure 1

Instantaneous transverse distributions of intensity (a),(b) and trajectories of center of mass (c),(d) of a strongly coupled rotating pair of two vortices with opposite charges [(a),(c), $d=0.06$)] and the core-one satellite structure [(b),(d), $d=0.12$; 1: the first revolution of the satellite, $t=(73710,78110)$; 2: the sixth revolution, $t=(95310,99710)$]. Arrows in (a),(b) indicate direction of structure rotation, and arrows in (c) indicate directions of averaged Poynting vector, $⟨{\mathit{S}}_{\perp }⟩$, in different moments; $g_0=2.108$.

Figure 2

Transverse distributions of intensity (a) and phase (b) for a core-two satellite structure. The rotation period is 1100 for the core and 11 000 for the satellites. The arrow indicates rotation direction. Phase images are scaled from $-\pi$ (black) to $\pi$ (white); $d=0.12$, $g_0=2.108$.

Figure 3

Energy flows for the stable localized structure given in Fig. 2, at $t=0$. Closed trajectories correspond to limit cycles. Two insets represent the vicinity of the weak overlapping of the core and satellites, and include nodes $N$ and saddles $S$ with separatrices given by dashed curves. The large arrow indicates rotation direction.

Figure 4

Dynamics of restoration of opposite positions of two satellites after their initial perturbation. Parameters are $d=0.15$ and $g_0=2.108$.