Stable Spatiotemporal Solitons in Bessel Optical Lattices

We investigate the existence and stability of three-dimensional solitons supported by cylindrical Bessel lattices in self-focusing media. If the lattice strength exceeds a threshold value, we show numerically, and using the variational approximation, that the solitons are stable within one or two intervals of values of their norm. In the latter case, the Hamiltonian versus norm diagram has a swallowtail shape with three cuspidal points. The model applies to Bose-Einstein condensates and to optical media with saturable nonlinearity, suggesting new ways of making stable three-dimensional solitons and “light bullets” of an arbitrary size.

Figure 1

(a) The propagation constant cutoff vs the lattice strength, shown for the cylindrical potentials of both types, $J_0$ and $J_0^2$. (b), (d) The soliton’s norm vs the propagation constant for the potentials $J_0$ and $J_0^2$, respectively. (c) The perturbation growth rate vs the propagation constant for the $J_0$ potential. Here and below, solid and dashed curves correspond, respectively, to stable and unstable branches.

Figure 2

The Hamiltonian vs norm diagrams for $p=5.5$ (a) and 8 (b). Here and below, all the figures are shown for the $J_0$ potential.

Figure 3

Isosurface plots for stable solitons: (a) $p=5$, $b=0.11$, $U=6.477$; (b) $p=5.5$, $b=0.85$, $U=3.677$; (c) $p=6$, $b=2$, $U=3.591$.

Figure 4

The evolution of a stable soliton under a random perturbation, for $p=5$, $b=0.11$, $U=6.477$: (a) $\xi =0$, (b) $\xi =200$, (c) $\xi =500$.