Channel-guided light bullets

We construct solitons for two-dimensional (2D) spatiotemporal solitons [light bullets (LBs)] in models of a planar optical layer with an intrinsic guiding channel. We demonstrate that LBs may be stabilized, instead of an ordinary index-guiding channel, by a structure generated through localized transverse modulation of the group velocity dispersion (GVD) and χ(3) (nonlinearity) coefficients. Such GVD- and χ(3) -guiding channels can be induced by a change of the layer's thickness. In addition, the model with only the nonlinearity coefficient subject to the transverse modulation may be realized in terms of Bose-Einstein condensates. Stability regions for 2D solitons in these settings are identified in a numerical form, and explained by means of a variational approximation (VA). Since the transverse GVD nonuniformity destroys the Galilean invariance, boosted (moving) solitons are constructed too, in both numerical and variational forms, and a maximum boost, past which the solitons do not exist, is found. In the model based on the usual index-guiding channel, head-on collisions between boosted LBs are studied. Simulations demonstrate that fast solitons collide elastically, while slow ones merge into a breather. The transition between quasielastic collisions and the merger is explained by means of a dynamical variant of the VA.