Propagation and collisions of semidiscrete solitons in arrayed and stacked waveguides

摘要

We consider shapes and dynamics of semidiscrete solitons (SDSs) in the known model of the set of linearlyncoupled waveguides with intrinsic cubic nonlinearity. The model applies to the description of a planar array ofnoptical fibers or of a stack of parallel planar waveguides, in the temporal and spatial domains, respectively, asnwell as to the self-attractive Bose-Einstein condensate (BEC) loaded into an array of parallel tunnel-coupledncigar-shaped traps. It was found previously that the interplay of the group-velocity dispersion, discrete diffractionn(in the longitudinal and transverse directions, respectively), and intrinsic self-focusing gives rise to SDSs in thenarray. We here develop the variational approximation (VA) and additional analytical methods for the descriptionnof the SDSs, and study their mobility and collisions by means of systematic simulations. The VA and an exactnsolution of the linearized equation in the cores adjacent to the central one produce an accurate description for thenfamily of stable fundamental on-site-centered SDS solutions, as well as of surface SDSs in the semi-infinite array.nThe VA is also presented for transversely unstable intersite-centered solitons. In simulations, the solitons arennot mobile in the discrete direction (nonsoliton semidiscrete modes may be mobile across the array). Collisionsnbetween SDSs traveling in the longitudinal direction feature a threshold separating the passage and mergernor destruction. The exact shape of the threshold, considered as a function of the solitons’ energy, featuresnirregularities, while its average form is explained analytically. “Shifted” collisions between SDSs centered atnadjacent cores are also studied.