Enhanced mobility of discrete solitons in anisotropic two-dimensional waveguide arrays with modulated separations

Abstract

We consider two-dimensional waveguide arrays with anisotropic coupling coefficients. We show using numerical and variational calculations that four stationary soliton types exist: Site-Centered, Bond-Centered, Hybrid-X and Hybrid-Y. For the isotropic case the last two modes become identical and equivalent to the known hybrid soliton. With a variational calculation using a gaussian trial function and six variational parameters corresponding to the soliton's position, width, and velocity components, the four stationary soliton types are reproduced and their equilibrium widths are accounted for accurately for a wide range of anisotropy ratios. We obtained using the variational calculation the Peierls-Nabarro potential and barrier heights for the four soliton types and different anisotropy ratios. We have also obtained a phase diagram showing regions of soliton stability against collapse and subregions of mobility in terms of the initial kick-in speed and anisotropy ratio. The phase diagram shows that 2D solitons become highly mobile for anisotropy ratios larger than some critical values that depend on the initial kick-in speed. This fact was then exploited to design tracks within the 2D waveguide array along which the soliton can be accelerated and routed. We have calculated the actual waveguide separations needed to realist the proposed guided trajectories of 2D solitons.