Walking Spatial Solitons in Nonlinear Quadratic Media

Both, spatial and temporal solitons (more properly, solitary waves) exist in bulk crystals and in optical waveguides made of nonlinear quadratic media [1]-[3]. Bright spatial solitons have been already observed in second harmonic generation experiments [4]-[5]. Families of stationary soliton solutions of the governing are known to exist under ideal conditions, namely when there is no walk-off betwen the interacting waves [2]-[3]. Temporal walk-off is due to different group velocities of the waves forming the soliton, while spatial beam walk-off is due to different propagation directions of energy and phase fronts in anisotropic media. Beam walk-off is always present in the experiments when birefringence-tuning phase-matching techniques are used. Numerical experiments indicate that solitonlike propagation occurs in the presence of walk-off [2], but physically relevant soliton solutions are not known at present.