Quadratic solitons in nonlinear dynamical lattices

Abstract

We propose a lattice model, in both one- and multidimensional versions, which may give rise to matching conditions necessary for the generation of solitons through the second-harmonic generation. The model describes an array of linearly coupled two-component dipoles in an anisotropic nonlinear host medium. Unlike this discrete system, its continuum counterpart gives rise to the matching conditions only in a trivial degenerate situation. A system of nonlinear evolution equations for slowly varying envelope functions of the resonantly coupled fundamental- and second-harmonic waves is derived. In the one-dimensional case, it coincides with the standard system known in nonlinear optics, which gives rise to stable solitons. In the multidimensional case, the system proves to be more general than its counterpart in optics, because of the anisotropy of the underlying lattice model.