Spatial Solitons in Quasi-Phase-Matched Quadratic Media

摘要

Recently there has been interest in producing "cubic-like" effects, such as self-focusing, in materials engineered to have a rapidly oscillating quadratic nonlinearity. If the nonlinearity oscillates on a fast enough scale, the governing quadratic equations can be effectively averaged to give cubic equations. We propose a multiple scales approach in which diffraction is neglected at leading order. In doing so, we obtain exact solutions to the leading order system and solvability conditions on the slow evolution and transverse spatial dependence which, ensure that the higher order corrections are periodic. Using a variational approach, dynamics and stability of the solutions to the slow envelope equations are described.