Up- and down-conversion at three-wave interaction in medium with combined nonlinear response

摘要

In this paper we construct the solution of nonlinear Schrdinger equations, describing the three-wave interaction in medium with combined (cubic and quadratic) nonlinear response under the condition of long pulse duration and plane wave approximation. The main feature of applied approach concludes in using of Hamiltonian of the equations set to find the algebraical equation with respect to difference of phases of interacting waves without the solution of the corresponding differential equation. For three-wave interaction we write the integral which depends on mismatching of wave-vectors and on input intensities of interacting waves. The evolution of intensity of each wave is express by the elliptical function