Counterpropagating geometries in periodically poled crystals

Summary form only given.Crystals whose quadratic susceptibility, /spl xi//sup (2)/, is modulated periodically in space can be used to phase match two or more counterpropagating beams of different frequencies provided that the wave vector of the modulation is sufficiently large. In this paper we analyze two very simple models of twoand four-wave mixing in a modulated /spl xi//sup (2)/ system. In the first model, a single pump beam pictured traveling from left to right interacts with a single second-harmonic beam traveling in the opposite direction. In the second model, there are two pump and two second-harmonic beams. We assume that the fields can be represented by plane waves and that all dispersion effects can be neglected.