Simultaneous optical wavelength interchange with a two-dimensional second-order nonlinear photonic crystal

We present a theoretical analysis for simultaneous optical wavelength interchange and isolation of a pair of collinear input optical signals by use of two concurrent difference-frequency-generation processes in a two-dimensional second-order nonlinear photonic crystal. We have derived a set of relations, including a general nonlinear Bragg condition, that we use to determine the parameters of the nonlinear lattice, given the input wavelengths and desired exit angles of the wavelength-interchanged outputs.