A steady state solution to four-wave mixing utilising the SU(2,2) group symmetry with mixed gratings in a Kerr type media

Abstract

Backward four-wave mixing in a Kerr type media with mixed refractive gratings of equal coupling strength are described by a set of nonlinear coupled wave equations. These are formulated into a compact matrix representation which then allows the identification of the four-dimensional symmetry group SU(2,2). When considering the two-point boundary value problem it is found that the mixed grating analysis reduces to the solution of a transmission only grating. This formulism is then used to find a solution for steady state phase conjugation and plots of reflectivity show the multiplicity of the solutions.