General scattering matrix solutions to vector four wave mixing

In this paper, a scattering matrix method to solve the fully nonlinear vector four wave mixing problem in nonoptically active photorefractive materials is presented. Specific solutions are given for anisotropic and isotropic media as utilised in standard four wave mixing systems and in ring passive phase conjugate resonators. Paraxial wave equations and an optimally (pi /2) phase shifted transmission grating are assumed. The theory is developed for linear polarisations and accounts for pump depletion. Solutions for arbitrary orientation of beams are used to explore the conditions by which vector phase conjugation can be simply achieved. (C) 2000 Elsevier Science B.V. All rights reserved.