FWM in One-dimensional Nonlinear Photonic Crystal and Theoretical   Investigation of Parametric Down Conversion (Steady State Analysis)
  The light propagation through one-dimensional photonic crystal using Four-wave mixing (FWM) nonlinear process is modeled. The linear and nonlinear indexes of refraction are approximated with the first Fourier harmonic term. Based on this approximation, a complete set of coupled wave equations, including pump fields depletion, for description of FWM process and conversion efficiency from pump to signal and idler waves for periodic structures is presented. The derived coupled wave equations are evaluated numerically. Some of important system parameters effects on FWM performance are investigated. The obtained relations are suitable and can easily be applied for description of Wavelength Division Multiplexing (WDM) optical signals transmitted through (parametric process) nonlinear fiber Bragg Gratings compatible to optical fiber communications. 
A. Rostami and M. Boozarjmehr