Analysis of three-wave mixing in one-dimensional nonlinear multilayer structures with pump depletion

Abstract

We present a general theoretical approach that combines the iterative technique with the nonlinear transfer matrix method to solve the general problems of three-wave mixing with pump depletion in nonlinear multilayer structures. The theoretical model is directly derived from nonlinear coupled wave equations, shows fast numerical convergence and maintains conservation of total energy perfectly for general structures. We have employed this approach to discuss second harmonic generation in photonic bandgap crystals with slow light effect and obtained a conversion efficiency of about 25% for both the forward and backward second harmonic waves. The detailed wave evolution process and energy conversion mechanism of sum frequency generation and difference frequency generation in perfect and imperfectly quasiphase-matching structures have been systematically investigated and their subtle and strong dependence on the initial conditions of incident waves has been revealed. The developed theoretical approach can be very useful for efficient and quantitative analysis of various nonlinear optical problems and help to design optimum nonlinear multilayer structures for specific high-efficiency nonlinear three-wave mixing processes.