An effective nonlinear susceptibility model for general three-wave mixing in quasi-phase-matching structure

We develop an effective nonlinear susceptibility model (ENSM) to solve analytically the general three-wave mixing nonlinear optical interaction problem under the quasi-phase-matching (QPM) scheme. The nonlinear processes including sum-frequency generation, difference-frequency generation and second harmonic generation are discussed in both periodic poled lithium niobate (PPLN) and chirped PPLN (CPPLN) structures. The analytical ENSM results show great consistency with rigorous numerical simulation based on direct solution of the nonlinear coupled-wave equations. This indicates that the ENSM is a brief, convenient, accurate, and efficient theoretical tool to quantitatively evaluate the performance of various three-wave mixing interactions in general QPM structures such as PPLN and CPPLN and to design and optimize the QPM structures for many specific functionalities of nonlinear frequency conversion.