Transfer Matrix and Fourier Transform Methods for Simulation of Second-Order Nonlinear Interactions in a PPLN Waveguide

A new method for the simulation of nonlinear processes of sum-frequency generation (SFG), difference-frequency generation (DFG) and cascaded SFG/DFG (cSFG/DFG) in complex periodically poled lithium niobate (PPLN) gratings for continuous wave signals is proposed and numerically validated. It is based on the transfer matrix method and shows better performance in comparison with traditional numerical solving methods of ordinary differential equations, in particular when nonuniform PPLN are considered. In addition, a Fourier transform method to compute SFG, DFG, cSFG/DFG, and also some cascaded second-harmonic generation/difference-frequency generation interactions of modulated signals is presented. This new algorithm considerably decreases the computing time in comparison with well-known finite-differences methods.