Application of Transfer Matrix Method to Second-Harmonic Generation in Nonlinear Photonic Bandgap Structures: Oblique Incidence

Generalization of the transfer matrix method is developed to analyze Type I second-harmonic generation in linear–nonlinear multilayer one-dimensional photonic bandgap structures for oblique incidence of a nondepleted fundamental. The advantage of the transfer matrix method is that it takes into account reflections and interferences between all forward and backward propagating fundamental and second-harmonic waves. The conversion efficiency is calculated as a function of the incident angle of the fundamental and the thicknesses of the linear and nonlinear layers. Specific incident angles and thicknesses may generate relatively high conversion efficiency inside nonlinear material. Our analytical and numerical analyses show that the conversion efficiency of second-harmonic generation depends on the fundamental pump power, second-order susceptibility, and field enhancement in the photonic bandgap structure. Upper bounds on pump intensity can be found for a given incidence angle and sample thickness where the nondepleted pump approximation can be used to model such a nonlinear structure