Recursive transfer-matrix method for second-harmonic generation in a one-dimensional nonlinear photonic crystal at arbitrary incidence angle

Abstract

Abstract In this paper, we derive a recursive transfer-matrix method (RTMM) and use the method to analyse the problem of second-harmonic generation (SHG) in a one-dimensional nonlinear photonic crystal (1D-NPC) under oblique incidence of fundamental-frequency (FF) wave and nondepleted pump approximation. This method is very simple and useful for determining SHG conversion efficiency at various incident angles of FF wave and thicknesses of nonlinear layer. The RTMM calculation results show that a maximum SHG conversion efficiency can be produced by the strong local FF field confinement in 1D-NPC due to optimal incidence angle and nonlinear layer thickness.