Recursive-formula for second-harmonic generation problem in photonic hypercrystal

Abstract

In this work, we proposed a recursive-formula based on transfer-matrix method to solve problem of second-harmonic generation by obliquely incident fundamental-harmonic wave in a photonic hypercrystal, which is composed of one-dimensional periodically alternating arrangement of nonlinear hyperbolic metamaterial layer with anisotropic permittivities: εaxx, εazz and layer thickness: a and linear dielectric layer with isotropic permittivity: εa and layer thickness: b. This proposed formula was very simple and accurate for calculating conversion efficiency of second-harmonic generation at various incident angles of fundamental-harmonic wave and thicknesses of nonlinear hyperbolic metamaterial layer. The numerical results showed that the maximum conversion efficiency can be achieved by the strong local field confinement of fundamental-harmonic wave in the photonic hypercrystal and phase-matching due to optimal values of hypercrystal layer thickness and incident angle of fundamental-harmonic wave. © 2022 Elsevier GmbH