Nonlinear frequency conversion in two-dimensional nonlinear photonic crystals solved by a plane-wave-based transfer-matrix method

Abstract

We develop the plane-wave-based transfer-matrix method, which is a formalism that has been extensively used to calculate the scattering of electromagnetic waves by usual linear photonic crystals, to solve the quasi-phase-matched (QPM) second-harmonic generation (SHG) in two-dimensional (2D) nonlinear photonic crystals. Using this method, we can calculate the conversion efficiency of high-order collinear and noncollinear QPM second-harmonics. We apply this method to evaluate the SHG conversion efficiency in the 2D periodically poled ${\text{LiNbO}}_{3}$ crystal with rectangular lattice. The high-order collinear and noncollinear QPM SHGs are observed. The wavelengths at which various orders of QPM SHGs occur and their relative conversion efficiencies predicted by the current theoretical method are in fairly good agreement with those found in experiments. This indicates that the developed method is effective and efficient in handling nonlinear light diffraction in nonlinear photonic crystals.