Enhancement of second-harmonic generation in an air-bridge photonic crystal slab: simulation by spectral element method

Abstract

The enhancement of second-harmonic generation (SHG) across a 2D photonic crystal (PC) slab consisting of GaP is investigated in this study with the three-dimensional spectral element method (SEM). The in-plane band structure is calculated, and it is compared with the peaks of the SHG to reveal the mechanisms behind the enhancement. The numerical result from the SEM shows that, under normal incidence, the scattered power of the SHG is enhanced for the eigenstates with large decay rates, while the stored energy of the SHG is enhanced for the eigenstates with a zero decay rate. The SHG is enhanced under two conditions: (i) phase matching between the fundamental and second-harmonic (SH) fields and (ii) symmetry matching between the field pattern of the resonant eigenstate and the generated SH polarization field. Compared with a homogeneous dielectric slab, the air-bridge PC slab can enhance the SHG by 4 orders of magnitude.