Optimizing doubly-resonant photonic crystal cavity modes for second harmonic generation

We optimize a photonic crystal slab for the generation of second harmonic. The optimization consists in two steps. In the first step a regular photonic crystal, consisting in a triangular lattice of circular holes in a dielectric slab, is optimized by allowing for holes of three alternating radii, with the objective of obtaining a high-frequency bandgap doubly resonant with the fundamental one. The second step consists in modeling a L3 defect cavity in such a photonic crystal where, by further varying the radii and positions of a few neighboring holes, doubly resonant modes at the fundamental and second harmonic frequencies are obtained, with maximal Q-factors and field overlap. The structure emerging from this optimization procedure has Q-factors of 3400 for the fundamental mode and of 430 for the doubly resonant one. Due to the localized nature of those modes and hence their large field overlap, efficient second-harmonic generation is expected in a material with a chi((2)) non-linearity