Theoretical bandgap modeling of two-dimensional square photonic crystals fabricated by the interference of three noncoplanar laser beams

Abstract

We have investigated numerically the photonic bandgap (PBG) and spectral properties of two-dimensional (2-D) square structures fabricated by holographic lithography. Based on the block-iterative frequency-domain method and on the nonorthogonal finite-difference time-domain method, we have calculated band structure as a function of intensity threshold and shown that the PBG of 2-D titania arrays opens only for TM polarization and that directional PBGs can be obtained simultaneously for TE- and TM-polarized waves. In addition, we have shown that symmetry reduction of the atom introduced by holographic lithography can lift the band degeneracies and create an absolute PBG for a square lattice of dielectric rods in air.