Opening of simultaneous photonic and phononic band gap in two-dimensional square lattice periodic structure

Abstract

We discuss two points related to the simultaneous existence of phononic and photonic band gaps in a two-dimensional crystal constituted by a square array of holes drilled in a matrix. In a first part, using the case of a sapphire sample in the microwave range, we show that in addition to the phononic gap, an absolute photonic gap may be obtained making use of the high values as well as the anisotropy of the dielectric matrix elements in the microwave regime. In a second part, using the case of silicon in the telecom frequency range, we demonstrate that absolute photonic and phononic gaps may be obtained by making a combination of two crystals having slightly different filling factors. The calculations of the band structures and transmission coefficients were mainly computed using the finite difference time domain method.