Simulation of simultaneous photonic and phononic band gaps in Sapphire

The simultaneous existence of photonic and phononic band gaps in a simple square periodic array of holes drilled in sapphire substrate is investigated theoretically. The investigations are focused in a first part on a photonic gap obtaining with a phononic gap in the same time making use of some specific parameters. In the second part, using a cavity defect in which the strong confinement of acoustic and optic waves enhances the interaction, we obtain photonic and phononic modes classified according to their symmetry (even or odd), also allowed bands in gaps, which has led to the propagation of waves appropriate. The frequencies of the localized modes in the first band gap are computed with a finite element method.