Photonic and phononic surface and edge modes in three-dimensional phoxonic crystals

We investigate the photonic and phononic surface and edge modes in finite-size three-dimensional phoxonic crystals. By appropriately terminating the phoxonic crystals, the photons and phonons can be simultaneously guided at the two-dimensional surface and/or the one-dimensional edge of the terminated crystals. The Bloch surface and edge modes show that the electromagnetic and acoustic waves are highly localized near the surface and edge, respectively. The surface and edge geometries play important roles in tailoring the dispersion relations of the surface and edge modes, and dual band gaps for the surface or edge modes can be simultaneously achieved by changing the geometrical configurations. Furthermore, as the band gaps for the bulk modes are the essential prerequisites for the realization of dual surface and edge modes, the photonic and phononic bulk-mode band gap properties of three different types of phoxonic crystals with six-connected networks are revealed. It is found that the geometrical characteristic of the crystals with six-connected networks leads to dual large bulk-mode band gaps. Compared with the conventional bulk modes, the surface and edge modes provide a new approach for the photon and phonon manipulation and show great potential for phoxonic crystal devices and optomechanics.