Simultaneous photonic and phononic band gaps in a two-dimensional lithium niobate crystal

The possibility to obtain hypersonic phononic band gaps in artificial crystals presenting submicron lattice parameters has shown that phononic and photonic crystals can be made of comparable dimensions, hence opening the way to simultaneous elastic and electromagnetic band gaps. We here focus on the theoretical investigation of air/lithium niobate 2D phoxonic crystals. The conditions for the existence of a full photonic band gap in this material are demanding, due to its relatively low refractive index and its elastic anisotropy which slightly hinders the opening of large phononic band gaps. The most commonly used single-atom lattices, i.e. square and hexagonal, as well as multiple-atom hexagonal lattices were considered. In each case, photonic and phononic band structures were computed independently. It is observed that decreasing the symmetry of the lattice by adding atoms of different sizes inside the unit cell leads to larger phoxonic band gaps. Examples of designs for operation at an optical wavelength of 1.55 ¿m are given. The corresponding phononic frequencies are in the Gigahertz range.