Negative refraction and omni directionality in 2D photonic quasicrystal superstructure

Omni-directional negative refractive index is a desirable feature that may be hard to achieve by using conventional periodic structures. In 2D periodic photonic crystals, where rotational symmetry is four- or six- fold, negative refraction index can be achieved but it is highly anisotropic. Another way to achieve negative refraction in 2D arrays is by using photonic crystal superlattices consisting of rods with two different diameters. In this study we employ this method to build a 2D quasicrystal superlattice based on Penrose tiling. The omnidirectionality of the bandgaps that results from the quasicrystalline structure, while the effective negative index results from the superlattice. Together, these two features produce an omnidirectional negative refractive index. We demonstrate this effect by tracing the directions of phase and group velocities in the prism made of the photonic quasicrystal superlattice.