Abstract
This paper presents a theoretical investigation on the anisotropic negative index states of a two-dimensional photonic crystal with an asymmetrical unit cell. Such a photonic crystal behaves similar to a bulk anisotropic medium in the vicinity of a photonic band gap with effective negative principal refractive indices. In particular, we studied a photonic crystal with a rectangular basis in a two-dimensional hexagonal lattice, which forms states with elliptical isofrequency contours near the band edge frequencies. By varying the filling ratio, it is possible to force such an anisotropic state to an accidental isotropic state. Further, by reorienting the basis and continuously varying the filling ratio, the orientation of the elliptical states can be continuously tuned.
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