SPEED OF LIGHT IN A 2D PHOTONIC CRYSTAL IN THE LOW-FREQUENCY LIMIT

We consider an arbitrary 2D periodic structure in the low-frequency li mit and demonstrate that it exhibits birefringence for propagation in the plane of periodicity. For polarization parallel to the cylinder ax is the effective dielectric constant, epsilon(eff) is just the average of the constituents, as known. On the other hand, for in-plane polari zation, epsilon(eff) is a function of the propagation direction. Numer ical calculations have been performed for triangular cylinders forming a square lattice. This leads to an anisotropy as large as 20%, much i n excess of anisotropy observed in natural crystals.