Photon density of states for a 2-D lattice of air holes

Consider a 2-D array of holes in a material with a relative dielectric constant ε_r = 13. The relative dielectric constant in the holes is ε_r = 1. For this array the lattice constant is taken to be a = 0.5 μm and the radius of the holes is R = 0.24 μm.

The plane wave method was used to calculate the dispersion relation for this case. The details of the calculation are given here.