Analytical treatment of two-dimensional photonic crystals with rectangular geometry

The dispersion relation for two-dimensional photonic crystals with rectangular geometry is analyzed, using analytical techniques. Both E-polarization and H-polarization are considered. By comparing with accurate numerical calculations, we show that the presented approach, with its derived expressions, can be used as a good approximation for various photonic crystals with a wide range of parameters. The degenerate bands, anticrossing effect and band gap creation can be analyzed, using the presented method. This approach provides not only a fast way for photonic crystal calculations, but also can be employed for investigating various physical effects, as well as for the design and analysis of new photonic crystal devices.