Approximate analysis of two-dimensional photonic crystals with rectangular geometry. I.E polarization

Using analytical techniques the dispersion relations for two-dimensional photonic: crystals with rectangular geometry are analyzed. In this part of the work E polarization is presented. By comparing with accurate numerical calculations, we show that our analysis provides a good description of the physical properties for this type of photonic crystal. Besides the significantly shorter calculation time, the analytical treatment provides an important insight into the photonic bands' formation and their properties. The presented approach and derived analytical expressions can be useful for the investigation of photonic band structures as well as for the design of novel photonic crystal devices.