Analytical approach for complex-shaped two-dimensional photonic crystals

An approximate perturbation based method for fast calculation and investigation of complex-shaped two-dimensional photonic crystals is presented. Both E- and H-polarizations are analyzed. Useful analytical formulas for calculating the dispersion relations are developed. The accuracy of the approximations is examined against numerical calculations, showing good match for a wide range of photonic crystal parameters. The present approach can be useful for the investigation of various physical effects inside photonic crystal structures as well as for the design of new photonic crystal devices. (C) 2010 Optical Society of America