The Computation of Spectra of Some 2D Photonic Crystals

Using analytical methods we develop an accurate and efficient algorithm for computation of the spectrum and eigenmodes for a 2D photonic crystal which comprises a periodic array of parallel rods of air of a square cross section embedded in a background lossless medium of higher dielectric constant. The numerical analysis of dependence of the spectral bands on the parameters of the 2D photonic crystal is carried out. It gives a reliable base for the optimal design of 2D photonic crystals.