Transmission line formulation for the full-wave analysis of two-dimensional dielectric photonic crystals

Using a matrix formulation it is shown how the full-wave analysis of multilayer photonic crystals can be reduced to the analysis of an equivalent multiconductor transmission line (TL). In the special case of single-layer two-dimensional photonic crystals the inductance and capacitance matrices of this equivalent TL provide the propagation characteristics of the crystal under investigation. Specifically, the determinants of these matrices contain the required information for determining propagation constants and consequently the field distribution of TM and TE propagation modes inside the crystal. Comparison of the numerical results presented in this work with those available in the literature verifies the soundness of the TL formulation introduced. Although the numerical results are presented for lossless isotropic dielectrics, the method is applicable to photonic crystals made of lossy and/or anisotropic dielectrics.