Analysis of 2-D periodic structures using the FD-FD method

The finite-difference in the frequency-domain (FD-FD) method is used in the analysis of the dispersion characteristics of guided waves in periodic structures such as: photonic crystals and dielectric gratings. The propagation is considered along an arbitrary direction and the analysis of the propagating modes is divided into two cases: (1) longitudinal propagation, where the guided waves are hybrid modes; and (2) transverse propagation, where the guided waves are TE or TM modes. The structure consists of a lossless biaxial anisotropic dielectric and the refraction index profile may vary continuously. The formulation is developed in such a way as to transform the problem into a conventional eigenvalue problem. The formulation is then applied to various cases where the active mode coupling and forbidden propagating bands are identified.