FDTD analysis of the dispersion characteristics of the metal PBG structures

Abstract

Two dimensional metallic photonic band gap (PBG) structures, which have higher power handling capability, have been analyzed for their dispersion characteristics. The analysis has been performed using finite difference time domain (FDTD) method based on the regular orthogonal Yee's cell. A simplified unit cell of triangular lattice PBG structure has been considered for the TE and TM modes of propagation. The EM field equations in the standard central-difference form have been taken in FDTD method. Bloch's periodic boundary conditions have been used by translating the boundary conditions along the direction of periodicity. For the source excitation, a wideband Gaussian pulse has been used to excite the possible modes in the computational domain. Fourier transform of the probed temporal fields has been calculated which provides the frequency spectrum for a set of wave vectors. The determination of eigenfrequencies from the peaks location in the frequency spectrum has been described. This yields the dispersion diagram which describes the stop and pass bands characteristics. Effort has been made to describe the estimation of defect bands introduced in the PBG structures. Further, the present orthogonal FDTD results obtained have been compared with those obtained by a more involved non-orthogonal FDTD method. The universal global band gap diagrams for the considered metal PBG structure have been obtained by varying the ratio of rod radius to lattice constant for both polarizations and are found identical with those obtained by other reported methods. Convergence of the analysis has been studied to establish the reliability of the method. Usefulness of these plots in designing the devices using 2-D metal PBG structure has also been illustrated.