Photonic band structures of finite thickness: theory and experiment

There has been a great deal of interest in photonic band structures (PBS). In the literature, the PBSs considered are usually infinite periodic dielectric lattices. These lattice structures exhibit frequency bands over which propagation can not occur for any direction. The type of structures which have been theoretically analysed to date have been infinite, two- and three dimensional periodic dielectric structures. The analysis technique has been an expansion of the wave equation in plane waves and its solution obtained through eigenvalue techniques [Plihal and Maradudin, 1991]. However, there has been little attention given to the problem of PBSs with finite thickness. The present authors provide a new analysis based on the FDTD method and experimental measurements of a physically realizable, finite thickness PBS. These results reveal the existence of evanescent modes in the bandgaps as well as a passband ripple.<>