Dyadic Green's function study of band structures of dispersive photonic crystals

We present here in terms of a dyadic Green's function (DGF) a general description of optical phenomena in photonic crystal (PC) structures, described particularly by frequency-dependent components, assuming that PC structures are decomposed into their relatively simple constituent parts via conductivity tensors. We demonstrate this approach by explicitly calculating the DGFs for electromagnetic waves propagating in the one- and two-dimensional dispersive PCs consisting of a periodic array of identical metallic quantum wells and a periodic square array of identical metallic quantum wires, each embedded in a three-dimensional dispersive medium. By means of the explicit analytic dispersion relations, which result from the frequency poles of the corresponding DGFs, we also calculate the band structures of these dispersive PCs by simple numerical means. Our analysis shows that the band structures calculated from our DGF approach conform well with those calculated from the traditional computational methods.