Photonic band gaps for three-dimensional face-centred cubic lattices

We show that the photonic analogue of the Korringa-Kohn-Rostoker method is a viable alternative to the plane-wave method for analysing the spectrum of electromagnetic waves in a three-dimensional periodic dielectric lattice. Firstly, in the case of a fcc lattice of homogeneous dielectric spheres, we reproduce the main feature of the spectrum obtained by the plane-wave method, namely that for a sufficiently high dielectric contrast a full gap opens in the spectrum between the eighth and ninth bands if the dielectric constant ^es of the spheres is lower than the dielectric constant ^eb of the background medium. If ^es>eb, no gap is found in the spectrum. The maximal value of the relative band-gap width approaches 14% in the close-packed case and decreases monotonically as the filling fraction decreases. The lowest dielectric contrast ^eb/es for which a full gap opens in the spectrum is determined to be 8.13. Eventually, in the case of a fcc lattice of coated spheres, we demonstrate that a suitable coating can enhance gap widths by as much as 50%.