Photonic band gaps of 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 meth od, namely that for a sufficiently high dielectric contrast a full gap open s in the spectrum between the eighth and ninth bands if the dielectric cons tant epsilon(s) of the spheres is lower than the dielectric constant epsilo n(b) of the background medium. If epsilon(s) > epsilon(b), no gap is found in the spectrum. The maximal value of the relative band-gap width approache s 14% in the close-packed case and decreases monotonically as the filling f raction decreases. The lowest dielectric contrast epsilon(b)/epsilon(s) for which a full gap opens in the spectrum is determined to be 8.13. Eventuall y, in the case of a fcr lattice of coated spheres, we demonstrate that a su itable coating can enhance gap widths by as much as 50%.