Photonic Band Gaps of Three-Dimensional Face-Centered Cubic Lattices

摘要

We show that the photonic analogue of the Korringa-Kohn-Rostocker method is aviable alternative to the plane-wave method to analyze the spectrum ofelectromagnetic waves in a three-dimensional periodic dielectric lattice.Firstly, in the case of an fcc lattice of homogeneous dielectric spheres, wereproduce the main features of the spectrum obtained by the plane wave method,namely that for a sufficiently high dielectric contrast a full gap opens in thespectrum between the eights and ninth bands if the dielectric constant$\epsilon_s$ of spheres is lower than the dielectric constant $\epsilon_b$ ofthe background medium. If $\epsilon_s> \epsilon_b$, no gap is found in thespectrum. The maximal value of the relative band-gap width approaches 14% inthe close-packed case and decreases monotonically as the filling fractiondecreases. The lowest dielectric contrast $\epsilon_b/\epsilon_s$ for which afull gap opens in the spectrum is determined to be 8.13. Eventually, in thecase of an fcc lattice of coated spheres, we demonstrate that a suitablecoating can enhance gap widths by as much as 50%.