Photonic bands: Convergence problems with the plane-wave method

Abstract

The problems associated with the poor convergence of the Fourier transform of the hard-sphere dielectric function are discussed. A significant band gap between the eighth and ninth levels has been found for air spheres in fcc. We also consider a periodic array of Gaussian spheres, which converges well and allows a consistent and reliable determination of the general features of photonic bands. It is found that when \ensuremath{\epsilon}(r) is sharply peaked, photonic levels become almost degenerate throughout the Brillouin zone, corresponding to standing waves.