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 ε(r) is sharply peaked, photonic levels become almost degenerate throughout the Brillouin zone, corresponding to standing waves.

• Received 7 October 1991

DOI:https://doi.org/10.1103/PhysRevB.45.13962