Abstract

We use plane wave method that correctly treats the vector nature of the photon to calculate the photonic band structure of a medium consisting of a face-centered cubic array of spheres embedded in a host material. Results are calculated for various volume-filling fractions of spheres, f, and refractive-index ratios for both the dielectric- and air-atom cases. Variations of the effective long wavelength refractive index with f is in excellent agreement with experimental data.¹ The band gaps for the air-atom case at the Land X-points in the Brillouin zone as a function of f are also in accord with experiments. In particular, we found the X-gap to go to zero for f = 0.66, which is close to the experimental value of 0.68. However, in the case of an 86% volume-filling fraction of air-atoms, we did not find a common gap, and this is in disagreement with experimental findings. The primary problem seems to be caused by symmetry, which requires the bands to be degenerate at the W-point. Extensive numerical calculations for refractive index ratios varying from 1/4 to 4 have not produced a common gap for the present model.

© 1990 Optical Society of America