Abstract

We have examined several methods of performing photonic band structure calculations, compared those methods with one another, and studied their rate of convergence. When the medium has a host/guest topology we found that the convergence rate is vastly different for the different methods we studied. The wrong method choice for a given medium can lead to inaccuracies of as much as 50%. This is a direct consequence of the discontinuous nature of the dielectric function and the electromagnetic fields. In the diamond lattice,¹ which was reported to have a 15% band gap between the second and third bands, we find at most a 3% band gap at the maximum volume filling fraction and none for the lower filling fractions. We attribute these discrepancies to inadequate numerical convergence of the previous calculations.² Our approach is novel in that it looks for consistency between the various methods while gradually employing up to 1100 plane waves. The trend thus observed shows that the gap is closing. Results are also reported for spheroidal particles on an FCC lattice. We found that when the medium has a host/guest topology, the effective dielectric constant is well modeled by the Maxwell-Garnett theory. The enhancement of the nonlinear optical response of the particles is also examined.

© 1991 Optical Society of America