Abstract

Recent experimental and theoretical studies have shown that, by introducing defects into a photonic crystal, defect states can exist within the forbidden photonic band gap.¹ The defect structure of interest occupies only a small volume within a unit cell, and the fields associated with the defect extend no more than a few lattice constants. Theoretical calculations were carried out by using the hypercell method. Here an alternate approach for treating highly localized defect states by introducing vector Wannier functions and using a Green's function is reported. The reason for the use of vector Wannier functions is that they are expected to be highly localized around each atomic site and therefore form ideal basis functions. The eigen problem for the defect state frequency and fields turns out formally to have exactly the same form as that of the corresponding electronic problem.

© 1992 Optical Society of America