Green's-function theory for row and periodic defect arrays in photonic band structures.

Abstract

The defect modes associated with a row or a periodic array of defects in a two-dimensional photonic band structure are studied using exact Green's-function methods. Specifically, we consider the above-described defect problems created in a pure photonic band-structure system that models an experimental system recently investigated by McCall et al. This is a square lattice array of cylindrical rods formed of linear dielectric material with \ensuremath{\epsilon}=9 surrounded by vacuum and of filling fraction f=0.4488. In one study a row of rods is replaced in the photonic band structure by a row of impurity rods that may be of either linear or nonlinear dielectric material, and conditions are determined for the existence of impurity modes, associated with the impurity array, in the photonic band gap. The electric fields of the impurity modes are computed for impurity modes in the gaps. In a second study, a two-dimensionally periodic array of defects is introduced into the photonic band structure such that the periodicity of the defect array may or may not coincide with the periodicity of the original photonic band structure. The defect rods are treated in the cases for which the impurities are formed from both linear and nonlinear dielectric materials, and the conditions necessary for defect modes to exist in the photonic band gaps are determined. \textcopyright{} 1996 The American Physical Society.