Impurity Modes from Frequency Dependent Dielectric Impurities in Photonic Band Structures

Abstract

A recent problem of interest in the study of photonic band structures has been that of a single dielectric impurity in an otherwise periodic photonic band structure. This problem has been studied using supercell methods [1], transfer matrix methods [2,3], and Green’s function methods [4–6]. In this paper we will look at the exact solution of the single impurity problem using Green’s function methods. Results will be presented for one-dimensional (layers) and two-dimensional (periodic array of rods) systems for impurities with frequency dependent dielectric constants substituted into periodic dielectric media composed of frequency independent dielectric materials. The impurities will be substitutional impurities (replacement of a single slab or rod by that of another dielectric composition). Particular attention will be given to obtaining theoretical results using dielectric constants appropriate to materials which have been used in recent experimental studies of photonic systems.