Defect modes in otherwise perfect photonic crystals and photonic crystal fibers

Abstract

Many of the applications of photonic crystals and photonic crystal fibers require the periodic structure to have some type of defect. In photonic crystal fibers a point defect defines the fiber core, whereas in photonic crystals a line defect acts as a waveguide, and point defects act as cavities. The modeling of these defects usually either makes use of periodic boundary conditions, by which the defect is replicated periodically, or models a photonic crystal of finite extent. However, some applications, for example the cut-off behavior of a defect mode where the field extends very widely, require methods that can model a defect in an otherwise infinite and perfectly periodic structure. Here we present such a method. It combines the method of fictitious sources with averaging over the Brillouin zone, and we apply it to study the long-wavelength behavior of the fundamental mode of photonic crystal fibers.