Coupled defects in photonic crystals

We present a theoretical and numerical description of coupled defects in ph otonic-bandgap crystals, expandable to cover a wide range of applications. Based on a weak interaction approach, explicit expressions are derived for defect interaction. The basis is formed by a system of coupled ordinary dif ferential equations for the field amplitudes for individual defects. The ac tual configuration of the defects (chain, lattice, bend, or anything else) enters the equations as a linear coupling between neighboring defects. The strength of this method is that many solutions of this system are known ana lytically; the band structure as well as the transmission response of a def ect chain, or of a defect lattice, can be determined. The results for the s uperlattice of defects are compared with widely accepted numerical methods, the transfer matrix method, and finite-difference time domain.