Coupled Defects in Photonic Crystals

We present a theoretical and numerical description of coupled defects in photonic-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 differential equations for the field amplitudes for individual defects. The actual 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 analytically; the band structure as well as the transmission response of a defect chain, or of a defect lattice, can be determined. The results for the superlattice of defects are compared with widely accepted numerical methods, the transfer matrix method, and finite-difference time domain.