Convergence of the supercell method for computation of defect modes in one-dimensional photonic crystals

In this paper, we analyze the spectrum induced by the supercell method for studying locally defected one-dimensional photonic crystals. By using the propagation matrix method, we show that the continuous spectrum of the periodic structure of the supercell converges to that of the defected photonic crystal. Also, it can be shown that frequencies of localized defected modes in the bandgap are included in a narrow interval (whose length diminishes exponentially with increasing size of the supercell) of the continuous spectrum of the supercell method.