Computation of localized modes in a defect-containing photonic crystal by the method of periodic continuation of solution

The applicability of the method of periodic continuation of solution for computing the spatial distribution of an electromagnetic field in a photonic crystal with a defect is analyzed. The accuracy of the method is estimated. The crystal eigenmodes are classified, and the method is shown to be applicable only for states localized on the defect. The results of numerical calculations based on expansion of electromagnetic field in plane waves are presented, and the details of the expansion method are described.