Localization of light in lossless inhomogeneous dielectrics

The localization of electromagnetic waves in lossless inhomogeneous dielectric media is studied. We consider a three-dimensional lossless periodic medium (photonic crystal) having a gap in the frequency spectrum (photonic bandgap). If such a medium is perturbed by either a single defect or a random array of defects, exponentially localized electromagnetic waves arise with frequencies in the gap. For a single defect, we derive equations for these midgap frequencies and estimate their number. For a random medium, we show the occurrence of Anderson localization for electromagnetic waves.