Propagation inhibition and localization of electromagnetic waves in two-dimensional random dielectric systems

We rigorously calculate the propagation and scattering of electromagnetic waves by rectangular and random arrays of dielectric cylinders in a uniform medium. For regular arrays, the band structures are computed and complete bandgaps are discovered. For random arrays, the phenomenon of wave transmission and scattering is investigated and compared in two scenarios: (1) Wave propagating through the array of cylinders; this is the scenario which has been commonly considered in the literature, and (2) wave transmitted from a source located inside the ensemble. We show that within complete band gaps, results from the two scenarios are similar. Outside the gaps, however, there could be a distinct difference, that is, wave transmission can be inhibited by disorders in the first scenario, but such an inhibition may not prevail in the second scenario.