Photon focusing, internal diffraction, and surface states in periodic dielectric structures

Several analogies between electrons and phonons in semiconductors and electromagnetic waves in periodic dielectric structures are used to demonstrate the existence of (i) surface or edge states at the boundaries between the periodic structure and air, (ii) focusing of the electromagnetic energy emitted by a point source, and (iii) the existence of internal diffraction as known for coherent acoustic waves. In addition, the inclusion in phonon or electron band structures, is briefly discussed.