Photonic band-gap structures

The analogy between electromagnetic wave propagation in multidimensionally periodic structures and electron-wave propagation in real crystals has proven to be a fruitful one. Initial efforts were motivated by the prospect of a photonic band gap, a frequency band in three-dimensional dielectric structures in which electromagnetic waves are forbidden irrespective of the propagation direction in space. Today many new ideas and applications are being pursued in two and three dimensions and in metallic, dielectric, and acoustic structures. We review the early motivations for this research, which were derived from the need for a photonic band gap in quantum optics. This need led to a series of experimental and theoretical searches for the elusive photonic band-gap structures, those three-dimensionally periodic dielectric structures that are to photon waves as semiconductor crystals are to electron waves. We describe how the photonic semiconductor can be doped, producing tiny electromagnetic cavities. Finally, we summarize some of the anticipated implications of photonic band structure for quantum electronics and for other areas of physics and electrical engineering.