Pholonic band-gap slruclures

The analogy between electromagnetic wave propagatian in multidimensionally periodic structures and electron­ wave propagat ion in real crystals bas proven ta be a fruitful one. Initial efforts were motivate<! by the prospect of a photanic hand gap. a frequency band in three-dimensional dielectric structures in which electromagnetic wave. are forbidden irrespective of the propagation direction in space. Today many new ideas and applicatians are being pursued in two and three dimensions and in metallic. dielectric. and &coustic structures. We review the early motivations for this researob. which were derived from the need for a photonic band gap in quantum optic.. This need led ta a series of experimental and theoretical searches for the elusive photonic band-gap structures. tbose three-dimensionally periodic dielectric structures that are ta photan waves as semiconductor crystals are ta electron waves. We desaibe how the photanic semiconductor can be doped. producing tiny elec­ tromagnetic 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. In this paper we pursue the rather appealing analogy 1.2 between the behavior of electromagnetic waves in artifi­ cial. three-dimensionally periodic, dielectric structures and the rather more familiar behavior of electron waves in natural crystais. These artificial twa- and three-dimensionally periodic structures we caII photonic crystals. The familiar nomen­ c1ature of real crystals is carried over to the electromag­ netic case. This means that the concepts of reciprocal space, Brillouin zones <BZ's). dispersion relations, Bloch wave functions, Van Hove singularities, etc. must be ap­ plied to photon waves. It then makes sense ta speak of photonic band structure I PBS) and of a photonic recipro­ cal space that has a BZ approximately 1000 times smaller than the BZ of electrons. Because of the periodicity, photons can develop an effective mass. but this implica­ tion is in no way unusual, since it occurs even in one­ dimensionally periodic. optically layered structures. We frequently leap back and forth between the conventional meaning of a familiar concept such as conduction band and its new meaning in the context of PBS's. Under favorable circumstances a photonic band gap can open up. a frequency band in which electromagnetic waves are forbidden irrespective of propagation direction in space_ lnside a photonic band gap optical modes, sponta­ neous emission, and zero-point fluctuations are a1l absent. Because of its promised utility in controlling the sponta­ neous emission of light in quantum optics. the pursuit of a photonic band gap has been a major motivation for study­ ingPBS.