Photonic band structure: observation of an energy gap for light in 3-D periodic dielectric structures

Abstract

By analogy to electron waves in a crystal, light waves in a 3-D periodic dielectric structure should be described by band theory. Recently, the idea of photonic band structure1 has been introduced. This means that the concepts of reciprocal space, Brillouin zones, dispersion relations, Bloch wave functions, Van Hove singularities, etc. must now be applied to optical waves. If the depth of index of refraction modulation is sufficient, a photonic band gap can exist. This is an energy band in which optical modes, spontaneous emission, and zero point fluctuations are all absent. Therefore, inhibited spontaneous emission can now begin to play a role in a semiconductors and solid-state electronics. It makes sense then to speak of photonic band structure and of a photonic reciprocal space, which has a Brillouin zone ~1000 times smaller than the Brillouin zone of the electrons. If the dielectric constant is periodically modulated in all three dimensions, it is possible to have a photonic band gap which overlaps the electronic band edge and for spontaneous electron-hole recombination to be rigorously forbidden. Indeed the photonic band gap is essentially ideal since the dielectric response can be real and dissipationless. It is interesting that the most natural real space structure for the optical medium is face centered cubic (fee), which is also the most famous atomic arrangement in crystals. The comparison between electronic and photonic band structure is revealing: (a) The underlying dispersion relation for electrons is parabolic, while that for photons is linear. (b) The angular momentum of electrons is 1/2, but the scalar wave approximation is frequently made; in contrast, photons have spin 1 and the vector wave character will likely play a major role in the band structure. (c) The band theory of electrons is only an approximation due to electron-electron repulsion, while photonic band theory is essentially exact since photon interactions are negligible.