When the Schrödinger equation is solved for periodic potentials, the allowed energies are confined to a series of energy bands. That predicted energy structure is familiar from metals, semiconductors, and insulators. A similar but less well-known prediction follows when Maxwell’s equations are applied to materials in which the dielectric function varies periodically: The frequencies of light that can propagate through the medium are confined to prescribed bands. Light with frequencies in the gaps between those photonic bands reflects off the medium’s surface.
Materials with periodic dielectric structures are called photonic crystals, and they have been constructed with periodicities in one, two, and three dimensions. In dimensions greater than one, a considerable challenge is to fabricate structures that block the propagation of light in all directions. The challenge has been met, first by UCLA’s Eli Yablonovitch in 1991. Since then, and especially in the past five years, the technology for making...
