Localization of Light: Theory of Photonic Band Gap Materials

Abstract

There are at least two technological revolutions in the twentieth century which owe their existence to atomic and condensed matter physics. The first was the semiconductor revolution which resulted in the emergence of the electronics industry. The second was a direct consequence of the invention and applications of the laser. A third revolution, may yet emerge from the discovery of “high temperature” superconductivity. In each of these developments, the fundamental elementary particles or “actors” are electrons and photons. The properties of semiconductors, lasers, and superconductors are fundamentally a consequence of the dynamical and cooperative behaviour of electrons and photons in carefully controlled environments. Electrons are strongly interacting fermions which are readily localized by the positive charge of an atomic nucleus. The semiconductor crystal facilitates a highly controlled delocalization of the electronic wavefunction. This selective flow of charge enables a semiconductor device to perform its function. Photons are weakly interacting bosons which propagate readily. The laser facilitates the emergence of a cooperative or coherent state of a large collection of photons. In a superconductor, electrons in a metal form bosonic, Cooper pairs which condense into a cooperative state analogous to the coherent state of photons in a laser field.