Abstract

By analogy to electron waves in a crystal, electromagnetic waves in a 3-D periodic dielectric structure should be described by band theory. The idea of photonic band structure¹ is rapidly^2–5 gaining acceptance. The concepts of reciprocal space, Brillouin zones, dispersion relations, Bloch wave functions, Van Hove singularities, etc., are now being applied to optical waves. If the depth of refraction index modulation is sufficient, a photonic band gap can exist. This is a frequency band in which electromagnetic modes, spontaneous emission, and zero point fluctuations are all absent. Indeed, a photonic band gap cam be essentially ideal provided the dielectric response is real and dissipationless. In addition to the obvious uses in atomic and laser physics, photonic band structure can now begin to play a role in microwave and millimeter wave electronics. Defects can be introduced into the otherwise perfect 3-D structures, creating electromagnetic donor modes and acceptor modes. Effectively, these defects are purely dielectric single-mode high-Q cavities suitable for a range of frequencies from microwaves to the visible. At the outset it was realized¹ that a face-centered-cubic (FCC) array in real space would produce the most spherelike Brillouin zone in reciprocal space. This spherelike geometry increased the likelihood that a forbidden gap would overlap all the way around the surface of the Brillouin zone. But is was unclear what should be the shape in real space of the atoms in this FCC array. The history of this field has been a search for that optimal 3-D dielectric geometry, favored by nature and by Maxwell’s equations. During this same period, electronic band theorists began calculating photonic band structure. It rapidly became apparent that the familiar scalar wave band theory, so frequently used for electrons in solids, was in utter disagreement with experiment on photons.⁷–¹⁰ Recently³–⁵ a full vector-wave band theory became available, which not only agreed with experiment, it successfully highlighted some discrepancies in the experiment.

© 1991 Optical Society of America