Abstract
Many major discoveries in physics this century originate from the study of waves in periodic structures. Examples include X-ray and electron diffraction by crystals, electronic band structure and holography. Analogies between disciplines have also led to fruitful new avenues of research. An exciting example is the recent discovery of three-dimensionally periodic dielectric structures that exhibit what is called a "photonic band gap" (PBG), by analogy with electronic band gaps in semiconductor crystals. Photons in the frequency range of the PBG are completely excluded so that atoms within such materials are unable to spontaneously absorb and re-emit light in this region; this has obvious beneficial implications for producing highly efficient lasers. Given that electrons and photons obey almost the same differential wave equation, the idea of a PBG is clearly far from crazy. It does, however, demand a radical rethink of how light behaves in periodic structures.