In this paper, we review the early motivation for photonic crystal res
earch which was derived from the need for a photonic bandgap in quantu
m optics. This led to a series of experimental and theoretical searche
s for the elusive photonic bandgap structures: those three-dimensional
ly periodic dielectric structures which are to photon waves, as semico
nductor crystals are to electron waves. We shall describe how the phot
onic semiconductor can be 'doped', producing tiny electromagnetic cavi
ties. Finally, we shall summarize some of the anticipated implications
of photonic band structure for quantum electronics and the prospects
for the creation of photonic crystals in the optical domain.