Epilogue

Abstract

The history of photonic crystals is not very long. In 1979, Ohtaka [27, 28] formulated the vector-spherical-wave expansion method, or the vector KKR (Koringa-Kohn-Rostker) method, to calculate the dispersion relation and the transmittance for the regular array of dielectric spheres. To the author’s knowledge, this is the first self-consistent treatment of electromagnetic eigenmodes in 3D dielectric systems with large periodic modulation of the dielectric constant. A remarkable step was made by Yablonovitch in 1987 [95] who pointed out the possibility of the realization of photonic bandgaps, localized defect modes, and their applications to various optoelectronic devices. His idea stimulated many researchers, and energetic research activities including his own studies were initiated. The process to realize the photonic bandgaps is described in [96]. In the same year, John [97] discussed the strong localization of electromagnetic waves in disordered photonic crystals. He also predicted many interesting quantum optical phenomena that can be realized in photonic crystals such as the bound state of photons [98] and non-exponential decay of spontaneous emission [99]. The summary of early studies can be found in [100, 101]. Also see [102] and special issues of JOSA [103] and J. Mod. Phys. [104].