Analyzing and Designing Photonic Crystals

Abstract

In this chapter, various methods for analyzing and designing photonic crystals are introduced. Since the possibility of controlling spontaneous emission using the PBG was first discussed in 1987, development of the methods for analyzing photonic crystals has progressed rapidly. In particular, the foundation for photonic crystal analysis has been strengthened by the work of theoretical researchers of solid state physics, including research groups individually headed by Leung, Zhang and Ho. They used the plane wave expansion (PWE) method to calculate energy bands, which is an optical version similar to the method used in solid state physics. In 1990, using this PWE method, Ho et al. calculated the band configuration of a diamond structure, and first showed that it is possible to obtain a complete PBG. In addition to the calculation of PBGs, the PWE can be applied to analyze the other aspects of photonic crystals, which have been discussed in Sections 2.4 and 2.5 as band engineering. The PWE calculation provides the contour map of frequency called the dispersion surface. It is the analogy to the Fermi surface of the electron system. In addition to providing a basic physical understanding of these phenomena, this technique is of general use in a wide range of application fields.