Abstract

Ever since the first practical demonstration by Yablonovitch and Gmitter¹ of the existence of a complete three-dimensional photonic band gap, strenuous efforts have been made by many researchers to characterise and quantify the propagation properties of proposed photonic crystal structures. With the notable exception^2,3 of one-dimensionally-periodic dielectric structures, however, analysis of such materials has been confined to numerical treatments. Although numerical routines provide the most versatile way forward for the study of two- and three-dimensional periodic media, they are subject to the usual problems of algorithm convergence and accuracy associated with finite wordlength arithmetic, the termination of infinite series, or finite discretisation of continuous functions. Clearly, an exact analysis of the electromagnetic fields in a photonic crystal would be of value for several reasons: these include numerical benchmarking, optimisation, and the direct computation of further necessary quantities such as densities of states.

© 1994 IEEE