Kazuaki SAKODA

Research Institute for Electronic Science, Hokkaido University, North 12 West 6, Kita-ku, Sapporo, 060-0812 Japan

(Received July 4, 1999; Accepted July 16, 1999)

In this article, a general theoretical framework to describe and analyze the optical properties of photonic crystals is presented. In addition to the analytical treatment of their optical response based on the method of Green's function, numerical tools to calculate the dispersion relations and the eigenfunctions of the radiation field, transmission spectra, localized midgap modes, and lasing threshold are introduced and applied to some typical examples. Group theory to analyze the symmetry of the eigenmodes is also introduced, and the existence of uncoupled modes that cannot be excited by external plane waves is shown. The presence of the enhancement effect of nonlinear optical processes and stimulated emission due to the small group velocity which is easily realized in the photonic crystals is pointed out, and the possibility of low-threshold lasing in the photonic crystals is discussed.

Key words : photonic crystal, dispersion relation, symmetry, group theory, Green's function, dipole radiation, sum-frequency generation, stimulated emission, localized mode, lasing

sakoda@es.hokudai.ac.jp