Huge group-velocity dispersion in a photonic crystal

We investigated the group-velocity dispersion of a one dimensional uniform photonic crystal by the optical transmission method. For application in optical communications, the wavelength should be near one of the two edges of a photonic bandgap. Four kinds of
dispersion-compensation may be obtained with a photonic crystal. Huge negative and positive group-velocity-dispersion (GVD) about a
zero-dispersion-point as large as 5.1 Tera- ps/nm/km by a photonic crystal of 100 periods can be realized. Such a value is about 50 Giga times the GVD of conventional dispersion-compensation fibers. The GVD reaches a maximum when the optical length ratio of the high refractive index material to the low refractive index material is 1.2 for given operating parameters. When we keep the optical length of each layer being constant, the GVD is found to increase rapidly with the refractive index ration of the high refractive index material to the low one and even more rapidly with the number of periods of a photonic crystal. Under quite common operating parameters, a thin piece of photonic crystal of 100 periods may play the role of an ordinary dispersion-compensation fiber with a length over 158
kilo-meters.