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.
We propose a kind of planar photonic crystal micro-cavity which is truly two-dimensional and is composed of a line of periodic air-holes and a set of periodic air grooves both with defect. Unlike the photonic crystal micro-cavity formed by distributed Bragg reflection (DBR) layers and two dimensional holes in a semiconductor substrate, the micro-cavity proposed is a true two-dimensional planar structure that is easy for mass-production through die-press copying. Numerical simulations by the FDTD method show that there exist resonance modes inside the photonic bandgap. The resonance wavelength is mainly decided by the period and radius of the holes. The quality factor of the cavity is mainly decided by the number of periods of the holes and the grooves.
We investigate a complex cavity composed of three simple cavities, which are formed by three simple defects in a one-dimensional photonic crystal (PC), by the optical transmission method. We set two of the simple cavities to be the same, and let the cavity-length of the third one vary. Generally, two or more narrow resonant transmission modes emerge in the bandgap region; the position of one of them is basically fixed with different fine structures, in which exists a fixed crest, while the other modes wander in the bandgap region as the cavity-length of the third cavity varies. We find the optimized the relative coupling length being 0.447 for the complex cavity. Introducing the parameter - degree of rectangularity, we find that the complex PC cavity is much more close to an ideal narrow band-pass filter than a simple PC defect cavity. It is surprising that the degree of rectangularity is insensitive to the number of periods in the structures.
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