The effects due to disorder in the applications of photonic band gap materials

By using the multiple-scattering method, we have studied the effects due to various kinds of disorder in the applications of photonic band gap (PBG) materials. In particular, we have studied the disorder effects on the quality of following devices:1) optical waveguides, 2) high-Q microcavities, 3) wave demultiplexer and 4) "superprism". The systems we considered are two-dimensonial PBG materials with cylindrical inclusions. In our study, we consider two kinds of randomness. In the first kind, the position of each cylinder can be randomly displaced within certain range from its lattice point. In the second kind, while the position of each cylinder is fixed in its lattice point, its radius becomes a random parameter. In addition, for devices 1) to 3 ) we also consider three random cases: (a) all cylinders are random, (b) only the cylinders in the first layer close to the devices are random, and (c) all cylinders except those in the first layer close to the devices are random. Our results show that for both the cases of position and size randomness the quality of the first three devices is insensitive to the disorder in case (c) but very sensitive for cases (a) and (b). Thus, we can conclude that the uniformity of the cylinders in the first layer close to the devices are extremely important to ensure the quality of the devices