Effects of geometric and refractive index disorder on wave propagation in two-dimensional photonic crystals

The effects of disorder in the geometry and refractive index on the transmi ttance of two-dimensional photonic crystals composed of dielectric circular cylinders are considered, including randomness of radii, positions of the cylinder centers, and thickness of each layer of the photonic crystal. The effects of combinations of different types of strong disorder are also cons idered. The localization and homogenization properties of disordered photon ic crystals are investigated. Analytical expressions for the two-dimensiona l localization length in the form of integrals are presented for both polar izations. It is shown numerically that the slope of the exponential diverge nce of the localization length in two dimensions is proportional to the inv erse of the square of randomness for strong disorder and proportional to th e inverse of the randomness for weak disorder. The effective dielectric con stants for both polarizations in the case of strong disorder are also found . The transition from localization to homogenization is discussed and the t erms responsible for this transition are identified and investigated.