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 transmittance 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 considered. The localization and homogenization properties of disordered photonic crystals are investigated. Analytical expressions for the two-dimensional localization length in the form of integrals are presented for both polarizations. It is shown numerically that the slope of the exponential divergence of the localization length in two dimensions is proportional to the inverse of the square of randomness for strong disorder and proportional to the inverse of the randomness for weak disorder. The effective dielectric constants for both polarizations in the case of strong disorder are also found. The transition from localization to homogenization is discussed and the terms responsible for this transition are identified and investigated.