Effects of disorder on wave propagation in two-dimensional photonic crystals

The electromagnetic transmittance of disordered two-dimensional photonic cr ystals composed of circular cylinders is investigated as a function of wave length and polarization. At short wavelengths, the transmittance shows a ba nd structure similar to that found in the optical absorption spectrum of am orphous semiconductors, with impurity states increasingly appearing on the long wavelength side of the band gaps as the degree of disorder is increase d. In the long-wavelength limit, Anderson localization of waves is found, p rovided that the wavelength is not so large that the random photonic crysta l can be viewed as homogeneous. The localization properties in this regime are studied and an analytic expression for the dependence of the localizati on length on wavelength is derived. In the limit of extremely long waveleng ths, the system homogenizes and can be replaced by an equivalent one with u niform effective refractive index, whose form is derived for both polarizat ions. Analysis of the crossover between localization and homogenization is also presented. [S1063-651X(99)18510-6].