Disorder-induced modification of the attenuation of light in a two-dimensional photonic crystal with complete band gap

We report on the modeling of light transmission in disordered two-dimensional photonic crystals (formed by air cylinders etched in a dielectric slab) with a complete photonic band gap. The disorder leads to a decrease in the light attenuation in the transmission dip corresponding to the photonic band gap, both for straight and scattered transmission, but the dependence of the attenuation length on the disorder is quite different for straight and scattered transmission. In the case of the straight transmission, there is a threshold degree of disorder required for the increase of the attenuation length. Disorder leads to a substantial modification of the spectral shape in the frequency region, corresponding to the photonic band gap, in particular, to the decrease of the width of the spectral dependence of the inverse attenuation length. We also demonstrate the appearance of photonic mini-bands in the photonic band gaps in the case of disorder represented by randomly distributed 'vacancies' of the air-cylinders.