Disorder plays a key role in the understanding of discrepancies between experimental results and theoretical predictions elaborated for perfect photonic crystals. The two-dimensional structures obtained by lithography, always contain roughness of the surfaces of the etched elements. We have investigated the effect of radius disorder on complete and incomplete photonic band gaps. We have considered the incomplete gap of a two-dimensional hexagonal photonic crystal of air cylinders for the TM electromagnetic modes (for which electric field is parallel to the cylinders and magnetic field lies in the plane perpendicular to the cylinders). The refractive index of the material is 3.6 and radius of the cylinder r{sub}0 = 0.4 d (where d is distance between centers of the two neighboring cylinders). An incomplete band gap exists in the F-M direction of the Brillouin zone, centered at the frequency fd / c ≈ 0.2212, with a relative width of about 0.15. We separate straight and scattered transmission, as shown in Figure 1. We have studied various "amount of the disorder", described by a deviation 8m the cylinder radius, which is uniformly distributed in the interval from r{sub}0(1-δ) to r{sub}0(l+δ).
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