It is known that photonic Bloch states can become strongly localized near the band edges in a disordered photonic crystal. We show that Bloch states are disrupted and another localization regime establishes when local fluctuations of the band-edge frequency caused by randomization of refractive index profile becomes as large as the band-gap width. Transmission experiments performed on opal photonic crystal have shown the exponential decay of light throughout the gap region, which is ascribed to building up of the second regime of light localization.

The eigenmode spectrum and transmission properties of a certain class of one-dimensional disordered photonic crystals have been studied statistically. It is shown that the relative fluctuation of the optical width of the period of the photonic crystal is a universal parameter allowing a quantitative description of the disordered photonic crystal for various models of disorder. It is shown that the tail of the density of states is characterized by a certain penetration depth and a quantitative relation between the penetration depth, the relative band gap width, and the disorder parameter is obtained. It is found that a threshold level of disorder exists, below which the density of states in the center of the photonic band gap vanishes, and the ensemble-averaged transmission coefficient does not change significantly with increasing disorder. Also, the standard deviation of the transmission coefficient is less than its mean value. Above threshold, the ensemble averaged transmission coefficient and density of states increase with the level of disorder rapidly, and the standard deviation of the transmission coefficient exceeds its mean value. A scaling formula is presented, which relates the logarithm of the transmission to the periodic refractive index modulation and the disorder.

The photonic eigenmodes near a band gap of a type of one-dimensional disordered photonic crystal have been investigated statistically. For the system considered, it is found that the tail of the density of states entering the band gap is characterized by a certain penetration depth, which is proportional to the disorder parameter. A quantitative relation between the relative penetration depth, the relative width of the photonic band gap, and the disorder has been found. It is apparent that there is a certain level of disorder below which the probability of the appearance of photonic eigenstates at the center of the photonic band gap essentially vanishes. Below the threshold, the ensemble-averaged transmission at the center of the photonic band gap does not change significantly with increasing disorder, but above threshold it increases much more rapidly. A simple empirical formula has been obtained which describes how the logarithm of the transmission relates to the periodic refractive index modulation and the disorder.

The modification of the bandgap structure of optical Fibonacci lattices that arises from an increase in the system size is analyzed. It is found that there is a minimum critical size of the Fibonacci...

A transfer-matrix method has been developed for cylindrical waves. Expressions are obtained for reflection and transmission coefficients of cylindrical light waves by an isolated cylindrical boundary...