Photonic heterostructures with Levy-type disorder: statistics of coherent transmission

We study the electromagnetic transmission $T$ through one-dimensional (1D) photonic heterostructures whose random layer thicknesses follow a long-tailed distribution --Lévy-type distribution. Based on recent predictions made for 1D coherent transport with Lévy-type disorder, we show numerically that for a system of length $L$ (i) the average $<-\ln T> \propto L^α$ for $0<α<1$, while $<-\ln T> \propto L$ for $1\leα<2$, $α$ being the exponent of the power-law decay of the layer-thickness probability distribution; and (ii) the transmission distribution $P(T)$ is independent of the angle of incidence and frequency of the electromagnetic wave, but it is fully determined by the values of $α$ and $<\ln T>$.

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