We study the electromagnetic transmission $T$ through one-dimensional (1D) photonic heterostructures whose random layer thicknesses follow a long-tailed distribution --Levy-type distribution. Based on recent predictions made for 1D coherent transport with Levy-type disorder, we show numerically that for a system of length $L$ (i) the average $<-ln T> propto L^alpha$ for $0<alpha<1$, while $<-ln T> propto L$ for $1lealpha<2$, $alpha$ 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 $alpha$ and $<ln T>$.
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