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We study the electromagnetic transmission $T$ through one-dimensional (1D)photonic heterostructures whose random layer thicknesses follow a long-taileddistribution --L\'evy-type distribution. Based on recent predictions made for1D coherent transport with L\'evy-type disorder, we show numerically that for asystem of length $L$ (i) the average $<-\ln T> \propto L^\alpha$ for$0<\alpha<1$, while $<-\ln T> \propto L$ for $1\le\alpha<2$, $\alpha$ being theexponent of the power-law decay of the layer-thickness probabilitydistribution; and (ii) the transmission distribution $P(T)$ is independent ofthe angle of incidence and frequency of the electromagnetic wave, but it isfully determined by the values of $\alpha$ and $<\ln T>$.

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