We study the electromagnetic transmission $T$ through one-dimensional (1D) photonic heterostructures whose random layer thicknesses follow a long-tailed 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 $\langle -\ln T\rangle \propto L^{\alpha }$ for $0<\alpha <1$, while $\langle -\ln T\rangle \propto L$ for $1⩽\alpha <2$, $\alpha$ being the exponent of the power-law decay of the layer-thickness probability distribution, and (ii) the transmission distribution $P\left(T\right)$ is independent of the angle of incidence and the frequency of the electromagnetic wave, but it is fully determined by the values of $\alpha$ and $\langle \ln T\rangle$. Additionally we have found and numerically verified that $\langle T\rangle \propto L^{-\alpha }$ with $0<\alpha <1$.

• Received 16 January 2012

DOI:https://doi.org/10.1103/PhysRevA.85.035803