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

Abstract

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 $<-\ln T>\propto L^{\alpha }$ for $0<\alpha <1$, while $<-\ln T>\propto L$ for $1\le \alpha <2$, $\alpha$ 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 $<\ln T>$.

4 pages, 4 figures

References in corpus (2)

• Nonalgebraic length dependence of transmission through a chain of barriers with a Levy spacing distribution
• Conductance through quantum wires with Levy-type disorder: universal statistics in anomalous quantum transport

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