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

TL;DR

This paper investigates how Levy-type disorder in 1D photonic heterostructures affects electromagnetic transmission, revealing distinct scaling laws and distribution characteristics depending on the disorder's power-law exponent.

Contribution

It numerically confirms theoretical predictions about the scaling of transmission and distribution independence in Levy-disordered photonic structures.

Findings

<- ln T> scales as L^α for 0<α<1 and linearly with L for 1≤α<2

Transmission distribution P(T) is independent of incidence angle and frequency

Distribution determined solely by α and <ln T>

Abstract

We study the electromagnetic transmission $T$ through one-dimensional (1D) photonic heterostructures whose random layer thicknesses follow a long-tailed distribution --L\'evy-type distribution. Based on recent predictions made for 1D coherent transport with L\'evy-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 $<\ln T>$.