Beyond Anderson localization: Anomalous transmission of waves through media with Lévy disorder

Abstract

It is widely known that the presence of disorder leads to an exponential localization of waves in one-dimensional random media, as predicted by Anderson. In this work, however, we provide experimental evidence that waves can be anomalously localized, in relation to the standard Anderson localization, by introducing random configurations of the disorder that follow a distribution with a power-law tail, i.e., a Lévy-type distribution. Using a microwave waveguide with dielectric slabs randomly placed, we show that if the spacing between slabs follow a Lévy-type distribution, unconventional properties in the microwave-transmission fluctuations appear, revealing the presence of anomalous localization. Our analytical model describes the experimental results for the statics of the transmission fluctuations. Effects of anomalous localization on the transmission are compared with those from the standard Anderson localization as well.

Information-Length Scaling in a Generalized One-Dimensional Lloyd’s Model

“…Consequently, disorder characterized by Equation ( 1 ) is commonly known as Lévy-type disorder. In addition, the recent experimental realizations of the so-called Lévy glasses [ 31 ] as well as Lévy waveguides [ 32 , 33 ] has refreshed the interest in the study of systems characterized by Lévy-type disorder; see some examples in Refs. [ 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 ].…”