Beyond Anderson Localization in 1D: Anomalous Localization of Microwaves in Random Waveguides

Abstract

Experimental evidence demonstrating that anomalous localization of waves can be induced in a controllable manner is reported. A microwave waveguide with dielectric slabs randomly placed is used to confirm the presence of anomalous localization. If the random spacing between slabs follows a distribution with a power-law tail (Lévy-type distribution), unconventional properties in the microwave-transmission fluctuations take place revealing the presence of anomalous localization. We study both theoretically and experimentally the complete distribution of the transmission through random waveguides characterized by α ¼ 1=2 ("Lévy waveguides") and α ¼ 3=4, α being the exponent of the power-law tail of the Lévy-type distribution. As we show, the transmission distributions are determined by only two parameters, both of them experimentally accessible. Effects of anomalous localization on the transmission are compared with those from the standard Anderson localization.

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

“…(2) are in contrast to the known results in the Anderson localization problem: ⟨T ⟩ decays exponentially with L and ⟨− ln T ⟩ ∝ L. Therefore, the above dependencies of ⟨T ⟩ and ⟨− ln T ⟩ on L reveal the presence of anomalous localization. Numerical simulations were performed firstly in order to design the random waveguides.…”

“…1(left), with a probability density of spacing ρ(d) between scatterers (slabs) with a power-law tail, i.e., for large d, ρ(d) ∼ c/d 1+α , where c is a constant and 0 < α < 1, we have found that the distribution of the transmission P (T ) is given by [1]- [2]:…”

Heat conduction in harmonic chains with Lévy-type disorder

“…A remarkable situation occurs when α = 2, since due to the logarithmic correction of the localization length, the asymptotic scaling law of the thermal conductivity acquires a non-closed form which represents an unusual situation because the typical scaling law of the thermal conductivity for 1D systems is κ ∼ N α1 , where the value of the exponent α 1 depends on the particular one-dimensional model [5,10]. Moreover, this logarithmic correction may be tested experimentally by measuring the electromagnetic transmission through onedimensional photonic heterostructures whose random layer thicknesses follow a long-tailed Lévy-type distribution since now there exist experimental devices where the anomalous localization of waves can be induced in a controllable manner [26]. The same phenomenon, may have some implications to the transmission T of light in Lévy glasses as a function of their thickness L since it may appear some corrections to the typical diffusive behavior for which T ∼ L 2 , L ≫ 1, however, this corrections will be not easy to observe, and an extension of the model analyzed in this work to higher dimensions is needed to provided a firmer theoretical background to the phenomenon of light in Lévy glasses.…”

Quantum evolution in disordered transport

“…In that sense, it may complement other established methods to treat disordered quantum systems, e.g., based on Green's functions. Attractive systems for scrutiny tests are ultracold atoms in optical waveguides [29,30], microwave waveguides [31,32], and classical light in the paraxial approximation [33,34], which all allow high control over disorder properties and state readout with excellent spatial resolution.…”