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

TL;DR

This study experimentally and theoretically demonstrates anomalous wave localization in microwave waveguides with Le9vy-type disorder, revealing unconventional transmission properties distinct from standard Anderson localization.

Contribution

It provides the first controlled experimental evidence of anomalous localization in microwave waveguides with Le9vy-type disorder and characterizes the transmission distribution using only two accessible parameters.

Findings

Anomalous localization occurs in waveguides with Le9vy-distributed disorder.

Transmission distributions depend on two key parameters.

Distinct transmission behavior compared to standard Anderson localization.

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 (L\'evy-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 $\alpha=1/2$ ("L\'evy waveguides") and $\alpha=3/4$, $\alpha$ being the exponent of the power-law tail of the L\'evy-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.