Experimental validation of the theoretical prediction for the optical $S$ matrix

TL;DR

This paper experimentally validates a recent theoretical prediction for the optical scattering matrix in wave scattering systems, using torsional wave experiments in a quasi-1D elastic system, and confirms its accuracy even under strong disorder.

Contribution

It provides the first experimental validation of a new theoretical prediction for the optical matrix in wave scattering, extending its applicability to disordered systems.

Findings

The theoretical optical matrix prediction matches experimental results.

The prediction remains valid under strong disorder conditions.

The study demonstrates the applicability of the theory in elastic wave systems.

Abstract

Scattering of waves is omnipresent in nature in systems with sizes varying from $10^{-15}$ to $10^{25}$ m. Within this 40 orders of magnitude, in a great number of systems, the scattering can be separated in an averaged response that crosses rapidly the scattering region and a fluctuating delayed response. This fact is the basis of the optical model; the averaged response, represented by the optical matrix $\langle S\rangle$, is composed with the fluctuating part that can be taken as a random matrix. Although the optical model was developed more than 60 years ago, a theoretical prediction for the optical matrix was obtained until very recently. The validity of such prediction is experimentally demonstrated here. This is done studying the scattering of torsional waves in a quasi-1D elastic system in which a locally periodic system is built; the distribution of the scattering matrix is calculated completely free of parameters. In contradistinction to all previous works, in microwaves and in elasticity, in which the value of $\langle S\rangle$ is obtained from the experiment, here the theoretical prediction is used to compare with the experiment. Numerical simulations show that the theoretical value is still valid when strong disorder is present. Several applications of the theoretical expression for the optical matrix in other areas of physics are proposed. Possible extensions of this work are also discussed.