Anomalous transmission through periodic resistive sheets

TL;DR

This paper explores anomalous acoustic wave transmission through periodic resistive sheets, revealing conditions for high transmission peaks at Bragg frequencies and linking the phenomenon to exceptional points in transfer matrix eigenvalues.

Contribution

It introduces the acoustic analogue of the Borrmann effect, combining theoretical and experimental analysis to identify conditions for anomalous transmission in dissipative media.

Findings

High transmission peaks occur at Bragg frequencies.

Optimal conditions involve many thin resistive sheets.

Anomalous peaks relate to eigenvalue coalescence at exceptional points.

Abstract

This work investigates anomalous transmission effects in periodic dissipative media, which is identified as an acoustic analogue of the Borrmann effect. For this, the scattering of acoustic waves on a set of equidistant resistive sheets is considered. It is shown both theoretically and experimentally that at the Bragg frequency of the system, the transmission coefficient is significantly higher than at other frequencies. The optimal conditions are identified: one needs a large number of sheets, which induce a very narrow peak, and the resistive sheets must be very thin compared to the wavelength, which gives the highest maximal transmission. Using the transfer matrix formalism, it is shown that this effect occurs when the two eigenvalues of the transfer matrix coalesce, i.e. at an exceptional point. Exploiting this algebraic condition, it is possible to obtain similar anomalous transmission peaks in more general periodic media. In particular, the system can be tuned to show a peak at an arbitrary long wavelength.