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.
References
An EP is defined as a point in parameter space such that two eigenvalues as well as the corresponding two eigenvectors of a matrix coalesce (see Ref. 19 for details). Since a single eigenvector exists at the EP, a basis can be obtained by adding a generalized eigenvector. In our case (a matrix) it means that such a vector satisfies but . Notice that because Mc is 2 × 2, any vector not aligned with the eigenvector will satisfy this.