Higher mode filtering: optimum attenuation in a continuum of exceptional points

Abstract

Exceptional points (EPs) occur when two (EP2) or more, say, <i>N</i> (<i>EP</i> <i>N</i>), modes coalesce causing a collapse of the eigenbasis in the underlying eigensystem. This phenomenon, which is associated with optimal attenuation, can arise in acoustic waveguides for which the eigensystem contains two or more parameters. This study focuses on mode filtering in a horizontal, rigid waveguide comprising an inlet duct (containing a point source) and an outlet duct, together with a finite-length component containing one/two horizontal wire-mesh perforate(s). The eigensystem has three/five parameters and the aim is to determine the best configuration to filter higher-order modes leaving only the plane wave. The initial tenet is that optimum filtering corresponds to EP2 (or EP3 when present) conditions. In fact, the results are surprising. For the case of one wire-mesh perforate, there exists a non-EP configuration that can perform as well or better than the EP2 case. For two wire-mesh perforates, the eigensystem exhibits a finite number of EP3s and a continuum of EP2s. An optimum EP2 occurs when the attenuation of an EP2 mode merges with that of the next least attenuated mode. One such configuration consistently performs as well or better than an EP3 configuration.