Passively achieving mode coalescence in acoustic waveguides with simple resonators

Abstract

A double root, commonly referred to as an exceptional point (EP), for modal frequencies in a 2-D or 3-D waveguide can exhibit almost perfect absorption over a relatively broad frequency range. The key to the phenomenon is that the wall impedance is such that modes coalesce at a complex-valued frequency. In this talk we consider a novel approach to feasibly achieve the aforementioned wall impedance with the use of simple resonators, which can be shown to exhibit mode coalescence at distinct frequencies when treated as a unit cell component of a larger metasurface. In order to evaluate each unit cell design, an efficiency parameter, EP density, was created which quantifies the number of double root frequencies within a given range all while satisfying the following constraints: realizable resonator dimensions, scale separation, and target absorption/attenuation goals. Strategies capable of deriving the necessary resonator parameters for this effect are given. The impact of these strategies on feasibility and performance are discussed via simulated and numerical results. An experiment design consisting of additively manufactured Helmholtz resonators incorporated onto a custom-made impedance tube to simulate the resonant metasurface is discussed along with preliminary results. [Work supported by NSF.]