A feasibility study on achieving mode coalescence in acoustic waveguides

Abstract

In a previous talk at ASA it was shown that the 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 how to feasibly achieve the aforementioned wall impedance with the use of simple resonators. Within the frequency ranges supporting scale separation, it can be shown that a wall aligned with resonators can be modelled as an effective surface with a unique admittance. It is with this concept that we arrive at results showing distinct frequencies at which mode coalescence can occur. Strategies capable of deriving the necessary resonators parameters, and therefore, its dimensions are given. Numerical results are shown for reflection and transmission from a waveguide with the tuned effective surface composed of resonators in addition to the theoretical impedance boundary associated with constant EP behavior. Computer simulations and preliminary experimentation of the phenomena are referenced. Future attempts of utilizing more complicated metasurface designs are discussed for next iterations. [Work supported by NSF.]In a previous talk at ASA it was shown that the 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 how to feasibly achieve the aforementioned wall impedance with the use of simple resonators. Within the frequency ranges supporting scale separation, it can be shown that a wall aligned with resonators can be modelled as an effective surface with a unique admittance. It is with this concept that we arrive at results showing distinct frequencies at which mode coalescence can occur. Strategies capable of deriving the necessary resonators parameters, and therefore, its dimensions are given. Numerical results are shown for reflection and transmission from a waveguide with the tuned effective surface composed of resonators in addition to th...