Bioinspired Fano-like resonant transmission: frequency selective impedance matching

Abstract

The study of the impedance mismatch between the device and its surroundings is crucial when building an acoustic device to obtain optimal performance. In reality, a high impedance mismatch would prohibit energy from being transmitted over the interface, limiting the amount of energy that the device could treat. In general, this is solved by using acoustic impedance matching layers, such as gradients, similar to what is done in optical coatings. The simplest form of such a gradient can be considered as an intermediate layer with certain qualities resting between the two media to impedance match, and requiring a minimum thickness of at least one quarter wavelength of the lowest frequency under consideration. The desired combination(s) of the (limited) available elastic characteristics and densities has traditionally determined material selection. Nature, which is likewise limited by the use of a limited number of materials in the construction of biological structures, demonstrates a distinct approach in which the design space is swept by modifying certain geometrical and/or material parameters. The middle ear of mammals and the lateral line of fishes are both instances of this method, with the latter already incorporating an architecture of distributed impedance matched underwater layers. In this paper, we develop a resonant mechanism whose properties can be modified to give impedance matching at different frequencies by adjusting a small set of geometrical parameters. The mechanism in question, like the lateral line organ, is intended to serve as the foundation for the creation of an impedance matching meta-surface. A computational study and parameter optimization show that it can match the impedance of water and air in a deeply sub-wavelength zone.