Design of highly-efficient acoustic waveguide couplers using impedance-tunable transformation acoustics

Abstract

In this paper, the theory of impedance-tunable transformation acoustics in the geometric-acoustics limit is proposed to design efficient two-dimensional acoustic waveguide couplers. By choosing suitable impedance functions in the original space, impedance matching between the transformation medium and the background medium becomes possible, and the reflection at the boundary is reduced. The theory can be used to enable efficient acoustic coupling between waveguides of different sizes and different embedded media. By selecting an appropriate impedance function and a tunable acoustic refractive index, the transformed medium in the coupler can become a simplified parameter medium, for which the bulk modulus is a constant. This makes the experiment substantially easier. The problem of a reduced coupling-efficiency at low frequencies (a deviation from the geometric acoustic approximation) can be mitigated by selecting a large acoustic refractive index. Our two-dimensional numerical simulations indicate that this theoretical design works very well. The method can be extended to other transformation acoustic designs including three-dimensional cases.