Transmedia transmission enhancement based on transformation acoustics

Transmission enhancement of sound waves across the interface between media with different impedances is a classical problem in acoustic communication, for instance in the case of the water-air interface. Different strategies, including bubble-embedded metasurfaces or impedance-matched metamaterials, have been developed to render the interface transparent. Transmedia wave enhancement is up to now either broadband or incorporating customized wavefront manipulation. In this paper, we explore the use of transformation acoustics and gauge transformation to realize both goals simultaneously. Transformation acoustics is first argued to provide lossless transmedia sound enhancement, although at the expense of adapting the cross section to respect power-flow conservation. It is specifically proven that a gradient anisotropic metamaterial provides perfect transmission between two media in two dimensions and that perfect steering of sound waves is allowed as well. Gauge transformation theory is then adapted from transformation elasticity to provide one-dimensional perfect sound transmission via a gradient Willis-like acoustic metamaterial. Finally, the two transformations are combined together to implement broadband perfect acoustic transmission and focusing at the water-air interface. The lens designed by the proposed method is achromatic. This paper is expected to provide alternative solutions for transmedia communication.