Abstract
Devices based on transformation acoustics (TA) designed to control radiation of acoustic waves in water will be described. By restricting the TA mapping to a two-dimensional conformal transformation, it is shown that the properties in the physical device have constant density equal to the background density, while the effective acoustic medium must have spatially varying compressibility with values proportional to the area mapping. The talk will concentrate on the application of these ideas to a conformal TA device, the circle-to-square lens. A practical design procedure based on unit solid cylinder metamaterial elements will be described. The selection of elements is simplified using an Ashby-type chart of properties in terms of effective cylinder density vs. compressibility. Unlike previous gradient index lens devices of this type, the present design is almost optimally impedance and index matched. Analytical, numerical, and experimental results will be presented for a device with only 49 elements showing broadband focusing with positive gain in the preferred directions. [Work supported by ONR.]
Published Version
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