Illusion Elastics in a Fluid Background

Abstract

Applying principles of transformation optics to acoustic systems continues to gain traction. It has been shown that transformation elastics, or $i\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}s\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}n$ $e\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}s\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}s$, is challenging, as the elastodynamic wave equation will change its form after coordinate transformation. Here the authors use transformation acoustics based on Fabry-P\'erot (FP) resonances, to obtain an illusion such that an arbitrary solid object sounds like a different object in a fluid background. This elastic illusion is confirmed analytically using Mie theory, for both two and three dimensions. This approach could be important in underwater acoustic communication, $e.g.$ sonar.