Acoustic cloaking in three dimensions using acoustic metamaterials

A scheme to achieve two dimensional (2D) acoustic cloaking is proposed by Cummer and Schurig [New J. Phys. 9, 45 (2007)] by mapping the acoustic equations to Maxwell’s equations of one polarization in the 2D geometry. We find that the acoustic equation can be mapped to the direct current conductivity equation in three dimensions, which then allows the design of three-dimensional acoustic cloaking using the coordinate transformation scheme. The perfect cloaking effect is confirmed by solving for the scattering problem using the spherical-Bessel function series expansion method.