Problem On The Acoustic Cloak By $0$ to $R_1$ Transformation

Abstract

The $0$ to $R_1$ radial spherical coordinate transformation method can be making electromagnetic (EM) invisible cloak. However the cloak by transformation optic has infinite speed and exceeding light speed etc fundamental difficulties. In this paper, we discover problem on acoustic cloak by transformation and prove that in the $0$ to $R_1$ radial spherical coordinate transformation, the pressure wave field $P(r_p)=P(r)$ is invariant, in the physical inner spherical surface boundary $r=R_1$, $P(R_1)$ is not zero. the acoustic field propagation penetrate into the inner sphere $r < R_1$.Therefore, the inner sphere $r < R_1$ can not be cloaked. The GL simulation figures of the pressure acoustic wave propagation penetrate into the inner sphere $r \le R_1$ are presented in figure 1 to figure 12.The pressure wave is setting to zero that cause the scattering wave to disturb incident pressure acoustic wave outside of the outer sphere $r \ge R_2$ that make the whole sphere $r \ge R_2$ will be deltected. GL method simulation is presented in figure 13. we discovered and proved that $0$ to $R_1$ sphere radial transformation can not be used to induce acoustic no scattering cloak.