The $0$ to $R_1$ cylinder radial coordinate transformation can not be used to make cylinder layer electromagnetic cloak

Abstract

In this paper, we discover and proved that the $0$ to $R_1$ cylinder radial coordinate transformation can not be used to make cylinder layer electromagnetic EM cloak. Because in the $0$ to $R_1$ cylinder radial coordinate transformation, the value area of the electric wave field $E_z (\rho,\phi,z)$ and magnetic wave field $H_z (\rho,\phi,z)$ are invariant. After $0$ to $R_1$ cylinder radial transformation,$\rho _q = R_1 + Q(\rho)$, $E_z (\rho _q,\phi,z) = E_z (\rho,\phi,z)$,$H_z (\rho _q,\phi,z) = H_z (\rho,\phi,z)$ . in the physical inner cylinder boundary, $E_z (R_1,\phi,z) \ne 0$,$H_z (R_1,\phi,z) \ne 0$, The cylinder EM wave field will propagation penetrate into the inner cylinder $\rho < R_1,\left| z \right| < \infty $ .Therefore, the inner cylinder $\rho < R_1,\left| z \right| < \infty $ . can not be cloaked. In many published papers on EM cylinder cloak, the $0$ to $R_1$ cylinder radial transformation is wrongfully used for their EM cylinder layer cloak.