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

TL;DR

This paper proves that the common $0$ to $R_1$ cylinder radial coordinate transformation cannot be used to create an effective electromagnetic cloak because it allows wave penetration into the inner cylinder, invalidating cloaking.

Contribution

The paper provides a rigorous proof that the $0$ to $R_1$ transformation is unsuitable for electromagnetic cloaking, correcting a widespread misconception in the field.

Findings

The $0$ to $R_1$ transformation preserves electric and magnetic field values, preventing cloaking.

Wave fields penetrate into the inner cylinder, making cloaking impossible with this transformation.

Many published EM cloaks incorrectly use this transformation, which the paper discredits.

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.