The problem for hiding an object which is placed outside an external invisibility cloak is usually solved by determining the characteristics of the structure and its dielectric properties by transformation optics method. After that the numerical simulations (usually full wave simulation with finite element method) confirm the desired optical properties of the cloak. In this paper, we find the analytical solution of the wave equation and plot the electric field distribution in order to justify the performance of the external invisible cloak. Under this circumstances, the plane electromagnetic waves which is transmitted through the cloak without any scattering effect is confirm that our solution is correct.

Keywords: External invisibility cloak, Maxwell\' wave equation, Theoretical solution, Transformation optics

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