In the past few years, a great interest has arisen in electromagnetic cloaking, a technology often associated with science fiction or fantasy [1-6]. An electromagnetic cloak, first proposed by Pendry et al. [1], is a coating made of exotic materials that can bend radio frequency (RF), infrared (IR), or visible electromagnetic radiation around an object. Rather than interacting with the cloaked object to produce either a reflection from the object or a shadow behind the object, incident wave will render the interior effectively "invisible" to the outside. Coordinate transformation is the initial way to design the cloak. An optical conformal mapping method has also been used to design a medium that creates perfect invisibility in the ray tracing limit [6-7]. Alu et al. have been working on the electrically small object's cloaking [8-11], which is constructed by metamaterial with negative or low-permittivity and/or permeability. Also, there are many simulations reported on cloaking [9-12], but the analytical demonstrations reported so far are mostly on the geometrical optics limit or in the electrostatic or magnetostatic limit. As we all know, both of the two limits include the approximations in Maxwell's theory, so it is necessary to demonstrate analytically whether perfect cloaking is achievable under any wavelength condition. Further more, since Pendry's design approach is based on Maxwell's equations, it indicated that such cloaking should be effective at all frequencies. Chen et al. have analyzed the interaction of the plane wave with the spherical metamaterial cloak through Mie scattering model [13]. In this paper, we demonstrated the interactions between plane electromagnetic wave and the cylindrical cloak analytically, and derived the analytical expression of the fields inside the cloak.
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