Analytical modeling of conformal mantle cloaks for cylindrical objects using sub-wavelength printed and slotted arrays

Abstract

Following the idea of “cloaking by a surface” [A. Alù, Phys. Rev. B 80, 245115 (2009); P. Y. Chen and A. Alù, Phys. Rev. B 84, 205110 (2011)], we present a rigorous analytical model applicable to mantle cloaking of cylindrical objects using 1D and 2D sub-wavelength conformal frequency selective surface (FSS) elements. The model is based on Lorenz-Mie scattering theory which utilizes the two-sided impedance boundary conditions at the interface of the sub-wavelength elements. The FSS arrays considered in this work are composed of 1D horizontal and vertical metallic strips and 2D printed (patches, Jerusalem crosses, and cross dipoles) and slotted structures (meshes, slot-Jerusalem crosses, and slot-cross dipoles). It is shown that the analytical grid-impedance expressions derived for the planar arrays of sub-wavelength elements may be successfully used to model and tailor the surface reactance of cylindrical conformal mantle cloaks. By properly tailoring the surface reactance of the cloak, the total scattering from the cylinder can be significantly reduced, thus rendering the object invisible over the range of frequencies of interest (i.e., at microwaves and far-infrared). The results obtained using our analytical model for mantle cloaks are validated against full-wave numerical simulations.