Designing near-perfect invisibility cloaks

Abstract

Invisibility cloaks are a favorite device used by science-fiction and fantasy authors. Yet, despite the fact that invisibility fascinates many people, its practical realization has rarely been treated as a serious research topic in science and technology. Very recently, researchers noticed that one can deduce the exact material requirement for making a completely passive cloaking device using the theory of transformation optics.1, 2 The basic principle is illustrated in Figure 1. Even for the simplest cylindrical cloak structure, however, the ideal material parameters prove difficult to match with current metamaterial fabrication technology. Therefore, one would prefer to simplify the material required for a cloak. Here we describe two promising approaches for constructing a simplified cylindrical invisibility cloak that should ease implementation while retaining good performance. In a cylindrical coordinate system (r, θ, z), one can simplify the cloak’s materials parameters ez, μθ , and μr for normal wave incidence—with a single transverse electric (TE) polarization (in which the electric field is solely aligned along the axial or z direction of the cloak)—by keeping intact the products ezμθ and ezμr. In the simplest case, a cylindrical cloak can be obtained through linear radial spatial mapping, i.e. r′ = (r− a) b b−a , where a and b are the cloak’s inner and outer radii, respectively, and r′ and r are the radial coordinates in electromagnetic and physical spaces, respectively. The corresponding ideal material parameters are shown in the left column of Table 1. Based on this ideal cloak, a simplified version, as proposed by John Pentry’s group3, has material parameters shown in the middle column in Table 1. However, such a simplified cloak still scatters electromagnetic fields considerably, largely due to its unmatched impedance to free space.4 Wepropose a new version of a simplified cylindrical cloak that restores impedance matching to the space outside the cloak. We do not vary the products ezμθ and ezμr. This improved set of Figure 1. Formatting a cloak of an arbitrary shape by transformation optics (a): and (b) depict correlated coordinates’ lines in electromagnetic space and physical space, respectively. A void region S2 in (b) has appeared, which is obtained by blowing up a point (or a line, if the structure is invariant along the paper-normal direction) of zero size in (a). The annular shape bounded by S1 and S2 in (b) is electromagnetically equivalent to the region bounded by S1 in (a). However the regions’ material parameters are different owing to a change of coordinate. The region bounded by S1 and S2 in (b) constitutes a cloak, whose interior can conceal objects. Notice that the coordinate changes only for a finite spatial region bounded by S1 in both panels. As a consequence, the material outside S1 (which we assume is air) remains the same in both panels.