Effectiveness and improvement of cylindrical cloaking with the SHS lining

We analyze, both analytically and numerically, the effectiveness of cloaking an infinite cylinder from observations by electromagnetic waves in three dimensions. We show that, as truncated approximations of the ideal permittivity and permeability tensors tend towards the singular ideal cloaking fields, so that the anisotropy ratio tends to infinity, the D and B fields blow up near the cloaking surface. Since the metamaterials used to implement cloaking are based on effective medium theory, the resulting large variation in D and B will pose a challenge to the suitability of the field averaged characterization of ε and μ. We also consider cloaking with and without the SHS (softand-hard surface) lining, shown in [6] to be theoretically necessary for cloaking in the cylindrical geometry. We demonstrate numerically that cloaking is significantly improved by the SHS lining, with both the far field of the scattered wave significantly reduced and the blow up of D and B prevented.