Cloaking a bump inside a single isotropic lossless dielectric

In this work, we determine the suitable parameters (permittivity and thickness) of a lossless dielectric superstrate slab layer, covering an infinite perfect electric conducting (PEC) plane on which lies a two-dimensional PEC bump, such that, simultaneously: (i) the plane wave reflection by the overall configuration in the absence of the bump resembles closely that by the infinite PEC plane, and (ii) the bump´s contribution on the scattered far-field radiated over all directions becomes as small as possible. The scattered field is determined by a semi-analytic integral equation methodology. Optimal superstrate´s parameters, achieving both objectives (i) and (ii) within significant numerical accuracy, are computed.