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.