Cloaking an object on a dielectric half-space

Cloaking an object on a dielectric half-space for an observer in air is studied. The proposed cloaking configuration has two vertical matching strips of isotropic and homogeneous material under the two bottom surfaces of a semi-cylindrical cloaking cover. Simple expression for the material parameters of the matching strips is derived. The theoretical results of cloaking are verified numerically for the incidence of plane wave and line current source. The vertical matching strips can be terminated with a finite depth by introducing some loss to the matching material.