Metamaterial-Coated Plates for Emulating Non-Specular Reflection and Antenna Reflectors

The optical transformation is generally used to deform free space in order to obtain novel effects on waves. Such effects can be realized by replacing the deformed region by a “metamaterial” characterized by \mbi ε and \mbi μ tensors that are determined by the transformation. A new type of transformation is proposed which not only deforms a free space region, but transforms a non-trivially shaped conducting surface that bounds this region as well. The deformations are designed to map the original region into a planar slab of metamaterial, and to map the conducting surface into a plate which bounds this slab. Since the fields outside the deformed region-which include the fields scattered by the original conducting surface-are unaffected by the transformation, they can, in effect, be produced by scattering from the planar metamaterial-coated plate created from the transformation. This substitution of a non-trivially shaped conducting surface by a planar metamaterial-coated plate is applied to (a) a face of a wedge to produce reflection from the planar metamaterial-coated plate that is not in the specular direction, and (b) a parabolic reflector antenna to design a planar system which produces the same radiation pattern as the reflector. Both devices are numerically validated.