  In this study, the design of a directional cloaking based on the Luneburg
lens system is proposed and its operating principle is experimentally verified.
The cloaking concept is analytically investigated via geometrical optics and
numerically realized with the help of the finite-difference time-domain method.
In order to benefit from its unique focusing and/or collimating characteristics
of light, the Luneburg lens is used. We show that by the proper combination of
Luneburg lenses in an array form, incident light bypasses the region between
junctions of the lenses, i.e., the "dark zone." Hence, direct interaction of an
object with propagating light is prevented if one places the object to be
cloaked inside that dark zone. This effect is used for hiding an object which
is made of a perfectly electric conductor material. In order to design an
implementable cloaking device, the Luneburg lens is discretized into a photonic
crystal structure having gradually varying air cylindrical holes in a
dielectric material by using Maxwell Garnett effective medium approximations.
Experimental verifications of the designed cloaking structure are performed at
microwave frequencies of around 8 GHz. The proposed structure is fabricated by
three-dimensional printing of dielectric polylactide material and a brass
metallic alloy is utilized in place of the perfectly electric conductor
material in microwave experiments. Good agreement between numerical and
experimental results is found.
