Inhomogeneous lens antenna 002

The Luneburg lens^[23] is an inhomogeneous symmetrical spherical lens where the relative index profile  varies with the square of the radius, , where  is the radius from the center point and  is the outer radius of the lens. This type of lens is very useful in antenna and scattering applications^[7,13,24].

The Luneburg lens design is extracted from the transformation optics theory. Transformation optics is a method to design lens antennas that is realized by controlling the electromagnetic field at the desired coordinates to obtain complex materials^[25–28].

The lenses in most of the mentioned Letters have a symmetrical shape and index profile. So the radiation pattern of a three-dimensional (3D) model lens is the same as a pencil beam. Two-dimensional (2D) model realization is more convenient than 3D model realization, so the radiation pattern of a planar form fabrication lens is like a fan-beam pattern. It produces a beam that is wide in the narrow plane and narrow in the wide plane of an asymmetrical lens. In this type of planar model, the control of the beam width is possible in one plane, but there is no control over the other planes of the radiation pattern beam width.

Wide angle searches are required in some modern radar and satellite systems operating at millimeter-wave and microwave-frequency bands, such as weather radar, tracking systems, and remote sensing applications. Parabolic reflectors and array antennas can be designed to radiate asymmetrical patterns in vertical and horizontal planes because of their special shape and feeding structures.