In this Letter, a broad-band inhomogeneous asymmetrical lens is presented based on geometric optics and the Eikonal equation[29], resulting in a special fan-beam radiation pattern. The vertical and horizontal planes of this fan-beam radiation pattern can be controlled separately. This is the main improvement of this method compared to others based on transformation optics. It is suitable to have a lens antenna that works in a broad-band frequency application. This feature is another aspect that is considered in this method. We design a 3D asymmetrical lens that has a fan-beam radiation pattern in which the half-power beam width of the pattern in the narrow plane is twice that in the wide plane.
The size of the lens antenna is approximately inversely proportional to the free-space wavelength. So, the size of the antenna is reduced at mm wavelengths. The center frequency of operation is considered equal to 10 GHz for a 3D asymmetrical lens.
First, the refractive index of the inhomogeneous asymmetrical lens is proposed, based on geometric optics and the Eikonal equation. Then, the proposed refractive index is validated in some cutting planes by using the FDTD scheme. The refractive index profile is approximated in CST commercial software, and the performance of the radiation pattern for this type of lens is discussed.
A fan-beam radiation pattern can result from a lens antenna having an asymmetrical aperture. A typical structure of this type of lens is shown in Fig. 1, which has an elliptical aperture with diameters 2a and 2b. It is assumed that the refractive index is inhomogeneous and has a continuous and gradual change. So, to analyze the lens, we consider it as many planes, all of them crossing the -axis. The length of theoutput side of each plane is 2d, which is between 2a for the XZ plane and 2b for the YZ plane. The lens is excited by a point source located at point (0, 0, ). The point source emits many rays of rising angle with respect to the -axis, as shown in Fig. 2.
