# Dielectric Slabs-Based Lens for Millimeter-Wave Beamforming
## 1 Introduction  
The use of millimeter-wave bands for next-generation wireless communication networks, such as fifth-generation (5G) mobile systems, has piqued the interest of researchers as the demand for high data rates grows. [1]. However, millimeter-wave communications pose many diverse challenges due to the large channel bandwidth, unique channel characteristics, hardware constraints, the concrete path, and penetration losses at millimeter wavelengths [2, 3]. As a result, antenna beamforming is proposed for establishing and maintaining a reliable millimeter-wave communication link. Beamforming in 5G is the modern, powerful technique for the intended user/direction coverage using the narrow beamwidth radiation patterns [3]. Beamforming techniques are based on steering the direction of the main lobe of the radiation by switching the elements of an antenna array or by changing the relative phases of radio frequency (RF) signals driving the array elements. The beamforming antenna array technologies are combined with massive multiple-input multiple-output (MIMO) systems and multi-beam antenna array systems to play a crucial role in 5G wireless communication systems [4, 5]. However, despite high directivity and beam scanning of antenna array beamformers, their practical implementation at millimeter-wave frequencies is complex and expensive [6]. So, researchers focus on innovative lenses to be used in beamforming systems of 5G millimeter-wave to reduce the cost and the complexity [7]. The passive phase shifter lens enables beamforming without a heavy network of phase shifters of antenna array beamformers, while the energy-focusing property of the lens achieves gain and directivity. In spherical or semi-spherical lenses, the beam traveling along the principal axis of the lens is focused on a spot, known as the focal point. Conversely, an EM radiation source placed at the focal point can be converted into a directional beam by the lens, so an object with an image at infinity and vice versa. Besides using these lenses as passive phase shifters,they are used for beam collimation and deflection in the microwave range [8] and cloaks in the optical range [9]. The most common lenses used at the millimeter-wave frequencies are the Luneburg and Maxwell fisheye lenses [10]. The effective refractive index varies in the range 1\(-\sqrt{2}\) for classical Luneburg lenses and in 1-2 for Maxwell fisheye lenses [10]. Variation of similar lens types is generally designed based on the transformation optics theory. The Graded refractive index of the material lens can achieve different focusing properties. The diameter of the spherical lens is inversely proportional to the achievable half-power beam width (HPBW). Theoretical conversion of 3D lens action on the 2D surface was demonstrated via focusing beam in a limited azimuthal or elevation plane [11]. Metallic parallel-plate waveguide (PPWG) structures represent the simplest periodic artificial sub-wavelength structures of graded refractive index (GRIN) metamaterials implemented for designing lenses in both microwave and sub-terahertz ranges [12; 13]. The gradient refractive index of the PPWG cells can be attained by gradually modifying their geometrical parameters. A metasurfaces-based lens with field control capabilities to achieve a similar graded-index principle is presented in [14]. A broadband low-loss lens was designed based on metamaterials [15]. Another metamaterial-based thin planar lens is presented in [16] to be used with linear substrate integrated waveguide antenna array for spatial beamforming. A 3D metasurfaces-based lens is realized in [17] machined by drilling inhomogeneous holes in multilayered dielectric plates. Although, spherical or semi-spherical dielectric lenses are isotropic and focus the radiation in both azimuthal and elevation planes. However, these lenses are challenging to be fabricated and need specific mechanical or printing devices.