## 1 Introduction  
Three-dimensional (3D) printing technology has been widely utilized in engineering production due to its properties of rapid prototyping, being lightweight, low cost, etc. This trend is also true for antenna engineering, not only for the stated reasons but also for its ability to shape any 3D form in space. Three-dimensional printing enables the realization of complex structures for effective radiation at a relatively lower cost and a lighter weight. Examples include small antennas, waveguide antennas, horn antennas, and slotted antennas, to mention only a few [1; 2; 3; 4; 5]. So-called 3D printed antennas are generally prototyped in the following steps. First, the antenna structure, whether it is a wire, planar, or waveguide, is printed with plastic-based materials, such as (acrylonitrile butadiene styrene) ABS or poly-powder. The printed plastic is then plated with metallic spray, polycrystalline copper sputtering, or chemical plating. In many studies, it has been found that the electrical conductivity of the antenna after the subsequent plating process nearly approaches that of bulk metals [2; 5; 6; 7]. Although the speedy production time for a prototype is an advantage of 3D printed antennas [6; 7; 8; 9; 10; 11; 12], the plating process is still the most challenging and time-consuming part of 3D printing technology-based antenna fabrication. This is because selective plating requires a pre- and post-process of wrapping the printed plastics. In addition, realizing a uniform coated metal surface with acceptable roughness is a sophisticated work. It would not be a big issue for low-frequency applications as long as a metal layer thicker than the skin depth is formed [13], but may affect antenna performance in high frequencies, such as mmWave or even higher ones [14; 15; 16]. In this case, additional chemical processes for better roughness may be carried out, and conductivity can be reduced, resulting in degraded antenna efficiency [17; 18]. Metallic 3D printing based on selective laser sintering methods can be attempted but they cannot meet the high conductivity desired for electrical engineering, as the technology is evolving to focus on rigidity or stiffness. Among the topics of 3D printed antennas, dielectric lens antennas for improved directivity are certainly free from plating difficulties. Furthermore, the resolution of the current 3D printing technology level is precise enough for millimeter-scale lens printing. Therefore, 3D printing technology is being intensively used in lens antenna designs, even at mmWave and THz frequencies, regardless of its electrical size [19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34]. For example, in [19], the lens is composed of cube units, with each edge length ranging from 0.1 mm to 2 mm. The dielectric constant of the lens can be adjusted with different cube sizes. In [27], a comb-like dielectric lens configuration was implemented with 0.6 mm spacing of the 3D printed parts. A circular polarizer was achieved with a 3D printed dielectric lens in [29], with 1 mm spacing of the 3D printed parts. A basic working principle of a dielectric lens antenna is to passively manipulate the spherical wave emitted by the source radiator into a planar wave by the shape of the solid lens [19]. When the lens is composed of a single permittivity material, however, it can be long, as the distance from excitation to each area of the spherical lens for the in-phase wavefront is different [31; 32; 33]. In other words, the lens height can be reduced by controlling the phase velocity of each wavefront independently. This can be realized when a lens is composed of more than a single permittivity [19; 27; 28; 29]. However, a single lens composed of multiple materials requires a complex fabrication process. Therefore, in this paper we propose realizing different effective dielectric constants at the lens by changing each area of the lens structure. The final lens design is found to have a reduced height when compared to the reference lens with a single permittivity.