# Additive Manufacturing of Variable Density Lenses for Radio Frequency Communications in X-Band
## 1 Introduction  
In recent years, additive manufacturing (AM) has emerged as a transformative technology with profound implications across various industries, including aerospace, healthcare, automotive, and beyond [1]. The unique capabilities of AM--particularly in terms of material diversity, precision, and design freedom--have opened the way for novel applications in the field of communication systems. The communications industry increasingly demands higher frequency devices capable of handling the complex requirements of modern wireless systems [2]. Additive manufacturing offers several advantages in meeting these demands. First, it enables rapid prototyping and iterative testing, allowing engineers to optimize designs in shorter time frames [3]. This rapid design-to-manufacture process is essential for the fast-paced communications sector, where technologies are continuouslyevolving to support new standards like 5G and 6G [4]. Secondly, AM facilitates the production of highly intricate structures that are difficult to machine or mold. For example, horn antennas and GRIN lenses with complex internal geometries can be manufactured as single components, reducing the need for assembly and the potential for alignment errors, which are critical factors in RF applications [5]. Antenna design has evolved significantly in response to the ever-growing demand for high-performance communication systems. Traditionally, antennas are fabricated from metals such as copper or aluminum, chosen for their high electrical conductivity and robustness in high-frequency applications. The horn antenna, a staple in RF communications, is particularly valued for its simplicity, directivity, and broadband capabilities [6]. With the advent of AM, researchers have explored new methods to manufacture these antennas, often focusing on materials and processes that allow for high precision and reduced weight. Metallic coatings can be applied to 3D-printed polymer structures to achieve the necessary conductivity [7]. [PERSON] et al. [8] offers a more versatile manufacturing process for complex designs. This approach not only reduces the weight of the component but also lowers material costs by limiting the use of expensive metals to surface coatings, customizing antenna properties without the constraints of conventional subtractive manufacturing. By enabling the use of composite polymer-based materials, AM also enhances the thermal management of devices, which is especially important for high-power applications in the communications field [9]. Gradient Index (GRIN) lenses are widely used in communications to manipulate the propagation of electromagnetic waves. By gradually varying the refractive index of the lens material, GRIN lenses focus or direct RF energy in a controlled manner, enhancing the performance of antennas in terms of gain and beam shaping [10]. Traditionally, these lenses are made from homogenous dielectric materials, with their refractive index modified by altering their geometry [11]. This often requires a labor-intensive shaping of dielectric materials to achieve the desired index gradient, which limits design flexibility and increases production time. However, AM provides the ability to adjust the refractive index more flexibly by changing the density or porosity of the polymeric material within a single component during fabrication. This method also allows for the integration of stochastic and gyroid mesh structures, which offers an additional degree of control over material properties. By adjusting the porosity of the material, designers can achieve specific permittivity values across the lens profile, as in [12; 13]. This capability opens up new possibilities in lens design, enabling devices that are both lightweight and capable of complex wavefront shaping. There are several AM techniques that are particularly suited to the polymer-based fabrication of RF components, for instance, Vat Photopolymerization (VPP) and Powder Bed Fusion (PBF).