# Methodology for Improving Scanning Performance Loading an Array Element with a 3D All-Metal WAIM
## 1 Introduction  
Wide scanning capabilities are usually required when using radar systems, modern communication systems, such as in 5G applications [1], or communications with low earth orbit (LEO) satellites [2]. As it is well known, while steering the beam, the coupling between the elements in the array may deteriorate the antenna active matching, possibly resulting in scan blindness [3]. It is particularly difficult to conceive an element for a phased array that scans at a wide angle, because its periodicity has to be smaller than \(0.5\lambda\) to avoid grating lobes. Some methods have been developed to avoid these problems, such as the use of mechanical steering [4]. Other methods try to alleviate the problem while allowing for electrical scanning, which consist of the use of matching networks in the antenna elements [5], reconfigurable active structures [6; 7] or matching layers placed above the antenna. Such layers are commonly known as wide-angle impedance matching (WAIM) surfaces. This article proposes an innovative topology and the associated design methodology for a WAIM that can be built employing only metal. Indeed, 3D additive manufacturing methods allow to build a full structure in just one metallic piece, avoiding the use of connections or welds that could cause problems or deformations in the final response, as well as increasing the fabrication process speed. In addition, it avoids the use of dielectric materials in the structure, preventing problems such as intrinsic losses in these materials and the outgassing phenomenon [8] that dielectrics may suffer when they are used in space. The use of these innovative manufacturing technologies results in a large number of 3D all-metal structures that are used in a wide range of applications. It can be found in frequency selective surfaces (FSS) acting as spatial filters [9; 10; 11], or as polarizers [12; 13; 14], metallic antennas [15; 16; 17] as well as metallic arrays [18; 19; 20]. Lenses are also being made as 3D metallic structures [21; 22; 23] and microwave filters as well [15; 24]. To the best knowledge of these authors, there is no proposal for a metallic WAIM in the literature yet. Classical WAIM solutions can be classified according to their topology, such as single dielectric layers [25; 26; 27; 28], single layer metamaterials [29; 30; 31; 32; 33], multilayer metamaterials [34; 35; 36] and 3D WAIMs [37]. Their design methodologies can also be classified into those that make use of optimization algorithms during all of the design process [30; 34; 38], or others that use an equivalent circuit (EC) [29; 36; 37] with which the cell is modeled. The optimization algorithms take into account all the degrees of freedom from a unit-cell and adjust them until obtaining the desired response. On the other hand, the ECs change the geometrical parameters of the unit-cell according to the EC elements required (an optimization process is also present but at the end of the design). This strategy is very useful to know the response of the global structure (antenna plus WAIM) without the need for a full-wave simulation, which highly reduces the computing time and the needed resources. It should be noted that other alternative techniques (analytical and quasi-analytical) have been proposed in the literature to model the discontinuities in waveguides or open structures [39; 40]; however, they have not been considered here for the sake of simplicity. The WAIM proposed in this article is based on a 3D structure that has been proposed by some of the authors [14]. It works as a simple waveguide that allows the excitation of low dispersive transverse-electromagnetic (TEM) modes. Thus far, the structure has been employed as a polarizing radome, and it was modeled by an EC that was only valid for normal incidence. In order to synthesize the WAIM, this paper proposes an improved EC that also accounts for the incident angle. This extension is a great contribution because characterizing the structure for oblique incidence is necessary for WAIM applications.