# On Modeling Antennas Using MoM-Based Algorithms: Wire-Grid versus Surface Triangulation
## 2 Materials and Methods
### Wire-Grid  
#### 2.2.1 Wire-Grid: Overview  
A lot of work has been done on investigating the properties of wire-grid. To the best of our knowledge, the first were the studies by [PERSON] 1823, [PERSON] 1889, and [PERSON] 1898. Since then, the researchers have considered various aspects of wire-grid. In general, they have studied their electromagnetic properties, like in [41; 42; 43; 44]. In particular, they have investigated for example, the influence of the gap between wires on the transmission and reflection coefficients [45; 46; 47]. Moreover, they developed many ways to evaluate the reflection and transmission coefficients of a dense grid like the second-order averaged boundary conditions proposed by [PERSON], and of a sparse grid like the higher order impedance boundary conditions [48]. Another way has been based on the representation of the grid of wires as an impedance shunted across an infinite transmission line [49; 50]. The investigations also included the radiation from wire-grid [51], and even its use to enhance the radiation efficiency of other antennas [52]. In addition, some studies confirm the possibility of using a number of metallic wire grids in order to replace the metallic plate. For example, they used wire-grid to build a multi-segments wire-grid bounded wave simulator model [53], where they also investigated the effect of the grid parameters (the wires and sections numbers) on the results accuracy. The influence of other wire-grid parameters has also been investigated in many works. For example, the researchers in [54] experimentally proved that the aperture of a grid reflector is not always a consistent quality indicator of its performance. The studies also cover some novel creative direction in using the concept of wire-grid. For example, in designing planar meta-surface unit cell to obtain thin antenna structure and simplify its manufacturing process [55]. Another example is a closely coupled metallodielectric electromagnetic band-gaps design approach, which depends on using a grid of wires to form compact electromagnetic band-gap structured materials, that can be used as filters for both plane and surface wave propagation [56]. The researchers also effectively used a grid of reactively loaded wires in building electromagnetic crystals that can be successfully used as elements of polarization antenna reflectors and lenses [57; 58]. The use of wire-grid also reached the development of complex artificial material that can be used as wire mediums with specific propagation characteristics [59]. Moreover, wire-grid was also implemented to improve the accuracy of the conventional methods of measuring the harmonic output of high-power microwave transmitters at high frequencies, even the more advanced one, as shown in [60]. Applying the wire-grid approach in the design configuration for such purposes proved its effectiveness and turned out to be more stable and reproducible [61]. Adding loaded wires in the wire-grid design has widely been used since they enable precise controlling of the structure characteristics [62], and in some cases improving them [63]. The loaded wires are especially common in combination with the frequency-selective surfaces (FSS) to design, for example, surfaces with tunable reflection and transmission characteristics [64]. Furthermore, wire-grids showed that they are very suitable for designing lens antennas [65]. Such antennas can be used in high frequency communication applications, which has been proved experimentally in [66; 67; 68]. The wave propagation properties of high frequency wire-grid lens antennas have been studied well. Many works were devoted to enhancing their characteristics by receiving a signal on a pair of adjacent beams instead of one [69] or by using the hexagonal mesh type after investigating these characteristics with different mesh types (square, hexagonal or triangular mesh) [70]. Another approach that evolved from the traditional wire-grid has been applied on reflector antennas that can be used in many satellites and ground antenna systems.