# Generation of Beam Tilt through Three-Dimensional Printed Surface
## 2 Unit Cell Analysis and Surface Generation  
To verify the concept of deflection of the beam through 3D printed surfaces, we have chosen four layers of cubes that are held by three perpendicular cylindrical rods that are stacked one after another, as shown in Figure 1. The cubes present along each layer are x2, x1, x2, x3 from top Port 2 to bottom Port 1, as depicted in Figure 1a for a four-layer arrangement of cubes, whereas for a five-layer cube arrangement, as shown in Figure 1b, we have x1, x2, x3, x2, x1, whose relative size varies from a minimum of 0.5 mm (0.02\(\lambda\)) to a maximum of 7.5 mm (0.3\(\lambda\)). The x1, x2 and x3 represents relative size of cubes. The distance between the ports to the top surface of the cylindrical rod is h, the transmission coefficient is denoted by \(\tau\) and the reflection coefficient by \(\partial\). In the horizontal plane, we have x1 and x2, whereas in the vertical plane, we have x3. It is noted from Figures 2 and 3 that for the smaller sizes of cubes, we have higher transmission magnitude values, whereas the larger cubes size show higher phase values. These unit cells are operating at the design frequency of 12 GHz (\(\lambda\) = 25 mm). The relative size of cylindrical rods along with cube size is detailed in [31]. The maximum length of three perpendicular cylindrical rods is 7.5 mm, which holds the respective cubes. Variation in cube size from 0.5 to 7.5 mm\({}^{3}\) in intervals of 0.5 mm\({}^{3}\) is able to show the transmission coefficient magnitude and phase values. The four and five layers of cube arrangement have generated magnitude and phase plots in degrees, as shown in Figures 2a,b and 3a,b, respectively. The cube dimensions are shown by x1, x2 and x3. The database of the transmission coefficient magnitude and phase in degree is generated through the specific arrangement of these cube distributions for four- and five-layer configurations. The respective cube dimensions are shown along the x-axis, y-axis and z-axis, as depicted in Figures 2 and 3. The transmission magnitude highlights the fact that its value is closer to unity for relatively smaller cube sizes, as noted from Figure 2a, and interestingly, transmission phase plots depict that a higher phase value of above 300\({}^{\circ}\) is obtainable for relatively higher cube sizes, as shown in Figure 2b. Interestingly, for the five-layer cube arrangement, we have found that the transmission magnitude tends to be closer to unity for smaller cube sizes, as noted in Figure 3a, and the successive transmission phase is higher than 300\({}^{\circ}\), which is highlighted in Figure 3b. Thus, we have created the database for both transmission magnitude and phase values for five- and four-layer cubes, which act as building blocks for the generation of BDS that is described in a later section of this article. Figure 1: Unit cell arrangement with a two-port network: (**a**) four-layer (**b**) five-layer. Figure 3: Variation in (**a**) transmission magnitude plots: (**b**) transmission phase (degrees) plots against the relative cube sizes for x1, x2 and x3 for five-layer cube arrangement. Figure 2: Variation in (**a**) transmission magnitude plots, (**b**) transmission phase (degrees) plots against the relative cubes size for x1, x2 and x3 for four-layer cube arrangement. The unit cell is analyzed in a two-port network to generate the required database of transmission coefficient magnitude and phase values, which are used to design the proposed BDS prototype, and is excited by a feed horn. The field propagates throughout all the layers of arranged cubes and is radiated in free space. The field phase across the radiating surface can be controlled by electronically tuning the characteristics of the individual cells to achieve beam tilting [34].