# Digitized Reconfigurable Metal Reflectarray Surfaces for Millimeter-Wave Beam-Engineering
## 2 Reconfigurable Metal Reflectarray  
A single unit groove in Figure 1a is shown as a metal reflectarray antenna building block. All waveguides are placed in a ground metal, an aluminum. The sizes of unit cell for the metal reflectarray are \(a\) = 1.8 mm, \(b\) = 1.4 mm, \(T_{a}\) = 2.3 mm, and \(T_{b}\) = 1.9 mm. The depth of a metal rectangular waveguide, \(d\), is changed for steered-beam metal reflectarray antennas. The period of unit cell is accepted by the minimization of mutual coupling between arrays. The mentioned isolated element analysis is valid when the distance between the edges of the adjacent patches is larger than 0.25\(\lambda\), also assuming the array elements spacing is larger than 0.6\(\lambda\)[17]. Thus, the mutual coupling between the elements can be neglected. Figure 1b shows simulated reflection phases of the unit cell in degree varying the depth of unit cell for some frequency components.  
The depth of phase element is tuned and the antenna frequency is also changed to confirm the sensitiveness of reflected phases from 80 to 110 GHz. The antenna frequency is selected by 95 GHz to reduce atmospheric propagation loss. The depth of each waveguide, \(d\), is changed for under half of the guided wavelength for the antenna frequency (\(0\leq\mathrm{d}<\lambda_{g}/2\)). The reflected phase can be fully satisfied from \(-\pi\) to \(\pi\) due to the ground-plane reflection, which is the round trip propagation in each metal waveguide. A perfect electric and magnetic conductor with a periodic boundary condition of a \(TM\)-polarized wave is used for electromagnetic full-wave simulation, CST Microwave Studio. Rectangular metal waveguide grooves are equally spaced arrays in an aluminum metal plate.  
The required phase at the \(i\)th element for beam-steering reconfigurable metal reflectarray antennas to focus a beam in the direction \((\theta_{b},\phi_{\mathrm{b}})\) with N elements in each column and M elements in each row is calculated [18]:  
\[\phi(m_{i},n_{i})=-k_{0}\sin\theta_{b}\cos\phi_{b}m_{i}-k_{0}\sin\theta_{b}\sin \phi_{b}n_{i} \tag{1}\]  
where \(k_{0}\) is the free space propagation constant and \((m_{i},n_{i})\) are coordinates of the element \(i\). The calculated phase shift on each reflectarray element can be expressed as:  
Figure 1: (**a**) Single unit waveguide as a metal reflectarray building block with a = 1.8 mm, b = 1.4 mm, \(T_{a}\) = 2.3 mm, and \(T_{b}\) = 1.9 mm and (**b**) simulated reflection phase values of the unit cell in degree varying d, the depth of a waveguide for some frequency components.  
\[\phi_{i}^{R}=k_{0}(d_{i}-(m_{i}\cos\phi_{b}+n_{i}\sin\phi_{b})\sin\theta_{b}). \tag{2}\]  
\(d_{i}\) is the distance from the phase center of the feed to the element. For uniform amplitude distribution, four required phase patterns for millimeter-wave beam-steering metal reflectarray antennas from \(\theta=-20^{\circ}\) to \(20^{\circ}\) are shown in Figure 2. The required phases are calculated by the relation of each groove location and feed location. There are 1147 (M \(\times\) N, 31 \(\times\) 37) elements constructed on 71.8 mm \(\times\) 70.8 mm \(\times\) 10 mm size aluminum metal plate.  
Figure 3 show the simulated far-field radiation characteristics when each main beam is independently directed from \(\theta=-20^{\circ}\) to \(20^{\circ}\). The radiation patterns at working frequency are an efficiently directed changing beam-steering angle in H-plane. The antenna maximum gains are rarely changed. The gain of bore-sight and \(-20^{\circ}\)-steered antennas are 33.44 and 33.41 dB and half-power beam width are 2.44\({}^{\circ}\) and 2.45\({}^{\circ}\) in the H-plane, respectively. There is no dramatic change when the beam-steering angle is changed. The designed reconfigurable metal reflectarray antennas rarely change the characteristics of bore-sight antennas.  
Figure 3: Simulated far-field patterns in H-plane of reconfigurable millimeter-wave reflectarray antennas when observation angles are changed from \(\theta=-20^{\circ}\) to \(20^{\circ}\).