Design of Alvarez Beam Scanning Reflectarray With Inversely Proportional Focal Length

In this letter, a beam scanning Alvarez reflectarray (RA) metasurface with its focal length (F) inversely proportional to the phase distribution on the Alvarez RA aperture is presented for ±45° beam scanning coverage and less than 3 dB gain loss. The beam scanning mechanism is based on mechanically tilting the Alvarez RA panel to the desired direction to steer the beam. Compared to a conventional RA where F is directly proportional to the parabolic phase distribution, the proposed Alvarez RA shows a wider 1 and 3 dB gain bandwidth, higher aperture efficiency (AE), and wider scanning range with less than 3 dB gain loss. The proposed RA has adopted an Alvarez phase distribution, which is a summation of two shifted cubic phase profiles. Pancharatnam– Berry (PB) meta-atoms of subwavelength periodicity were utilized to provide the 360° phase range and to enhance the bandwidth of the RA. An Alvarez RA consisting of 38 × 38 PB meta-atoms has been designed, fabricated, and tested for ±45° beam scan coverage with less than 3 dB gain loss. The simulated and measured results show that the gain of the proposed Alvarez RA metasurface is 29.1 dBi at 19.5 GHz, which corresponds to an AE of 44.2%. The 3 dB gain variation of the Alvarez RA is from 15 to 23.4 GHz, which corresponds to a 3 dB gain bandwidth of 43.7%. The 1 dB gain bandwidth was 27.8% from 17.3 to 22.9 GHz.

2-D, or even 3-D beam scanning [11], [12], [13], [14], [15]. Beam scanning of an RA can be implemented either electronically or mechanically [16]. The beam scanning speed of RAs based on electronic phase tuning elements is faster compared to the mechanical scanning. However, it requires complicated external dc biasing and control circuitry, and this will in turn increase the cost of the RA. The benefits of mechanical bean scanning are that it can be implemented at low-cost with ease of fabrication. As can be seen in the literature realizing more than a ±30°beam scanning range with less than 3 dB gain loss using classical RAs with conventional parabolic phase distributions is still a big challenge, particularly when the RA's focal length (F) is directly proportional to the phase distribution on its aperture. To extend the beam scanning range of an RA to more than ±30°, various kinds of phase distributions have been utilized in the literature based on using complicated optimization algorithms other than a parabolic phase only. Some of those techniques include, phase matching methods [17], spherical phase distributions [18], bifocal phase distributions [19], [20], and four focal points designs [21], [22].
This letter proposes a thin single-layer, circular polarization (CP) beam-scanning Alvarez RA where the focal length (F) is inversely proportional to the reflection phase distribution on the Alvarez RA aperture. A 2-D Alvarez phase distribution, which is the summation of a pair of shifted cubic phase profiles, is applied to all the Pancharatnam-Berry (PB) [23] meta-atoms across the proposed Alvarez RA aperture. Compared to those classical RAs where F is directly proportional to the phase distribution, the proposed Alvarez RA with focal length (F) inversely proportional to the phase distribution shows improved 1 (27.8%) and 3 dB (43.7%) gain bandwidths, higher aperture efficiency (AE = 44.2%), and wider beam scanning range (±45°) with less than 3 dB beam scan gain loss. The proposed RA can be designed without the need for any complicated and time-consuming optimization algorithms to find the optimum phase distribution for wider scanning angles.

II. HIGH-EFFICIENCY REFLECTIVE PB META-ATOM DESIGN
Conventional RAs consist of a 2-D array of meta-atoms (also called unit cells) with a quantized phase distribution. The requirements for high-efficiency meta-atoms are as follows: high reflectivity, can provide the required 360°reflection phase variation, and be of subwavelength periodicity. The structural diagram of the PB meta-atom used in this work is shown in Fig. 1(a) which is composed of a single dielectric layer (RO4003C, ε r = 3.55, h = 2 mm) with a full copper ground layer on the bottom side. A copper resonator was etched at the upper side of the dielectric layer. The reflection performance of the 1536-1225 © 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See https://www.ieee.org/publications/rights/index.html for more information. meta-atom was evaluated by conducting a series of simulations in CST Microwave Studio. In the simulations, the meta-atom was surrounded by periodic boundary conditions in the x-and y-directions, while a Floquet port was assigned in the z-axis direction. The optimized dimensions of the meta-atom are P = 5, w = 5, L = 5, and R = 5 mm. When a CP plane wave is normally incident in the −z direction with the meta-atom placed in the xy-plane, a strong copolarized (co-pol) reflection was dominant and was close to 0 dB from 10.9 to 24.2 GHz as shown in Fig. 1(b). Over this frequency range, the cross-polarized (cross-pol) reflection was reduced to less than −11.2 dB. The relation between the copol reflection phase and the rotation angle (β) was studied carefully. As can be seen in Fig. 1(c), when the top copper resonator was rotated from β = 0°to β = 180°, the reflection phase of the copol reflection component is always equal ±2β ("+" and "−" signs represent the LHCP and RHCP incident waves) and the required 360°phase shift of the RA can be realized. Thus, reflection phase compensation of each unit cell between 0°and 360°, can be obtained by rotating the top copper resonator to the required angle.

III. ALVAREZ CP REFLECTARRAY METASURFACE DESIGN
Alvarez phase distribution is a focusing phase composed of two subphases (positive and negative subphases), and the focusing capability of the Alvarez RA can be controlled by the relative shifting of the two subphases [24], [25], [26]. The positive and negative phase distributions of the two subphases can be calculated using the famous Alvarez phase (1) and (2) [24].
In (1) and (2), x c and y c are coordinates of the PB meta-atom on the Alvarez RA aperture in the xy-plane, λ o is the free  (1) and (2), respectively. (c) Final Alvarez phase distribution calculated using (4) which is inversely proportional to the focal length. space wavelength at 19 GHz, A is a parameter that relates the Alvarez phase distribution to the focal length (F) and can be calculated using (3) where d is a parameter representing the cubic phase shifting which affects the centerline of the 2-D phase distribution. The parameter d should be optimized carefully to ensure that the centerline of the 2-D phase distribution is approximately at the center of the RA. As can be seen in (3), the Alvarez phase distribution is inversely proportional to F, which is totally opposite to the classical RA in which the parabolic phase distribution is directly proportional to F. The distribution of the two subphases has been calculated using MATLAB code based on (1) and (2) and presented in Fig. 2(a) and (b). The Alvarez RA contains 38 × 38 PB meta-atoms distributed in the xy-plane, F = 0.9D, D = 190 mm, λ o = 19 GHz, and d = 10. The final Alvarez phase distribution, which is the summation of the two sub-phases was calculated using (4) and shown in Fig. 2(c). This Alvarez phase distribution was achieved with F was inversely proportional, i.e., φ RA (x, y) Ý 1/F. Based on the phase distribution in Fig. 2(c), an Alvarez RA has been constructed as shown in Fig. 3(a) and fed by a RHCP horn antenna which was designed using a septum polarizer [27], as shown in Fig. 3(b). The copper resonator of each PB meta-atom was rotated by an angle β according to the required phase compensation with the help of the reflection phase results in Fig. 1(c). First, the 3-D simulated RHCP radiation patterns of the Alvarez RA were computed using CST Microwave Studio and are presented in Fig. 4. When centrally fed by an RHCP horn antenna, the Alvarez RA shows a high gain directive beam from 15 to 23.4 GHz as shown in Fig. 4. The simulation results show that the maximum gain of the proposed Alvarez RA metasurface is 29.1 dBi at 19.5 GHz, which corresponds to AE of 44.2%. The 3 dB gain variation of the Alvarez RA metasurface is from 15 to 23.4 GHz, which corresponds to a 3 dB gain bandwidth of   Next, the beam scanning capability of the Alvarez RA metasurface was investigated carefully. The beam scanning was realized by keeping the CP horn feed fixed at the center of the Alvarez RA with a distance F in front of the Alvarez RA and exactly at the focal point, and tilting the Alvarez RA panel to an angle θ T with respect to the x-or y-axes to steer the main reflected beam to an angle θ b = 2θ T while the CP feed antenna remains fixed as shown in Fig. 5(a). The simulated RHCP scanned beams are shown at various frequencies in Fig. 5(b)-(d) for θ T = 0°, 7.5°, 15°, and 22.5°. It can be noticed that the  Alvarez RA metasurface can efficiently steer the beam from 0°t o ±45°with less than 3 dB gain loss over this scanning range. When the tilting angle increased to more than ±22.5°, the scan gain loss increased to more than 3 dB. To further understand the relation between the titling angle θ T and the beam steering angle θ b , the 2-D far-field distribution was computed for all scanned beams and are presented in Fig. 6. An important parameter in dealing with scanned beams of an RA is the beam deviation factor (BDF) which is defined as the ratio between the direction of the scanned beam and the titling angle and can be calculated [14], [17]. It been noticed that the θ b = 2θ T relation is valid for the proposed beam scanning Alvarez RA with very slight deviation. Details of the scanned beams including the computed BDF for all scanned beams at 19 and 22 GHz are shown in Tables I and II. As can be seen, the Alvarez RA metasurface can efficiently steer the beam from 0°to ±45°w ith gain variation less than 3 dB for all scanned beams, the sidelobe level (SLL) is less than −16.7 dB, the BDF is close to unity, and it has a stable half-power beamwidth (HPBW).

IV. FABRICATION AND MEASUREMENTS
For experimental verification and to verify the beam scanning performance, the Alvarez RA designed in the previous section has been fabricated using PCB technology with the size of 190 × 190 mm 2 as shown in Fig. 7(a). The RHCP horn antenna shown in Fig. 7(a)    characteristics of the Alvarez RA were measured using the farfield method inside an anechoic chamber to reduce the unwanted reflections and noise from the surroundings. The measurement setup used is shown in Fig. 7(b). The Alvarez RA and the RHCP horn antenna were placed at the same height with respect to the reference horn antenna (Horn#2) as shown in Fig. 7(b). A distance R was maintained between the Alvarez RA and the reference horn antenna in order to satisfy the far-field formula [28]. The measured gain versus frequency curve is shown in Fig. 8(a) and demonstrates good agreement with the simulated results. The maximum gain shifted from 19.1 GHz in the simulations to 18.35 GHz in the measurements. The measured axial ratio of the Alvarez RA is shown in Fig. 8(b) and the AR is less than 3 dB for all frequencies. The small deviation between the simulated and measured results can be attributed to many factors. For instance, the alignment between the antenna under test and the reference antenna, the fabrication tolerance of the RA panel and the 3D printed horn antenna, the uncertainty of the dielectric constant of the substrate at this frequency band. The measured scanned beams at 19 and 22 GHz are shown in Fig. 9. As can be seen, the Alvarez RA can successfully steer the beam over ±45°with less than 3 dB gain loss. A comparative study of closely related works in the literature where F was directly proportional to the phase distribution has been conducted and the results are tabulated in   Table III. It is shown that the proposed Alvarez RA with F is inversely proportional to the phase distribution achieved wider beam scanning range, higher AE, and wider 1 and 3 dB gain bandwidths.

V. CONCLUSION
In summary, an Alvarez RA has been designed and realized for high-gain wide-angle beam scanning from 15 to 23.4 GHz. It is shown that the Alvarez RA where F is inversely proportional to the phase distribution, can help in improving the radiation characteristics and can achieve a wider-beam scanning range compared to those RAs based on phase distributions directly proportional to the focal length. Compared to other works in the literature, the proposed technique can help to design wide-angle beam scanning RA up to ±45°without requiring complicated and time-consuming optimization algorithms to find the optimum phase distribution. The proposed Alvarez RA achieved improved 1 and 3 dB gain band widths and higher AE compared to conventional unifocal and bifocal reflectarrays in the literature.