Multibit Electrically Reconfigurable Circularly Polarized Reflectarray Elements Based on Pancharatnam–Berry Phase Principle

1. 引言：1-bit 的天花板约 10 分钟

Abstract—P-i-n diode-based reconfigurable reflectarray antennas have gained attention for their flexible beam-steering, simplified design, and cost effectiveness. However, many existing designs offer only 1- or 2-bit phase reconfigurability, limiting radiation performance. In this letter, we present Ku-band reflectarray elements with both 2-bit and 3-bit electrical phase control for circular polarization. By leveraging the Pancharatnam–Berry phase principle, dynamic phase control is achieved through p-i-n diode switching. The proposed design is validated using a waveguide simulator (WGS), which confirms the 2-bit phase responses and shows excellent agreement with full-wave simulations. Measured results demonstrate 2-bit phase quantization over an 11.1 GHz to 12.5 GHz range (11.9% bandwidth) with insertion losses below 1.0 dB and cross-polarization levels under −15 dB. Furthermore, simulated performance of the 3-bit element reveals consistent 45° phase intervals. To verify array-level performance, 16 × 16 RRAs based on both 2-bit and 3-bit elements are implemented. This multibit reconfigurable strategy enhances reflectarray performance and offers increased design versatility for advanced Ku-band applications.

Reconfigurable reflectarray (RRA) antennas with dynamic beam control have garnered significant attention for applications in wireless communications and sensing systems [1]. These antennas enable versatile manipulation of electromagnetic waves, supporting beam steering, information sensing, and imaging functionalities. In contrast to conventional phased arrays [2], [3], [4], which require bulky feeding networks and expensive transceiver modules, 1-bit RRAs employing spatial feeding techniques offer a cost-effective solution for wide-angle beam scanning [5], [6], [7]. RRAs are typically implemented using various tuning elements, including p-i-n diodes, varactors, radio-frequency microelectromechanical systems (RF-MEMS), graphene, and liquid crystals [1]. Among these, PIN diode-based 1-bit RRAs have attracted considerable interest due to their affordability, simplicity, and widespread availability [8]–[12]. As demonstrated in [9], altering the state of a p-i-n diode enables tuning of the resonant frequency and induces phase reversal, thereby achieving 1-bit phase adjustment for linearly polarized (LP) operation.

Researchers have further explored 1-bit circularly polarized (CP) RRAs based on p-i-n diodes [13], [14], [15] and by employing an element rotation method [16], which utilizes physical or mechanical rotation for phase tuning. However, 1-bit designs inherently suffer from phase quantization errors, resulting in reduced aperture efficiency and elevated sidelobe levels (SLLs). To mitigate these limitations, multibit phase control is essential. Existing approaches for multi-bit or continuous CP phase tuning include mechanical methods [17], [18], [19] and varactor-based designs [20]. In comparison, p-i-n diodes present a cost-effective alternative characterized by lower insertion losses and simpler biasing requirements, rendering them highly suitable for multibit CP RRAs.

To date, only one study has demonstrated a p-i-n diode-based wideband 2-bit CP RRA with ±60° scanning and improved efficiency [21]. A similar principle has been applied using MEMS technology for 2-bit LP reconfigurability; however, this approach introduces additional complexity [22]. In this work, we present a Ku-band 2-/3-bit electrically controlled CP RRA element based on an innovative design approach that is scalable to multibit phase control. The key innovation involves the integration of multiple p-i-n diodes around the reflective patch, enabling simulation of physical rotation via controlled diode switching to achieve the desired phase response.

This letter also presents the use of the waveguide simulator (WGS) method for CP element testing. Section II details the design and operating mechanism. Section III outlines the measurement setups and experimental results, and Section IV concludes the letter.

2. PB 相位：转一倍，得两倍约 6 分钟

The proposed RRA element adopts the Pancharatnam–Berry (PB) phase principle [23], [24], [25], where the CP reflection phase equals twice the element's rotation angle. For clarity, we briefly introduce the PB principle used here. As shown in Fig. 1(a), under left-hand circular polarization (LHCP) excitation along the $-z$-direction, the incident electric fields ($\vec{E}^{inc}$) is written as

Here, $\vec{E}_i$ denotes the vector electric of the incident wave, $k$ is the free-space wave number, $\omega$ is the angular frequency.

According to the basic rotational transformation matrix [24], when the element is rotated counterclockwise by an angle $\theta$ [Fig. 1(b)], the corresponding rotation matrix is $T = \begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{pmatrix}$. Then, the reflected wave can be written as

where $\varphi_x$ and $\varphi_y$ represents the reflection phases for x- and y-polar components. If $\varphi_x = \varphi_y + \pi$, we have

This represents an LHCP reflected wave with a phase shift of $\varphi_x - 2\theta$, showing the CP reflection phase varies twice the cell's rotation angle. Conversely, under right-hand circularly polarized (RHCP) excitation, the phase shifts as $\varphi_x + 2\theta$.

3. 2-bit 单元：四根延时线伪造旋转约 12 分钟

As shown in Fig. 2, the proposed 2-bit CP RRA element uses a dual-layer substrate without air gap, comprising a reflective patch and bias circuit separated by a ground plane. The upper substrate is Arlon AD255 (εr = 2.55, tanθ = 0.0014, h1 = 1.5 mm), and the lower is FR-4 (εr = 4.4, tanθ = 0.02, h3 = 0.5 mm), bonded with an FR-4 adhesive film (h2 = 0.1 mm). A regular octagonal patch on the upper layer connects to ground via a blind via, acting as the main scatterer for CP phase control. Four identical phase delay lines at 45° intervals integrate p-i-n diodes (P#1–P#4) to dynamically adjust current paths and electrical lengths for precise phase tuning.

The DC bias circuit on the lower layer connects to delay lines through metallic vias. We employed the flip-chip MACOM MADP-000907-14020 PIN diode, modeled as an equivalent series circuit in simulations (Fig. 2). To save space, traditional quarter-wavelength radial stubs for RF signal choking were replaced by inductors. Each bias line includes two muRata LQW15AN3N2C00D (3.2 nH, SRF = 14 GHz) inductors, providing 6.4 nH for RF suppression.

Fig. 3(a) presents the simulated element response under two orthogonal incident waves, x′- and y′-polarizations, with P#2 "ON" and all other diodes "OFF," showing that the y′-polarized component follows an extended current path. The green dashed line indicates a roughly constant phase difference of 180° ± 10° between x′- and y′-components across 11.15 GHz to 12.2 GHz. Within this range, Sx′x′ and Sy′y′ magnitudes remain above −1 dB and approximately balanced, enabling the generation of a CP reflected wave with an axial ratio (AR) below 3 dB.

To achieve 2-bit phase quantization with uniform 90° steps, the element emulates four rotational states at 45° intervals by electronically controlling integrated p-i-n diodes, while retaining a fixed physical structure. In operation, one diode is ON and the others are OFF, forming an asymmetric current path on the otherwise symmetric element. As shown in Fig. 3(b), selective diode switching effectively emulates physical rotation, enabling discrete 2-bit reflection phase control. With ON/OFF represented as binary 1/0, phase states are encoded using 4-bit control logic (Table I). Under LHCP illumination, the element provides four reflection phases (0, π/2, π, 3π/2), corresponding to 2-bit quantization. These states, S#1–S#4, represent virtual rotations defined in the idealized configuration of Fig. 2(b).

Simulation results were obtained in Ansys HFSS using Floquet excitation and primary–secondary boundaries. Fig. 4 shows the performance of four states under LHCP illumination. Owing to symmetry, states S#1 and S#4 exhibit similar amplitudes, as do S#2 and S#3. Fig. 4(a) shows copolarized (SLL) magnitudes above −1 dB and cross polarized (SRL) below −15 dB, yielding an AR under 3 dB from 11.17 GHz to 12.15 GHz. Fig. 4(b) confirms ∼90° phase differences among the four states across the band, verifying effective 2-bit CP phase quantization. Additionally, the response of state S#2 under oblique LHCP incidence shows stable copolarized magnitude and phase, with cross-polarized components below −15 dB up to 25°, demonstrating excellent angular stability. These results confirm the element's reliable 2-bit phase quantization under CP excitation, making it highly suitable for electronically scanned reflectarray applications.

4. 3-bit 扩展与波导模拟器实测约 12 分钟

Building on the PB phase principle and the 2-bit implementation in Section II-A, a 3-bit CP RRA element is developed by adding four more phase delay lines, each integrated with a PIN diode, as shown in Fig. 5. The design features a circular reflective patch and eight identical delay lines with PIN switches (D#1–D#8). According to the PB principle, this design yields a theoretical 22.5° phase interval between adjacent lines. Similar to the 2-bit case, reflection phase control is achieved by switching the diodes. Fig. 5(b) and (c) shows the simulated coefficients and phases under LHCP incidence. From 11.3 GHz to 12.52 GHz, adjacent states exhibit ∼45° phase spacing, with copolarized magnitudes exceeding −1 dB and cross-polarized levels maintained below −15 dB.

Recent studies have validated the reliability of WGS for element testing [9], [12], [26], but CP reflectarray characterization in waveguides remains limited. Here, we adopt an orthomode transducer (OMT)—previously used for cross polarization and transmissive CP wave tests [9], [26]—to separate orthogonal linear polarizations.

To validate the proposed RRA element, a 2 × 2 array was fabricated [see Fig. 6(a)], enclosed by ground planes and periodic metallic vias to suppress substrate modes. As shown in Fig. 6(b), the test setup includes the device under test (DUT), a waveguide transition, two coax-to-WR75 adapters, and the OMT. Operating from 10.6 GHz to 12.8 GHz, the OMT offers 30 dB isolation and features an 18 mm test port, while the prototype measures 24 mm × 24 mm. An ad-hoc waveguide transition with a length of 20 mm (0.76λ0) and a tapered circular-to-square cross section was designed to ensure impedance matching. Bias voltages were set to ±3.3 V for forward and reverse operation.

Calibration of the waveguide transition and OMT was performed via the short-circuit line method. After calibration, the elements (DUT) were placed at the test port. Full characterization involved measuring the S-parameters ($S_{mea}$), including magnitudes $|S_{nm}^{mea}|$ and phases $∠S_{nm}^{mea}$ ($n, m = 1, 2$), with port definitions shown in Fig. 6(b). As both ports are linearly polarized, the orthogonal components were combined with a ±90° phase shift to derive the CP reflection coefficients, as defined in [26]:

where R represents the RHCP component and L signifies the LHCP component.

5. 成绩验收：单元、阵列与同行对比约 12 分钟

Fig. 7 compares simulated and measured results under CP incidence. In Fig. 7(a), the minimum measured insertion losses for states S#1–S#4 are 0.62 dB, 0.42 dB, 0.43 dB, and 0.65 dB, closely matching simulated values of 0.38 dB, 0.33 dB, 0.36 dB, and 0.42 dB. Across 11.1 GHz to 12.5 GHz (11.9% bandwidth), measured losses stay below 1 dB, with simulations showing similar performance over 10.8 GHz to 12.25 GHz. Additionally, the measured cross-polarized components for all states remain below −15 dB (AR < 3 dB) over the frequency range of interest.

Fig. 7(b) shows strong agreement between measured and simulated reflection phases. The phase differences between adjacent states remain near 90° across the band: S#1–S#2, 83°–99°; S#1–S#3, 185°–210°; and S#1–S#4, 275°–295°. These phase differences align well with simulation, confirming the element's 2-bit phase reconfigurability under CP excitation.

The measured magnitude responses exhibit a slight shift toward higher frequencies compared to simulations. This discrepancy is attributed to the integration of an ad-hoc waveguide transition, calibration errors, manufacturing tolerances, and assembly misalignment. Nonetheless, the WGS method accurately captures the CP RRA element's phase states, thereby validating the method's overall accuracy in reproducing the intended phase characteristics.

To further validate the feasibility of the proposed RRA element, 2-bit and 3-bit CP 16 × 16 RRAs (7.4λ0 × 7.4λ0) were designed and illuminated by an LHCP horn (−20° offset, F/D = 1.23), as shown in Fig. 8(a). The phase compensation diagrams for different beam directions are shown in Fig. 8(b).

Fig. 8(c) presents the simulated broadside gains and ARs of both RRAs, with key metrics summarized in Table II. The AR < 3dB bandwidth range from 10.1 GHz to 12.6 GHz (22%) and 10.5 GHz to 12.8 GHz (19.7%) for the 2-bit and 3-bit CP RRAs, respectively. Furthermore, the performance of the 2-bit RRA integrated with the complete bias network is evaluated, indicating minimal impact and validating the effectiveness of the bias network design. Therefore, the trade-off—greater design complexity in exchange for enhanced multibit phase tunability—is considered acceptable. Fig. 8(d) demonstrates 2-D beam scanning at 11.6 GHz, achieving ±60° steering with a scanning loss below 3.35 dB and a sidelobe level under −15.5 dB at broadside direction. Due to the inherent symmetry of the proposed element, RHCP performance can be obtained by replacing the LHCP horn without altering the RRA.

Table II compares the proposed p-i-n diode-based RRA with related works. Compared with the design in [21], which uses eight PIN diodes, the proposed element achieves stable 2-bit phase quantization with only four diodes, thereby reducing complexity and cost. The peak gain of the 2-bit CP RRA reaches 24.1 dBic at 11.3 GHz, with an aperture efficiency of 39.1%. Moreover, by increasing the number of p-i-n diodes per element to eight based on the same design concept, 3-bit phase quantization is realized. This novel design approach can be easily extended to arbitrary-bit element configurations, enabling flexible and scalable phase control.

In this letter, we propose a novel method for designing arbitrary-bit phase RRA elements. As a proof of concept, a 2-bit element is first designed and validated using a 2 × 2 prototype. The measurements based on the WGS method closely match the simulation predictions. A stable 2-bit phase quantization is achieved over the 11.1 GHz to 12.5 GHz band, with insertion losses below 1 dB. Furthermore, by extending the same design principle and implementation mechanism, a 3-bit element is also developed, exhibiting clear 45° phase steps in simulation. To verify array-level performance, 16 × 16 RRAs are implemented for both 2-bit and 3-bit cases. The results demonstrate wide AR bandwidths, ±60° beam scanning, and high aperture efficiency. These results validate the scalability of the proposed approach to arbitrary-bit electrically reconfigurable CP elements. With robust performance and wide bandwidth, the design strategy shows strong potential for advanced space and satellite communication applications.