Compact Reflective Metasurface: Production of Broadband Vortex Beams in Millimeter Waves

Abstract

A low-profile reflectarray has been designed in the Ka-band to efficiently generate wideband orbital angular momentum (OAM) vortex beams. The proposed design employs a reflective phase-shifting patch etched onto a dielectric substrate, featuring a three-square loop structure intersected by two transverse dipoles. This unit cell achieves a 440° phase shift at 30 GHz with a minimal magnitude loss of (−0.25 dB), enabling high-efficiency reflectarray performance. The OAM vortex beam supports high-order phase distributions ($l=+1,+2,+3,+4$) modes, though fabrication and experimental validation focused on the $+1$ mode. Measurements confirm that the reflectarray produces a high-purity OAM vortex beam for +1 mode, covering the operational frequency range from 27 to 39 GHz, and achieving a 40% bandwidth with a peak gain of 23.39 dBi at 33 GHz and an aperture efficiency of 17.38%. These results demonstrate the ability of the reflectarray to produce broadband directive OAM beams with robust performance, making it ideal for Ka-band communication systems.

1. Introduction

Spectrum resources are becoming increasingly crowded as wireless communication technology develops [1]. Vortex beams carrying OAM have garnered significant attention in communication research due to their potential to increase transmission capacity [2]. In the microwave range, vortex waves are produced using a variety of techniques, including holographic substrates [3], spiral-phase plates [4], and array antennas [5]. Another approach in super-oscillation-based lenses offers the potential for high-resolution imaging with reduced sidebands, enabling more effective electromagnetic manipulation and improved wavefront control [6]. Vortex waves are identified by their spiral-shaped phase wavefronts. However, these techniques frequently encounter difficulties with prominent patterns or intricate feed networks. Reflective metasurfaces provide an alternative to these drawbacks in producing OAM vortex waves. Electromagnetic waves can have their phase wavefront, amplitude, frequency, and polarization state precisely controlled using metasurfaces [7]. Based on distinct concepts, various techniques can regulate the phase of reflected electromagnetic waves. The first technique, the propagation phase (or resonant phase), works with circular and linear polarized waves. It modifies the element’s geometry to vary the phase. However, because of the resonant part’s inherent dispersion, OAM generators that use this method frequently have narrow bandwidths [8]. Another method, the Pancharatnam–Berry (PB) phase, rotates the element to alter the phase. This method’s generators typically offer broadband features, although they are limited to CP waves [9,10]. The detour phase method generates vortex waves but is limited by narrow bandwidth and compatibility only with linearly polarized (LP) waves, restricting their versatility in broader applications [11]. An independent LHCP- and RHCP-controlled translational transmission metasurface (TM) for dual-circularly polarized vortex beam generation is presented. Measurements confirm their efficacy; however, the challenges are polarization sensitivity and fabrication complexity [12]. To improve the performance of modern communication systems, a 1-bit reflecting RIS is proposed for the Ka-band, utilizing triangular patches and active switching elements. However, the 1-bit resolution limits its precision, and using active components could increase losses and power consumption [13]. Thermally switchable reflecting metasurfaces were created using Z-shaped resonators. Because of these resonators, the metasurface can produce numerous OAM (orbital angular momentum) modes by adjusting its properties in response to temperature variations. This means that the metasurface is adaptable for a range of applications because it can switch between different OAM beams by simply adjusting its temperature, which can limit stability and control in dynamic environments [14]. A wideband circularly polarized OAM vortex beam generator with $l=1$ mode is presented using a reflectarray. With steady phase responses and sound polarization isolation, it is restricted to specific polarization modes (CP) [15]. A CCTA for OAM vortex wave generation with a double C-shaped grating metasurface is presented, which achieves sound transmission and 360° phase coverage. Its performance is validated through measurements, although issues like surface distortion and fabrication complexity still exist [16]. A compact system is produced by employing high-order modes to transform a single antenna element into an array. At 2.4 GHz, a patch antenna produces an OAM beam that is circularly polarized in the right direction and has a topological charge of OAM $l=-1$. Still, high-order modes often lead to more significant phase errors and reduced mode purity [17]. A spider-shaped unit cell is designed to generate OAM modes using a single-layer reflector that maintains high mode purity. The unit cell’s multi-resonance characteristics enable a linear reflection phase response, allowing for broad bandwidth OAM generation, but complexity arises with this in unit cell design and fabrication [18]. A dual-polarized reflectarray is proposed for generating dual OAM beams with minimal inter-band interaction. Simulations and measurements confirm their feasibility, but there are issues with element coupling, bandwidth limitations, and the absence of dynamic beam control [19]. The compact reflectarray metasurface has a planar design, stability, and polarization insensitivity. Though it has potential for development, its limited beam coverage and low gain make it unsuitable for applications requiring high-performance beam shaping or wide-area coverage [20]. A compact cascaded metasurface system is introduced for efficient OAM vortex wave synthesis with customized SAM and polarization conversion. Its design enhances integration and enables multi-mode OAM generation, but challenges remain in alignment sensitivity and fabrication complexity [21]. The design integrates the reflection polarization conversion metasurface with the propagation phase and employs a low Q-factor C-shaped element. In addition to supporting linear and circularized polarized waves, the recommended OAM generator exhibits extensive bandwidth coverage in the microwave range, spanning from 12 to 18 GHz (40%) operations. Still, a broader bandwidth can increase the overall susceptibility to phase errors and losses [22].

Although these metasurfaces are innovative and effective in their particular domains, they face significant challenges in high gain, operational bandwidth, aperture efficiency, flexibility, and the cost and complexity of their design and fabrication processes. Overcoming these limitations is critical, and future research should focus on improving aperture efficiency and gain, achieving wider bandwidths, enhancing polarization versatility, and simplifying manufacturing processes to achieve practical and cost-effective deployment in real-world applications. This paper introduces a phase-shifting element design to enhance the mode purity, gain, aperture efficiency, and operational bandwidth of an OAM reflectarray antenna. The aperture phase distribution of the reflectarray vortex beam is precisely controlled using a variable-size adjustment technique. At the center frequency of 30 GHz, the proposed unit cell shows a low magnitude loss of −0.25 dB and achieves a phase range of 440°. Its symmetric structure enables dual-polarization functionality. Simulation results confirm that the reflectarray achieves improved mode purity, high aperture efficiency, and significant gain across a wide frequency range.

2. Element Design and Analysis

The dimensions of the reflectarray element are shown in Figure 1a shows the front view of the element, highlighting its geometric configuration and planar structure, and Figure 1b shows the side view of the element, highlighting the layer stack-up, including metallic patch, the dielectric substrate, an air gap, and a ground plane. The element has a periodicity (P) of 5 mm ($\lambda /2$ at 30 GHz) to ensure effective interaction with electromagnetic waves. The air gap ($H_1$) and the substrate thickness (H) are both 0.5 mm, contributing to the overall phase response and ensuring structural stability. The parameters are defined as follows: the patch width ($W_p$) is 0.28 mm, $L=M-W_p$, $L_p$ is an adjustable parameter used to achieve the desired phase shifts, and $M=L_p-W_p$. The elements are fabricated on an FR4 substrate with a relative permittivity of ${\epsilon }_r=2.65$ and a low loss tangent ($tan\delta =0.001$), supporting compact element design while maintaining wide bandwidth. The moderate dielectric constant ensures efficient impedance matching and phase accuracy. At the same time, the low-loss tangent minimizes dielectric losses, preserving signal integrity and efficiency at high frequencies, making FR4 a suitable choice for Ka-band OAM vortex beam generation.

The electromagnetic properties of the reflectarray element are analyzed using ANSYS HFSS 2023 R2 software. A comprehensive parametric analysis is performed to optimize the element dimensions by changing the value of A from 3.5 mm to 5 mm. Figure 2 shows the reflective phase and the magnitude loss of the unit cell dependent on the parameter $L_p$ at the center frequency. The analysis reveals that varying $L_p$ allows the unit cell’s phase response to be extended up to 440° with a −0.25 dB reflection loss. Therefore, the proposed single-layer design achieves a reflective phase response greater than a full $2\pi$ cycle, significantly enhancing the element’s linear phase bandwidth. The unit cell bandwidth is determined by [23].

$$\mathrm{BW}={\displaystyle \frac{2(f_u-f_l)}{f_u+f_l}},$$

(1)

where $f_u$ indicates the highest frequency where the system operates effectively and $f_l$ indicates the lowest frequency where the system operates effectively. Figure 3 shows the phase and magnitude loss of the element at various frequencies. The phase response curves at various frequencies are nearly symmetrical and show good linearity, a key feature for wideband reflectarray design. So, it is essential to consider the reflecting phases and magnitudes of the element under normal and oblique wave incidences. Figure 4 shows the reflective phases and magnitudes of the element at various incidence angles. The differences in reflective phases across these angles are minimal. As a result, the reflective phase under normal incidence serves as the foundation for the reflectarray design.

3. Advanced Reflectarray Design and Evaluation Techniques

The geometry of the antenna goes through a structured process. First, element simulations are performed to obtain the phase-shifting curve. Then, we select the focal diameter ratio (F/D) and the feed position based on beam width and aperture size. After that, we derive the compensated phase distribution using the aperture phase optimization. Finally, we calculate the geometric parameters of the reflectarray by converting the compensated phase into unit geometry with the help of the phase-shifting curve. We can fine-tune the reference phase to optimize the array beam performance. This method designs a square-shaped $10\lambda \times 10\lambda$ dielectric reflectarray consisting of $20\times 20$ elements at the Ka-band. The overall design of the reflectarray antenna is illustrated in Figure 5.

The structure comprises $A\times B$ elements, which are explained by a horn antenna for operation. Here, A and B represent the number of elements along the X and Y axes. The reflective phase for each $AB\mathrm{th}$ reflectarray element, required to produce an OAM vortex wave, is determined as follows [24]:

$$\delta (A,B)={\displaystyle \frac{2\pi }{\lambda }}\left(\sqrt{x^2+y^2+F^2}-F\right)+l·arctan\left({\displaystyle \frac{y}{x}}\right)$$

(2)

Here, F is the distance between the geometric center of the reflecting metasurface and the phase center of the horn, $\lambda$ represents the free-space wavelength, and $(x,y)$ is the unit elements’ location coordinates. The variable l represents the preferred OAM mode number. The aperture efficiency depends on the feed distance, and the reflectarray’s feed source is a standard waveguide horn. Reducing F can reduce spillover loss but also reduce the reflectarray’s illumination efficiency. To maximize gain, an optimal value of F is established at $3\lambda$. The designed unit structure’s phase shift is sufficient to generate a reflectarray that produces OAM beams with the required mode and beam direction. To achieve OAM modes ($l=+1,+2,+3,+4$) at 30 GHz, a software-based approach was used to calculate the overall phase distributions for the reflectarray for all four modes.

4. Simulated and Measured Results

The simulated phase and magnitude of the electric field produced by the proposed reflectarray are shown in Figure 6. In the reflection spectra, the phase patterns show a complete $2\pi$ phase shift around the reflectarray’s center. In the meantime, the magnitude distribution forms a characteristic doughnut shape with a central singularity, a key feature of orbital angular momentum (OAM) vortex beams, confirming the predicted behavior of the OAM modes ($l=+1,+2,+3,+4$). These results verify that the reflectarray successfully produces the desired OAM vortex beam and demonstrates its ability to radiate an OAM vortex wave efficiently in the specified mode.

The mode purity of each mode is shown in Figure 7. The mode purity was evaluated using a numerical Fourier transform of the aperture phase function, as defined in [25] below, to validate the accuracy of the proposed OAM waves:

$$P_{l_q}={\displaystyle \frac{1}{2\pi }}{\int }_0^{2\pi }\mathsf{\Psi }\left(\psi \right)e^{-k{l}_q\psi }d\psi$$

(3)

$$\mathrm{Purity}={\displaystyle \frac{|P_{l_q}|}{{\sum }_{w=-\infty }^{\infty }\left|P_{l_w}\right|}}$$

(4)

At an operating frequency of 30 GHz, the results of the simulations indicate impressive mode purities: 97% for mode $+1$, 94% for mode $+2$, 88% for mode $+3$, and 84% for mode $+4$. These confirm the generation of OAM waves for the modes ($l=+1,+2,+3,+4$). Simulated phase and magnitude responses from 27 to 39 GHz are presented in Figure 8. Furthermore, the purity of the mode consistently remains above 78% for the $+1$ mode across a frequency range, highlighting the wideband performance of the proposed design. This demonstrates the design’s ability to generate high-purity OAM waves over a wide range, as seen in Figure 9. Orbital angular momentum (OAM) waves are inherently resilient to feed obstructions due to their helical phase fronts, which distribute phase and radiation uniformly across the wave. This feature reduces the impact of localized disturbances on mode purity, as the spiral structure effectively preserves the wave’s overall phase coherence and energy integrity. As a result, the generated OAM modes maintain high purity and performance, ensuring the precision and reliability of the system in advanced communication applications.

Figure 10 shows the fabricated reflective metasurface designed with OAM mode $l=+1$. (a) A perspective view highlights the overall structure, while (b) a close-in view shows the unit cell patterns and fabrication intricacies. The prototype and measurement setup is illustrated in Figure 11. Measured phase and magnitude responses from 27 to 39 GHz are presented in Figure 12, showing how well the proposed design performs over a wide range of frequencies. The measured results exhibit a single-arm spiral phase distribution, typical of orbital angular momentum (OAM) beams, and an intensity profile displaying the characteristic doughnut-shaped pattern. This indicates that the reflectarray continuously generates an excellent OAM beam over the entire frequency spectrum in the $+1$ mode. The results confirm that the design is suitable for wideband OAM beam-generating applications, as it maintains steady performance with decisive phase and magnitude characteristics.

Normalized radiation patterns at 30 GHz, derived from measurements and simulations, are presented in Figure 13a,b. These patterns exhibit distinct conical beams in both H-plane and E-plane, characterized by a pronounced null at the center. The 2D radiation patterns show the significant orthogonal planes; the center null remains consistent across the E-plane and the H-plane at the operating frequency.These results confirm the efficient and reliable generation of the OAM $+1$ mode.

The measured gain and aperture efficiency of the proposed reflectarray at various frequencies are presented in Figure 14. The reflectarray shows an exceptional performance at 33 GHz, achieving a peak gain of 23.39 dBi. At this gain, the equivalent aperture efficiency is 17.38%, indicating effective conversion of the available aperture area into radiated power. Furthermore, the reflectarray achieves a wide OAM bandwidth of 40%, covering a wide range of frequencies from 27 to 39 GHz. This extensive bandwidth highlights the reflectarray’s ability to sustain consistent OAM mode generation and excellent performance across a significant portion of the spectrum, making it suitable for various applications within this range.

Table 1. Performance comparison: This work vs. existing OAM antennas.

Ref.	Frequency	Antenna Type	Element Phase	Profile	Mode	Mode Purity	OAM BW	Gain dBi	Aperture Efficiency
[15]	10 GHz	Reflectarray	400°	0.13${\lambda }_0$	1	N/A	20%	19.9	7.2%
[18]	5.75 GHz	Reflectarray	750°	0.12${\lambda }_0$	1	50%	N/A	N/A	N/A
[20]	5.8 GHz	Reflectarray	377°	0.11${\lambda }_0$	1	N/A	N/A	15.4	22.6%
[22]	15 GHz	Reflectarray	360°	0.18${\lambda }_0$	1	N/A	40%	18.42	N/A
[26]	10 GHz	Reflectarray	360°	0.10${\lambda }_0$	1	N/A	40%	20	14.35%
[27]	30 GHz	Reflectarray	360°	0.5${\lambda }_0$	1	62.6%	21.7%	20.5	N/A
This Work	30 GHz	Reflectarray	440°	0.10${\lambda }_0$	1	78%	40%	23.39	17.78%

N/A: not available; BW: bandwidth.

shows the performance of the proposed OAM reflective metasurface compared to state-of-the-art OAM antennas. Previous studies, such as [15] (10 GHz), [18] (5.75 GHz), [20] (5.8 GHz), and [26] (10 GHz), have primarily focused on generating OAM beams in the microwave range. In contrast, this work advances OAM technology into the millimeter-wave spectrum (27–39 GHz) to meet the growing demand for higher bandwidth and resolution in applications such as 5G/6G networks and radar systems. While the authors of [22] reported a 40% bandwidth at 15 GHz, the efficiency and gain remain lower than this design’s. Similarly, ref. [27], operating at 30 GHz, targeted millimeter-wave frequencies and achieved a bandwidth of 21.7% and a peak gain of 20.5 dBi, but the profile was very high. The proposed reflectarray offers a 40% bandwidth and a peak gain of 23.39 dBi while maintaining an aperture efficiency of 17.78%, ensuring stable and efficient OAM beam generation across the Ka-band. Additionally, its low-profile structure provides a compact and practical solution for high-frequency communication and sensing applications by enhancing phase stability and mode purity. The proposed metasurface effectively bridges the gap between microwave and millimeter-wave OAM technologies, making it well-suited for next-generation wireless and radar systems.

5. Conclusions

This work has developed a compact, low-profile reflectarray metasurface for wideband OAM wave generation in the Ka-band. The innovative unit cell design, comprising square loops with dipole cuts, achieves a 440° phase shift with negligible magnitude loss, enabling efficient reflection and OAM beam synthesis. Experimental validation for the $+1$ mode demonstrates exceptional performance, including a 40% bandwidth (27–39 GHz), a peak gain of 23.39 dBi, and an aperture efficiency of 17.38%. The proposed reflectarray’s high gain, wide bandwidth, and excellent mode purity position make it a promising solution for advanced Ka-band applications, such as 5G/6G millimeter-wave communications, satellite links, and radar systems requiring multiplexed OAM channels. Future work will explore reconfigurable unit cells with tunable materials like liquid crystals, varactor diodes, and graphene-based metasurfaces to enhance the reflectarray’s adaptability. These advancements could enable real-time OAM beam tuning, frequency agility, and adaptive mode selection, enhancing its versatility for wireless communication applications.