Wide-Angle Stable Transmissive Focusing Metasurfaces for OAM Vortex Waves in Wireless Communications

Abstract

Orbital angular momentum (OAM) vortex waves have become a promising technology for future 6G high-capacity wireless communications. However, the inherent propagation divergence and performance degradation under angular deviation severely restrict their practical applications. This paper proposes a transmissive focusing metasurface that maintains stable OAM vortex wave generation under angular deviation. By employing a quadratic phase distribution, the proposed design fundamentally eliminates the axial focal shift caused by oblique incidence and maintains stable focusing performance. A three-metal-layer transmissive unit is developed to achieve high cross-polarization transmittance and full 2π phase coverage. By combining the quadratic focusing phase and OAM spiral phase, the metasurface enables stable generation of high-purity focused OAM beams under angular deviation. A prototype is fabricated and experimentally characterized, which verifies the theoretical predictions under the designed incident angle and angular deviation scenarios. Furthermore, a wireless communication system based on the Universal Software Radio Peripheral (USRP) is constructed in this work, which achieves reliable transmission and demodulation verification of 16-quadrature amplitude modulation (16-QAM) signals. The proposed metasurface provides a feasible solution for short-to-medium distance robust transmission of OAM waves and shows good application potential in practical wireless communication systems.

Introduction

The rapid development of 6G wireless communications toward space-air-ground-sea integrated networks and the ubiquitous Internet of Things (IoT) has posed unprecedented demands for higher transmission rates, spectral efficiency, and link reliability. Vortex beams carrying orbital angular momentum (OAM) offer a new degree of freedom for wireless communications: the inherent orthogonality between OAM modes with different topological charges enables infinite-dimensional multiplexing, making it a promising solution to break through the capacity bottleneck of conventional systems. To date, OAM technology has been widely investigated in various fields, including high-resolution imaging, − radar detection, , and high-capacity wireless communications. − However, conventional OAM generators, such as spiral phase plates (SPPs), , circular antenna arrays, , and metallic cavity structures, , suffer from inherent drawbacks of bulky volume, low efficiency, or poor integration, which severely limit their practical applications.

Metasurfaces, planar artificial structures composed of subwavelength meta-atoms, have enabled unprecedented precision in tailoring the amplitude, phase, and polarization of electromagnetic waves. − Leveraging this unique capability, metasurfaces have emerged as a competitive solution for high-efficiency generation and flexible manipulation of OAM vortex beams. − Compared with traditional OAM generators mentioned above, metasurfaces offer significant advantages of low profile, compact footprint, and low insertion loss, making them widely investigated for OAM-assisted wireless communication systems. −

While metasurfaces exhibit prominent advantages in OAM wave manipulation, the inherent divergence of OAM beams, combined with the oblique incidence and angular deviation inevitably caused by noncollinear transceiver arrangement and alignment errors in practical systems, jointly impair beam focusing performance and degrade mode purity. To resolve these problems, conventional hyperbolic/Fresnel focusing metasurfaces work well under normal incidence but suffer from inherent axial focal shift and progressively worsening aberration under oblique illumination. Another mainstream route corrects focal shift at a specific angle via a superimposed linear phase gradient, ,, yet this compensation is only valid at the nominal design angle; angular deviation induces residual phase coupling with high-order hyperbolic terms, causing recurrent axial focal shift, wavefront distortion, and severe OAM mode purity degradation. A detailed comparison of representative transmissive-focusing OAM metasurfaces is summarized in Table . In addition, previous studies have systematically characterized the performance degradation mechanism of microwave focusing metasurfaces under oblique incidence, where the resulting off-axis aberrations are also ubiquitous in OAM-focusing metasurfaces. Thus, existing methods cannot fundamentally resolve the focal shift issue under wide-angle oblique incidence, leaving the stable transmission under angular deviation and the long-distance focusing performance of OAM metasurfaces to be further improved.

1. Comparison of Representative Transmissive Focusing OAM Metasurfaces.

Reference	Focusing Phase Mechanism	Verified Angular Range	OAM Modes	Communication Validation
Bai et al.	Conventional hyperbolic phase	Normal incidence (array) with 30° unit-level tolerance	l = +1	No
Tian et al.	Conventional hyperbolic phase	Normal incidence only	l = +1, +2	No
Bai et al.	Conventional hyperbolic phase	Normal incidence (array) with 45° unit-level tolerance	l = −2 ∼ +2	No
This work	Quadratic phase distribution	15° oblique incidence (15° deviation, array) with 60° unit-level tolerance	l = ±1	16-QAM via USRP

In this work, a stable transmissive focusing metasurface adopting quadratic phase distribution is presented to tackle the aforementioned critical bottlenecks. We first theoretically reconstruct the phase modulation mechanism of the metasurface: replacing the conventional linear focusing phase with a quadratic phase profile, which fundamentally eliminates the focal plane shift under oblique incidence. A “three-layer metal grating + two-layer dielectric” meta-atom is designed to achieve high-efficiency cross-polarization transmission, full 2π phase coverage, and excellent angular stability. By integrating the quadratic focusing phase with the spiral phase of vortex waves, the metasurface array enables stable focusing and high mode purity of vortex beams under wide oblique incidence. Full-wave simulations and prototype measurements validate the excellent performance of the design. As shown in Figure , a USRP-based wireless communication system further demonstrates its reliable signal transmission capability in complex oblique incidence scenarios. This work provides an effective technical solution for stable medium-to-long distance transmission under angular deviation of OAM vortex waves and has important reference value for the engineering application of OAM technology in next-generation 6G wireless communication systems.

1.

Conceptual diagram of OAM wireless communication system architecture based on a stable transmissive focusing metasurface.

Results and Discussion

Principle

The electric field distribution of a vortex electromagnetic wave carrying OAM in the cylindrical coordinate system is expressed as:

$$E(r,\theta ,z)=A(r,\theta ,z)e^{jl\varphi }{e}^{-j{k}_{0}z}$$ 1

where A(r, θ, z) denotes the complex electric field amplitude at spatial position (r, θ, z); r, θ, and z are the radial distance, polar angle, and propagation distance along the beam axis, respectively; l is the topological charge of the OAM mode; ϕ is the azimuthal angle; k ₀ = 2π/λ is the free-space wavenumber, and λ is the operating wavelength.

To suppress the inherent beam divergence of OAM waves, conventional focusing metasurfaces adopt a hyperbolic phase profile to achieve energy concentration:

$$\phi (r_{mn})=k_0(\sqrt{r_{mn}^2+f^2}-f)$$ 2

where f is the preset focal length, and $r_{mn}=\sqrt{x_{mn}^2+y_{mn}^2}$ is the radial distance from the (m, n)-th unit cell to the array center.

Conventional designs achieve operation at any nominal incident angle θ₀ by superimposing a linear phase gradient φ _g = −k ₀ x _mn sin θ₀ to compensate for the spatial phase difference of the incident wave. However, when the actual incident angle deviates from the nominal value by Δθ, the residual linear phase term will couple with the third- and higher-order terms of the hyperbolic phase, generating noneliminable cross terms. Through Taylor series expansion and ray tracing analysis (detailed derivation in Supporting Information Section S1.1), the total residual phase of the conventional design can be approximated as:

$$\begin{array}{ll}\mathrm{\Delta }{\phi }_{\mathrm{total}}\approx & k_0{x}_{mn}\mathrm{\Delta }\theta \cos {\theta }_0+\frac{k_0{x}_{mn}^2}{2f}+\frac{k_0{y}_{mn}^2}{2f}\\ & -\frac{k_0{x}_{mn}^4}{8f^3}-\frac{k_0{x}_{mn}^2{y}_{mn}^2}{4f^3}-\frac{k_0{y}_{mn}^4}{8f^3}\end{array}$$ 3

This nonuniform phase distortion not only destroys the helical phase front of the OAM beam, leading to a sharp degradation in mode purity, but also causes the focal plane to axially deviate from the designed position z = f. Moreover, the severity of the axial focal shift increases significantly and nonlinearly with the angular deviation Δθ.

To fundamentally eliminate the axial focal shift caused by angular deviation, we propose replacing the conventional hyperbolic phase with a quadratic phase distribution as the focusing foundation:

$${\phi }_{\mathrm{focus}}(r_{mn})=k_0\frac{r_{mn}^2}{2f}$$ 4

Consistent with conventional designs, we also introduce a linear phase gradient φ _g = −k ₀ x _mn sin θ₀ to enable operation at the nominal incident angle θ₀. When the incident angle deviates by Δθ, the residual linear phase term is given by:

$$\mathrm{\Delta }\phi =k_0{x}_{mn}(\sin ({\theta }_0+\mathrm{\Delta }\theta )-\sin {\theta }_0)=A{x}_{mn}$$ 5

where A = k ₀ (sin­(θ₀ + Δθ) – sin θ₀) is a constant coefficient independent of spatial coordinates. We perform a completing the square transformation on the total phase, which converts the residual linear phase term into a pure lateral shift term without introducing any higher-order aberrations (detailed algebraic derivation in Supporting Information Section S1.2):

$${\phi }_{\mathrm{total}}=\frac{k_0}{2f}{(x_{mn}-x_0)}^2+\frac{k_0}{2f}{y}_{mn}^2+C$$ 6

where x ₀ = −f (sin­(θ₀ + Δθ) – sin θ₀) is the lateral focal shift, and C is a constant phase term that does not affect the wavefront. Regardless of the magnitude of the angular deviation Δθ, the transmitted wave is always focused onto the precisely designed axial plane z = f (detailed derivation in Supporting Information Section S1.3). The angular deviation only induces a linear lateral shift x ₀ of the focal point within the focal plane, which can be easily compensated by fine-tuning the receiving antenna position. Meanwhile, the helical phase front of the OAM beam remains intact, ensuring stable high mode purity.

For an M × N metasurface array, the position vector of the (m, n)-th unit cell is defined as r⃗ _mn = (x _mn , y _mn , 0), where $x_{mn}=(m-\frac{M+1}{2})p$ , $y_{mn}=(n-\frac{N+1}{2})p$ , and p is the periodicity of the unit cell. The total compensation phase required for the (m, n)-th unit cell is given by:

$$\phi (m,n)=-{\mathit{k⃗}}_{inc}·{\mathit{r⃗}}_{mn}+k_0\frac{r_{mn}^2}{2f}+l·{\mathrm{\Phi }}_{mn}+\mathrm{\Delta }\phi$$ 7

The four terms on the right-hand side sequentially correspond to the oblique incidence phase matching term −k⃗ _inc · r⃗ _mn for precompensating the wavefront spatial phase difference of obliquely incident waves; the quadratic focusing phase term $k_0\frac{r_{mn}^2}{2f}$ for wide-angle stable beam focusing; the OAM spiral phase term l · Φ _mn , where Φ _mn = arctan 2­(y _mn , x _mn ) denotes the azimuthal angle of the (m, n)-th unit cell, for generating the helical phase front of vortex waves; and the phase calibration term Δφ for compensating phase deviations from dielectric loss, fabrication, and assembly error.

OAM Metasurface Design

The superior stable focusing performance of the proposed metasurface is achieved by elaborately designing a transmissive unit cell composed of three metallic layers and two dielectric layers. As schematically illustrated in Figure a–b, the unit operates based on a cross-polarization conversion mechanism, where an x-polarized incident wave is converted into a y-polarized transmitted wave. The top and bottom orthogonal metallic gratings act as polarization filters: the top layer selects the incident polarization, while the bottom layer purifies the output cross-polarized wave. Their cooperative effect enables high polarization conversion efficiency. The middle resonant layer consists of a diagonally symmetric notched split ring integrated with a metallic rod, and adjacent metallic layers are separated by dielectric spacers. The meta-atom has a periodicity of p = 13 mm, and all metallic patterns are fabricated from high-conductivity copper with a thickness of t = 0.035 mm. For the grating structures, the line width of each metal strip is a = 3.5 mm, and the gap between adjacent strips is d = 3.1 mm. For the middle resonant structure, the line width of the split ring is r = 2 mm, the line width of the metallic rod is w = 1 mm, and the initial values of the angular parameters α and β are set to 65° and 45°, respectively. The combination of the orthogonal polarization gratings and the middle split-ring resonator enables multiple reflections and transmissions of electromagnetic waves inside the unit cell, which significantly enhances the cross-polarization conversion efficiency of the proposed structure. The dielectric spacers are made of F4B substrate with a relative permittivity of ε _r = 2.65 and a single-layer thickness of h = 4 mm.

2.

Stable transmissive focusing metasurface unit cell.(a) Schematic diagram of the transmissive unit structure. (b) Planar structure of the unit cell and metallic gratings. (c) Schematic diagrams of the middle-layer metallic resonant structures of the four coding units (00, 01, 10, 11). (d) Co-polarization and cross-polarization characteristics of the unit cell. (e) PCR of the unit cell as a function of incident angle. (f) Simulated transmission coefficients and transmission phase curves of the four units in the 3–7 GHz frequency band.

Before performing full-wave simulations in CST Microwave Studio to characterize the electromagnetic response of the wide-angle transmissive meta-atom proposed in this work, we first define the polarization conversion rate (PCR) to quantify the polarization conversion performance of the unit cell, with its mathematical expression given as follows:

$$\mathrm{PCR}=\frac{{|t_{yx}|}^2}{{|t_{xx}|}^2+{|t_{yx}|}^2}$$ 8

where t _yx represents the cross-polarization transmission coefficient, and t _xx is the copolarization transmission coefficient for the incidence of polarization x. Figure d plots the simulated scattering parameters of the unit cell. Over the ultrawide frequency band of 3–7 GHz, the cross-polarization transmission coefficient t _yx stably maintains above 0.8, with a peak value of 0.99 at the central operating frequency of 5 GHz. Meanwhile, the PCR exceeds 95% across the entire band, and all undesired scattering parameters are suppressed below 0.2. These results confirm that the designed unit cell achieves high-efficiency cross-polarization conversion with negligible energy loss. The wide-angle stability of the proposed unit cell is also validated via simulation of the PCR across the incident angle range from −60° to +60°, with results plotted in Figure e. The PCR maintains above 0.75 over the entire angular range, reaches nearly 1.0 at normal incidence, and shows no significant degradation even at ±60° oblique incidence, which guarantees stable operation of the metasurface array. Subsequently, we perform parametric sweeps on the structural angles α and β of the middle-layer split-ring resonator to characterize the phase modulation capability of the meta-atom under different angle configurations. When β is fixed at 45°, tuning α from 30° to 80° yields a continuous linear phase shift from 0° to 180°; by reversing β to −45° and sweeping α over the same range, the remaining 180°–360° phase coverage is realized. Notably, the transmission coefficient of the unit cell remains above 0.8 throughout the entire 2π phase tuning range, achieving an excellent balance between high transmission efficiency and full-range continuous phase modulation. This lays a solid foundation for the subsequent wide-angle focusing OAM metasurface array design.

Based on the above parameter sweeping results, four unit cells with a phase gradient of approximately 90° are selected, and the detailed parameters of these structures are listed in Table . Figure c intuitively shows the middle-layer metallic resonant structures of the four coding units (00, 01, 10, 11). Figure f clearly presents the transmission coefficients and transmission phase curves of the four units in the frequency band of 3–7 GHz. At the operating frequency of 5 GHz, the transmission coefficients of all four units remain above 0.8, indicating excellent transmission efficiency. Meanwhile, the transmission phases of the units exhibit an equal-interval gradient distribution of approximately 90° at the operating frequency.

2. Parameters of the Four Coding Unit Cells.

Unit	α(deg)	β(deg)	Transmission Coefficient	Transmission Phase
00	–45	40	0.98	0°
01	45	65	0.97	90°
10	45	40	0.99	180°
11	–45	65	0.98	270°

Simulation and Experiment

Using the optimized unit design and a focal length f set to 600 mm, we accurately calculate the required compensation phase for each unit in the metasurface array according to theoretical eq . Consequently, the ideal OAM phase distribution corresponding to mode l = +1 was obtained, and its phase distribution under oblique incidence is presented in Figure a. Figure b depicts the phase distribution after 2-bit quantization. By comparing the simulation results in Figure c–h, it can be observed that, compared with the original vortex radiation field without the introduction of convergent phase, the diffraction and divergence effects of the vortex electromagnetic wave during spatial propagation are significantly suppressed after the introduction of convergent phase compensation modulation. Specifically, the beam energy becomes more concentrated, the amplitude distribution is more uniform and compact, and the phase singularity and spiral distribution characteristics are more distinct and regular, which further ensures the structural integrity of the target vortex mode.

3.

Performance comparison of stable transmissive focusing metasurface. (a) Phase distribution of the wide-angle focusing vortex metasurface. (b) Quantized phase distribution. (c)–(e) Amplitude distribution, phase distribution, and mode purity of the nonfocusing metasurface. (f)–(h) Amplitude distribution, phase distribution, and mode purity of the focusing metasurface.

To quantitatively compare the focusing performances between the conventional convergent vortex metasurface and the proposed wide-angle convergent vortex metasurface, we first calculate the phase distributions of the two metasurface arrays for the l = +1 mode under 30° oblique incidence based on two distinct focusing phase principles, respectively. Conventional focusing typically employs a hyperbolic phase profile, given by $\phi (r)=\frac{2\pi }{\lambda }(\sqrt{r^2+f^2}-f)$ . Subsequently, full-wave numerical simulations of the conventional focusing metasurface and the proposed focusing metasurface are performed in CST. To verify the angular offset robustness of the proposed metasurface, the actual incident angle for both metasurfaces is set to 20° in the simulation, which deviates 10° from the designed incident angle. As clearly observed from Figure of the simulation results, compared with the traditional convergent vortex metasurface, the wide-angle convergent vortex metasurface effectively constrains the beam propagation path and significantly suppresses the free-space diffraction effect by introducing a wide-angle phase compensation mechanism, enabling more efficient axial energy convergence toward the focal plane and a substantial reduction in energy loss during propagation. In the focal plane region, the metasurface achieves a compact and regular focal spot morphology, with a significantly reduced central null depth region, a marked improvement in the continuity and integrity of the annular energy distribution, and a substantial enhancement in the focal plane energy density, while completely retaining the unique phase singularity of the vortex beam. Furthermore, benefiting from the modulation mechanism of the quadratic phase gradient, the transmitted wave can be stably focused onto the same predefined focal plane even when the incident angle deviates from the designed value, exhibiting only a regular lateral shift within the focal plane. In contrast, the conventional focusing metasurface suffers from severe axial focal shift, resulting in significantly degraded performance. This observation is in good agreement with the theoretical analysis presented above.

4.

Performance comparison of OAM focusing metasurfaces under oblique incidence angle deviation. (a)–(c) OAM propagation, amplitude distribution, and phase distribution of conventional focusing metasurfaces under angular deviation of the incident angle. (d)–(f) OAM propagation, amplitude distribution, and phase distribution of the stable transmissive focusing metasurface under angular deviation of the incident angle.

Having validated the superior focusing performance of the proposed design via numerical simulations, we then fabricated two representative prototypes to experimentally characterize its practical performance under 30° oblique incidence for OAM mode l = ±1. Photographs of the fabricated metasurface prototype are depicted in Figure a–c. The prototype has an overall physical size of 390 mm × 390 mm and is composed of 30 × 30 periodically distributed independent coding unit cells. The schematic illustration of the near-field measurement setup is shown in Figure d. A horn antenna radiates a horizontally polarized Gaussian beam that impinges on the metasurface at a 30° oblique angle. The metasurface converts the incident plane wave into a focused vortex electromagnetic wave carrying orbital angular momentum with topological charge l = +1. The electric field amplitude and phase distributions over a 400 mm × 400 mm region are measured by a near-field scanning probe mounted on a 2D scanning stage, which is positioned 300 mm away from the metasurface and connected to a vector network analyzer. Figure a–c shows the near-field measurement results of the fabricated metasurface in an anechoic chamber. In the amplitude distribution, a typical hollow donut-shaped vortex beam profile can be clearly observed, with distinct characteristics of the central zero-field intensity region, and the number of amplitude nulls fully corresponds to the target OAM mode number l = +1, which intuitively confirms the effective generation of the vortex mode. In the phase distribution, the number of vortex arms is consistent with the OAM mode number, the spiral phase profile is clear, and the mode purity reaches 83%, demonstrating excellent mode stability and regulation accuracy. Correspondingly, Figure d–f shows the measured amplitude, phase, and mode purity of the generated OAM beam when the incident angle deviates from the designed value by 15°. The change in the incident angle leads to a corresponding shift in the amplitude and phase distributions. Nevertheless, the amplitude and phase profiles still agree well with the characteristics of the l = +1 OAM mode, indicating that the vortex beam can be generated stably without obvious wavefront distortion. Meanwhile, the mode purity remains above 0.73, which demonstrates that the proposed quadratic-phase-based focusing metasurface exhibits strong stability and reliable wavefront manipulation capability under angular deviation.

5.

Fabricated metasurface prototype and near-field measurement setup. (a)–(c) Photographs of the fabricated 30 × 30 array metasurface prototype. (d) Schematic of the near-field OAM measurement system under 30° oblique incidence. (e) Schematic of the metasurface demodulation measurement system under 30° oblique incidence.

6.

Near-field measurement results of the fabricated metasurface. (a)–(c) Amplitude, phase, and mode purity under normal incidence. (d)–(f) Amplitude, phase, and mode purity under oblique incidence. (g)–(i) Amplitude, phase, and mode purity of the outgoing wave after phase cancellation.

Subsequently, as shown in Figure e, the receiving metasurface was placed at a distance of 600 mm along the +z direction from the transmitting end. Based on the fundamental principle of phase cancellation, inverse phase compensation for the modulation-end metasurface was implemented, thereby achieving phase cancellation of the vortex electromagnetic waves propagating in the channel and completing channel demultiplexing. As shown in Figure g–i, the receiving metasurface demultiplexes the OAM signal in the channel into a focused plane wave signal, whose phase exhibits a concentric annular distribution analogous to that of a spherical wave. From the mode purity spectrum obtained via inverse Fourier transform analysis of the sampled data, it can be observed that the energy is almost entirely concentrated in the l = 0 mode, and the vortex beam in the channel is completely converted into a pencil beam that can be efficiently received by a standard horn antenna.

Given the great application potential of OAM beams in next-generation wireless communications, an experimental OAM wireless communication system is built on the USRP platform to validate the transmission performance of the proposed wide-angle focusing metasurface in realistic communication scenarios. The system consists of three parts: the transmitting end, the metasurface modulation end, and the receiving end, operating at a central frequency of 5 GHz and adopting 16-QAM. In the experiment, the transmitting horn antenna is placed 300 mm away from the transmitting metasurface and illuminates its geometric center at an oblique incidence angle of 30°. The receiving metasurface is positioned 600 mm behind the transmitting metasurface at the preset focal plane to receive the modulated focused vortex signals. In this configuration, the receiving end fully captured the transmitted signal that contains the vortex mode information and performed error-free demodulation and data recovery. The specific experimental configuration is shown in Figure a. It can be observed that the corresponding constellation diagram exhibits a compact and well-defined distribution with clearly distinguishable constellation points, which intuitively validates that the proposed metasurface has excellent polarization demultiplexing and signal transmission performance in near-field communication scenarios. Subsequently, we gradually increased the transmission distance between the transmitting and receiving metasurfaces to characterize the communication performance and verify the focusing effect of the proposed OAM metasurface. The error vector magnitude (EVM) is adopted to quantitatively evaluate signal transmission quality. As labeled in Figure b–e, the EVM values are 26%, 19%, 10%, and 31% at transmission distances of 200 mm, 400 mm, 600 mm, and 1250 mm, respectively. The minimum EVM of 10% is achieved at the designed focal distance of 600 mm, which matches well with the focusing performance of the metasurface. When the distance D = 200 mm, the characteristic helical phase front of the electromagnetic wave of the vortex has not been fully developed. The excessively close spacing between the receiving and transmitting metasurfaces severely disturbs the near-field distribution. In this case, forced phase cancellation leads to significant degradation of the output Gaussian beam quality and a disordered constellation diagram. As the distance is adjusted to an appropriate range, the constellation becomes increasingly clear and regular, and the communication quality is improved accordingly. However, as the distance further increases, the inherent phase divergence of the OAM wave becomes pronounced, resulting in gradual dispersion of the constellation points. When the distance reaches 1.25 m, the receiver cannot demodulate more effectively. At the optimal distance of 600 mm, the measured signal-to-noise ratio (SNR) reaches 18.2 dB. For 16-QAM modulation, the corresponding theoretical bit error rate (BER) is better than 10^–6 under additive white Gaussian noise channels, which satisfies the requirement of reliable wireless communication. To evaluate the link reliability, a simplified link budget analysis is performed based on the measured received power. With the USRP transmit power set to +10 dBm and the receiver sensitivity rated at −70 dBm, the measured received power at the optimal focal distance of 600 mm is approximately −45 dBm, accounting for free-space path loss, metasurface transmission loss, and the gain of the transmit and receive horn antennas. This corresponds to a measured link margin of 25 dB. Such a positive margin ensures robust signal reception in the presence of environmental fluctuations and multipath interference, validating the practical feasibility of the proposed metasurface-based OAM communication link.

7.

16-QAM communication experiment scenarios and results. (a) 16-QAM communication experimental setup. (b)–(e) Constellation diagrams and EVM at different communication distances.

Conclusion

In summary, this paper proposed, fabricated, and experimentally verified a transmissive focusing metasurface for OAM vortex waves that could operate stably under angular deviation. By introducing a quadratic phase distribution, the axial focal shift induced under oblique incidence was fundamentally resolved, enabling robust and stable focusing of OAM beams even when the incident angle deviated from the designed value. The designed transmissive unit cell featured high cross-polarization transmittance and full 2π phase modulation capability, which supported the stable generation of high-purity OAM vortex beams. Measured results demonstrated that the metasurface maintained favorable amplitude, phase, and mode purity under oblique incidence and angular deviation, without obvious wavefront distortion or performance degradation. Furthermore, the OAM beam could be efficiently demodulated back into a Gaussian-like beam through phase cancellation, and the reliable transmission and demodulation of 16-QAM signals were experimentally verified. In future work, the proposed design can be extended to active metasurfaces to achieve flexible adjustment over a wide angular range. Illuminated by a single feed source, multimode OAM multiplexing can be realized by superimposing spiral phases with distinct topological charges, quadratic focusing phases, and linear deflection phases over a unified metasurface aperture. Each resultant OAM beam is focused at a separate lateral position on the shared focal plane and propagates along an exclusive spatial direction. At the receiving side, dedicated OAM metasurfaces loaded with conjugate modes are deployed at corresponding spatial positions to implement beam demodulation. This architecture supports parallel independent multichannel transmission and physical-layer encrypted communication. This work is of great value for the practical deployment of OAM technology in future 6G high-capacity wireless communication systems.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.6c05118.

• Full phase derivation and ray-tracing analysis to verify the wide-angle focusing stability of the proposed OAM metasurface (PDF)

The authors declare no competing financial interest.