Introduction

The advancement of scalar phase-vortex beams has revolutionized classical and quantum information processing1,2, with their spatial mode orthogonality offering substantial potential for capacity scaling in optical communications3,4. However, their spiral phase fronts are prone to distortion in conventional single-mode or multi-mode fiber transmission, restricting deployment to free-space links or specialty fibers5,6. Recently, attention has shifted to vectorial polarization-vortex beams7, such as cylindrical vector beams (CVBs)8,9, which are emerging as transformative enablers for next-generation optical communications and networks. Their inherently orthogonal eigenvector modes with inhomogeneous polarization gradients demonstrate superior resilience to propagation impairments10, making them ideal for both high-capacity long-haul fiber transmission11,12 and dynamic network node interconnections3,13. Owing to the intricate polarization topologies involved in manipulation14, current CVB generation and multiplexing predominantly thrive in free space15,16,17. Prevailing long-distance communication and node data access demands, however, are fundamentally reliant on optical fibers for implementation. Accordingly, efficiently coupling multiplexed CVBs from free space into optical fibers with engineered ring-core index profiles becomes imperative, which represents a pivotal procedure for bridging free-space to fiber-optic communications. Traditional direct free-space-to-fiber coupling scheme, achieved by lens-based reduced-beam focusing11,12,18, encounters persistent challenges due to the dynamic uncontrollability of mode-order-dependent divergent beam expansion in CVBs. The diffraction-induced divergence disparities during free-space propagation19 cause composite CVB mode-field mismatch at the fiber interface upon coupling, thereby scrambling mode orthogonality and amplifying channel crosstalk in multiplexed fiber transmission. Concurrently, the inability to dynamically adjust the beam ring radii typically poses suboptimal alignment between coupled CVBs and fiber cores, degrading coupling efficiency20. This limitation considerably compromises its adaptability and applicability in fiber-optic node interconnections, where diverse core diameters necessitate reconfigurable beam control for precise matching.

In this research, we address these problems by employing a twisted moiré transformation strategy that develops ring radius-adjustable perfect cylindrical vector beams (PCVBs) with consistent annular profiles for fiber coupling. Created by axicon-modulated Fourier transformation of CVBs, the PCVBs exhibit uniform far-field structures irrespective of mode orders21,22,23,24,25,26,27. This treatment mitigates the differential expansion and divergence of various vector modes, enhancing both multi-mode-field overlap-matching and compatibility at the fiber coupling interface. On the other hand, dynamically manipulating the ring radii of the resulting PCVBs can promote their efficient alignment with fiber cores, which can be approached as a switchable axicon phase modulation issue. The optical twisted moiré effect28,29, achieved through spatial coordinate engineering of superimposed transmission profiles, unlocks tunable creation of joint phases by rotating two constituent elements relative to each other30,31,32,33. This mechanism facilitates the switchable construction of axicon phase profiles, complete with tunable radial periods, thereby establishing a one-to-one correspondence between rotation angles and the generated PCVBs’ ring radii. Consequently, multiplexed CVBs with mode-order-dependent divergence can be consistently transformed into PCVBs, with their ring radii meticulously adjusted through twisted switching of the matched axicon phase distributions.

To implement the presented twisted moiré transformation, a paired of twisted moiré meta-devices were precision-engineered and fabricated using two-photon nanolithography (TPN) technology, demonstrating their efficacy in achieving the ring radius-adjustable PCVBs within a compact, cascading configuration. Through in-plane twisted actuation, the moiré meta-devices enabled continuous alteration of axicon phase patterns across 20° to 160° angular displacement, permitting the dynamically tunable ring radii of PCVBs to be averaged from 0.0955 mm to 0.7430 mm. Compared to conventional direct CVB coupling, the introduction of ring radius-adjustable PCVBs provides ~80.7% enhancement in free-space-to-fiber coupling efficiency, simultaneously leading to ~2.75 dB improvement in crosstalk suppression. These outcomes collectively facilitate 14.1 Tbit s−1 quadrature phase shift keying (QPSK) signal transmission over 5 km multi-mode fiber (MMF) in a 282-channel multi-dimensional multiplexing communication system, with bit error rates (BERs) of 1 × 10−6. This work suggests a near-ideal CVB fiber coupling paradigm by enabling controllable transformation of ring radius-adjustable PCVBs via twisted moiré engineering, demonstrating capabilities of enhanced coupling efficiency, reduced channel crosstalk, and dynamically reconfigurable operation. Our findings highlight substantial progress in advancing free-space-to-fiber CVB multiplexing communications, offering benefits for the practical deployment of advanced optical networks and interconnections.

Results

Principle of twisted moiré transformation

Efficient connecting of multiplexed CVB mode channels from free space into optical fibers for subsequent transmission is a feature crucial within optical communication systems and networks. Traditional executions are typically challenged by low coupling efficiency, as the uneven beam size and divergence across distinct mode orders cause mode-field mismatch19,34 during the coupling process, as depicted in Fig. 1a. This introduces disparities in power allocation and propagation dynamics among these mode channels over fiber transmission, leading to a degradation in the overall communication performance. Completing the conversion of CVBs into PCVBs with consistent annular profiles and mode divergence at a given spatial depth35 is poised to mitigate these issues and enhance coupling [see Fig. 1b]. However, the fixed ring radius size often disables to optimally align with fibers of varying core dimensions, potentially restricting their applicability and effectiveness in realistic fiber couple systems. This work presents an innovative technique for controllably adjusting the ring radii of PCVBs, facilitating precise matching with a diverse array of fiber profiles that possess various cladding and core ratios at their cross-sections, as delineated in Fig. 1c. This achievement signifies a near-ideal CVB fiber coupling paradigm, holding the promise of enhancing both the transmission efficiency and practical utility of free-space-to-fiber-optic communication systems and networks.

Fig. 1: Schematic description of efficient dynamic free-space-to-fiber coupling with ring radius-adjustable PCVBs.
Fig. 1: Schematic description of efficient dynamic free-space-to-fiber coupling with ring radius-adjustable PCVBs.The alternative text for this image may have been generated using AI.
Full size image

a Representation of CVBs (red circles) possessing different beam size and divergence along with propagation dynamics over fiber transmission. b The situation of PCVBs (uniformly sized red circles) obtained by conversion of CVBs. c Detail of ring radius-adjustable PCVBs (red circles) capable of matching various fiber profiles (gray and blue circles). d A pair of twisted moiré meta-devices (shown in purple) facilitates the consistent conversion of multiplexed CVBs into PCVBs for subsequent fiber coupling. The resulting combined phase profiles, achieved via twisting, are equivalent to that of various axicon configurations, as illustrated in the bottom-right panel.

In clarifying that the axicon-modulated Fourier transformation is the key element for genesis of PCVBs from CVBs, we discern that alteration in ring radii of PCVBs hinges on the applied axicon distributions. The detailed illustration and analysis are provided in Supplementary Note 1. Herein, a twisted moiré transformation mechanism is introduced to enable the ring radius-adjustable PCVBs for purposes, which incorporates a pair of rotary doublet meta-devices to function as a dynamically tunable axicon modulator (see Fig. 1d). To be specific, the paired and independent phase elements are subjected to linear superposition to construct the desired axicon phase distributions with tunable parameter via the relative rotation of both components, showing the capacity of ring radius adjustability in PCVBs. The phase profiles Ψ1 and Ψ2 designed for the first and second meta-devices can be deduced in polar coordinates (r, θ) as follows, respectively:

$${\Psi }_{1}(r,\theta )=-\theta \cdot round(ar)+{b}_{1}$$
(1)
$${\Psi }_{2}(r,\theta )=\theta \cdot round(ar)+\frac{\pi {r}^{2}}{\lambda f}+{b}_{2}$$
(2)

where a is the variable parameter, and λ denotes the wavelength. b1 and b2 are the initial constants, both set to zero in our designs. The round(·) function is applied to convert the operand’s value to the nearest integer to mitigate the sectoring effect28. f represents the focal length of a flat quadratic lens phase for fulfilling the Fourier transformation. Thereafter, a mutual twisted movement around the optical axis is imparted to afford the dynamic manipulation behavior for the meta-devices, creating a continuously switchable axicon phase. The joint phase profile Ψjoint can be obtained as:

$${\Psi }_{{{\rm{joint}}}}(r,\theta )={\Psi }_{1}(r,\theta )+{\Psi }_{2}(r,\theta -\vartheta )=-\vartheta \cdot round(ar)+\frac{\pi {r}^{2}}{\lambda f}$$
(3)

in which ϑ represents the relative rotation angle between the paired meta-devices. It can be concluded that the selection of the rotation angle offers direct control over the combined axicon phase distribution, affecting its radial period, which is equivalent to different physical axicons traditionally used, as shown visually in Fig. 1d. This switchable axicon phase further determines the annular intensity profile of PCVB. Hence, a one-to-one mapping relationship can be established between the rotation angle ϑ and the ring radius R of the generated PCVB, characterized by a linear proportionality expressed as R ~ aϑf/k when ϑ ∈ (0, π). It is evident that for a certain parameter a, incident wavelength λ, and Fourier transformation depth f, the ring radius R of PCVB solely depends on the rotation angle ϑ. In a nutshell, in-plane twisting one of the meta-devices with respect to the other will form a continuously changing axicon phase, thereby enabling the continuously adjustable ring radius for the converted PCVB. The detailed mathematical derivation and description of the proposed twisted moiré transformation mechanism have been outlined in Supplementary Note 2.

Design of twisted moiré meta-devices

The paired twisted moiré meta-devices were precisely manufactured utilizing the TPN method to demonstrate the above mechanism, wherein the positive photoresist (IP-Dip, Nanoscribe) was directly structured as the meta-units with varying height H on a dielectric silicon dioxide (SiO2) substrate, as indicated in Fig. 2a. The elaborate description of fabrication process can be found in Supplementary Note 3. In this approach, phase modulation relies on light propagation theory, i.e., the transmissive output phase φ can be calculated by φ = φ0 + (n−1)kH. φ0 represents the initial phase of incident light wave, k is the wave number, and n denotes the refractive index of the meta-unit. Thus, optimizing these meta-units’ height can effectively modulate the transmissive phase of output light field, shaping the desired wavefront. In accordance with this principle, the height H of the meta-unit is meticulously tailored to span from 0 to 3.1 μm, with a total of 16-level discrete phase states to cover a full 2π range. Combining the finite difference time domain (FDTD, Lumerical Solutions) technique to perform full-wave simulations, Fig. 2c visualizes this inference by numerically calculating the phase shifts of the 16-level discrete structure units with different heights under the illumination of a right-handed circularly polarized plane wave. Both the x- and y-direction components of transmitted light exhibit the matched phase responses with the structural heights, and the mean transmittance across these structures exceeds 94.6%. This indicates that these chosen meta-units satisfy the demands for a 2π phase modulation and concurrently maintain relatively low transmission loss. Figure 2d, e further reveal their broadband responses at six selected discrete wavelengths (1495 nm, 1515 nm, 1535 nm, 1555 nm, 1575 nm, 1595 nm). The phase shifts all display a strong linear correlation with the structural heights, and the transmittances converge towards an average of 93.2%. These characteristics highlight the meta-units’ capability in manipulating multiple wavelength components, holding the potential for supporting broadband optical applications.

Fig. 2: Design and characterization of the bilayer twisted moiré meta-devices.
Fig. 2: Design and characterization of the bilayer twisted moiré meta-devices.The alternative text for this image may have been generated using AI.
Full size image

a Schematic of the designed meta-devices comprising IP-Dip-based meta-units positioned on a SiO2 substrate, with a lattice constant of 4 μm (Px = Py). b SEM images showcasing the fabricated second meta-device. c Simulated phase shifts (ϕx, ϕy) and transmittance T as a function of the meta-unit’s height H at the wavelength of 1550 nm. The broadband d phase shift and e transmittance characteristics of these meta-units with a x-polarized plane wave excitation at six discrete wavelengths. The inset in panel e provides an enlarged view of the transmittance parameter as a function of the meta-unit’s height H, ranging from 1.5 μm to 2.5 μm.

In our designs, we have set a to 3.5 × 104 and f to 30 mm, followed by properly solving the phase distribution functions (Ψ1, Ψ2). The phase profiles of each layer were converted into the corresponding height maps and then fabricated as a pair of samples to serve as the proof-of-mechanism meta-devices, both with a 2-mm diameter and array format of 500 × 500. The comprehensive definition of parameters and phase engineering pertinent to both experiments and simulations are delineated in Supplementary Note 2. Figure 2b shows scanning electron microscope (SEM) images of one of the fabricated meta-devices (the second one), and supplementary characterizations involved the use of a metallurgical microscopy (ECLIPSE LV150N) and a three-dimensional optical profilometer (TuoTuo Technology, MV-1000) have been included in Supplementary Note 3. Moreover, the simulation outcomes presented in Supplementary Note 2 affirm the feasibility of our approach, demonstrating the flexible transformations of the ring radius dimensions in PCVBs.

Analysis of the ring radius adjustability in PCVBs

For experimental validation purposes, a dedicated measurement setup was constructed in conjunction with the fabricated meta-devices. The generation of the targeted CVBs is achieved through interaction of linearly polarized input Gaussian beams with Q-plates featuring distinct q-values, enabling the conversion of the fundamental Gaussian modes into inhomogeneous vector modes via the principle of spin-dependent orbital interactions36. Additionally, a custom-designed experimental apparatus, outfitted with a rotating scale, is employed to dynamically manipulate the paired meta-devices, providing the in-plane rotatably twisted behavior. The meta-devices are closely cascaded with a properly optimized interstitial gap to enable the cumulative summation of their respective phase profiles, thereby reconstructing a total axicon phase distribution. After conducting the transformation of CVB to PCVB and the fine-manipulation of its ring radius, a charge-coupled detector is introduced to gather the output light field amplitude. A comprehensive description of the experimental setup is given in Supplementary Note 4.

A investigation into the adjustability of the ring radius in PCVBs is demonstrated, with the experimental findings displayed in Fig. 3 for cases of four chosen polarization orders of m = 1, 2, 4, 6. Notably, the inherent ambiguity concerning the rotation angle between |ϑ |and |ϑ|−2π leads to a theoretically symmetrical intensity distribution within the obtained PCVBs throughout the full 360° rotation range, representing an effective twisted tunable angle scope of 180° for this axicon moiré system (see Supplementary Note 2 for the detailed analysis). To elucidate this point, we captured the intensity and polarization distributions of output light fields for PCVB+1 and PCVB+2 (subscript denotes the polarization order) over a range of discrete rotation angles from 20° to 160°, for PCVB+4 and PCVB+6 over a range of sampled rotation angles from 200° to 340°, as illustrated in Fig. 3a. As anticipated, manipulating the relative rotation angle ϑ of the paired meta-devices effectively alters the ring radius dimensions of the resulting PCVBs through far-field transformations, forming a twisting-matched annular intensity profile and facilitating their adjustability. By switching the rotation angle within less than 180° and more than 180°, the ring radii of the PCVBs can be symmetrically scaled along both rotation states. Specifically, the ring radii expand as the rotation angles increase (0° < ϑ < 180°) but contract when 180° < ϑ < 360°, irrespective of their polarization orders. This observation is well-aligned with our numerical simulations presented in Supplementary Fig. S3a. And the accurate polarization detection outputs also substantiate the validity of our method, underscoring the robustness of the vector distribution upon beam transformations.

Fig. 3: Experimental findings highlighting the ring radius adjustability in PCVBs.
Fig. 3: Experimental findings highlighting the ring radius adjustability in PCVBs.The alternative text for this image may have been generated using AI.
Full size image

a Measured intensity and polarization detection results of the transformed PCVBs, detailing the correlation between the ring radius sizes versus the rotation angles. The white double arrow indicates the direction of polarization detection, and the normalized intensity colorbar refers to all panels. b Distribution of the measured normalized intensity along the horizontal central x-direction with y = 0; a.u., arbitrary unit. c Theoretical, simulated and experimental results of the ring radii R versus the rotation angles ϑ.

Another noteworthy phenomenon is the non-uniform intensity distribution observed along the circumference of the annular intensity ring in the captured PCVBs. Taking PCVB+1 as an example, Fig. 3b quantifies this explanation by extracting the cross-sectional curves of the measured intensity distributions and normalizing them as a function of the well-defined rotation angles. The appearance of this phenomenon arises from the inherent ambiguity in the joint axicon phase obtained, which indicates the residual azimuthal phase variations introduced through discrete sampling of the effective axicon phase during twisted moiré superposition. When the relative rotation angle between the paired meta-devices is not an exact rational multiple of the moiré periodicity, the joint phase profile acquires a weak azimuthal modulation alongside the dominant radial term, thereby producing the observed annular non-uniformity. This intrinsic effect is also reproduced in simulations, referring to Supplementary Fig. S3b. Additionally, fabrication-induced deviations within the 3D photonic-structured meta-devices also contribute to this effect37, inadvertently exacerbating the azimuthal intensity non-uniformity. Overall, the discrepancies between the experimental and simulated results can be attributed to system errors, involving fabrication instability, cascaded alignment inaccuracy, and imperfect perpendicular illumination of the incoming beam. The simulated effects of in-plane lateral misalignments and inclination angle on the PCVB generation are discussed in Supplementary Note 2. Despite these aberrations, the intensity peaks consistently shift outward with increasing rotation angles, confirming that the PCVBs’ ring radii can be precisely adjusted by actively controlling the twisting of the meta-devices. Figure 3c further illustrates this tunability by measuring the correlation between the ring radius R and the rotation angle ϑ in both simulation and experimental data. In spite of minor fluctuations between the simulation and experimental results, both sets of data show agreement with the theoretical approximation adhering to an expression of aϑf/k. And, Supplementary Fig. S9 offers complementary quantitative characterizations of the remaining three polarization orders (m = 2, 4, 6). Conversely, for rotation angles exceeding 180°, the linear correlation for resizing the ring radius dimension is governed by the expression of |ϑ−2π|af/k (see Supplementary Note 4). Our findings confirm the accuracy and reliability of both the experimental deployment and theoretical model, affirming the ring radius adjustability in PCVBs. Although our demonstration includes only a few discrete rotation angles, this method empowers continuous adjustment of the ring radii of PCVBs by continuously regulating the twisted attitude of the meta-devices.

In addition, we have verified the broadband optical response properties of our approach, which are accessible in Supplementary Note 4. Using the transformed PCVB+3 as an object, the favorable results exhibit the stable intensity and polarization detection patterns across three selected wavelengths (1530 nm, 1550 nm, 1570 nm). And, Supplementary Fig. S11 presents the diffraction efficiency of the meta-devices based on the measured intensity outputs of the PCVBs. When calculating the ratio of the output optical power to the input one, we have demonstrated that the measured diffraction efficiency exceeds 84.1%, achieving an insertion loss below 0.75 dB. This finding indicates the superior performance of the proposed meta-devices in achieving PCVB transformation. Properly minimizing the separation between the paired meta-devices can reduce diffraction loss and enhance light transmission efficiency38. However, an excessively small distance may result in undesirable electromagnetic coupling and evanescent field coupling. Therefore, a trade-off must be considered in practical implementation.

Verification of the “perfect” performance in PCVBs

Apart from the pursuit of an adjustable ring radius, the fundamental “perfect” attribute of the PCVBs is also to be sought after. Here, we conducted a verification to attest the “perfect” performance in PCVBs. As indicated in Fig. 4a, eight vector modes with polarization orders ranging from 1 to 8 are selected to perform the axicon moiré transformation for yielding PCVBs at two rotation angles of 50° and 130°, respectively. The eight input CVBs are obtained through a cascading configuration of two spatial light modulators (SLMs). Apparently, the created PCVBs exhibit a constant and stable toroidal intensity distribution, with polarization detection outputs displaying an axisymmetric rosette ring pattern, which comprises several petals related to the mode order. Figure 4b depicts the distribution curves of the measured normalized intensities as a function of the polarization orders. Despite the presence of peak offsets, the experimental results fit well with the numerical simulations (refer to Supplementary Fig. S4), demonstrating an approximate overlap. These sets of data pertaining to the ring radius parameters from both experimental measurements and simulated calculations are presented in Fig. 4c, with specific values detailed in Supplementary Table 3. It shows that the differences between the experimentally measured and theoretical ring radii are less than 0.012 mm. These results suggest the dependable “perfect” performance of the transformed PCVBs, exhibiting good consistency in beam intensity profiles.

Fig. 4: Experimental results verifying the “perfect” performance in PCVBs.
Fig. 4: Experimental results verifying the “perfect” performance in PCVBs.The alternative text for this image may have been generated using AI.
Full size image

a Measured intensities and polarization detection distributions of the transformed PCVBs at ϑ = 50° and 130°, respectively. The white double arrow indicates the direction of polarization detection, and the normalized intensity colorbar refers to all panels. b Distribution of the measured normalized intensities as a function of the polarization orders; a.u., arbitrary unit. c Theoretical, simulated and experimental results of the ring radii R versus the polarization orders.

282-channel multi-dimensional multiplexing communication from free space to MMF fiber

To elucidate the practical utility of the proposed approach in enhancing free-space-to-fiber coupling efficiency and communication performance, a dedicated prototype optical communication system was developed and evaluated, which is detailed in Supplementary Note 5. Incorporated with wavelength- and polarization-division multiplexing techniques, this system can support a 282-channel multi-dimensional hybrid multiplexing communication, encompassing three distinct vector modes (m = 1, 2, 4), two orthogonal linear polarization states (x- and y-components), and a broad spectrum of 47 wavelengths (spanning from 1542.14 nm to 1560.61 nm with an approximate interval of 0.4 nm). Each of these multiplexed channel carries decorrelated 50 Gbit s−1 QPSK signals, thus achieving a total communication rate of 14.1 Tbit s−1 (282 × 50 Gbit s−1) for data transmission over both 1 m of free space and 5 km of MMF.

We first evaluated the enhancement in coupling efficiency without merging wavelength- and polarization-division multiplexing. Figure 5a−c compares the received optical power levels for three distinct CVBs (m = 1, 2, 4) when coupled to the 5 km MMF: one through direct beam coupling (marked as red dotted line) and the other via transformation to ring radius-adjustable PCVBs using the meta-devices prior to coupling (represented as column chart). The coupling process was performed using a collimator to facilitate free-space-to-fiber coupling, thereby directing the beam to the fiber interface. The employed MMF exhibited a core diameter of 50 ± 2.5 μm and a cladding diameter of 125 ± 1 μm. These figures reveal that introducing the twisted meta-devices to convert CVBs into PCVBs results in increased received power as the ring radii decrease. In particular, at a rotation angle of 20°, this treatment realizes average 2.56 dB (equivalent to 80.7%) efficiency improvement over conventional direct coupling. When excluding the insertion loss of the meta-devices, the coupling efficiency can surpass 3.31 dB. This efficiency enhancement is primarily attributed to reduced annular beam dimensions enabling improved core alignment during fiber coupling, thereby confining more optical energy within the fiber for total internal reflection. In addition, another noteworthy phenomenon related to channel equilibrium deserves emphasis. For direct CVB coupling, the received optical power deviates by approximately 0.87 dB. In contrast, when PCVB is introduced as an intermediary, power fluctuations are reduced to below 0.29 dB, with a minimum level of 0.08 dB at the rotation angle of 40°. This underlying reason is that the PCVBs maintain consistent beam size and divergence across distinct mode orders within the coupling process. This approach ensures power equalization across multiple mode channels, which is of importance for enabling long-distance multi-mode multiplexing and efficient transmission in optical communication systems. For a three-mode multiplexed transmission, the channel crosstalk analysis detailed in Supplementary Note 5 also affirms the above findings, which underscores ~2.75 dB improvement in crosstalk suppression. Overall, our scheme enables dynamically tuning of the fiber coupling efficiency for multiplexed CVB mode channels, promising near-ideal coupling performance. This finding can be extended to other fiber types, affording optimal coupling solution for fiber-optic network node interconnections by transforming and adjusting the ring radii of PCVBs.

Fig. 5: Results of free-space-to-fiber coupling efficiency and communication performance with/without the PCVB coupling scheme.
Fig. 5: Results of free-space-to-fiber coupling efficiency and communication performance with/without the PCVB coupling scheme.The alternative text for this image may have been generated using AI.
Full size image

a–c Measured received optical power levels to evaluate the coupling efficiency improvement of three distinct CVBs when coupled to a 5 km MMF. The red dotted lines indicate the measured received optical powers using the conventional lens-based direct coupling method, while the column charts represent the counterparts via PCVB coupling across varying ring radii. d, e Communication metrics of direct CVB coupling with 282 multiplexed channels, including BER curves, constellation diagrams, and EVM values. f, g Communication metrics of PCVB coupling at a twisted angle of 20° versus received optical powers. h, i Performance comparison for elaborating PCVB coupling scheme’s effect at different rotation angles. In figures, “1550.12, x2” represents the CVB+2 channel at the wavelength of 1550.12 nm with a x-polarization input, and the others can be inferenced similarly. The color gradient in the constellation diagram reflects the density distribution of the converged signal points, with the transition from blue to yellow indicating regions of higher point concentration, which corresponds to improved signal convergence.

To demonstrate the impact of enhanced fiber coupling efficiency on communication performance, we assessed BER metrics for the transmitted 14.1 Tbit s−1 QPSK signals, obtaining outcomes as reflected in Fig. 5d−i. A comparative analysis with and without the proposed PCVB coupling scheme highlights its utility in improving communication performance. The communication measurement using direct CVB coupling is initially shown in Fig. 5d, e, sketching several BER curves and constellation diagrams of the 282 channels versus received optical powers. Apparently, when the received power exceeds −21 dBm, the BERs remain below the hard-decision forward error correction (FEC) threshold of 3.8 × 10−3. As the received power increases to −15 dBm, the BERs decrease to near 1 × 10−6 for these sampled channels. It can be depicted that under identical received power conditions, the maximum variation in BERs across different channels reaches approximately half an order of magnitude, a phenomenon that can be primarily ascribed to differing propagation dynamics arising from variations in beam divergence characteristics. Despite this, the close clustering observed in constellation diagrams and their corresponding error vector magnitudes (EVMs) collectively demonstrate favorable signal quality. For the scheme taking advantage of PCVB coupling, Fig. 5f, g characterizes the communication performance metrics of the meta-devices with a rotational twist angle of 60°. Comparative analysis with Fig. 5d, e reveals that the BER magnitudes maintain consistent cross-channel proximity, demonstrating effective inter-channel equalization performance thanks to uniform beam divergence in fiber coupling. The capability of our PCVB coupling strategy is also corroborated by demonstrating more convergent constellations and lower EVM levels [see Fig. 5g]. Furthermore, an analysis of the experimentally measured optical spectrum of 47 wavelengths before and after PCVB coupling is supplied in Supplementary Note 5. To conclude that the PCVB coupling affects communication performance in different twisting states, we evaluated metrics for a “1550.12, x2” channel, as stated in Fig. 5h, i. The BER curves indicate that PCVB coupling confers an approximate 1 dB signal gain for the communication system’s sensitivity at a rotational twist angle of 20°, representing a ~0.5 order of magnitude improvement over direct CVB coupling. However, an increased signal deterioration occurs in improper twisting states of ϑ = 80° and 100°. As a consequence, PCVB coupling effectively improves both receiver sensitivity and operational reliability in the free-space-to-fiber CVB multiplexed link, demonstrating its valuable impact on channel equalization and signal optimization within multi-mode optical communications.

Discussion

Diffraction during free-space propagation causes multiplexed CVBs to inevitably expand and diverge, leading to mode-field mismatch and efficiency reduction during free-space-to-fiber beam coupling. Reduced spatial coherence also disturbs the mode power distribution of CVBs upon fiber coupling39, thereby posing diminished signal strength and increased crosstalk. Traditional direct coupling strategies11,18 struggle to maintain an optimal consistent beam ring radius, which results in considerable coupling loss and constrained multiplexing capacity for CVBs, particularly with realistically limited-size receiver apertures. This study addresses these challenges in CVB-based free-space-to-fiber-optic communications by introducing a reconfigurable beam transformation methodology that converts multiplexed CVBs into ring radius-adjustable PCVBs. Its implementation demonstrates an ~80.7% improvement in free-space-to-fiber coupling efficiency, a ~2.75 dB enhancement in crosstalk suppression, and dynamically adaptable beam configuration with ring radii ranging from 0.0955 mm to 0.7430 mm. With twisted moiré engineering, the proposed deployment not only effectively mitigates the divergence of multiplexed CVBs but also creates dynamically adjustable consistency, emphasizing its near-ideal coupling capability and practical benefits in real-world communications. Our efforts are dedicated to developing ring radius-adjustable PCVBs, and a comparative alternate solution is outlined in Supplementary Note 6 for this purpose. This approach adjusts the ring radii of PCVBs by strategically engineering moiré varifocal lenses, yet the induced spatial output variability limits its practicality in applications like stationary fiber couplers or devices. Harnessing twisted axicon moiré modulation, our solution operates at the same spatial depth, making it more compatible with practical communication systems and offering extended potential for fiber-tip integration40,41.

A promising advantage of the proposed strategy lies in its scalability spanning beam objects, parameterization, device implementation, and functional applications. Despite the current validation in the ring radius adjustability of PCVBs, this principal engineering architecture can be extended to other centrosymmetric light beams such as prefect orbital angular momentum beams42, prefect hybrid-order poincaré sphere beams43, or even emerging grafted perfect vector vortex beams22,27 and fractional-order modes44. With simultaneous elliptic coordinate transformations45, such a scheme affords potential for manipulating elliptical beam wavefronts to enable size scaling and ellipticity modulation. In terms of parameterization, precision-altering parameters (a, f) in Eq. (3) can modify the scaling scope of PCVBs’ ring radii against the twisted rotation control. Furthermore, device implementation can be scaled up to Si- or TiO2-based metasurface platforms46,47, enabling adaptable operation across multiple spectral regimes, such as visible and mid-infrared bands, through nanoscale structural configuration. While both SLMs and liquid crystal-integrated metasurfaces48 could theoretically implement the proposed twisted moiré mechanism, they are constrained by the requirement for active electrical control, narrow operational bandwidth, and polarization-dependent performance. In contrast, our presented passive, phase-only modulation twisted moiré meta-devices operate without electrical control, offering broadband capability, universal multi-mode support, and inherent compactness, thus representing a promising implementation approach. When incorporating superimposed gradient phases for multi-beam assignments, a ring radius-adjustable PCVB array is obtained, numerically validated in Supplementary Note 6. This functionality could provide valuable insights for prevailing multi-core fiber coupling, thereby reducing multi-channel coupling loss and enhancing light transmission efficiency. In addition, by establishing deterministic encoding relationship between twisted angular parameter and ring radius dimension, the proposed work might show potential applications for encrypted data transmission and secure key management.

Conclusion

To summarize, we are dedicated to developing a near-ideal CVB fiber coupling paradigm, which exploits the twisted moiré-engineered axicon modulation technology to efficiently transform multiplexed CVBs into PCVBs with dynamically adjustable ring radii. This innovation allows for precise free-space-to-fiber coupling, addressing the challenges of mode-field mismatch and suboptimal alignment previously encountered in direct CVB coupling. Our experimental outcomes confirm the strategy’s efficacy by harnessing a pair of twisted moiré meta-devices, achieving continuous dynamic tuning of PCVB ring radii from 0.0955 mm to 0.7430 mm with a diffraction efficiency over 84.1% and a 40 nm bandwidth (1530−1570 nm). The successful transmission of 14.1 Tbit s−1 QPSK signals over a 5 km MMF, with improved coupling efficiency (~80.7%) and decreased channel crosstalk (~2.75 dB), underscores the practical potential of our approach. These findings not only advance the field of CVB multiplexing communications but also pave the way for the integration of free-space-to-fiber-optic networks, offering a versatile platform for future high-capacity robust fiber couple systems and node interconnections.

Methods

Full-wave simulation with FDTD

The commercially available software FDTD Solutions (Lumerical Solutions Corp.) was employed to perform full-wave electromagnetic simulations of the selected 16-level meta-units, analyzing their phase shift and transmittance properties. For each meta-unit of distinct height, a three-dimensional (3D) FDTD calculation model with a simulation domain of 4 μm × 4 μm × 8 μm was established. Within this domain, the perfectly matched layer (PML) boundaries were applied along the z-direction, while periodic boundary conditions were implemented along the x- and y-directions to simulate an infinite array. The complex amplitude of the output light field was collected at a detection plane positioned 6 μm above the SiO2 substrate, enabling characterization across different incident wavelengths and polarizations.

Fabrication of IP-Dip-based meta-devices

The designed twisted moiré meta-devices were fabricated via the TPN method, comprising five main steps: plasma cleaning of the square SiO2 substrate; dispensing a droplet of IP-Dip photoresist; femtosecond pulsed laser nanolithography; solidification of the target structures; and degumming the resulting samples. Detailed procedures are outlined in Supplementary Note 3.