Metasurfaces, as planar arrays of subwavelength nanostructures, have revolutionized photonics and electromagnetics by enabling unprecedented control over light and wavefronts [1–8]. Their ultra-compact, lightweight, and multifunctional properties have unlocked transformative applications across diverse fields such as holography [9–12], beam steering [13,14], biosensing [15,16], and communications [17,18]. THz technology has emerged as a pivotal frontier in modern photonics, offering transformative potential across applications such as imaging [19–22], sensing [23–25], and wireless communications [26,27]. A critical challenge in this domain lies in achieving dynamic and efficient control over THz wavefronts, particularly with regard to polarization-multiplexed tunable manipulation. The evolution from static to dynamic control in THz metasurfaces has been driven by stimuli-responsive materials and mechanisms. Optically tuned metasurfaces leverage photoexcitation in phase transitions in materials like Ge2Sb2Te5 (GST) to modulate THz waves via carrier density or refractive index changes, achieving ultrafast responses but suffering from thermal damage and limited modulation depth [28–30]. Thermally tuned designs, such as VO2-based metasurfaces, exploit insulator-to-metal phase transitions under heating, offering high modulation contrast but facing slow response and high energy consumption [31–33]. Electrically controlled metasurfaces, utilizing graphene or liquid crystals, enable tuning via carrier injection or molecular alignment under electric fields, yet require high voltages and complex electrode integration [34–36].

A promising alternative lies in Moiré metasurfaces, which leverage rotational misalignment between cascaded metasurface layers to achieve dynamic phase modulation without external stimuli. By rotating cascaded metasurface layers, the effective phase profile can be continuously modulated, enabling reconfigurable optical responses. Zhang et al. demonstrated a Moiré meta-device using cascaded dielectric metasurfaces to dynamically tune Bessel beam order and non-diffraction length via mutual rotation; experimental results validate high-quality Bessel beam generation with reconfigurable parameters [37]. Xiao et al. introduced adaptive aberration correction during focal scanning using two rotating cascaded silicon metasurfaces. Optimized phase functions enabled dynamic focus control on custom planar and conical surfaces in the terahertz regime without external components [38]. Chen et al. proposed twisted dielectric metasurfaces that achieve on-demand subwavelength focusing localization through rotational interlayer coupling, enabling dynamic control of focal position and intensity without mechanical adjustments. Experimental validation demonstrates spatially reconfigurable focusing with diffraction-limited precision [39]. Despite these advances, existing Moiré-based designs face two critical limitations. On the one hand, they predominantly focus on single-polarization-state manipulation, neglecting the independent control of orthogonal polarization channels. On the other hand, their zoom ranges and NAs remain constrained, limiting their utility in applications requiring high-resolution and polarization-multiplexed functionalities.

In this work, we address these challenges by introducing a cascaded all-dielectric Moiré metasurface platform that achieves simultaneous focal-length tuning and independent polarization control in the THz regime. Our design combines polarization-insensitive and polarization-sensitive sub-metasurface layers, enabling decoupled manipulation of orthogonal circular (Moiré device 1) or linear (Moiré device 2) polarization states. Here, Moiré device 1 generates focused beams carrying topological charges l=0 and l=1 in the LCP→RCP and RCP→LCP channels, respectively, under orthogonal circularly polarized illumination. In contrast, Moiré device 2 produces focused beams with l=1 and l=0 in the co-polarized channels under x-LP and y-LP illumination, achieving polarization-dependent phase control. As an example, the feasibility of the proposed design strategy is further verified using a THz near-field imaging system with the metasurface under linearly polarized illumination. By rotating the layers relative to one another, the effective phase profile is reconfigured, allowing continuous focal-length adjustment from 8.42 mm to 3.11 mm and a zoom ratio exceeding 2.7 times, while simultaneously tailoring polarization responses. This dual functionality is achieved without external stimuli, relying solely on the phase and interlayer rotational coupling. These findings demonstrate twisted metasurfaces’ capacity to minimize conventional optical dependencies, advancing cost-effective and sustainable communication technologies.

Figure 1 presents a schematic illustration of the proposed Moiré device 1 for on-demand wavefront shaping. This meta-device comprises two coaxially arranged all-dielectric metasurfaces with precise alignment: the upper metasurface, referred to as Layer 1, and the lower metasurface, referred to as Layer 2. This configuration enables the generation of a focused vortex beam with a topological charge of l=1 under RCP illumination, while simultaneously producing a focused Gaussian beam with l=0 under LCP illumination, as depicted in Fig. 1(a). The described wavefront shaping process can be mathematically expressed as [40,41] {O⌢MS|σL⟩=exp(il1ζ)|σR⟩,O⌢MS|σR⟩=exp(il2ζ)|σL⟩.(1)

Here, σL=[1i] denotes LCP and σR=[1−i] denotes RCP; l1 and l2 present the topological charges carried by the LCP and RCP channels, respectively. In this context, we set l1=0, while l2=1, and ζ denotes the azimuthal angle. The focal length of the generated beam can be dynamically modulated by rotating Layer 1 relative to Layer 2, introducing a controlled twist angle between the two metasurfaces. This tunable configuration enables the derivation of a functional relationship between the relative twisted angle and the resulting focal length. Such a design underscores the versatility and robustness of the proposed strategy, allowing for precise tailoring of beam properties through polarization control and spatial phase manipulation.

The functionality of the proposed Moiré device 1 relies on meticulous phase engineering. Based on the Moiré effect, the phases of the two metasurfaces constituting the composite lens are complex conjugate to each other. In polar coordinates, their original phases can be expressed as ϕ1(r,α0)=−round(r2λf)(α0),(2)ϕ2(r,α0)=round(r2λf)(α0),(3)where r and α0 are the polar coordinate parameters, λ is the operating wavelength, and f represents the predefined focal length. The round (•) function converts the value of the operand to the nearest integer to avoid sectorization effects. For Layer 1, the design must enable dynamic focusing as the layer rotates, whereas for Layer 2, the phase distribution is tailored to achieve polarization multiplexing. According to Eq. (2), when Layer 1 is rotated around the axis by an angle θ relative to Layer 2, the phase profile of Layer 1 can be written as [42,43] ϕ1(r,α0;α)=−round(r2λf)(α0−α),(4)where α denotes the mutual twisted angle. For the phase design of Layer 2, its primary function is to independently encode the orthogonal circularly polarized channels and to enable generation of vortex beams for orthogonal circularly polarized channels, where helical phase lζ is introduced. Based on Eq. (3), the encoded phase distribution at Layer 2 can be mathematically expressed as ϕ2L→R(r,α0)=round(r2/λf)α0+l1ζ and ϕ2R→L(r,α0)=round(r2/λf)α0+l2ζ, where the parameters l1 and l2 represent the topological charges assigned to the LCP→RCP and RCP→LCP channels, respectively. The variable ζ=arctan(y/x) denotes the polar angle used to encode the vortex phase. In this design, the topological charges are set as l1=0 and l2=1. Based on Eq. (4), the total phase of the Moiré device 1 for RCP/LCP can be expressed as ϕJointL→R(r,α0;α)=round(r2λf)α+l1ζ,(5)ϕJointR→L(r,α0;α)=round(r2λf)α+l2ζ.(6)

Based on the total phase distribution, it can be seen that by superimposing the phase profiles of the two metasurfaces with a relative rotation (angle α), the interferences in the phase distribution generate dynamic effective phase gradients, which modulate the wavefront characteristics. Under RCP illumination, Moiré device 1 generates a vortex beam carrying a topological charge of l=1, whereas LCP excitation produces a focused Gaussian beam (l=0), demonstrating polarization-dependent phase modulation for selective structured field generation. To clarify the operational mechanism of the proposed design, the encoded phase distributions of Layer 1 and Layer 2 at a relative twisted angle of 90° are illustrated in Fig. 1(b). These phase profiles demonstrate the independent encoding of orthogonal circular polarization channels and the corresponding joint phase distributions. The orthogonal circularly polarized channels exhibit phase profiles consistent with the assigned topological charges, facilitating the selective generation of distinct beam types. Moreover, the electric field distributions in the xoy- and xoz-planes for the corresponding polarization channels are evaluated at the designed focal plane. As shown in Fig. 1(c), within the LCP→RCP channel, the device generates a focused Gaussian beam, while in the RCP→LCP channel, a vortex beam with a characteristic spiral phase profile is observed. According to Eqs. (5) and (6), the relationship between the focal length and the relative twisted angle α can be derived, enabling precise control over the focal properties. This functional relationship, which forms the foundation of the device’s tunable focusing capabilities, is expressed as F(α)=πCλα,(7)where C is a constant and can be adopted as 1/λf; λ is considered a constant value. Therefore, it can be concluded that the focal length F varies with twisted angle α. Consequently, the NA can be expressed as NA=sin(arctanL2·F(α)).(8)

Here, L denotes the diameter of the Moiré device 1, which plays a critical role in determining the transmitted performance. As shown in Fig. 1(d), an inverse relationship is observed between the focal length and the twisted angle α (depicted by the green curve). Specifically, as the angle α increases, the focal length gradually decreases, indicating a compression of the beam’s focal region. Conversely, a direct proportional relationship is evident between the NA and the twisted angle, as illustrated by the red curve in Fig. 1(d). The NA parameter expands steadily with increasing twisted angle, which suggests an enhanced focusing capability and a reduction in the focal spot size. This behavior underscores the tunable property of the proposed meta-device, as both focal length and NA can be dynamically adjusted through precise control of the relative twisted angle.

Given that the primary function of Layer 1 is to achieve dynamic focal adjustment (zoom), polarization-insensitive cylindrical pillars were deliberately chosen for the design of the meta-atoms. Figure 2(a) illustrates the side and top views of the cylindrical dielectric pillar, characterized by a height H=200μm and a variable radius r, fabricated on a silicon substrate with a periodicity P=150μm. To achieve full 2π phase modulation at the target frequency of 0.9 THz, a comprehensive parameter sweep for r was performed using the CST Microwave Studio software. From the simulation results, eight distinct meta-atoms were selected to provide a complete phase coverage ranging [−π,π]. As shown in Fig. 2(b), the selected meta-atoms exhibit consistent transmission amplitude and phase response under linearly polarized illumination, ensuring uniform performance for both x-LP and y-LP incidences. Figure 2(c) presents the normalized magnetic field distribution of the cylindrical dielectric pillars monitored under periodic boundary conditions, by utilizing the time-domain solver. Apparently, the EM energy carried by the incident THz wave is localized mainly inside the dielectric pillars with high refractive indices, suggesting that the coupling between neighboring meta-atoms is negligible.

Layer 2, on the other hand, is specifically designed for polarization conversion. Anisotropic rectangular pillars were introduced to achieve polarization-multiplexing functions. This configuration employs meta-atoms composed of rectangular nano-pillars with a height H=200μm, fabricated on a silicon substrate with a periodicity P=150μm. The characteristic parameters Lx and Ly are predefined for manipulating the orthogonal polarization channels and the desired meta-atoms are obtained in the time-domain solver by utilizing a parametric scanning process. The x- and y-directions along the dielectric pillars are set as periodic boundary conditions, while the z-direction is set as an open boundary condition. To enable independent encoding for orthogonal circular polarization channels, the design leverages the principle of a spin-decoupling mechanism. This approach ensures that the meta-atoms independently manipulate the phase profiles of LCP and RCP waves, expressed as [40,44–46] {φxx=(φLCP+φRCP)/2,φyy=(φLCP+φRCP)/2−π,θ=(φRCP−φLCP)/4.(9)

Here, φxx (φyy) represents the propagation phase at x(y)-LP incidence, φLCP (φRCP) represents the phase distribution of the LCP (RCP), and θ is the rotation angle of the meta-atom. The details of the calculations corresponding to the spin-decoupled phase engineering are presented in Appendix A. Using CST software for parameter scanning (varying the Lx and Ly of the rectangular pillar structure), we simulated the transmission amplitude and phase shift of the meta-atom. Based on the requirements set forth by Eqs. (9) and (A5), meta-atoms were selected to enable independent phase modulation for incident LCP and RCP waves. The transmission amplitudes and phase shifts of these selected meta-atoms are illustrated in Figs. 2(e) and 2(f). Notably, the corresponding phase distributions φxx and φyy exhibit complete 2π coverage within the range of −π to π, ensuring comprehensive phase modulation capability. Additionally, the transmission amplitudes remain within the range of 0.6 to 0.8 and display a relatively smooth variation across the selected meta-atoms. As depicted in Fig. 2(g), the rotation angle θ demonstrates a well-defined function relationship with both the phase distribution and the meta-atom orientation. To gain deeper insights into the electromagnetic response, the normalized magnetic field distribution of structural units with periodic boundary conditions was analyzed. The results, shown in Fig. 2(h), reveal that the energy of the incident electromagnetic wave is strongly confined within the high-refractive-index medium columns. This indicates minimal interlayer coupling, thereby preserving the independent functionality of the metasurfaces and ensuring high design robustness.

Figure 3(a) presents the phase distribution of Layer 2 within the LCP channel, where each discrete pixel represents a precisely engineered anisotropic rectangular silicon pillar. These meta-atoms were optimized to encode the required phase profile, ensuring accurate polarization control and phase manipulation. Figure 3(b) systematically demonstrates the phase distribution of Layer 1 under various twisted angles. As the twisted angle α increases from 90° to 240° in 30° increments, the phase profile exhibits a counterclockwise rotational shift around the central axis of the image, highlighting the tunable characteristic of the metasurface and its ability to dynamically reconfigure the phase distribution through simple mechanical rotation. The joint phase distribution of Layer 1 and Layer 2, corresponding to the LCP channel, is shown in Fig. 3(c). This joint phase profile is computed by superimposing the phase contributions from both Layer 1 and Layer 2 under the respective rotation angles. The resultant combined phase pattern demonstrates precise control over the spatial phase distribution. Under LCP illumination, the incident wave traverses the meta-device, enabling electric field distributions to be analyzed in terms of their RCP components using a field monitor in transmission mode [Fig. 3(d)]. Notably, as the rotation angle α increases from 90° to 240°, the focal length of the generated focused beams decreases from 9.28 mm to 3.22 mm. In parallel, Fig. 3(e) shows the phase distribution of Layer 2 within the RCP→LCP channel, while the corresponding phase distribution of Layer 1 [identical to Fig. 3(b)] is shown in Fig. 3(f). The joint phase distribution for the RCP channel, obtained as the Fourier sum of the phases from Layer 1 and Layer 2, is presented in Fig. 3(g). This phase distribution adjusts dynamically with changes in α, creating distinct interference patterns that enable the emitted waves to generate vortex beams focused at specific points on the focal plane [Fig. 3(h)]. The electric field distributions in the xoz-plane monitored with the time-domain solver are presented in Appendix B, with increasing relative rotation angles from 90° to 240°. Figure 3(i) demonstrates the inverse correlation between focal length and rotation angle α, coupled with a direct proportionality of NA to α, aligning qualitatively with theoretical predictions. Specifically, as α increases from 90° to 240°, the NA rises from 0.54 to 0.88. In addition, we further quantified the operating performance of the Moiré device 1 by introducing the APE parameter, the details of which are demonstrated in Appendix C. Apparently, the average APEs of focal length and NA between the theoretically predicted and numerically simulated values are 25.2% and 15%, respectively, which indicates the effectiveness of the proposed design strategy. The reason for the higher APE values is the complex near-field coupling between the layers and the sensitivity of the phase control to structural tolerances, which are reflected in the simulations but less directly in the theoretical model. Nonetheless, the device shows a consistent trend in focal length adjustment, validating the design principle of rotating Moiré phase engineering. Figure 3(j) quantifies the focusing efficiency of the Moiré device 1, defined as [47] ηf=E˜f/E˜sum=∬Ef(Ef≥(Emax/e))/∬Ef, where E˜f denotes the integral of the focused field distribution over a range greater than Emax/e, and E˜sum denotes the integral of the field distribution at the entire focal plane. With the gradual increase of parameter α, the focusing efficiency of the focused beam carrying topological charge l=1 generated within the LCP component exhibits a monotonic efficiency reduction, while the trend of the focusing efficiency of the focused beam carrying topological charge l=0 generated within the RCP component maintains near-constant. Further calculated results indicate an average focusing efficiency of approximately 35%, primarily affected by diffraction losses, discrete phase control defects, and material losses. To further evaluate the polarization isolation capability of the Moiré device 1, we quantified the crosstalk between LCP and RCP through numerical simulations, as detailed in Appendix D.

While the above results demonstrate successful dynamic control of orthogonal circular polarization channels, the practical implementation of polarization-selective meta-devices often requires compatibility with both circularly polarized (CP) and linearly polarized (LP) systems depending on application scenarios. In order to validate the generality of the cascaded metasurface design across different polarization bases, as well as to satisfy different application requirements, we further designed Moiré device 2 with the aim of verifying the versatility and flexibility of this design framework. The schematic of the designed Moiré device 2 is illustrated in Fig. 4(a). Layer 1 of the metasurface is identical to the design presented in Fig. 1(a), while Layer 2 consists of rectangular pillar units engineered based on propagation phase principles, distinct from Layer 2 in Moiré device 1. This configuration facilitates the generation of a focused beam with a topological charge of l=0 in the y-LP channel under y-LP illumination. Simultaneously, a focused vortex beam carrying a topological charge of l=1 is produced in the x-LP channel under x-LP illumination. The described wavefront shaping process can be mathematically expressed as {O⌢MD2|σx⟩=exp(il1ϕ)|σx⟩,O⌢MD2|σy⟩=exp(il2ϕ)|σy⟩.(10)

Here, σx=[10] denotes x-LP incidence and σy=[01] denotes y-LP incidence; l1 and l2 present the topological charges associated with the x-LP and y-LP incidence, respectively. In this context, we set l1=1, while l2=0, and ϕ denotes the azimuthal angle. Furthermore, the ability to dynamically adjust the focal length of the generated beams is achieved by rotating Layer 1. The range of rotation angles is defined as (0°, 360°).

The simulation results for x-LP incidence are shown in Fig. 4(b), where a focused vortex beam is generated within the x-LP channel. This beam exhibits a characteristic intensity profile with zero intensity at the phase singularity, surrounded by a ring-shaped intensity distribution. As the mutual twisted angle α between the two metasurfaces (Layer 1 and Layer 2) increases, the phase distribution region corresponding to the focal area has diminished, and the phase transition has become more localized. Similarly, Fig. 4(c) demonstrates the response under y-LP incidence, where a conventional focused beam is observed within the y-LP channel. Unlike the vortex beam, this beam features a Gaussian-like intensity profile at the focal point. Further, the electric field distribution (xoz-plane) generated by the Moiré device 2 under orthogonal linearly polarized wave illumination is exhibited in Appendix E. Apparently, the focal length of the transmitted beam is inversely related to the relative rotation angle. Due to the device’s ability to manipulate phase fronts through relative rotational alignment, both the focusing range and spatial phase distribution are systematically reduced, enabling dynamic tuning of the focal properties.

Figure 5(a) presents a schematic diagram of the THz near-field scanning spectroscopy system, which was employed to measure the proposed Moiré meta-devices. The employed experimental system is equipped with microprobes that can record the complex amplitude information at the focal plane, pixel by pixel, under LP illumination. Sample fabrication was performed using ultraviolet (UV) lithography and inductively coupled plasma (ICP) etching [48,49]. High-resistivity silicon with a thickness of 500 μm was used as the substrate to optimize the device’s optical performance and minimize signal loss. The scanning electron microscope (SEM) images of the fabricated metasurfaces (Layer 1 and Layer 2) are shown in Figs. 5(b) and 5(c). The dimensions of the samples are 1.4cm×1.4cm, with a central circular region composed of 80×80 silicon pillars. For Layer 1, the magnified detail images highlight that its basic unit consists of cylindrical silicon pillars, which are characterized by sharp boundaries and smooth surfaces, reflecting a high level of fabrication precision. In contrast, Layer 2 is composed of rectangular silicon pillars, which also demonstrate excellent fabrication quality, as evidenced by the magnified detail images presented herein. To ensure sub-wavelength precision in aligning cascaded metasurface architectures, the experimental setup employed a GCT-090101 multi-axis rotational control system with integrated phase-sensitive feedback mechanisms [37]. The dual-layer configuration features independent rotational stages—Layers 1 and 2 are mounted on aerostatic bearing platforms incorporating high-resolution radial gratings (360° circumferential division). Details of the cascaded metasurfaces constructed with the assistance of the GCT-090101 components are shown in Appendix F. Interlayer spacing optimization follows an inverse proportionality principle derived from coupled-mode theory simulations. The parametric study reveals that the critical coupling distance dc between adjacent metasurfaces scales inversely with their respective phase gradients (ΔΦ), obeying dc≈λ2/(4πΔΦ), when operating near the Rayleigh-Sommerfeld diffraction regime [37,38,50]. This counterintuitive relationship stems from the competition between near-field evanescent coupling and far-field propagation effects—steeper phase gradients effectively compress the Fresnel zone, necessitating reduced spacing to maintain phase continuity. The synergy between rotational alignment precision and gradient-dependent spacing adjustment enables unprecedented control over the proposed Moiré meta-devices.

To assess the simultaneous control of polarization and focal length in our Moiré device 2 for THz waves, experimental characterization was performed at discrete twisted angles between the metasurface Layer 1 and Layer 2, specifically at 90°, 120°, 150°, 180°, 210°, and 240°. Amplitude and phase distributions were systematically recorded at 0.9 THz (Fig. 6). Under x-LP incidence, Fig. 6(a) presents a characteristic doughnut-shaped pattern, with a dark core at the center, indicative of a phase singularity where the intensity is zero. The phase distribution around this singularity evolves along a closed, helical path, corresponding to a complete 2π phase winding, a hallmark of an optical vortex with topological charge l=1. As the relative twisted angle between the two metasurface layers increases from 90° to 240°, with a step size of 30°, the doughnut-shaped spots in the electric field distributions exhibit progressive radial contraction. Concurrently, the 2π phase winding in the phase distribution narrows, indicating a gradual reduction in the focal length. This experimental result aligns well with the simulation data shown in Fig. 4(b). Subsequently, the electric field distribution and phase profile of the Moiré device 2 under y-LP illumination were further measured under the same experimental conditions, as shown in Fig. 6(b). In the electric field distribution, a well-defined focused spot is observed, where the intensity reaches its maximum at the central point. The phase distribution at the focal region is nearly uniform, indicating coherent focusing with minimal phase variation. As the relative twisted angle α increases from 90° to 240°, the central focused intensity distribution gradually diminishes, which is indicative of a reduction in the effective focal length and a change in the beam’s NA. This experimental result aligns well with the simulation data shown in Fig. 4(c).

To further illustrate the zoom functionality of the Moiré device 2, Figs. 6(c) and 6(d) show the focal length and NA as a function of the relative twisted angle α, respectively, with theoretical predictions, simulations, and experimental measurements overlaid. It is evident that as the rotation angle increases from 90° to 240°, the focal length steadily decreases from 8.42 mm to 3.11 mm, demonstrating the dynamic focusing capability of the metasurface. The experimental results closely match the simulation data, exhibiting an APE for focal length of less than 5.9% and an NA of less than 3% (the details can be found in Appendix G), confirming the feasibility of the designed strategy of the Moiré device 2. Such behavior is consistent with the expected response that manipulates phase and polarization at the THz frequency, enabling effective and tunable beam control. As shown in Fig. 6(d), the results show a clear proportional relationship between the NA and the rotation angle α. As the rotation angle increases, the NA parameters obtained in the experiments gradually increase, which is consistent with the evolutionary trend of the theoretical and simulation results. This agreement further underscores the device’s tunable focusing capability. Figure 6(e) presents the focusing efficiency under x-LP and y-LP incidence. The measured focusing efficiencies in both orthogonal polarization channels exhibit a gradual decline with increasing rotational angle while consistently maintaining values above 15% across all tested configurations, which is constrained by fabrication tolerances and suboptimal rotational alignment between layers. This systematic characterization confirms the dual-polarization operational capability of Moiré device 2, validating its capacity for simultaneous polarization-multiplexed focal length tunability and independent polarization channel modulation. In conjunction with the previous discussion, device 1 simulations yielded average focusing efficiencies in excess of 35%, and experimentally measured focusing efficiencies in excess of 15% for device 2, a preliminary exploration for polarization-selective focusing metasurfaces. Further optimization of geometry and material selection and more precise fabrication techniques could lead to even higher efficiencies for both devices. More importantly, the results fundamentally establish that our phase-engineering strategy enables focal length customization while preserving efficient polarization-selective control, which is a critical requirement for advanced polarization-manipulation systems.

In summary, we have proposed a tunable-focus cascaded dielectric meta-device (Moiré device 1) employing rotational Moiré phase engineering to achieve simultaneous polarization-channel selectivity and focal-length modulation in transmitted THz beams without external stimuli. Through strategic layer design, that is, utilizing polarization-insensitive dielectric pillars in Layer 1 and polarization-anisotropic pillars in Layer 2, independent manipulation of orthogonal circular polarization states is achieved. Under circularly polarized illumination, distinct topological charges (l=0 in LCP→RCP channel, l=1 in RCP→LCP channel) are generated through spin-decoupled phase control. The rotational degree of freedom (α) between cascaded metasurfaces enables continuous focal length tuning from 9.28 mm (α=90°, NA=0.54) to 3.22 mm (α=240°, NA=0.88), while maintaining simulation accuracy with a mean APE of 25.2% for focal length and 15% for NA (based on comparison between theoretical design and simulation), thereby demonstrating a dynamically reconfigurable focusing paradigm that exhibits consistent trends with theoretical expectations.

To further demonstrate the versatility of rotational Moiré engineering, we extend this strategy to linear polarization control in Moiré device 2. Numerical simulations and experiments confirm its ability to generate distinct topological charges (l=1 and l=0) in co-polarized transmission channels under x-LP and y-LP illumination through propagation phase modulation. Experimental validation confirms the device’s dynamic focusing capabilities, achieving a continuous focal length tuning from 8.42 mm to 3.11 mm, which directly governs the corresponding NA enhancement from 0.54 to 0.88, while preserving measurement accuracy with APE of less than 5.9% and 3% for focal length and NA, respectively. Measured focal efficiencies exceeding 15% underscore the adaptability of Moiré phase engineering across polarization bases.

Collectively, these devices exemplify a unified design philosophy, leveraging interlayer rotation to reconfigure wavefronts without external stimuli. Device 1 prioritizes polarization-selective functionality for chiral light-matter interactions, while device 2 emphasizes compatibility with conventional linear polarization systems. This dual-device approach validates the broad applicability of Moiré engineering, laying the groundwork for future applications such as adaptive aberration correction, biomedical imaging, and multi-dimensional particle manipulation.