Metasurfaces are artificial two-dimensional (2D) structures composed of micro- and nanoscale patterns. They enable precise manipulation of optical fields at the subwavelength scale, including amplitude, phase, and polarization^[1]. Compared with traditional optical devices, metasurfaces are easier to integrate and capable of achieving broadband and high-efficiency polarization control through customized designs^[2,3]. In particular, the mechanisms of polarization control in metasurfaces combine geometric, propagation, and resonant phases to efficiently modulate polarization states. These features highlight their significant potential in applications such as holographic displays^[4], quantum communication^[5], and nonlinear optics^[6].

In recent years, optical-fiber-integrated metasurfaces have become an important branch of metasurface technology. The advent of “Lab-on-Fiber” technology has enabled the integration of micro- and nano-structures on the sides^[7], ends^[8,9], or insides^[10] of an optical fiber by technologies including laser direct writing, focused ion beams, electron beam lithography, and three-dimensional (3D) printing, facilitating the miniaturization and integration of all-fiber devices. Optical-fiber-integrated metasurfaces combine the flexibility, portability, and efficient transmission characteristics of optical fibers, demonstrating potential applications in complex optical field manipulation^[11], micro-nano sensing^[12], and fiber communication systems^[13]. They also enable the development of various functional devices, such as meta-tips^[14], metalenses^[15], and wavefront shaping elements^[16], paving the way for innovative applications in holographic displays, quantum optics, and communication technologies. Like the bulk optical systems, polarization control can be easily realized using polarization-maintaining fibers. Metasurfaces are typically introduced to effectively modulate one or more polarization modes in optical fibers. However, the polarization control based on the fiber-integrated metasurfaces still focuses on static wavefront shaping, fixed mode conversion, or single-state polarization manipulation without real-time tunability^[17,18], and the exploration of dynamic polarization is a major challenge.

In this work, we propose an optical-fiber-integrated dynamic polarization metasurface (DP-MS) for polarization-driven focal spot rotation. The DP-MS based on photonic spin-orbit interactions is used to decouple orthogonal polarization states and control phase differences. Thereby, dynamic polarization modulation is achieved, allowing the focal spots to rotate stably and precisely in response to variations in the polarization direction of the fundamental mode in the large mode fiber (LMF). Additionally, the introduction of a vortex phase makes the focal spot rotate both in phase and in intensity. Furthermore, combining the signal function for phase profile allows customizable and simultaneous rotation of multi-focal spots. The device improves dynamic polarization control ability and has high integration, miniaturization, and flexibility, which provides a new idea for its potential applications in the fields of optical manipulation, polarization detection, and optical micro-machining.

Figure 1 shows the schematic of the proposed optical-fiber-integrated DP-MS. An all-dielectric single-layer metasurface composed of an array of amorphous silicon (α-Si) nanobricks was designed for integration at the end of the LMF. In particular, the LMF core (radius: 29 µm, refractive index: 1.454) is immediately surrounded by a high-index annular layer (annular layer spacing d=2μm, refractive index: 1.458), followed by an outer cladding (n=1.45), as shown in the inset of Fig. 1. As a result, the fundamental mode of LMF, which is a linearly polarized quasi-plane wave (QPW) with a flat mode field distribution at a wavelength of 1.55 µm, is efficiently delivered to the metasurface for optimal performance. When the polarization direction of QPW is PD1, the DP-MS converts it into a focused beam, forming the focal spot FPD1. With the rotation of the angle θ1, the QPW’s polarization direction changes from PD1 to PD2, and the DP-MS generates a new focal spot FPD2. The included angle θ2 between FPD1 and FPD2 corresponds to the rotation angle θ1 of the QPW polarization directions PD1 and PD2. Due to the interaction of geometric phase and dynamic phases, the DP-MS enables independent phase modulation of orthogonal polarization states and precise control of the phase profile.

The DP-MS independently modulates the left-handed circular polarization (LCP) and right-handed circular polarization (RCP) lights to form a stable polarization-sensitive focal spot. To realize this dynamic rotational behavior, two key conditions must be satisfied: precise spatial overlap of LCP and RCP at the focal plane, ensuring constructive interference and circular symmetry of the phase profile to maintain the stability of the focal spot shape during rotation. The phase profile of a metasurface can be expressed as ϕ(x,y)=2πλ(f−x2+y2+f2),(1)where λ is the wavelength and f is the focal length. When a linearly polarized QPW is modulated by the DP-MS, two independent phase profiles ϕLCP(x,y) and ϕRCP(x,y) are generated. The response of the DP-MS can be described by the Jones matrix: J(x,y)=eiϕ+(x,y)|LCP⟩+eiϕ−(x,y)|RCP⟩,(2)where ϕ+(x,y) and ϕ−(x,y) represent the phase profiles corresponding to the LCP and RCP polarization states, respectively. For a single nanobrick unit cell, ϕx and ϕy describe the phase shift along two perpendicular symmetry axes (typically x and y) defined as ϕx=12[ϕ+(x,y)+ϕ−(x,y)+π] and ϕy=12[ϕ+(x,y)+ϕ−(x,y)−π]. The difference between ϕx and ϕy satisfies |ϕx−ϕy|=π; this ensures that the orthogonal polarization states independently contribute to each nanobrick unit cell.

The Pancharatnam-Berry (PB) phase introduced by the metasurface is determined by the rotation angle θ of the nanobrick unit cells and is expressed as ϕPB=2σθ, where σ=+1 for LCP and σ=−1 for RCP. The total phase profiles of the LCP and RCP are given by {ϕLCP(x,y)=ϕ(x,y)+ϕPB,ϕRCP(x,y)=ϕ(x,y)−ϕPB.(3)

The phase difference is key to ensuring stable interference: ΔϕPB=ϕLCP−ϕRCP=4θ.(4)

To meet the dynamic rotational conditions, this phase difference must equal π, leading to the optimal rotation angle θ=π/4. The target phase profile is defined as ϕtarget=(ϕLCP−ϕRCP2).(5)

Multi-focal metasurfaces play a crucial role in optical information processing, multi-channel imaging, and parallel computing. Traditional designs rely on stitching regions with different phase profiles, which lead to phase discontinuities, diffraction losses, and efficiency reduction. In this work, a signal function is added to the original phase profile to introduce a periodic phase jump, which decomposes the incident light into spatial frequency components. These components generate diffraction orders at different positions on the focal plane, forming multi-focal spots that rotate with changes in the input polarization direction. The phase profile modulated by a signal function is expressed as ϕ(x,y)=2πλ{f−[x+m(x)]2+[y+m(y)]2+f2},(6)where m(x) and m(y) are the periodic modulation functions along the x and y directions, respectively: {m(x)=A·sawtooth(2πxLx+ϕm(x))m(y)=A·sawtooth(2πxLy+ϕm(y)),(7)

Here, A is the modulation amplitude, which determines the distance between multi-focal spots. Lx and Ly are the periods of the modulation, controlling the number and positions of the multi-focal spots, while ϕm(x) and ϕm(y) are the phase offsets that adjust the starting spots of the modulation (more design details can be found in the Supplement 1, S1).

The working principle of DP-MS depends on the accurate polarization and phase control by adjusting the orientation and size of sub-wavelength nanobrick unit cells. Figures 2(a) and 2(b) illustrate the geometric parameters of a typical nanobrick unit cell, with the width W and length L both ranging from 0.15 to 0.6 µm. Using the finite-difference time-domain (FDTD) method at the wavelength of 1.55 µm, the phase shift ϕx and transmittance Tx distributions of the nanobrick unit cells were obtained (the phase shift difference between ϕx and ϕy satisfies |ϕx−ϕy|=π and transmittance Ty; see the Supplement 1, S2). These nanobrick unit cells are designed as anisotropic nanopillars with rectangular cross-sections, supporting waveguide modes with distinct refractive indices along the short and long axes. By adjusting the geometric dimensions of width W and length L, the nanobrick unit cells achieve tunable phase shift ϕx and high transmittance Tx. As shown in Figs. 2(c) and 2(d), the phase shift ϕx spans from 0 to 2π, while the transmittance Tx remains close to 100% over most parameter ranges. In this design process, we adopted the figure of merit (FoM) serving as an evaluation metric to optimize the unit cell database. The dataset was expanded from an initial 92×92 database to a 500×500 dataset, allowing for a more comprehensive analysis of the ϕx and Tx distributions, as shown in Figs. 2(e) and 2(f). The FoM is defined as the sum of squared differences between the simulated complex transmission coefficients and the targeted values for each pair of phase shifts (ϕx, ϕy) and transmittance. The optimal geometric parameters (L,W) are then selected as those corresponding to the minimum FoM value.

To realize effective polarization control in the optical-fiber-integrated device, we present three kinds of target phase profiles of DP-MS. Figure 3(a) shows the single focal spot phase profile calculated using Eqs. (1)–(5). Figure 3(b) illustrates the vortex spot design, realized by adding a vortex term lφ to Eq. (1), where l represents the topological charge and φ=arctan(y/x) denotes the azimuthal angle, generating a vortex beam with specific topological charges. Figure 3(c) presents the multi-focal phase profile generated by overlapping a signal function onto the original phase profile using Eqs. (6) and (7). The three metasurfaces mentioned above have the same focal length f=3μm, radius r=14.2μm, and numerical aperture NA=0.98. This design method is suitable for DP-MS with different numerical apertures (see the Supplement 1, S9).

Based on three types of target phase profiles, rotational polarization control of optical-fiber-integrated DP-MS was designed and demonstrated. Figure 4(a) shows the intensity distributions of LMF fundamental modes with different polarization directions. Figures 4(b)–4(d) present the three types of DP-MS that generate a single focal spot, a vortex spot, and multi-focal spots at the corresponding polarization directions in Fig. 4(a). We can find that all these focal spots exhibit elliptical profiles. As shown in Fig. 4(b), by precisely focusing the LCP and RCP at the same position on the focal plane to induce coherent interference, an elliptical-like single focal spot is formed. The rotation angle of the single focal spot is very consistent with the polarization direction of the fundamental mode. In Fig. 4(c), a vortex spot carrying orbital angular momentum is generated by adding a vortex phase. With the change of polarization direction, the vortex spot exhibits rotational characteristics in both intensity and phase, demonstrating the capability of the DP-MS to generate a vortex beam. Furthermore, this design method can be extended to other advanced beams, such as Airy beams and Bessel beams. As an extension of the single focal spot design, we propose a method of generating multi-focal spots by overlaying a signal function onto the original phase profile, as shown in Fig. 4(d). The multi-focal spots FP1 and FP2 rotate synchronously with changes in the polarization direction. The results above prove the dynamic polarization sensitivity of the DP-MS and its potential application in accurate optical field manipulation. In addition, the rotational characteristics of the focal spots are distinguishable across a broader spatial range, as demonstrated in Fig. S4 in the Supplement 1, S3.

In order to further analyze the dynamic polarization modulation of the proposed devices, we calculated the rotation angle curves of the output focal spots with polarization directions ranging from 0° to 180°, with an interval of 5°. The linearity of these curves emphasizes the precise rotation control ability of this device. Figure 5(a) shows that the single focal spot achieves remarkable linearity in its rotation angle curve, which can be attributed to the circular symmetry in the central region of the phase profile [see Fig. 3(a) and Fig. S1(a) in the Supplement 1, S1]. This symmetry effectively prevents deformation of the spot shape during rotation and maintains precise alignment between rotation angle and polarization direction. Figure 5(b) depicts the vortex spot with a reduced linearity, resulting from the vortex phase breaking circular symmetry in the central region of the phase profile [see Fig. 3(b) and Fig. S1(b) in the Supplement 1, S1], which leads to uneven intensity distribution and deviations of rotation angle. However, the varying intensity distribution of the vortex spot throughout the rotation process enables the identification of the polarization direction. Figure 5(c) shows the multi-focal spots design, and the two focal spots (FP1 and FP2) show a linear decrease due to the asymmetric phase modulation introduced by the signal function [see Fig. 3(c) and Fig. S1(d) in the Supplement 1, S1], which suppresses the specific spatial frequency, thus changing the rotation behavior. The underlying principle of these behaviors is that the phase profiles near the focal spots exhibit circular symmetry for circularly polarized light (LCP or RCP), leading to isotropic spot shapes (see the Supplement 1, S6). However, when linearly polarized light is incident, the simultaneous excitation of LCP and RCP will introduce interference, breaking the circular symmetry and creating directional modulation. This phase asymmetry near the focal spots leads to a dynamic response sensitive to the polarization direction, thus achieving accurate rotation control, so that the rotation angles of the three DP-MSs completely cover the polarization direction range.

To characterize the shape and stability of output focal spots during rotation, we calculated the full width at half-maximum (FWHM) of the major axis and minor axis of the focal spots and their ratio with the change of polarization direction. For the single focal spot, as shown in Fig. 6(a), the FWHM of the major axis shows periodic oscillations, while the FWHM of the minor axis remains stable, resulting in a consistently high FWHM ratio above 1.5. This phenomenon stems from the approximate symmetric phase profile [see Fig. 3(a)]. In Fig. 6(b), for the vortex spot, both the FWHMs of major and minor axes display more complex oscillation due to the vortex phase breaking symmetry of the phase profile [see Fig. 3(b)], leading to uneven intensity distributions. For FP1 and FP2 in multi-focal spots, as shown in Figs. 6(c) and 6(d), the FWHM ratio changes periodically, with a peak around 45° and a minimum around 135°, which is caused by two focal spot profiles along the 45° direction and two obvious side lobes along the 135° direction in the asymmetric phase profile [see Fig. 3(c)]. These results reveal that the global symmetry of the phase profile affects the periodic variations and stability of focal spot shapes. To further assess the performance of DP-MSs, we calculate the focusing efficiency of focal spots, as shown in Fig. S5 in the Supplement 1, S4.

In addition, multi-focal spot control can be realized by adjusting the parameters of the signal function. As shown in Figs. 7(a) and 7(b), as the amplitude A of the signal function increases, the distance between the two focal spots increases significantly. It is worth noting that the linear relationship between the distance of two focal spots and the amplitude A of sawtooth wave functions is shown in Fig. 7(c), demonstrating the control ability of the signal function for precise distance tuning. Moreover, Figs. 7(d)–7(f) show that three focal spots displaying dynamic rotational behavior are generated by overlapping sawtooth wave functions rotated at different angles [see Fig. S1(c) in the Supplement 1, S1]. This shows that if customized signal functions are applied to particle manipulation, the interaction of light and matter is enhanced. Compared with the traditional design, this method provides a periodic and continuous phase profile, reducing diffraction loss. It also allows precise control over the number, position, and distance of the focal spots, thus simplifying the design process and enhancing adaptability. It is worth noting that we further analyzed the performance of the DP-MS excited by elliptically polarized light to simulate its behavior under practical experimental conditions. As shown in Fig. S6 of the Supplement 1, S5, the DP-MS still demonstrates effective modulation capabilities under elliptical polarization.

In summary, we propose an optical-fiber-integrated DP-MS to achieve dynamic polarization modulation. The DP-MS decouples orthogonal polarization states through phase control, which allows precisely focusing LCP and RCP on the same position in the focal plane, forming an interference focal spot, breaking circular symmetry, and introducing directional modulation. This mechanism supports stable rotation behavior and dynamic polarization response. Additionally, the phase profile is optimized by overlapping signal functions to construct complex optical fields, which further enables precise control over the number, position, distance, and synchronized rotation of multi-focal spots. Simulation results confirm the feasibility of the proposed theory, showing that the three kinds of DP-MSs generate a single focal spot, a vortex spot, and multi-focal spots, all exhibiting shape stability and dynamic responses to polarization direction changes. This study promotes the transformation of polarization optics from static control to dynamic control, highlights the potential of fiber-integrated metasurfaces in polarization-sensitive applications, such as optical communication, super-resolution imaging, and sensing, and shows its prospects in beam shaping and multi-dimensional vector field manipulation.