Polarization is a fundamental property of light that describes the orientation of the oscillating electric field vector. It plays a critical role in scientific research and various optical technologies [1–4]. Accurately determining the polarization state of light is essential for applications such as remote sensing [5,6], quantum information [7], machine vision [8], and biomedical diagnostics [9,10]. Conventional polarization detection methods are typically classified into two main categories: time-division and spatial-division. The time-division approach sequentially analyzes different polarization components [11–13], thereby limiting real-time detection capabilities. The spatial-division method typically employs discrete optical devices, such as polarizers, beam splitters, and waveplates, to separate different polarization components into distinct optical paths. Multiple detectors or distinct regions of a single detector are then used to simultaneously capture the intensity from each path [14–16]. All of these techniques require a set of components that inevitably increases the bulk and complexity of the systems, thereby hindering the development of miniature and compact polarimeters.

As artificial two-dimensional electromagnetic materials, metasurfaces provide a versatile platform to effectively manipulate the amplitude, phase, wavelength, and polarization of light [17–24]. To date, numerous types of metasurface-based optical devices have been demonstrated, including metalenses [25,26], polarization converters [27–29], holograms [30], and structured optical field generators [31–34]. Additionally, there has been significant interest in metasurface-enabled polarimeters, and several innovative metasurface-based platforms for polarization detection have been proposed [35–46]. Despite these exciting results, the developed polarimeters still face several challenges. Current research primarily focuses on developing polarization-dependent filter arrays [35–39], meta-gratings [40,41], or metalens arrays [42–45], which capture the intensity of polarization components along different optical paths and enable the measurement of Stokes parameters. However, these spatial-division design methods encounter issues of crosstalk between different optical paths. Furthermore, variations in transmittance or diffraction efficiency across the optical paths hinder their ability to achieve high-accuracy polarization analysis. Although there have been several studies focusing on the realization of crosstalk-free polarization detection, they generally do not have full polarization measurement capability and operate in a narrow bandwidth [46–50]. Overall, a metrology method for high-accuracy and broadband full-Stokes polarization detection, which avoids crosstalk, is highly desired and remains elusive so far.

In this work, we propose a novel polarization detection method. Our strategy is based on real-time analysis of a vector beam whose polarization profile varies sensitively and corresponds one-to-one with the incident polarization, thus avoiding crosstalk and enabling high-accuracy detection without any calibration process. As a proof of concept, a geometric metasurface-based grafted perfect vector vortex beam (GPVVB) generator within silica glass is fabricated through femtosecond-laser-induced birefringence. The experimentally measured Stokes parameters have an average relative error of 2.25%. Moreover, the ability to detect the vector beam polarization profile is experimentally verified using a GPVVB-generating array. The metasurface GPVVB generator enables a high transmittance exceeding 95% and a broad operating wavelength range from 450 to 1100 nm, with a relative bandwidth of 83.87%. Our research showcases a practical approach to implementing high-accuracy, broadband, and real-time full-Stokes polarization detection based on vector beams. These advancements have the potential to revolutionize the field of polarization detection and vector optical field polarization profile detection across various applications, such as quantum-based optical computing, optical communication, and material characterization.

Figure 1 illustrates the schematic of our proposed vector-beam-based polarization detection strategy. High-accuracy and real-time polarization detection is achieved by constructing vector beams with a high degree of correspondence and a highly sensitive polarization response. As a demonstration, we designed a metasurface-based GPVVB generator to verify the feasibility of the approach. Here, we use the modulated intensity profile (obtained from the vector beam passing through an analyzer), which can be directly detected by the CCD detector, to reflect the GPVVB polarization profile.

In order to analyze the one-to-one correspondence between polarization profiles and incident polarization states, we start with the GPVVB generation. GPVVBs are created by the combination of two mutually orthogonal circularly polarized grafted perfect vortex beams (GPVBs), expressed as [31] EGPVVB=EReiφ0|RGPVB⟩+ELe−iφ0|LGPVB⟩,(1)where |RGPVB⟩=eiφgspiralRexp(−(r−R)2ω2)[1−i]and |LGPVB⟩=e−iφgspiralLexp(−(r−R)2ω2)[1i]are the right circularly polarized (RCP) and left circularly polarized (LCP) GPVBs, respectively. ER and EL are the RCP and LCP amplitudes, respectively. ω is the waist of the Gaussian beam in the focal plane, φ0 is the initial phase, and R represents the radius of the GPVBs. The φgspiralR and φgspiralL are the grafted spiral phases for RCP and LCP, respectively. The φgspiralL(R) are governed as φgspiralL(R)(r,θ)=∑j=1Nrect(Nθ2π−N+12+j)lL(R)jθ,(2)where N is the number of topological charges (TCs) used for grafting, and lL(R)j are the TCs.

Arbitrarily polarized light can be produced by modulating a combination of a line polarizer (LP) and a quarter-wave plate (QWP), denoted as [31] E=22[sinα−isin(α+2β)cosα−icos(α+2β)],(3)where α is the angle between the transmission axis of LP and the horizontal direction, and β is the angle between the fast axis of QWP and the horizontal direction. Under the illumination of arbitrarily polarized light, the electric field profile of GPVVB after passing through the analyzer (a linear polarizer whose transmission axis is fixed along the vertical direction) can be given as EGPVVB−A(r,θ)=22exp(−(r−R)2ω2)eilpjθ(cos(pjθ−α)−icos(pjθ−(α+2β)))[01],(4)where lpj=lRj+lLj2 and pj=lRj−lLj2 are topological Pancharatnam charge and polarization order to determine the phase profile and polarization profile, respectively. According to Eq. (4), when the TCs lRj and lLj are fixed, the profile of EGPVVB−A is related to the angle of LP and QWP. In other words, the intensity profile is related to the polarization state of the incident light.

In addition, GPVVBs exhibit uneven light ring intensity at the grafting joints. This is the result of the interference between the “scion” and “rootstock” (the concepts from plant grafting). The intensity has a rotation with respect to the spiral phase due to the combined effect of both azimuthal energy flow and radial energy flow [51,52]. We also discovered that the intensity mutations on the light ring are opposite with orthogonal circularly polarized incidence, as indicated in Fig. 2(a). For comparison, the non-grafted perfect vector vortex beam (PVVB) has nearly identical intensity profiles at orthogonal circularly polarized incidence, which has no capability to distinguish the spin. For quantitative evaluation, we further extract the intensity-angle profiles on the GPVVB and PVVB light ring. GPVVB has modulated intensity distribution corresponding one-to-one with the incident light polarization state owing to the intensity mutation caused by grafting, providing a new platform for polarization detection.

As a proof of concept, N=2 was used for grafting to demonstrate polarization detection. The two TCs were selected as 4 and −2, and the θ ranges of these two TCs were 0°–180° and 180°–360°, respectively. This is the result of combining the intensity fluctuation magnitude induced by the grafting and the polarization detection sensitivity (see Appendix A for details). In Fig. 2(b), the principle of the generated GPVVB for polarization detection is depicted. By extracting the intensity-angle profile at r=R and using the intensity valleys (1–4) and grafting joints (5 and 6) as the feature points, polarization detection can be achieved by resolving their positions and corresponding values.

To be specific, the transmission axis angle of the LP affects the angle position of the valleys, while the relative angle of the LP transmission axis and the QWP fast axis affects the intensity values of the valleys. The relation between the angle positions of the characteristic valleys 1–4 and the LP transmission axis (α, changing from −90° to 90°) can be expressed as follows: {θ1=90°+12α,θ2=225°−14α,θ3=270°−14α,θ4=315°−14α.(5)

To simplify the data processing process, the normalized intensities of characteristic valleys 1–4 are fitted by using a least square method: Ik=0.06573exp(|α−β|18.22121)−0.07996,(6)where the interval of variation of |α−β| is 0° to 45°, and k=1–4. On this basis, the intensity relationship between grafting joints 5 and 6 is used to determine the magnitude of LCP and RCP incident light, that is, to uniquely determine αk and βk. To minimize measurement error, the mean values αmean and βmean are taken as the final results for calculating the polarization states.

Due to the unique capability of flexible manipulation of light, a metasurface is able to integrate multiple functions of different optical elements into a monolithic device [33]. The phase profile of a GPVB generator in polar coordinates can be expressed as ϕGPVB(r,θ)=φgspiral(r,θ)+φaxion(r,θ)+φlens(r,θ),(7)where φaxion(r,θ)=−2π·NA·rλand φlens(r,θ)=−π·r2λ·fare the phase profiles of an axion and Fourier transform lens, respectively. NA is the numerical aperture of the axicon, λ is the operating wavelength, and f is the focal length of the Fourier transform lens. The phase design of GPVBs for LCP and RCP light is shown in Fig. 3(a). Here, the complex-amplitude superposition method is used to design the geometric metasurface for GPVVB generation; the phase profile is given by ϕGPVVB=arg(exp(iϕRGPVB)+exp(iϕLGPVB)),(8)where ϕRGPVB and ϕLGPVB are phase profiles to generate GPVBs of RCP and LCP, respectively. The designed geometric phase metasurface-based GPVVB generator has a diameter D=3mm, a focal length f=100mm, and numerical aperture NA=0.01 at the center wavelength λ=532nm. The phase profile of the metasurface GPVVB generator is showcased in Fig. 3(b).

The metasurface is fabricated using femtosecond-laser-induced birefringence within silica glass (7980, Corning) using a homemade processing system. The femtosecond laser (wavelength 1030 nm, pulse duration 450 fs) is generated by a Yb-doped potassium gadolinium tungstate-based mode-locked regenerative amplified femtosecond laser system (PH2-20, Light Conversion Ltd.). An objective lens (NA=0.26) focuses the femtosecond laser beam into the silica glass. The geometric metasurface exhibiting half-wave retardance at 532 nm is fabricated by a line-by-line laser direct writing process controlled by the movement of a 3D stage, while the line spacing is set at 1 μm. The unit cell of the fabricated metasurface is an elliptical nanopore array with the same orientation. Figure 3(d) reveals the SEM images of nanopores induced by femtosecond laser irradiation with four different polarization directions. Notably, the major axes of the nanopores consistently align perpendicular to the polarization direction of the femtosecond laser, as indicated by the white arrow. Based on this, the polarization direction of the femtosecond laser was dynamically controlled in real-time during the entire fabricating process to achieve the desired distribution of nanopore rotation angles, which is governed by the phase profile of the designed metasurface. For the geometric metasurface, the phase modulation capability arises from the direction-controllable elliptical nanopores. The fast-axis angle profile is measured using a commercial birefringence imaging microscope (Exicor MicroImagerTM, Hinds Instruments), as shown in Fig. 3(c). The value of the measured fast-axis angle is half of the value of the designed phase, which is a direct consequence of adhering to the geometric phase principle.

The transmittance of the fabricated metasurface is over 95% in the wavelength range of 450–1100 nm, which is characterized by using a UV-VIS-NIR spectrophotometer (LAMBDA 1050, PerkinElmer), as depicted in Fig. 3(e). We also theoretically calculated the transmission spectrum of nanopores with different diameters. The theoretical and measured results show good agreement (more details can be seen in Appendix B). A photograph of the fabricated device is shown in the inset of Fig. 3(e). Additionally, we assessed the laser-induced damage threshold (LIDT) of the fabricated metasurface, showing an LIDT up to 68J/cm2 (at 1064 nm, 6 ns). This indicates that our proposed method has the capability for polarization detection of high-power beams. The detailed LIDT test methodology and results are shown in our previous work [53].

We first validate the high-accuracy and broadband polarization detection ability with different polarization incidences. Figure 4(a) presents the experimental setup. The laser beam emitted from a supercontinuum laser (SuperK EVO, NKT Photonics) was passed sequentially through an LP and a QWP to generate light of arbitrary polarization, and then expanded by a beam expander. The GPVVB generated with the metasurface is imaged on the CCD after passing through an analyzer. The incident polarization state can be solved in real-time from the light field profile detected by the CCD.

Figure 4(b) demonstrates the simulated and experimental light field profile results for six polarizations states, including two orthogonal linear polarizations [(S1,S2,S3)=(1,0,0), and (S1,S2,S3)=(−1,0,0)], two orthogonal circular polarizations [(S1,S2,S3)=(0,0,1), and (S1,S2,S3)=(0,0,−1)], and two elliptical polarizations [(S1,S2,S3)=(0.866, 0,−0.5), and (S1,S2,S3)=(0.866,0,0.5)] at a wavelength of 532 nm. By extracting the intensity-angle profile of the GPVVB ring, it is observed that the experimental and simulated results show a high degree of consistency, as shown in Fig. 4(c). For linear polarizations, the intensity of the valleys is almost zero, and polarization detection relies on the angular positions of the valleys. For circularly polarized light, polarization detection is mainly based on the intensity fluctuations at the grafting joints. Although the experimentally measured intensity-angle profiles are not smooth enough, the intensities at the grafting joints perfectly match the simulation results and do not affect the polarization detection results since there are no regular valleys in the curves. Specifically, for elliptical polarizations, the situation is more complicated. Although two elliptical polarizations correspond to light intensity profiles with almost identical valley positions and values, the intensity magnitude relationships at the grafting joints are distinctly different, suggesting that they have opposite S3. In detail, for elliptically polarized state (S1,S2,S3)=(0.866,0,−0.5), the normalized intensities at grafting points 5 and 6 are 0.97 and 0.83, respectively; however, for elliptically polarized state (S1,S2,S3)=(0.866,0,0.5), the normalized intensities at grafting points 5 and 6 are 0.8 and 0.97, respectively. The experimental results for three representative polarization states illustrate the feasibility of our proposed polarization detection approach.

In order to characterize the precision of the measurement, we use a commercial polarimeter (PAX1000, Thorlabs) as a comparison. The Stokes parameters of incident beams measured by our method as well as by the commercial polarimeter are shown in Fig. 4(d). Define the relative error of the Stokes parameters as σS=(S1ref−S1exp)2+(S2ref−S2exp)2+(S2ref−S2exp)22S0ref.(9)

The average measurement relative error of the Stokes parameters is 2.25% for 31 polarization states. More light field profile results of other polarization states and detailed relative error calculations are shown in Appendix C.

By taking advantage of the broadband characteristic of the geometric phase and the high transmittance of the femtosecond-laser-induced birefringence nanopores, the constructed system is capable of achieving polarization detection at a broad operating wavelength range from 450 to 1100 nm. Figure 5(a) showcases the experimental light intensity profile results at different wavelengths (473 nm, 633 nm, 808 nm, and 1064 nm). The experimentally measured light intensity profiles are essentially the same when the incident light has distinct wavelengths but the same polarization state, as illustrated in Fig. 5(b). For vertical line polarized incidence at different wavelengths, the positions of intensity valleys 1–4 in the extracted GPVVB intensity-angle profiles are nearly consistent. For elliptical polarization at different wavelengths, the positions and intensity values of the intensity valleys 1–4, as well as the intensity values of grafting points 5 and 6, all remain almost identical. This indicates that our proposed method is capable of broadband high-accuracy polarization detection. The central spots in the 808 and 1064 nm intensity profiles are due to the reduced conversion efficiency when deviating from the design center wavelength significantly. However, this has almost no effect on polarization detection results. A comparison of the detection accuracy and operating bandwidth of state-of-the-art polarization detection methods is shown in Appendix D.

Although the demonstrations are conducted within 450–1100 nm, this bandwidth is not limited by our fabricated metasurface but by the light source and CCD used in the experiment. In fact, the operating wavelength range can be further extended. Moreover, our approach is compatible with other wavebands, including ultraviolet and infrared. We also note that the polarization conversion efficiency of our designed metasurface is upper bounded by 50% due to the conjugate symmetry of the geometric phase [54]. However, this is not intrinsically limited by our proposed vector-beam-based polarization detection method. By using other design approaches, such as geometric phase and propagation phase co-modulation [55,56], our approach can theoretically achieve 100% energy utilization, allowing for further improvements in detection accuracy and low-light-level detection capability.

In order to demonstrate the capability of detecting the polarization profile of vector beams, a metasurface polarization detection array was constructed by leveraging the integrable property of the metasurface. The dimension of each detection pixel is set to D=150μm with f=500μm and NA=0.1. In experiments, the linear polarization laser with a wavelength of 532 nm was passed through a commercially available S-waveplate (Workshop of Photonics) and formed a radial vector beam. Then this vector beam illuminated the metasurface array and was focused to the image plane in each detection pixel. An objective (10×, NA=0.25) accompanied by a linear polarization analyzer was further utilized to transfer the image to a CCD detector. Figures 6(a) and 6(b) show the simulated and experimental intensity profiles of 5×5 detection pixels, respectively. From these raw data, we derive the polarization profile according to Eq. (5). The results are depicted in Fig. 6(c), showing agreement between simulation and experiments. The black arrows correspond to the theoretical values, while the red arrows correspond to the experimental values. Insufficient sampling would result in inaccuracy or even invalidation of the measurements, which limits further reductions in the diameter of a single detection pixel. The utilization of neural networks and deep learning presents potential solutions to these challenges, enabling higher accuracy and resolution in polarization detection with advantages of speed and robustness [48,57,58].

In summary, we have demonstrated a novel platform for high-accuracy, broadband, and real-time polarization detection. This innovative approach is achieved by analyzing the polarization profile of a vector beam. To experimentally validate this method, a metasurface-based GPVVB generator was fabricated in silica glass using femtosecond-laser-induced birefringence. The capability for broadband and polarization profile detection has been experimentally demonstrated, proving the excellent performance of our proposed approach. The average relative error for the 31 polarization states is 2.25%, while the relative working bandwidth is 83.87%. Furthermore, the fabricated metasurface exhibits a high LIDT of 68J/cm2 (at 1064 nm, 6 ns), indicating that our method has the potential to be used for polarization detection of high-power beams. Given these advantages, our polarization detection platform is expected to become a leading candidate for future applications.