Metasurfaces are promising candidates for compact and versatile polarimetry. However, the highly dispersive nature of metasurfaces limits metasurface-based polarimetric devices to single-wavelength operation with narrow bandwidths. In this study, we employ a multi-target optimization method to realize, both theoretically and experimentally, a full-Stokes metasurface grating for dual-wavelength (1310 and 1550 nm) polarimetry. The metasurface grating exhibited high-level polarization efficiencies of 65.89% and 64.78% at the respective wavelengths and a notably low degree of polarization errors for fully polarized light detection (<0.1). Our work provides a solid foundation for future development of multi-wavelength/broadband polarimetric platforms with enhanced performance and broader applicability.
【AIGC One Sentence Reading】:We developed a full-Stokes metasurface grating for dual-wavelength polarimetry, achieving high efficiency and low errors.
【AIGC Short Abstract】:This study demonstrates a full-Stokes metasurface grating for dual-wavelength polarimetry at 1310 and 1550 nm, achieved through multi-target optimization. The device shows high polarization efficiencies and low error rates, laying a foundation for multi-wavelength/broadband polarimetric platforms with improved performance.
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High-precision polarimetry can not only improve additional valuable information acquisition, but also significantly enhances the target object identification. Full-Stokes polarimetry, a key technique for mapping polarization states across a scene, has found widespread applications in remote sensing[1], optical communication[2], medical diagnostics[3], etc. Conventional polarization measurement techniques[4–6] typically rely on bulky, discrete optical elements, such as polarizers and waveplates[7,8]. These systems suffer from high costs, large and complex systems, multiple measurements, and limited spatial or temporal resolution, impeding their applications in practical polarization-related optics[9,10]. Thus, the development of compact, efficient, and integrable polarization detectors is paramount to meet the growing demand for miniaturization and large-scale integration in on-chip optical architectures.
Metasurfaces, a new paradigm in free-space optics, are two-dimensional nanostructured interfaces that manipulate optical wavefronts at the subwavelength scale[11–13], enabling the fabrication of ultrathin and lightweight planar optical devices for light polarization processing and detection[14–20]. Therefore, the emergence of metasurfaces provides a new integrated platform to generate and analyze the polarized light in a more flexible manner[21–25]. Specifically, recent dielectric metasurfaces including metalenses[26–28] and metasurface gratings[29] with multifunctional responses have been credited for their high efficiency on light manipulation[30], enabling intricate and versatile applications such as polarization-dependent multiplexing[27,31–33], multichannel polarization control[34], holographic imaging[35,36], and optical information encryption[37,38]. However, the inherent bandwidth limitations and fixed wave manipulation hinder the widespread deployment of broadband functional polarimetric metasurfaces, which restricts the degree of freedom, information capacity, and system integration required for advanced polarization analysis[39,40]. Despite some progress in achieving polarization manipulation at two or more distinct wavelengths[26,39,41], the realization of broadband polarimeters remains elusive due to chromatic-aberration-induced polarization cross-talks. (Table S1 in the Supplement 1 summarizes and compares single/multi-wavelength polarimetry metasurfaces.) While efforts have been devoted to reducing chromatic dispersion in metalenses for wide bandwidth applications[42,43], the systematic study of chromatic aberration compensation in metasurface gratings is conspicuously lacking.
Metasurface grating, as a promising component for robust, cost-efficient, and integrated polarimetry[44–47], diffracts incident light into multiple orders encoded with polarization information. When subjected to full-Stokes vector analysis, these orders enable the determination of the incident light’s polarization state. Unlike previous polarization metasurfaces that rely on interleaved detection areas[29,48,49], metasurface gratings offer a single-layer approach to detect the polarization states in a more compact and straightforward manner[22,47,50]. To achieve multi-wavelength or broadband polarimetry metasurface gratings, effective suppression or manipulation of chromatic dispersion is critical. This poses a design challenge of ensuring consistent polarization state measurements across different wavelengths while maintaining high performance in terms of both efficiency and measurement precision.
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In this paper, we present a metasurface grating that synchronously achieves high-accuracy full-Stokes polarimetry at 1310 and 1550 nm, opening new avenues for the development of multi-wavelength/broadband metasurface grating polarimeters. Using a multi-target optimization process, we designed a metasurface grating that directed two wavelengths’ light into two sets of diffraction orders, with each set encoding the corresponding polarization state [Fig. 1(a)]. Experimental results suggest that our designed metasurface achieves high-accuracy simultaneous polarimetric measurements at both wavelengths, with polarization detection efficiencies up to 65.89% at 1310 nm and 64.78% at 1550 nm. Root mean square errors in the degree of polarization (DOP) are remarkably low, which are just 0.025 and 0.046 for linearly polarized light at 1310 and 1550 nm, respectively. Our demonstration paves the way for higher performance and broader functionality in simplified polarimetry and imaging systems, offering significant potential for near-infrared spectropolarimeter development across remote sensing, biomedical imaging, and industrial inspection.
Figure 1.(a) Schematic illustration of dual-wavelength (1310 and 1550 nm) imaging polarimetry using the designed metasurface grating. The bottom part shows the experimental image of the detected eight diffraction orders under illumination from 1310 and 1550 nm lights. The incident polarization is randomly chosen. (b) Schematic optimization routine for dual-wavelength (1310 and 1550 nm) polarization metasurface grating design. Unit cell of the dual wavelength metasurface grating, featuring silicon (Si) nanocuboids with an 800 nm height on the silica (SiO2) substrate. The width (Wx) and length (Wy) vary to enable independent and adjustable phase delays ϕx and ϕy for x- and y-polarized lights.
The single-wavelength metasurface grating has been designed based on the Fourier optics for polarimetric analysis through its four defined diffraction orders (, ), given the polarization states of the arbitrarily polarized incident beam[46]. For a given diffraction order of the metasurface grating, its diffraction angle is governed by the wavelength, which inspires the development of the dual-wavelength metasurface grating for polarization detection. Considering the crucial role of polarization detection in the near-infrared region[51] and the discriminability of the diffraction orders at different wavelengths, we chose 1310 and 1550 nm as two working wavelengths. Figure 1(a) shows the schematic illustration of the dual-wavelength polarimetry. When unknown polarized lights (whether fully or partially polarized light) at 1310 and 1550 nm illuminate the metasurface grating simultaneously, they will split into four diffracted orders for each wavelength, yielding a total of eight diffraction orders. The diffraction order with the larger angle corresponds to 1550 nm, and the smaller angle to 1310 nm. This enables synchronous determination and analysis of the polarization states of the incident light at both wavelengths.
The measurement accuracy of a metasurface grating is directly determined by its configuration[46]. Therefore, to ensure comparable accuracy across wavelengths in a dual-wavelength metasurface grating, the corresponding diffraction orders for two wavelengths should have a consistent detected polarization state. Additionally, achieving multi-wavelength or broadband polarimetry depends on the effective management of chromatic dispersion, which necessitates uniform polarization state detection across all operating wavelengths. Consequently, we propose a multi-target optimization process [Fig. 1(b)] for designing dual-wavelength metasurface gratings with high functionality, efficiency, and measurement precision.
The metasurface grating consists of a single layer of silicon (Si) nanocuboids, with varying lengths () and widths (), positioned on a silica () substrate. We start with one period metasurface grating with 20 800 nm height nanocuboids. Therefore, 40 phase parameters of () and () directions at each wavelength need to be designed. Every nanocuboid is placed within a grid with specified width and length. At the outset of the design, the influence of the nanocuboid material is ignored, and its transmittance is assumed to be one. The frequency spectrum of the -direction transmission of the grating is expressed as where is the th diffraction order. is a complex number that represents the th order Fourier coefficient of . The diffraction field distribution of the y direction can also be obtained using the above equation.
Firstly, the structural and phase parameters for two wavelengths were analyzed and simulated separately to determine each wavelength’s optimal structure for polarization detection. Random phase profiles , at 1310 nm and , at 1550 nm are generated. The overall efficiency of each diffracted order is calculated by
Designing a metasurface grating with four polarization detection channels requires establishing phase and amplitude constraint conditions for the diffracted wave at each order[46], which facilitates the preliminary design and control of the phase parameters and . When the Jones matrix is , the corresponding constraint conditions are calculated by
To ensure high polarization detection efficiency, the total energy of the diffracted beam should be concentrated as much as possible and distributed evenly among the four diffraction orders.
Before processing multi-target optimization of the phase, a parameter library is generated by the finite-difference time domain (FDTD) simulation, which reveals the relation of to the lengths and widths of the nanocuboid. The optimal nanocuboid structure, with ideal phase and transmission profiles at 1310 and 1550 nm, can be determined from the simulation results from Figs. 2 and S1 in the Supplement 1. The phase spans a range from to , and the majority of the parameter spaces have a high transmittance.
Figure 2.Simulated phase shift for x-polarized light as a function of the length (Wy) and width (Wx) of the nanocuboid at the wavelength of 1310 (a) and 1550 nm (b). Simulated transmission amplitude |tx|2 for x-polarized light as a function of the length (Wy) and width (Wx) of the nanocuboid at the wavelength of 1310 (c) and 1550 nm (d).
To screen out structures with required phase profiles for both 1310 and 1550 nm, a dual-wavelength figure of merit [Eq. (5)] is defined, in what we refer to as a multi-target optimization: where is the averaged transmittance of the total nanocuboid structures; , and , are optimized phase values of 1310 and 1550 nm from the first optimization. A global search in the parameter library is applied to minimize the ε for the identification of all dual-wavelength metasurface grating geometries , while simultaneously a constraint condition aiming to maximize the similarity of polarization detection performance across all wavelengths is taken into consideration. The transmittance is expressed as
By incorporating the multi-objective balancing procedure, flexible and comprehensive dual/multi-wavelength designs can be achieved. The final designed dual-wavelength metasurface grating generates four polarization states on and orders with equalized intensities under 45° linearly polarized incident light, aiming to approximate a tetrahedral configuration on the Poincaré sphere and thus maximize polarization detection precision. The final phase and structure parameters are given in Table S2 in the Supplement 1.
Once the design parameters are obtained, we simulate the whole grating structure in the FDTD to verify whether the polarization states of the four diffracted orders align with our design. As shown in Figs. 2(a)–2(d) and S1(a)–S1(d) in the Supplement 1, for one pillar structure, the phase of most of the geometries along -polarization ranges from to , and its transmission is high as desired. Figures S1(e) and S1(f) in the Supplement 1 depict the theoretical (dashed lines) and numerical optimization (solid lines) results. While the 1310 and 1550 nm outcomes are not perfect, they closely match the intended polarization states, and the performance of the two wavelengths shows minimal difference.
2.2. Metasurface polarimetric results
Silicon was chosen as the material for fabricating the near-infrared metasurface grating due to its high refractive index, low absorption loss, and compatibility with commercial image sensors. Figure 3 shows the optical and scanning electron microscope images of the designed metasurface. The detailed fabrication process is given in the Supplement 1. Due to the design principle, the metasurface grating functions independently of the material platform or wavelength regime; therefore, the absolute efficiency, i.e., transmission of the metasurface grating, is not a key consideration. Here, the polarization detection efficiencies of the metasurface grating are quantified by the fraction of incident power diffracted into the four designed orders (power as fraction of incident power) and the fraction of the total transmitted power distributed among those orders (power as a fraction of all orders)[46]. Simulated and experimental efficiencies of the metasurface grating at each wavelength are listed in Table S3 in the Supplement 1. It reveals that, for power transmitted to all orders at 1310 and 1550 nm, 65.89% light and 64.78% light are diffracted into the four designed orders, manifesting sufficient power for polarization detection at both wavelengths. Meanwhile, the power distribution across these four orders at each wavelength, as a constraint condition of the optimization scheme, is approximately uniform, with experimental performance exceeding simulated values. Detailed discussions are available in the Supplement 1.
Figure 3.(a) Optical image of the fabricated metasurface grating sample captured by a 20× microscope. (b) Scanning electron microscope (SEM) images of the fabricated metasurface grating sample.
When an unknown polarized light is incident on our designed analyzer, its intensity will be modulated by the four polarization-sensitive diffraction orders of the metasurface grating. By measuring the intensity of the transmitted light, the polarization state of the incident light can be determined using the following equation: where is a instrument matrix, with each row representing one of the four polarization diffraction orders of the metasurface grating. refers to the Stokes vector of the light incident on the metasurface grating, which represents the polarization state to be detected. is a column vector referring to the intensities of the four diffraction orders. When paired with imaging optics (i.e., lens sets and camera), the designed metasurface grating functions as a full Stokes polarimeter. Therefore, the Stokes vector of any incident beam can be determined from and the calculated intensities from the camera. is measured by the instrument calibration process. Details are discussed in the Supplement 1.
After the calibration, we first verify the fully polarized light detection ability of our designed dual-wavelength metasurface grating (Fig. S2 in the Supplement 1). Optical setups are discussed in the Supplement 1. When measuring the linearly polarized light, the half waveplate (HWP) is rotated from 0° to 90° with 2.5° intervals, i.e., changing the linear polarization state every 5°. For elliptically polarized light detection, the quarter waveplate (QWP) is rotated every 5° from 0° to 180°. Finally, the incident light Stokes vector can be recovered by Eq. (7). Every round of polarization detection was done three times.
Based on the calculated Stokes parameters, we use the degree of polarization () and azimuth [] to evaluate the performance of the metasurface grating on linearly polarized light detection. Figures 4(a) and 4(b) depict the measured values from the metasurface polarimeter, with the ideal correspondence line shown in gray. Accordingly, the mean absolute error () for the DOP at 1310 nm is within 0.04 and within 0.09 at 1550 nm [Fig. 4(c)]. Their corresponding root-mean-square errors (RMSEs) are 0.025 (1310 nm) and 0.046 (1550 nm), respectively. The MAE of azimuth, as seen in Fig. 4(d), is less than 1.0 for 1310 nm and 1.65 for 1550 nm, while the RMSEs are 0.42 and 0.77, respectively.
Figure 4.Linear polarization detection experimental results of DOP (a) and azimuth (b). Gray lines indicate the theoretical values of DOP and azimuth. Linear polarization detection mean absolute errors of DOP (c) and azimuth (d) at both 1310 nm (green spots) and 1550 nm (red spots). The shaded areas represent the error range (green for 1310 nm, red for 1550 nm).
The measured DOP, azimuth, and ellipticity [] plotted in Figs. 5(a)–5(c) are used to evaluate the elliptical polarization detection. Figures 5(d)–5(f) present the MAEs for the DOP, azimuth, and ellipticity, which range from 0.002 to 0.063, 0.21° to 9.50°, and 0.127° to 8.55° at 1310 nm, and from 0.026 to 0.078, 0.004° to 6.93°, and 0.075° to 6.352° at 1550 nm. The corresponding RMSE values at 1310 nm are 0.038, 4.30, and 2.80, and at 1550 nm are 0.06, 3.48, and 6.23. We observed that, as the polarization state of the incident light approached near circular polarization (), the measured azimuth and ellipticity values exhibited notable discrepancies from theoretical predictions. These deviations can likely be attributed to the non-ideal characteristics of our generated circular polarized light in the lab.
Figure 5.Circular polarization detection experimental results of DOP (a), azimuth (b), and ellipticity (c). Gray lines indicate the theoretical values of DOP, azimuth, and ellipticity. Circular polarization detection mean absolute errors of DOP (d), azimuth (e), and ellipticity (f) at both 1310 nm (green spots) and 1550 nm (red spots). The shaded areas indicate the error range, with green indicating 1310 nm and red indicating 1550 nm.
Given the importance of DOP in polarization detection evaluation, it is essential to study the performance of the dual-wavelength metasurface grating across a range of DOP values, i.e., partially polarized light measurement. A Mach-Zehnder-interferometer-based optical system shown in Fig. S2 in the Supplement 1 is established to produce partially polarized light[52]. Details are discussed in the Supplement 1.
During the measurement, the angle of the HWP is changed from 0° to 180° in 1.5° intervals. As shown in Fig. 6, a metasurface grating steered full DOP measurement at both 1310 and 1550 nm is achieved, with the DOP as a function of the θ aligning well with the theoretical relation. For 1310 nm, a DOP range of 0.024 to 1.009 is observed, while for 1550 nm, a DOP range of 0.018 to 1.106 is recorded. Both ranges are close to the ideal DOP values, confirming the effectiveness of our designed metasurface grating on dual-wavelength polarimetry. In alignment with the blue and orange images presented in Fig. 6, the calculated RMSEs of the minimum DOP for the 45° and 135° linear polarization are 0.025 at 1310 nm and 0.040 at 1550 nm, with a theoretical value of zero. These errors are comparable to the performance of previously reported single-wavelength metasurface gratings[46]. The slight difference in polarimetric analysis is due to the structural selection during the design process, which prioritized dual-wavelength functionality over optimal polarization detection performance. Detailed discussion about the errors can be seen in the Supplement 1.
Figure 6.DOP versus incident linear polarization orientation: theoretical (gray solid lines) and experimental data (green spots for 1310 nm and red spots for 1550 nm). The blue figure depicts the 45° linear polarizer; minimum measured DOP values for 1310 and 1550 nm are 0.024 and 0.055, respectively. The orange figure depicts the 45° linear polarizer; minimum measured DOP values for 1310 and 1550 nm are 0.026 and 0.0018, respectively.
In summary, the above experimental results confirm that our designed metasurface grating can work as a dual-wavelength polarimeter effectively. Although the polarization state detection abilities vary slightly between the wavelengths, the differences are not significant.
3. Conclusion
In this work, we have successfully designed and demonstrated a full-Stokes metasurface grating for high-precision dual-wavelength (1310 and 1550 nm) polarimetry. Compared with a single-wavelength metasurface grating, the fully polarized and partially polarized light detection accuracies are comparable: 1) for fully polarized light, the MAEs for the DOP at two wavelengths are less than 0.1; 2) for partially polarized light, the DOP ranges are 0.024–1.009 at 1310 nm and 0.018–1.106 at 1550 nm. This metasurface grating polarimeter is a robust, compact, and adaptable platform, offering increased capacity and flexibility for potential applications including remote sensing, bioimaging, industrial inspection, and optical communication.