Polarization is an important feature of light besides wavelength, amplitude, and phase. Different materials exhibit different polarization characteristics based on their intrinsic properties. By analyzing the changes in the polarization properties of light waves before and after being reflected by an object, information such as polarization angle and degree of polarization can be obtained. Compared to traditional spectrum detection techniques, polarization detection provides more target information, making it widely applied in fiber optic communication, remote imaging sensing, medical diagnosis, and military target recognition. However, traditional polarization detection systems are struggling to meet the trend of miniaturization and integration due to their large sizes and complexity. In recent years, the use of metasurfaces to generate and detect polarization has been proposed to realize fast and in-situ polarization detection for complex conditions. Metasurfaces are artificially designed arrays of subwavelength phase-shifting microstructures, and can flexibly control the polarization properties of light through design. Currently, the design and construction of metasurfaces with multifunctional and flexible polarization control capabilities have been carried out widely. However, the performance of metasurface diffraction gratings with different polarization configurations varies on polarization detection. In this paper, metasurface diffraction gratings with three different configurations are designed and fabricated by intelligent algorithm to analyze their influence on polarization detection.

An intelligent algorithm combined with a gradient descent method and simulated annealing algorithm are used to design metasurface diffraction gratings. Initially, the polarization state constraints of each diffraction order are obtained by an intermediate parameter C_n, and then the gradient descent optimization method is applied to obtain parameters that meet the preliminary phase requirements. Subsequently, to consider the influence of the device characteristics, finite-difference time-domain (FDTD) simulation is used to scan and construct an actual metasurface structure parameter database. Our metasurface design is based on a periodic array of rectangular nano-pillar unit structures with a constant height of 800 nm, using SiO₂ as the substrate and Si as the material for the top rectangular layer. The parameter database includes various dimensions of rectangular nano-pillars, their corresponding abrupt phase changes, transmittance, and other parameters. By using the annealing optimization algorithm to compare the metasurface parameters in the database, the initial phase parameters obtained from the first optimization are iteratively optimized multiple times to obtain the required phase and structural parameters. After optimization under different constraints, three metasurface diffraction gratings with different polarization configurations and 1550 nm working wavelengths are obtained and fabricated. A detection optical path of the completely polarized light is established to verify and evaluate the polarization detection capability of the three designed metasurface diffraction gratings. Before polarization detection, the instrument matrix of the polarization metasurface diffraction gratings is calibrated by using the intensity information of the outgoing light from incident linearly and circularly polarized light with known Stokes vectors to reduce the error. Subsequently, by inputting various unknown polarization states and using the intensity information of the output light along with the calibrated instrument matrix, the Stokes vector of the incident polarization state is recovered through matrix operations, enabling the detection of various polarization states. The polarization detection properties of the three metasurface diffraction gratings are quantified and compared by the degree of polarization (DOP), azimuth, and ellipse. The same experiments are conducted at 1540 nm and 1560 nm to verify the broadband performance of the metasurface diffraction gratings.

When 45° polarized light is incident on the metasurface diffraction gratings, four different polarization states can be produced at their -2, -1, 1, and 2 diffraction orders, corresponding to four polarization analysis channels. The first diffraction grating (sample 1, planar grating) forms a plane in the Poincaré sphere for its four polarization analysis channels [Fig. 5(a)]. The four polarization analysis channels of the second diffraction grating (sample 2, ordinary tetrahedral grating) form a tetrahedron on the Poincaré sphere [Fig. 5(b)]. The four polarization analysis channels of the third diffraction grating (sample 3, regular tetrahedral grating) form a regular tetrahedron on the Poincaré sphere [Fig. 5(c)]. The FDTD simulation results of the three diffraction grating fields are shown in Figs. 5(d), (e), and (f) respectively. Figure 7 is the error results of the experiment, which contains multiple sets of polarization-related parameters recovered by the detection calculation of three diffraction gratings. It can be seen that sample 3 has the smallest detection error among the three samples. At the same time, the root mean square errors (RMSE) of the DOP and polarization angle of the three samples are calculated, as shown in Table 1. The results show that the detection error of the sample is the smallest and has the best performance: the RMSE of the linear polarization angle is 0.79°, which is less than 1°. For elliptical polarization light, its RMSE of the azimuth and elliptic declination are 2.93° and 3.76°, respectively. Since the polarization of the three samples is calculated and recovered according to the instrument matrix, the stability of the matrix is directly determined by the number of conditions: a smaller number of conditions means more stable matrixes, leading to higher accuracy of the output results. Among the three samples, sample 3 has the smallest conditional number, so it is the most suitable metasurface grating for polarization recovery and detection. In addition, the designed metasurface diffraction gratings are proven to detect different polarization states at 1540 nm and 1560 nm, confirming their broadband polarization detection ability.

In this paper, three kinds of metasurface diffraction gratings with different polarization configurations are designed and fabricated by using intelligent optimization algorithms, and their detection performance for completely polarized light is verified and compared. For the detection of linear polarized light, the RMSE of the linear polarization angle is 0.7931°. For the detection of elliptical polarized light, the RMSE of azimuth angle and elliptical declination angle are 2.930° and 3.762°, respectively. The polarization detection performance of the metasurface diffraction grating is also verified at 1540 nm and 1560 nm, and the experiments show that the polarization detection performance of the designed tetrahedral and regular tetrahedral gratings at these two wavelengths is comparable to that of 1550 nm, demonstrating an acceptable polarization detection bandwidth of the designed metasurfaces. The work provides experimental guidance on the design of metasurface diffraction gratings with optimal polarization detection capabilities.