1Northwestern Polytechnical University, School of Physical Science and Technology, Ministry of Industry and Information Technology, Key Laboratory of Light Field Manipulation and Information Acquisition, Shaanxi Key Laboratory of Optical Information Technology, Xi’an, China
2Northwestern Polytechnical University, Analytical and Testing Center, Xi’an, China
Compact, single-shot, and accurate Stokes polarimetric imagers are highly desirable for imaging at all scales, from remote sensing to biological diagnosis. Recently, polarimetric imaging demonstrated on the metasurface platform is accelerating its realization and revolutionizing associated techniques and imagers. These breakthroughs, however, are greatly limited by the single operating wavelength and the complexity of metasurfaces. We present a minimalist yet powerful cascaded metasurface strategy to realize wavelength-insensitive snapshot Stokes polarimetric imaging. Two cascaded metasurface polarization gratings built into the 4f imaging system enable optical spin Hall momentum shifts and cross-polarization interference of incident light, which are wavelength-robust and free of polarization cross talk, allowing the 4f system to perform accurate and single-shot polarimetric imaging at an arbitrary wavelength and even low-coherence light. We demonstrate the feasibility and robustness of this cascaded metasurface architecture by characterizing diverse polarization objects. We open an avenue for polarimetric imaging and exhibit promising potential in emerging areas of applications such as biological diagnosis.
【AIGC One Sentence Reading】:A cascaded metasurface strategy enables wavelength-insensitive, single-shot Stokes polarimetric imaging, showing potential in diverse applications.
【AIGC Short Abstract】:A compact, single-shot Stokes polarimetric imager using cascaded metasurfaces is proposed. This strategy achieves wavelength-insensitive imaging by leveraging optical spin Hall effects and cross-polarization interference, eliminating polarization cross talk. Its feasibility and robustness are demonstrated, showing potential in diverse applications like biological diagnosis.
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Polarization is one of the intrinsic properties of a light wave that describes the vibration direction of the electric field and plays a critical role in light–matter interactions such as reflection, transmission, scattering, and reradiation. Measuring the polarization of light, namely, polarimetry, is an important means of detecting and acquiring intrinsic information of matter that cannot be acquired using traditional intensity imaging, e.g., surface morphology,1 structural orientation,2 physical and chemical properties of material,3 which has been widely used for remote sensing,4,5 biological diagnosis,6,7 material characterization,8 and vision enhancement.9–11 Various polarimetric techniques and devices have been proposed for fast and accurate polarization acquisition and imaging. The common strategy is observing the intensities of multiple polarization components sequentially in time and space and calculating the polarization information according to the Stokes formalism, namely, division-of-time Stokes polarimetry. This method requires bulk polarization dichroism elements and their mechanical rotation, making system miniaturization and high temporal resolution difficult; mechanical rotation could introduce measurement errors.12–16 Therefore, compact and real-time polarimetric imagers are highly desirable.
Metasurfaces, which are capable of flexibly modulating multiple parameters of the light field at a subwavelength scale,17–27 have been integrated into polarimetry and have subsequently garnered significant interest.28,29 Metasurfaces enable spatial division and focusing of multiple polarization components simultaneously, thereby performing single-shot full-Stokes polarization detection by calculating separated focal arrays in different polarization channels. Hence, researchers have proposed a variety of metasurface-based techniques and compact imaging systems for both visible and infrared polarimetry as well as polarimetric imaging,30–43 e.g., a metasurface polarization camera based on matrix Fourier optics33,43 and chip-integrated metasurface full-Stokes imaging sensors,32,42 enabling compact, high-speed, and single-shot polarimetric imaging. However, nonorthogonal polarization separation with the demand of low cross talk and high polarization extinction ratio is the fundamental basis of these strategies, which requires the rigorous design of meta-atom geometries, leading to a strict wavelength dependency, i.e., these imagers can only operate at specific wavelengths. Recently, a broadband single-chip full Stokes polarization imager has been proposed based on the six-channel orthogonal polarization separation enabled by a fan-shaped multiplexing metalens.34 Nevertheless, the complexity of geometry-varying meta-atoms on a large scale remains a great challenge. Cascaded metasurfaces that have a more controllable degree of freedom of light provide a solution to overcome this issue.44–49
Here, we present a cascaded metasurface architecture that enables wavelength-insensitive single-shot Stokes polarimetric imaging. Two geometric phase metasurfaces with minimalist two- (2D) and one-dimensional (1D) polarization gratings are cascaded into the imaging system to implement the splitting and cross-interference of two spin components. After a single shot of interferograms, we can obtain the quantitative amplitudes and phase retardation of two spin components in the measured light field according to digital holography, thus achieving the acquisition of Stokes vector information. This holographic interference strategy and spatial division of measured light generated by the geometric phase metasurface are robust for different wavelengths, low coherence, metasurface dislocation, and polarization cross talk removal, allowing for accurate measurement without taking into account wavelength drift and misalignment. Meanwhile, this method can directly measure the orientation angle of the light field through a single demodulation operation, effectively avoiding the accumulation of multiple errors caused by indirect measurements of nondirect physical quantities. As proofs of concept, Stokes polarimetric imaging of two typical optical polarization components, wave plates and depolarizer, and real-time polarimetric measurement of electrically controlled liquid crystal (LC) polarization grating are demonstrated.
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2 Results
2.1 Cascaded Metasurfaces Principle
Given the powerful modulation ability of the metasurface to the spin state as well as the robustness of the geometric phase principle at different wavelengths, we selected two opposite spin states as Jones vector bases to characterize the incident polarization state and utilized the optical spin Hall momentum shifts induced by the geometric phase metasurface with identical meta-atoms to manipulate the separation and interference of spin components. As the cascaded metasurface architecture obtains both interferograms and intensity images in a single exposure, to realize the stability of the system, gratings that have translation invariance are considered. Therefore, the geometric phase polarization grating is used, of which the structure is very simple while ensuring the uniformity of transmitted light in all orders.
The cascaded metasurface architecture, which mainly consists of 2D and 1D polarization gratings, is schematically shown in Fig. 1(a). The 2D metasurface polarization grating is located in the spatial spectrum plane of the imaging object, and the 1D metasurface polarization grating is placed in the plane behind the 2D one with a distance of . As shown in Fig. 1(b), the spin Hall momentum shifts induced by the 2D polarization grating generate four first-order light fields with left- (LCP) and right-handed circular polarizations (RCP) along the diagonal and antidiagonal directions in the imaging plane, which are depicted as , , , and , respectively. The idler light field directly transmitted from 2D polarization grating illuminates the 1D one after propagating a distance of and then is split into LCP and RCP components (depicted as and ) along the antidiagonal direction, which overlaps with the orthogonal spin components and at the imaging plane, respectively (see details in Notes 1 and 2 in the Supplementary Material). Under horizontal filtering, the overlapping spin components produce polarization interferences, and the corresponding interferograms and are expressed as where is the phase retardation between the LCP and RCP components, depicts the momentum shift induced by 2D polarization grating, and is the focal length of the lens that transforms the momentum shift to displacement.
Figure 1.Schematic illustration of cascaded metasurface architecture. (a) Schematic illustration of the principle. The object is placed at the input plane of the imaging system; an interferometer generates four intensity images at the imaging plane, which are the separated intensity images of LCP and RCP, as well as the intensity images of cross-polarization interferograms. By combining these four intensity images with the DHI method, it is possible to simultaneously obtain the amplitudes and phase retardation of two spin components, thereby obtaining polarization information. (b) Operation scheme of polarization division and interference induced by cascaded metasurfaces. and represent the RCP and LCP, respectively, and depicts the horizontal polarization. The incident light is split into four spin components (, , , and ) by the 2D polarization grating placed at the spectral plane, which shifts momentums along the diagonal and antidiagonal directions, respectively. The idler light directly transmitted from 2D polarization grating is split into two spin components ( and ) by the 1D polarization grating, which shift momentums along the antidiagonal direction and interfere with the orthogonal spin components and at the imaging plane after horizontal polarization filtering, generating interferograms and , respectively.
Hence, the camera placed in the image plane is able to obtain four intensity images from a single exposure, i.e., , , , and . From or , the phase retardation can be calculated through digital holography interferometry (DHI), as shown in Fig. 1(a). Combining the directly observed intensities and , the Stokes vector thus can be calculated by
In this principle, the imaging resolution of the interferometer depends on the size radius of the 2D polarization grating and the distance because determines the maximum spatial frequency of LCP and RCP, whereas determines the interference resolution of the phase retardation (see theoretical derivation in Note 3 in the Supplementary Material). According to the spin–orbit coupling principle of geometric phase metasurface, for the incidence of LCP or RCP, its transmitted light field is composed of the co- and cross-polarization components with an amplitude that is dependent on the birefringent phase retardation of polarization grating, i.e., and . The cross-polarization component shifts momentum with respect to the incident light, but the copolarization component directly propagates as an idler light. Considering the division efficiency of two metasurfaces, we set the conversion efficiencies of 2D and 1D polarization gratings as and 1, respectively.
2.2 Single-Shot Stokes Polarimetric Imaging
Figures 2(a) and 2(b) display the geometric phase distributions of 1D and 2D polarization gratings, respectively. The geometric phases of 1D and 2D polarization gratings corresponding to the RCP component are designed as and , respectively. Here we set momentum shift angle at wavelength . Notably, 2D polarization grating presents a linear distribution along the direction but a rectangular distribution (binary phases 0 and ) along the direction, as shown in Fig. 2(c). The duty cycle of the rectangular grating is , and the difference in the binary phase is ; this special structure can eliminate the zeroth-order diffraction and make the first-order diffraction the most efficient (see details in Note 4 of the Supplementary Material). The polarization gratings are prepared from the 300-nm-thick poly-Si film on a -thick fused silica substrate. Figures 2(d) and 2(e) are the micrographs and scanning electron microscope images of 2D and 1D polarization gratings, respectively. The overall size of the 2D polarization grating is a circle with a diameter of 2.5 mm, whereas the 1D grating is a square with a side length of 1.5 mm. We used the experimental setup shown in Fig. 2(f) to demonstrate the feasibility of this interferometer. In the experiment, lenses and , each with focal length , were used to perform the Fourier transform. The 2D polarization grating was located at the spatial spectrum plane of the system, and the 1D polarization grating was located at the plane behind the 2D one with a distance of . The combination of polarizer and CMOS camera (Hamamatsu C11440-42U40) was used to observe the interferograms and intensity images simultaneously. Figure 2(g) shows the background intensity images used for calibration in an incidence of horizontally polarized light without an object, and the inset is a locally enlarged image of the interferogram . By combining the focal length of the lens and the radius of the 2D polarization grating, the cutoff frequency of the coherent transfer function (CTF) can be calculated as . By imaging the 1951 USAF target (Thorlabs, R1DS1N, Newton, New Jersey, United States), the actual imaging resolution of the system was experimentally characterized, as shown in Fig. 2(h). The imaging system can distinguish a minimum line pair of Group 4 Element 5, which is and consistent with the theoretical one. To further accurately characterize the imaging resolution of the system, the point spread functions (PSFs) of the LCP and RCP components were experimentally measured to describe its resolution, as shown in Fig. 2(i). Quantitative characterization of system imaging resolution can be seen in Note 3 in the Supplementary Material.
Figure 2.Design of metasurface and experimental setup. (a), (b) Geometric phase distributions of the 1D and 2D polarization gratings, respectively. Scale bar: . The insets are the local phase distributions within a range. (c) Phase modulations of RCP (upper) and LCP (lower) components of the 2D polarization gratings along the and axes. (d), (e) Optical micrographs and SEM images of the 2D and 1D polarization gratings, respectively. Scale bar in micrographs: ; scale bar in SEM images: . (f) Experimental setup. (g) Background intensity images without objects for calibration. The inset is a locally enlarged image of the interference image . (h) 1951 USAF target (Thorlabs, R1DS1N) imaging resolution test. The inset is an enlarged view of Group 4 Element 4-6, with line widths of 22.62, 25.39, and , respectively. (i) Measured PSFs of the RCP and LCP light.
As a proof of concept, we first exhibit the polarimetry of three typical polarization elements, e.g., first- and second-order LC vortex wave plates (WPV10L-633 and WPV10-633), and an LC depolarizer. The experimental results at the 633-nm wavelength are shown in Figs. 3(a)–3(c), which display the optical images of the tested objects and measured Stokes parameter distributions , , , and from left to right. For these transparent objects, the measured results clearly present their polarization characteristics. As these wave plates are designed at 633-nm wavelength, the polarization ellipticity , whereas the orientation angle of polarization distribution obtained by reflects the change of local azimuthal angle of birefringence molecules within wave plates, that is, the angular orientation of LC molecules. Moreover, in the Stokes vector images, the defects of polarization singularities and dislocations are much more obvious due to contrast enhancement. The comparison with the traditional measurement method of time division strategy, that is, calculating the Stokes vector by measuring the intensity distributions of six polarization components , , , , , and , can be found in Note 6 in the Supplementary Material. Furthermore, we assessed the polarimetric accuracy by benchmarking the polarization ellipticity angle and orientation angle induced by the rotation angle of commercial quarter- and half-wave plates. Figures 3(d) and 3(e) show the ellipticity angle and orientation angle changes of the output light after the horizontally polarized light incident on a rotating quarter- and half-wave plate, respectively. In Fig. 3(d), the theoretical and measured Stokes parameter and polarization ellipticity angle of the outgoing light field with the quarter-wave plate rotation angle are shown. The experimental results are highly consistent with the theory, i.e., and ( is usually confined in the interval of ), exhibiting root mean square errors of 0.0157 rad for and 0.0273 rad for , and maximum absolute errors and 0.0914 rad, respectively. To benchmark the polarization orientation angle, we selected a half-wave plate, of which the rotation causes a double rotation of the incident light. The orientation of linearly polarized light is only dependent on the phase retardation between its LCP and RCP components, i.e., ( is usually confined in the interval of ). Figure 3(e) shows the theoretical and experimental results of the orientation angle, with a root mean square error of 0.0362 rad and a maximum absolute error of 0.0638 rad. Different from previous indirect measurements through four-intensity information, this method obtains the orientation angle from the high-precision phase information obtained by the digital holographic method, avoiding the accumulation of errors caused by indirect measurements.
Figure 3.Experimental results of cascaded metasurface strategy and benchmark of polarization measurement. (a)–(c) From top to bottom are the measured results of the first- and second-order LC vortex wave plates and an LC depolarizer, and from left to right are the optical micrographs and Stokes vector measurement results. These vortex wave plates are designed at the 633-nm wavelength. Scale length: 1 mm. (d), (e) Benchmarking the polarization ellipticity angle and orientation angle measurements of the output light after the horizontally polarized light incident on a rotating quarter- and half-wave plate, respectively. , , : theoretical results; , , : experimental results. The rotation angle intervals of wave plates are 5 deg.
To validate the real-time polarization measurement capability, the variation of the Stokes vector of a dynamic LC polarization grating was experimentally characterized.50 The LC element, consisting of distinct polarization gratings, is shown in Figs. 4(a) and 4(b). Figure 4(c) displays the polarization micrograph of a 1D polarization grating. Owing to the excellent electro-optic tunability of LCs, significant variation of LC birefringence occurs as the external electric field changes. A time-varying external electric field is applied to the LC element, as shown in Fig. 4(b), which produces a dynamic change in the output field of the 1D polarization grating. Figure 4(d) shows the Stokes parameter distributions of the transmitted light field from the 1D LC polarization grating when an external voltage is 2.5 V. Figure 4(e) shows the phase retardation distribution along the red dotted line in Fig. 4(d), and Fig. 4(f) depicts the unwrapping result. According to the geometric phase theory, , with depicting the azimuthal angle of LC molecules. The period of LC photoalignment within the 1D polarization grating is (pixel size is ), and the average period of measured results shown in Fig. 4(e) is , which is very consistent with the theoretical design, as the comparison of unwrapping phases shown in Fig. 4(f). Due to the high resolution of interferometry, it has a high sensitivity to circular birefringence, i.e., , the measured phase gradient shown in Fig. 4(f) is . In turn, external field voltage, and other relevant environmental factors, can be sensed through precise polarization and birefringence measurements (see Note 7 in the Supplementary Material). This real-time full polarization microscopic imaging capability has great potential for precise resolution of molecular spatial positions and angular orientations.51,52
Figure 4.Real-time characterization of LC polarization grating. (a) Physical image of LC element. Red box: 1D LC polarization grating to be measured. (b) Diagram of applying an external electric field to the LC element. (c) Polarization micrograph of a 1D LC polarization grating. Scale bar: . (d) Stokes parameter distributions. (e) Phase retardation between LCP and RCP components along the dashed line in panel (d). (f) Comparison of theoretical and experimental results after unwrapping the phase retardation . The external voltage is 2.5 V (Video 1, MP4, 2.6 MB [URL: https://doi.org/10.1117/1.AP.7.1.016008.s1]; Video 2, MP4, 2.4 MB [URL: https://doi.org/10.1117/1.AP.7.1.016008.s2]).
Different from the multipolarization channel imaging strategy, this method modulates the separation and interference of spin states through the optical spin Hall momentum shifts. Therefore, spatially separated LCP and RCP components have uniform amplitudes and phase transmittances. More importantly, this uniformity is well maintained when changing wavelengths, without the need for complex metasurface structure design and wavelength correction, because the wavelength only affects the ratio of diffractive and idler light. However, when the light wavelength is mismatched, the birefringence of the polarization grating does not satisfy the half-wave retardation condition, the amplitude of the idler light increases, and the amplitude of the diffractive light decreases; that is, the efficiency decreases. Therefore, without considering the influence of diffraction efficiency, changes in wavelength only affect the position of the captured images and have no impact on the measurement results. As the linear phase shift is independent of the wavelength, the period of the interference fringe does not change. Detailed theoretical derivations can be found in Note 2 of the Supplementary Material.
To verify the wavelength robustness, the Stokes vector distributions of outgoing fields from the second-order vortex wave plate incident with horizontally polarized light fields at wavelengths of 473, 552, and 633 nm were measured experimentally, as shown in Fig. 5(a). The desired operation wavelength of the vortex wave plate is 633 nm. When the incident beam wavelength is 633 nm, the birefringence phase retardation of the wave plate satisfies , so the theoretical is constant to 0. When the incident wavelength shifts, i.e., , it is intuitive that of the outgoing light field changes. Figure 5(b) shows the variation along the angular coordinate, and Fig. 5(c) shows the Stokes vector trajectories on the Poincaré sphere. As the vortex wave plate changes its local orientation angle of birefringence twin along the azimuthal direction, changes synchronously in the azimuthal direction, with the peak of presenting the dispersion of birefringence. The slight fluctuation of at 633 nm is the inhomogeneity of the second-order LC vortex wave plate. The validation by the traditional (time-divided) intensity measurement method is shown in Fig. S4 in Note 6 of the Supplementary Material. Figure 5(d) shows the diffraction efficiency and polarization splitting ratio of the system in a broadband range from 500 to 900 nm. As mentioned, this system has a uniform polarization splitting ratio in this broadband range, but the efficiency decreases as the wavelength deviates from 633 nm. In the experiment, considering the strong absorption of Si below 550-nm wavelength, we increased the power of the incident light to achieve polarimetric imaging with a high signal-to-noise ratio at 473 and 552 nm, used a checkerboard image to uniformly register experimental data of different wavelengths, and then analyzed the measurement results. These experimental results validate the feasibility of this polarization imaging strategy over broadband. Compared with the spatial multiplexing broadband polarization metalens,34 the circular polarization extinction ratios at 633, 532, and 514 nm are 61.4, 65.4, and 43.7, respectively. Meanwhile, this method does not require the complex design and precise fabrication of the metasurface.
Figure 5.Polarimetric imaging at different wavelengths. (a) Stokes parameter distributions of light fields output from a second-order vortex wave plate in the incidences of horizontal polarization but different wavelengths. From top to bottom, the wavelengths are 633, 552, and 473 nm, respectively. (b) Comparison of distributions along the angular coordinate at different wavelengths. (c) Variation trajectory of the Stokes vector along the red dashed line in panel (a) at three wavelengths. (d) Intensity ratio of the separated left- and right-handed circular polarizations (red) and diffraction efficiency (blue) with incidence of linearly polarized light at different wavelengths.
This polarimetry combines metasurfaces with the DHI method, providing a new Stokes vector measurement strategy for metasurface-integrated imaging systems. Although our strategy relies primarily on interferometry for polarization measurements, this common optical path interference device is compact and stable, allowing for effective measurement of polarization states when the coherence of the light source decreases. Figure 6 shows the polarimetry of a microscopy imaging scenario, where the lighting source is a light-emitting diode (LED) with 626-nm central wavelength and 9.2-nm bandwidth. As a partially coherent light source, LED light is a popular choice for microscopy imaging. The power spectrum of the LED source is shown in Fig. 6(a), and the single-shot intensity image and the enlarged view of one interferogram are presented in Figs. 6(b) and 6(c). Clearly, evident interferograms are observed. The measured Stokes parameter images are shown in Fig. 6(d), which indicates the interferometer suitability under low coherence conditions.
Figure 6.Polarimetric imaging of LED illumination scenario. (a) Power spectrum of an LED source with 626-nm central wavelength and 9.2-nm bandwidth. (b) Single-shot image of a second-order vortex wave plate under the illumination of an LED source with horizontal polarization. (c) Enlarged view of interferogram corresponding to the red box in panel (b). (d) Measured Stokes parameter distributions.
We further experimentally analyzed the impact of bandwidth on the capacity of this polarimetric imaging system. The polarimetric imaging of the second-order vortex wave plate and the visibility of the fringe pattern obtained under the illumination of an LED light source with a 14.4-nm bandwidth are shown in Fig. S8 in the Supplementary Material. It is noteworthy that Stokes images can be obtained in this bandwidth condition, but the lower visibility of the fringe pattern produces poorer image quality, indicating that using a narrowband LED light source will yield more accurate measurement results. On the other hand, when the single bandwidth is large enough, diffraction dispersion must also be considered. We measured the diffraction dispersion effect of light with the 31.8-nm bandwidth and a central wavelength of 520 nm. In such a broadband condition, the off-axis diffraction dispersion degrades the image quality, making it unsuitable for further polarization measurements, and the imaging results of a checkerboard pattern are validated in Fig. S9 in the Supplementary Material. Thereby, the bandwidth of this polarimetric imaging system is .
3 Discussion and Conclusion
This solution cascades 2D and 1D polarization gratings and introduces linear phase shifts through the longitudinal displacement of the 1D polarization grating, thereby achieving off-axis interference. Although the metasurfaces need to be integrated with a system and equipped within an imaging system, similar to the grating type polarimetric imager,33 this inversely reduces the requirements for its fabrication. Both lens-integrated polarimetric imagers31,34,37 and chip-integrated imaging sensors42 require large-aperture metasurfaces to improve the numerical aperture and field of view, but it remains a great challenge to fabricate large-scale geometry-varying nanostructures with high polarization extinction ratios and low polarization cross talk. On the other hand, thanks to the translation invariance of grating, the interferometer is easy to integrate with various imaging systems, without the consideration of metasurface dislocation. Moreover, the cascaded metasurface architecture no longer constrains the angle of the incident beam and can also work normally under oblique incidence without introducing additional measurement errors. Meanwhile, the interferogram period can be flexibly controlled by adjusting the interval of two metasurfaces for distinct application scenarios and image acquisition instruments with different imaging resolutions.
As this method enables the measurement of amplitudes and phase retardation of the LCP and RCP components simultaneously, the complex refractive index of the circular birefringence of the sample can be obtained, which provides great value for characterizing the circular dichroism. The phase retardation between LCP and RCP components is obtained by DHI, which derives the orientation angle from high-precision phase information directly, thereby avoiding the accumulation of errors from indirect measurements. Similar to all polarimetric imaging methods that refer to the division of polarization channel, the imaging field of view is lost; if the Kramers–Kronig relationship is used to solve digital holography,53 the spatial bandwidth product of the interferometer can be further improved. Limited by the material absorption of Si and the half-wavelength modulation effect of the meta-atom, this system exhibits variant efficiency in the whole visible range, which affects the signal-to-noise ratio of polarimetric imaging. Low absorption materials such as and an optimized meta-atom with flat half-wavelength retardation in the visible range are promising to solve this efficiency problem.
In summary, we proposed a cascaded metasurface strategy to address the key problem of operation wavelength within metasurface-based polarimetric imaging. Owing to the optical spin Hall effect induced by minimalist polarization grating, the cascaded metasurface architecture generates spin division and interference without strict wavelength dependence and polarization cross talk, allowing single-shot Stokes polarimetric imaging from the associated cross-polarization interferograms using digital holography. We demonstrated the feasibility and robustness of this architecture under multiple wavelengths and low-coherence light illumination conditions, indicating the potential for applications such as biological diagnosis involving precise resolution of molecular spatial positions and angular orientations.
4 Appendix: Videos
The following videos are mentioned in the caption of Fig. 4.
Video 1 The variation of Stokes vector of LC polarization grating with a time-varying external electric field (MP4, 2.6 MB).
Video 2 The retardation between LCP and RCP components of the outgoing field along the horizontal profile of the liquid crystal polarization grating (MP4, 2.4 MB).
Xuanguang Wu received his BS degree in optoelectronic information science and engineering from Northwestern Polytechnical University (NPU) in China in 2021. He is currently a PhD student in optical engineering at the School of Physical Science and Technology, NPU, China. His research is focused on multidimensional imaging of light fields based on metasurface.
Kai Pan received his BS degree in optoelectronic information science and engineering from Northwestern Polytechnical University (NPU) in China in 2020. He is currently a PhD student in optical engineering at the School of Physical Science and Technology, NPU, China. His research is focused on metasurface holography.
Xuanyu Wu received his BS degree in optoelectronic information science and engineering from Northwestern Polytechnical University (NPU) in China in 2021. He is currently a PhD student in optical engineering at the School of Physical Science and Technology, NPU, China. His research is focused on depth information perception based on metasurface.
Xinhao Fan received his MS degree in optics from Northwestern Polytechnical University (NPU) in China in 2021. He is currently a PhD student in optical engineering at the School of Physical Science and Technology, NPU, China. His research is focused on longitudinal control of the light field polarization state.
Liang Zhou received his BS degree in optoelectronic information science and engineering from Northwestern Polytechnical University (NPU) in China in 2020. He is currently a PhD student in optical engineering at the School of Physical Science and Technology, NPU, China. His research interests include metasurface holography and light field modulation.
Chenyang Zhao received her PhD in physics from Northwestern Polytechnical University of China in 2017. She is currently an associate researcher at the Analytical and Testing Center of Northwestern Polytechnical University, mainly engaged in the fundamental and applied research of micro-nano photonics.
Dandan Wen received his PhD from Heriot-Watt University in the United Kingdom in 2017. He is currently a professor at the School of Physical Science and Technology, Northwestern Polytechnical University, China. His research interests include optical field modulation, information perception, and optoelectronic devices that are based on metasurface.
Sheng Liu received his PhD in optical engineering from Northwestern Polytechnical University (NPU) in China in 2011. He is currently a professor at the School of Physical Science and Technology, NPU, China. His research interests include the generation and modulation of light fields, photonic lattices, and spatial solitons.
Xuetao Gan received his PhD in optical engineering from Northwestern Polytechnical University (NPU) in China in 2013. He is currently a professor at the School of Physical Science and Technology, NPU, China. His research interests include micro-nano photonics, optoelectronics of two-dimensional layered materials, and optoelectronic devices.
Peng Li is now a professor at the School of Physical Science and Technology, Northwestern Polytechnical University, China. His areas of research focus on optical field modulation, optical holography, and multidimensional information perception of light field based on metasurface.
Jianlin Zhao is now a professor at the School of Physical Science and Technology, Northwestern Polytechnical University, China. He received his PhD in optics from the Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, in 1998. He has published over 480 journal and international conference papers in the fields of digital holography, light field control and information processing, nonlinear optics, micro-nano photonics, and optical fiber sensors.