An ultra-stokes polarization detection superlens and a full stokes parameter recovery method thereof

Abstract

The application discloses a full-Stokes polarization detection superlens and a full-Stokes parameter recovery method thereof, the superlens comprising a superlens substrate and a nanostructure unit; the nanostructure units are staggered or randomly staggered on the superlens substrate; the superlens is configured to: after a polychromatic light source irradiates the superlens, the multiple nanostructure units focus polarized light of different polarization states to different positions, and different focusing focal points are formed on a focusing plane; the design method comprises a staggered arrangement design or a random staggered arrangement design step of the superlens and a full-Stokes parameter recovery step. The polarization recovery method can be used for the staggered arrangement or the random staggered arrangement, polarization recovery can be performed on a Stokes parameter superlens of any arrangement, the imaging quality is improved, the post-processing of pictures is facilitated, the method is easy to program and implement, can be used at any wavelength, such as ultraviolet, visible light, infrared and the like, and has wide application scenarios and strong expandability.

Description

Technical Field

[0001] This invention relates to the field of micro-nano optics technology, and in particular provides a metalens for all-Stokes polarization detection and a method for all-Stokes parametric recovery. Background Technology

[0002] In the field of optical engineering, polarization imaging can be considered a novel imaging method. Compared to traditional imaging, it obtains an additional dimension of scene information, making it highly valuable in industrial, biological, military, and aerospace fields. However, traditional polarization imaging devices require multiple lenses, optical paths, or polarizers, significantly increasing the size and weight of the imaging device and resulting in low efficiency. Metasurfaces are a newly developed type of metamaterial in recent years. They consist of subwavelength nanoscale structures arranged on a substrate. By adjusting the shape, size, and rotation direction of the nanounits, the amplitude, phase, and polarization of light can be flexibly controlled. Due to their small size and multiple functions, they offer the possibility of miniaturizing optical devices.

[0003] While numerous schemes combining metasurfaces and polarization imaging exist, several challenges remain in full Stokes imaging and Stokes parameter recovery. Existing polarization recovery methods are often limited to vertical or intermittent arrangements, which frequently fail to yield complete images. Furthermore, these methods are often ineffective for staggered or randomly staggered arrangements, significantly impacting both imaging results and post-processing. For instance, large errors may render the images unusable or result in missing image content. Additionally, current technologies lack Stokes parameter recovery methods for both staggered and non-staggered arrangements, which are crucial for imaging. These technological limitations hinder the application and expansion of full Stokes imaging technology in engineering fields. Summary of the Invention

[0004] Based on this, the present invention provides a metalens and design method for all-Stokes polarization detection to reduce errors in all-Stokes imaging and Stokes parameter recovery, and to improve image imaging quality by performing staggered and random staggered arrangement of nanostructure units.

[0005] To achieve the above objectives, in a first aspect, the present invention provides a metalens for all-Stokes polarization detection, comprising a metalens substrate and nanostructure units; the nanostructure units are arranged in an alternating or random alternating manner on the metalens substrate; the metalens is configured such that, after a polychromatic light source illuminates the metalens, multiple nanostructure units focus polarized light of different polarization states to different positions, forming different focal points on the focusing plane.

[0006] Furthermore, the focusing points include four points arranged in the focusing plane as follows: X-ray polarized light is focused at the upper left corner, Y-ray polarized light is focused at the upper right corner, 45° linearly polarized light is focused at the lower left corner, and left-handed circularly polarized light is focused at the lower right corner.

[0007] Furthermore, the focusing points include six points arranged on the focusing plane as follows: X-ray polarized light is focused at the upper left corner, Y-ray polarized light is focused at the upper left corner, 45° linearly polarized light is focused at the upper center position, 135° linearly polarized light is focused at the lower center position, left-handed circularly polarized light is focused at the upper right corner, and right-handed circularly polarized light is focused at the lower right corner.

[0008] To achieve the above objectives, in a second aspect, the present invention provides a method for designing a metalens for all-Stokes polarization detection, including a staggered or random staggered arrangement design of the metalens and a full-Stokes parametric recovery step.

[0009] Furthermore, the staggered or random staggered arrangement design of the meta-lens includes the following steps:

[0010] S110. Determine the number of focal points and the position where polarized light of different polarization states is focused onto the focal plane;

[0011] S120. Calculate the phase distribution value of polarized light with different polarization states relative to the entire metalens area when the polarized light is focused to different focal points;

[0012] S130. Based on the phase distribution value at each focal point, select the nanostructure unit most suitable for a certain polarization light using the principle of minimum error;

[0013] S140. Combine all nanostructure units to generate a pattern of polarized light for a specific polarization state;

[0014] S150. Multiple patterns for different polarized light are arranged in an alternating or random alternating manner.

[0015] Furthermore, in the process of calculating the focusing of polarized light with different polarization states to different focal points, the phase distribution of left-handed circularly polarized light is calculated, including:

[0016] An anisotropic nanostructure unit with high transmittance and a phase difference of π in the x and y directions is selected. Then, the nanostructure unit is rotated counterclockwise by a set angle. The required phase value φ at each position is calculated according to the following formula:

[0017]

[0018] in For the wavelength, , Let be the coordinates of the nanopillar. This is the focal length of the lens.

[0019] Furthermore, multiple layouts for different polarized light are arranged and combined in an interleaved manner, including:

[0020] Select the version at a specific location on the paper. Figure 1 The nanostructure unit at that location, selected at the next defined location on the canvas. Figure 2 The nanostructure unit at this location, selected at another location on the surface. Figure 1 The nanostructure units at that position are selected in different orders, and the order is changed in the next row or column, and so on, eventually forming an alternating metalens pattern.

[0021] Furthermore, multiple patterns for different polarized light are randomly interleaved and combined, including:

[0022] At a specific location on the image, a nanostructure unit of a pattern is randomly selected at that location. Then, another nanostructure unit of a pattern is randomly selected at the next location, and so on, until a randomly staggered metalens pattern is formed.

[0023] Furthermore, the full Stokes parameter recovery step includes:

[0024] S210. Polarized light with the same incident intensity but different polarization states;

[0025] S220. At each incident point, calculate the focal point intensity value at each designed position to construct a reconstructed light intensity matrix;

[0026] S230. Calculate the theoretical Stokes parameters of the corresponding incident polarized light and construct the known Stokes parameter matrix;

[0027] S240. Calculate the pseudo-inverse matrix of the reconstructed light intensity matrix. Multiply the known Stokes parameter matrix by the pseudo-inverse matrix to obtain the reconstructed Mueller matrix, thereby completing the reconstruction of the metalens.

[0028] Furthermore, the full Stokes parametric recovery step also includes: after obtaining the reconstructed Mueller matrix, incident polarized light of unknown polarization state, obtaining the focal intensity value at each design position, forming a reconstructed light intensity matrix, multiplying the reconstructed Mueller matrix by the light intensity matrix, normalizing the process, obtaining the Stokes parametric matrix of unknown polarization state, and then calculating the degree of polarization or polarization angle to obtain the polarization information of the object.

[0029] A method for full Stokes parametric recovery of metalenses using full Stokes polarization detection includes a method for staggered arrangement design of metalenses and Stokes parametric recovery.

[0030] The staggered arrangement design of metalenses first requires identifying the lens as a Stokes parametric metalens, possessing the complete ability to detect Stokes parameters. In design, it is generally considered to be a multifocal metalens. Multifocal metalenses can often be divided into four-focal and six-focal metalenses. For a four-focal metalens, X-ray polarized light, Y-ray polarized light, 45° linearly polarized light, and left-hand circularly polarized light (LCP) can be focused at different positions on the focal plane. Similarly, for a six-focal metalens, X-ray polarized light, Y-ray polarized light, 45° linearly polarized light, 135° linearly polarized light, left-hand circularly polarized light (LCP), and right-hand circularly polarized light (RCP) can be focused at different positions on the focal plane. In the design of staggered or randomly staggered metalenses, the first step is to calculate the phase distribution value of the polarization state relative to the entire metalens area when different polarization states are focused to different focal points. Then, based on the phase distribution value calculated at each position, the nanostructure most suitable for a specific polarization is selected using the principle of minimum error. All nanostructures are then combined to generate a pattern for that specific polarization. Finally, multiple patterns for different polarizations are staggered or randomly staggered. For staggered arrangements, the pattern is selected at a specific position on the lens surface. Figure 1 The nanostructure at this location, selected at the next specific location on the canvas. Figure 2 The nanostructure at this location is then selected at the next location on the next sheet of the image. Figure 1The nanostructure at this position is selected, and the selection order is changed in the next row or column, and so on, to eventually form an alternating arrangement of metalens patterns; for random arrangement, a certain pattern is randomly selected at a certain position on the image, and a certain pattern is randomly selected at the next position, and so on, to eventually form a randomly arranged metalens pattern. Taking a four-focal Stokes parametric metalens as an example, the lens itself needs to focus different polarized light to different positions. Here, it is set to focus the incident X-ray polarized light to the upper left corner of the lens, the incident Y-ray polarized light to the upper right corner of the lens, the incident 45° linearly polarized light to the lower left corner, and the incident left-handed circularly polarized LCP light to the lower right corner. The next step is to calculate the phase distribution under each polarization. For X and Y linearly polarized light, an anisotropic nanostructure is selected here. It is considered to multiplex the polarization of the X and Y orthogonal linearly polarized light into one nanostructure, that is, to use one nanostructure to simultaneously control the X and Y linearly polarized light. Of course, it is also possible not to multiplex the polarization of the X and Y orthogonal linearly polarized light and to use two structures instead. For 45° linearly polarized light, the design needs to be based on X-ray polarization, meaning only the response of the nanostructure to X-ray polarization is considered. Finally, the nanostructure designed for X-ray polarization is rotated counterclockwise by 45°. For left-handed circularly polarized light (LCP), an anisotropic nanostructure with high transmittance and a phase difference of π in the x and y directions needs to be selected. This nanostructure is then rotated counterclockwise by a certain angle, the magnitude of which is obtained by dividing the phase value calculated using the formula by 2. Note the conversion between radians and angles. The required phase value φ at each position is calculated using the following formula:

[0031]

[0032] in For the wavelength, , Let be the coordinates of the nanopillar. This is the focal length of the lens.

[0033] After calculating the phase under each polarization using formulas, a suitable anisotropic nanostructure is selected based on the principle of minimizing error for the corresponding phase distribution under each polarization. Specifically, for X and Y linearly polarized light, the phase of both X and Y linearly polarized light at the same position needs to be considered simultaneously, and the most suitable anisotropic nanostructure is selected to simultaneously modulate both linearly polarized lights. For 45° linearly polarized light, it is first considered as X-polarized light, then the most suitable nanostructure is selected, and finally, the nanostructure is rotated counterclockwise by 45°. For left-handed circularly polarized light (LCP), an anisotropic nanostructure with high transmittance and a phase difference of π in the x and y directions needs to be selected. This nanostructure is then rotated counterclockwise by a certain angle, the angle being obtained by dividing the phase value calculated using the formula by 2. Note the conversion between radians and angles. The selected structures for each polarization state are combined to form three patterns: one pattern is used to modulate X and Y linearly polarized light, one pattern is used to modulate 45° linearly polarized light, and one pattern is used to modulate left-handed circularly polarized light (LCP). These three images are identical in size and period, differing only in the structure at the same location. This is because different structures modulate different polarized light. Finally, these three images are interleaved or randomly interleaved to form new images. For interleaved arrangements, at a specific location on the image, a nanostructure from the image controlling X and Y linear polarization is selected; at the next specific location, a nanostructure from the image controlling 45° linear polarization is selected; at the next location, a nanostructure from the image controlling left-handed circularly polarized light (LCP) is selected; the order of image selection is changed in the next row or column, and so on, ultimately forming an interleaved metalens image. For random arrangements, at a specific location on the image, one of the three images' nanostructures is randomly selected; at the next location, another random nanostructure from the three images is selected, and so on, ultimately forming a random metalens image. This new map will simultaneously include the content of three maps and possess the ability to manipulate all three maps. This method can transform Stokes multifocal metalenses with arbitrary polarization combinations into staggered or random arrangements, and then perform Stokes parameter detection and recovery on such staggered or random Stokes parametric metalenses.

[0034] The proposed full Stokes parametric restoration method can not only restore multifocal staggered or randomly arranged Stokes parametric metalenses—such arrangements avoid problems like alignment difficulties and incomplete imaging—but also restore multifocal Stokes parametric metalenses with other arrangements. The following section will use a four-focal Stokes parametric metalens as an example to introduce this full Stokes parametric restoration method. This process is applicable to any arrangement and other multifocal Stokes parametric metalenses. First, incident X-polarized light, Y-polarized light, 45° linearly polarized light, 135° linearly polarized light, left-handed circularly polarized light (LCP), and right-handed circularly polarized light (RCP) with the same intensity value. At each incident point, the intensity value of the polarization focus at each designed position is calculated. The focus intensity value is taken as three times the full width at half maximum (FWHM) of the focus. The intensity of each polarization focus on the focal plane is calculated and recorded. Here, there are four designed polarization focuses, and a total of six different polarizations need to be incident. Finally, six sets of values ​​are calculated and obtained, forming a 4×6 light intensity matrix, which can be called the reconstructed light intensity matrix. Simultaneously, the theoretical Stokes parameters S0, S1, S2, and S3 for the corresponding incident polarized light are calculated, resulting in a total of six polarized light types, each with its own theoretical Stokes parameters. This forms a 4×6 known Stokes parameter matrix. Next, the pseudo-inverse matrix of the reconstructed light intensity matrix is ​​calculated, and multiplied by the Stokes parameter matrix to obtain a 4×4 numerical matrix, called the reconstructed Mueller matrix. At this point, the reconstruction aspect of the metalens is complete. Subsequently, polarized light of unknown polarization is incident, yielding focal intensity values ​​at four designed positions, forming a 4×1 matrix called the light intensity matrix. Multiplying the reconstructed Mueller matrix by the light intensity matrix and normalizing it yields the Stokes parameters for the unknown polarization state. This allows for the calculation of the degree of polarization or the polarization angle, thus obtaining the polarization information of the object.

[0035] Compared with existing technologies, the technical advantages of the metalens and design method for all-Stokes polarization detection in this invention are at least reflected in the following aspects:

[0036] Firstly, existing polarization restoration methods are often limited to vertical or intermittent arrangements, failing to obtain complete imaging results and hindering post-processing of the images. In contrast to existing technologies, this invention can perform polarization restoration on any arrangement of Stokes parametric metalenses. The polarization restoration method can be applied to staggered or randomly staggered arrangements, improving imaging quality and facilitating post-processing of the images.

[0037] Secondly, this invention can perform polarization restoration on any multifocal Stokes parametric metalens. As long as the multifocal point can be used for Stokes parametric restoration, it can be performed. The implementation process is theoretically clear, easy to program and implement, convenient to use, and can be used at any wavelength, such as ultraviolet, visible light, infrared, etc., with a wide range of applications and strong scalability. Attached Figure Description

[0038] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings:

[0039] Figure 1 A three-dimensional schematic diagram of an embodiment of the metalens for all-Stokes polarization detection provided;

[0040] Figure 2 A partial layout of an embodiment of the metalens for all-Stokes polarization detection provided;

[0041] Figure 3 A flowchart illustrating an embodiment of the staggered or random staggered arrangement design of the metalens for the provided Stokes polarization detector;

[0042] Figure 4 A flowchart illustrating an embodiment of the metalens full-Stokes parametric recovery step for full-Stokes polarization detection provided;

[0043] Figure 5 A schematic diagram showing how X-ray linearly polarized light, Y-ray linearly polarized light, 45° linearly polarized light, 135° linearly polarized light, left-handed circularly polarized light, and right-handed circularly polarized light incident on a metalens form four focal points on the focusing plane;

[0044] Figure 6 This is a schematic diagram of the 4×4 intensity matrix formed by the metalens for the all-Stokes polarization detection provided.

[0045] Figure 7 A schematic diagram of the nanostructure unit arrangement of the metalens for the provided all-Stokes polarization detection;

[0046] Figure 8 This is a flowchart of the polarization recovery process of the metalens for the provided all-Stokes polarization detection.

[0047] Explanation of reference numerals in the attached diagram:

[0048] 1-Polychromatic light source, 2-Nanostructure unit, 3-Lens substrate, 4-Focusing plane, 5-Focusing point. Detailed Implementation

[0049] In the field of optical engineering technology, existing technologies still have some technical problems to be solved in full Stokes imaging and Stokes parametric recovery. Existing polarization recovery is often limited to vertical or intermittent arrangement. Such arrangement methods often cannot obtain complete imaging results. Polarization recovery methods are also often unable to be used for staggered or randomly staggered arrangements. This will not only greatly affect the imaging results, but also affect the post-processing of the images.

[0050] To address this, the present invention provides a metalens and its design method for all-Stokes polarization detection, comprising a metalens substrate and nanostructure units; the nanostructure units are arranged in an alternating or random alternating manner on the metalens substrate; the metalens is configured such that after a polychromatic light source illuminates the metalens, multiple nanostructure units focus polarized light of different polarization states to different positions, forming different focal points on the focusing plane. The design method includes steps for designing the alternating or random alternating arrangement of the metalens and a step for all-Stokes parametric recovery. The provided metalens and its design method can reduce errors in all-Stokes imaging and Stokes parametric recovery, thereby improving image quality.

[0051] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0052] like Figure 1 , Figure 2 As shown, an embodiment of a metalens for all-Stokes polarization detection provided by the present invention includes a metalens substrate 3 and nanostructure units 2; the nanostructure units 2 are arranged in an alternating or random alternating manner on the metalens substrate 3; the metalens is configured such that after a polychromatic light source 1 illuminates the metalens, multiple nanostructure units 2 focus polarized light of different polarization states to different positions, forming different focal points on the focusing plane 4.

[0053] It should be noted that the provided lens is a Stokes parametric metalens, which has the ability to fully detect Stokes parameters. In design, it is generally considered to be a multifocal metalens. Multifocal metalenses can often be divided into four-focal metalenses and six-focal metalenses.

[0054] In some embodiments, the focus point 5 may include four or six, or other quantities. The following description focuses on four focus points and six focus points.

[0055] Specifically, in some embodiments, the focusing points 5 include four points arranged in the focusing plane as follows: X-ray polarized light is focused at the upper left corner, Y-ray polarized light is focused at the upper right corner, 45° linearly polarized light is focused at the lower left corner, and left-handed circularly polarized light is focused at the lower right corner.

[0056] Specifically, in some other embodiments, the focusing points 5 include six points and are arranged on the focusing plane as follows: X-ray polarized light is focused at the upper left corner, Y-ray polarized light is focused at the upper left corner, 45° linearly polarized light is focused at the upper center position, 135° linearly polarized light is focused at the lower center position, left-handed circularly polarized light is focused at the upper right corner, and right-handed circularly polarized light is focused at the lower right corner.

[0057] Compared to existing Stokes parametric metalenses, the metalens for full Stokes polarization detection provided by this invention has advantages such as complete image acquisition, convenient testing, and easy calibration. At the same time, it can recover Stokes parameters to obtain complete polarization information of the image, thereby increasing the dimensionality of the image information, which has practical significance for engineering applications.

[0058] Meanwhile, the present invention provides a design method for a metalens for all-Stokes polarization detection, including a staggered or random staggered arrangement design of the metalens and a full-Stokes parametric recovery step.

[0059] It is important to clarify the prerequisites for the proposed metalens design method: this method targets a fully Stokes metalens, which should possess the capability to completely detect Stokes parameters. Based on this, the Stokes parameters of an unknown beam are recovered using this metalens, allowing for the understanding of its polarization state, which is crucial for polarization imaging. This method is applicable to staggered or randomly staggered metalenses, and is also effective for other arrangement methods.

[0060] like Figure 3 As shown, the staggered or random staggered arrangement design of the meta-lens includes the following steps:

[0061] S110. Determine the number of focal points and the position where polarized light of different polarization states is focused onto the focal plane;

[0062] S120. Calculate the phase distribution value of polarized light with different polarization states relative to the entire metalens area when the polarized light is focused to different focal points;

[0063] S130. Based on the phase distribution value at each focal point, select the nanostructure unit most suitable for a certain polarization light using the principle of minimum error;

[0064] S140. Combine all nanostructure units to generate a pattern of polarized light for a specific polarization state;

[0065] S150. Multiple patterns for different polarized light are arranged in an alternating or random alternating manner.

[0066] Specifically, in some embodiments, the staggered or random staggered arrangement design of the metalenses includes the following steps:

[0067] First, determine the number of focal points 5 and the position where polarized light of different polarization states is focused onto the focal plane 4. Taking a four-focal Stokes parametric metalens in a multifocal system as an example, the lens itself needs to focus different polarized light onto different positions. Here, it is set to focus the incident X-ray polarized light onto the upper left corner of the lens, the incident Y-ray polarized light onto the upper right corner of the lens, the incident 45° linearly polarized light onto the lower left corner, and the incident left-handed circularly polarized LCP light onto the lower right corner.

[0068] Then, calculate the phase distribution of polarized light with different polarization states relative to the entire metalens area when focused at different focal points 5. Specifically, this involves calculating the phase distribution under each polarization state:

[0069] For X and Y linearly polarized light, anisotropic nanostructure units are selected here. Consideration is given to multiplexing the polarization of the X and Y orthogonal linearly polarized light into one nanostructure unit, that is, using one nanostructure unit to simultaneously control the X and Y linearly polarized light. Of course, it is also possible to choose two nanostructure units instead of multiplexing the polarization of the X and Y orthogonal linearly polarized light.

[0070] For 45° linearly polarized light, the design needs to be based on X-ray polarized light, that is, only the response of the nanostructure unit to X-ray polarized light is considered, and finally the nanostructure unit designed based on X-ray polarized light is rotated 45° counterclockwise.

[0071] For left-handed circularly polarized light, anisotropic nanostructure units with high transmittance and a phase difference of π in the x and y directions are selected. These nanostructure units are then rotated counterclockwise by a certain angle. The angle is obtained by dividing the phase value calculated using the formula by 2, paying attention to the conversion between radians and angles. The required phase value φ at each position is calculated using the following formula:

[0072]

[0073] in For the wavelength, , Let be the coordinates of the nanopillar. This is the focal length of the lens.

[0074] Then, based on the phase distribution value at each focusing point 5, the most suitable nanostructure unit 2 for a certain polarization is selected using the principle of minimum error. After calculating the phase under each polarization using the formula, the appropriate anisotropic nanostructure unit is selected according to the principle of minimum error for the corresponding phase distribution under each polarization. That is, for X and Y linearly polarized light, the phase of X and Y linearly polarized light at the same position needs to be considered simultaneously, and the most suitable anisotropic nanostructure unit is selected to simultaneously control the two linearly polarized lights. For 45° linearly polarized light, it is considered to first be X linearly polarized light, then the most suitable nanostructure unit is selected, and finally the nanostructure unit is rotated 45° counterclockwise.

[0075] For left-handed circularly polarized light LCP, it is necessary to select an anisotropic nanostructure unit with high transmittance and a phase difference of π in the x and y directions. Then, rotate the nanostructure unit counterclockwise by a certain angle. The size of the angle is obtained by dividing the phase value calculated by the formula by 2. Note the conversion between radians and angles.

[0076] Then, all nanostructure units 2 are combined to generate a pattern for polarized light of a specific polarization state. The selected structures for each polarization state are then combined to form three patterns: one pattern to control X and Y linearly polarized light, one pattern to control 45° linearly polarized light, and one pattern to control left-handed circularly polarized light (LCP). These three patterns are identical in size and period; the difference lies in the structure at the same location in each pattern, as different structures control different polarized light.

[0077] In some embodiments, combining multiple layouts for different polarized light in an alternating arrangement includes:

[0078] Select the version at a specific location on the paper. Figure 1 The nanostructure unit at that location, selected at the next defined location on the canvas. Figure 2 The nanostructure unit at this location, selected at another location on the surface. Figure 1 The nanostructure units at that position are selected in different orders, and the order is changed in the next row or column, and so on, eventually forming an alternating metalens pattern.

[0079] In other embodiments, multiple patterns for different polarized light are randomly interleaved and combined, including:

[0080] At a certain location on the image, a nanostructure unit 2 of a certain pattern is randomly selected at that location. At the next location, a nanostructure unit 2 of a certain pattern is randomly selected at that location, and so on, until a metalens pattern with random staggered arrangement is finally formed.

[0081] This method can transform Stokes multifocal metalenses with arbitrary polarization combinations into staggered or random arrangements, and then perform Stokes parameter detection and recovery on such staggered or random Stokes parametric metalenses.

[0082] Multiple patterns targeting different polarizations are arranged alternately or randomly to form a new pattern. For an alternate arrangement, at a specific position on the pattern, a nanostructure unit from the pattern controlling X and Y linear polarization is selected. At the next specific position, a nanostructure unit from the pattern controlling 45° linear polarization is selected. At yet another position, a nanostructure unit from the pattern controlling left-handed circularly polarized LCP is selected. The selection order is changed in the next row or column, and so on, ultimately forming an alternately arranged metalens pattern. For a random arrangement, at a specific position on the pattern, a nanostructure unit from one of these three patterns is randomly selected. At the next position, another nanostructure unit from one of these three patterns is randomly selected, and so on, ultimately forming a randomly arranged metalens pattern. This new pattern will simultaneously include the content of three patterns and possess the controllability of all three patterns.

[0083] The following section will use a quadfocal Stokes parametric metalens as an example to introduce the full Stokes parametric recovery method. This process is applicable to any arrangement and other multifocal Stokes parametric metalenses.

[0084] This invention provides a method for the full Stokes parameter recovery of metalenses with staggered or random staggered arrangements. By combining a designed full Stokes parameter lens with staggered or random staggered polarization multifocal arrangement with the Stokes parameter recovery method, the Mueller matrix of the Stokes parameter lens is calibrated using a known polarization state, thereby obtaining the Stokes parameter of the unknown polarized light to achieve the recovery of the Stokes parameter.

[0085] In practical implementation, for a four-focal metalens, X-ray polarized light, Y-ray polarized light, 45° linearly polarized light, and left-hand circularly polarized light (LCP) can be focused at different positions on the focal plane. For a six-focal metalens, X-ray polarized light, Y-ray polarized light, 45° linearly polarized light, 135° linearly polarized light, left-hand circularly polarized light (LCP), and right-hand circularly polarized light (RCP) can be focused at different positions on the focal plane.

[0086] The following section will use a quadfocal Stokes parametric metalens as an example to introduce the full Stokes parametric recovery method. This process is applicable to any arrangement and other multifocal Stokes parametric metalenses.

[0087] like Figure 4 As shown, the whole Stokes parameter recovery step includes:

[0088] S210. Polarized light with the same incident intensity but different polarization states;

[0089] S220. At each incident point, calculate the focal point intensity value at each designed position to construct a reconstructed light intensity matrix;

[0090] S230. Calculate the theoretical Stokes parameters of the corresponding incident polarized light and construct the known Stokes parameter matrix;

[0091] S240. Calculate the pseudo-inverse matrix of the reconstructed light intensity matrix. Multiply the known Stokes parameter matrix by the pseudo-inverse matrix to obtain the reconstructed Mueller matrix, thereby completing the reconstruction of the metalens.

[0092] Specifically, in some embodiments, the implementation steps of the full Stokes parameter recovery step are as follows:

[0093] First, incident polarized light with the same intensity but different polarization states; specifically, incident X-ray polarized light, Y-ray polarized light, 45° linearly polarized light, 135° linearly polarized light, left-handed circularly polarized light (LCP), and right-handed circularly polarized light (RCP) with the same intensity.

[0094] Then, at each incident point, the focal intensity value at each designed position is obtained. The focal intensity value is taken as three times the full width at half maximum of the focal point. The intensities of each focal point on the focal plane are calculated and recorded. There are four designed focal points here. A total of six different polarizations need to be incident. Finally, six sets of values ​​are calculated and obtained, forming a 4×6 light intensity matrix, which can be called the reconstructed light intensity matrix.

[0095] Then, the theoretical Stokes parameters of the corresponding incident polarized light are calculated to form a known Stokes parameter matrix. Specifically, the theoretical Stokes parameters S0, S1, S2, and S3 of the corresponding incident polarized light are calculated. There are a total of six types of polarized light, each with its own theoretical Stokes parameters, which ultimately form a 4×6 known Stokes parameter matrix.

[0096] Then, the pseudo-inverse matrix of the reconstructed light intensity matrix is ​​calculated. The known Stokes parameter matrix is ​​multiplied by the pseudo-inverse matrix to obtain the reconstructed Mueller matrix, thus completing the reconstruction of the metalens. Specifically, the pseudo-inverse matrix of the reconstructed light intensity matrix is ​​calculated, and the Stokes parameter matrix is ​​multiplied by the pseudo-inverse matrix of the reconstructed light intensity matrix to obtain a 4×4 numerical matrix, which is called the reconstructed Mueller matrix. At this point, the reconstruction of the metalens is completed.

[0097] Subsequently, the incident polarized light of unknown polarization state is used to obtain the focal intensity values ​​at each designed position, forming a reconstructed light intensity matrix. Multiplying the reconstructed Mueller matrix by the light intensity matrix and normalizing it yields the Stokes parameter matrix for the unknown polarization state. This allows for the calculation of the degree of polarization or the polarization angle, thus obtaining the polarization information of the object. Specifically, after obtaining the reconstructed Mueller matrix, the incident polarized light of unknown polarization state yields the focal intensity values ​​at four designed positions, forming a 4×1 matrix called the light intensity matrix. Multiplying the reconstructed Mueller matrix by the light intensity matrix and normalizing it provides the Stokes parameter for the unknown polarization state, which is then used to calculate the degree of polarization or the polarization angle, thus obtaining the polarization information of the object.

[0098] It should be noted that this method is applicable to Stokes parametric metalenses of any arrangement. It is necessary to keep the intensity value of the incident polarized light the same during the reconstruction process. This can be normalized to the intensity value of one type of incident polarized light or directly ensure that the intensity values ​​of all incident polarized light are the same.

[0099] The provided design method avoids problems such as alignment difficulties and incomplete imaging, improving image quality and facilitating post-processing. It features a clear theoretical implementation process, ease of programming, and convenient use, and can be used at any wavelength, such as ultraviolet, visible light, and infrared, making it suitable for a wide range of applications. Furthermore, this full Stokes parametric restoration method is highly scalable, capable of restoring not only multifocal staggered or randomly staggered Stokes parametric metalenses, but also multifocal Stokes parametric metalenses with other arrangements.

[0100] The technical solution of the present invention will be described in detail below with reference to specific embodiments, so that the solution can be better understood. It should be noted that the focus of the present invention is on the method of Stokes parametric recovery, taking a four-focal interlaced or randomly interlaced Stokes parametric metalens in a multifocal lens as an example. Of course, the invention is still applicable to other Stokes parametric metalenses.

[0101] Figure 2The diagram shows a partial layout of the metalens. Rectangles and ellipses are used as the shapes of the nanostructure units. There are a total of three types of nanopillar units with different control functions. Among them, the nanostructure units without rotation angle can control X-ray polarized light and Y-ray polarized light, the nanostructure units rotated 45° counterclockwise are responsible for controlling 45° linearly polarized light, and the nanostructure units with inconsistent rotation angles are responsible for controlling left-handed circularly polarized light LCP.

[0102] The Stokes parameters consist of four parameters, S0, S1, S2, and S3, defined as follows:

[0103]

[0104]

[0105]

[0106]

[0107] Among them I x I y I 45 I 135 I LCP I RCP These represent the light intensities of X-ray, Y-ray, 45°, 135°, left-handed circularly polarized (LCP), and right-handed circularly polarized (RCP) light in the incident polarized light, respectively. Ax and Ay represent the amplitudes of the X-ray and Y-ray polarized light in the incident polarized light, respectively. The parameter δ represents the phase difference between the Y-ray polarized component and the X-ray polarized component in the incident polarized light. These four parameters can be used to completely describe any polarization state.

[0108] List the Stokes parameters of the known incident polarized light into a matrix. For X-polarized light, Y-polarized light, 45° linearly polarized light, 135° linearly polarized light, left-handed circularly polarized light (LCP), and right-handed circularly polarized light (RCP) with the same incident intensity, each polarized light beam has four known Stokes parameters. The six polarized light beams can be written as a 4×6 known Stokes parameter matrix S, as shown below:

[0109]

[0110] Figure 5For the focal plane focus maps obtained from incident X-ray linearly polarized light, Y-ray linearly polarized light, 45° linearly polarized light, 135° linearly polarized light, left-handed circularly polarized light (LCP), and right-handed circularly polarized light (RCP), the focal intensity value at each designed position is calculated. The focal intensity value is taken as three times the full width at half maximum (FWHM) of the focal point. The intensities of each focal point on the focal plane are calculated and recorded. Here, there are four designed focal points, requiring a total of six different polarizations. Finally, six sets of values ​​are calculated and obtained, forming a 4×6 intensity matrix, which can be called the reconstructed intensity matrix I. all It should be noted that the incident intensity of the left-hand and right-hand circularly polarized light is twice that of other linearly polarized light. Therefore, when calculating the intensity, the intensity of the focal point generated by the left-hand and right-hand circularly polarized light should be divided by 2 to ensure that the incident light intensity is the same.

[0111] The intensity value within three times the full width at half maximum (FWHM) of the focal point is taken as the focal intensity value. From top to bottom, the matrix represents the intensity at the focal point of X-polarized light, the intensity at the focal point of Y-polarized light, the intensity at the focal point of 45° linearly polarized light, and the intensity at the LCP focal point of left-handed circularly polarized light. From left to right, the matrix represents the intensity components obtained from the incident X-polarized light, Y-polarized light, 45° linearly polarized light, 135° linearly polarized light, left-handed circularly polarized light (LCP), and right-handed circularly polarized light (RCP). Example: Reconstructed Intensity Matrix I all As shown in Table 1.

[0112] Table 1 Reconstructed Light Intensity Matrix I all

[0113]

[0114] After obtaining the reconstructed light intensity matrix, the Mueller matrix M of the metasurface can be obtained, which is derived from the following formula.

[0115]

[0116] Subsequently, polarized light of arbitrary polarization states is incident, and the focal intensity value at the corresponding designed focal point is obtained. Multiplying this value by the M matrix and normalizing it yields the Stokes parameter for the arbitrary polarization state. The following test obtains the light intensity values ​​at the focal positions of -30° elliptically polarized light, 30° linearly polarized light, 45° elliptically polarized light, and 60° linearly polarized light, respectively. Each beam of polarized light has four designed focal intensity values, as shown below. Figure 6 As shown, a 4×4 light intensity matrix is ​​formed, denoted as I. test .

[0117] It should be noted that the degree of elliptically polarized light at this point is the phase difference between Y polarization and X polarization in the elliptically polarized light. Furthermore, the intensity of the incident light does not need to be considered because it will undergo normalization. The resulting intensity matrix is ​​shown in Table 2.

[0118] Table 2. Test polarization light intensity matrix

[0119]

[0120] Then, the Mueller matrix M is compared with the intensity matrix I of the test polarized light. test By multiplying and normalizing, the Stokes parameter S of the tested polarized light can be obtained. test As shown below

[0121]

[0122] The ideal Stokes parameter S of the incident polarized light mentioned above theory As shown below

[0123]

[0124] It is clearly visible that the recovered Stokes parameters are almost identical to the ideal Stokes parameter values. The error (calculated by subtracting each recovered Stokes parameter value from the theoretical Stokes parameter value, summing the absolute values ​​of the differences, and then dividing by the sum of all theoretical Stokes parameters) is only 0.00844%, less than 0.01%, demonstrating the invention's remarkably high accuracy. Simultaneously, calculations were also performed on six-focal multifocal configurations, with an error of only 0.00688%. Calculations were also conducted for other different arrangements, such as... Figure 7 The layouts shown have very low errors and will not be listed individually here.

[0125] The final process can be roughly divided into four main parts, such as... Figure 8 As shown, other polarization states can be selected during reconstruction, but there should be more than four, and preferably a Platonic solid, while ensuring that the incident light intensity is the same.

[0126] The proposed method for full Stokes parametric polarization restoration based on staggered or randomly staggered metalenses can restore polarization for any Stokes parametric metalens, such as four-focal or six-focal multifocal Stokes parametric metalenses. It can also restore polarization for different arrangements, such as vertical, intermittent, or staggered arrangements, achieving extremely low restoration results with an error of less than 0.01%. It has the advantages of strong adaptability, high precision, and clear process.

[0127] Furthermore, this invention can perform polarization restoration on any multifocal Stokes parametric metalens, as long as the multifocal focal length can be used for Stokes parametric restoration. This paper will use four-focal or six-focal lenses as examples, both of which achieve near-zero error restoration results.

[0128] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for designing a metalens for all-Stokes polarization detection, characterized in that, This includes the design steps for the random staggered arrangement of metalenses and the full Stokes parametric recovery steps; The random staggered arrangement design steps of the meta-lens include: First, determine the number of focal points (5) and the position where polarized light of different polarization states is focused onto the focal plane; Then, the phase distribution value of polarized light with different polarization states relative to the entire metalens area is calculated when the polarized light with different polarization states is focused to different focal points; Then, based on the phase distribution value on each focal point (5), the nanostructure unit (2) most suitable for a certain polarization light is selected using the principle of minimum error. Then, all the nanostructure units (2) are combined to generate a pattern of polarized light for a certain polarization state; Finally, multiple layouts for different polarized light are combined in an alternating or random arrangement; multiple layouts for different polarized light are combined in a random alternating arrangement, including: At a certain position on the image, a nanostructure unit (2) of a certain pattern is randomly selected at that position. Then, a nanostructure unit (2) of a certain pattern is randomly selected at the next position. This process is repeated until a metalens pattern with random staggered arrangement is formed.

2. The design method of the metalens for all-Stokes polarization detection according to claim 1, characterized in that, Calculating the phase distribution of left-handed circularly polarized light includes: An anisotropic nanostructure unit with high transmittance and a phase difference of π in the x and y directions is selected. Then, the nanostructure unit is rotated counterclockwise by a set angle. The required phase value φ at each position is calculated according to the following formula: in For the wavelength, , Let be the coordinates of the nanopillar. This is the focal length of the lens.

3. The design method of the metalens for all-Stokes polarization detection according to claim 1, characterized in that, The whole Stokes parameter recovery steps include: First, incident polarized light with the same intensity but different polarization states; Then, at each incident point, the intensity value of the focal point (5) at each design position is calculated to form a reconstructed light intensity matrix; Then, the theoretical Stokes parameters of the corresponding incident polarized light are calculated to construct the known Stokes parameter matrix; Finally, the pseudo-inverse matrix of the reconstructed light intensity matrix is ​​calculated, and the known Stokes parameter matrix is ​​multiplied by the pseudo-inverse matrix to obtain the reconstructed Mueller matrix, thereby completing the reconstruction of the metalens.

4. The design method of the metalens for all-Stokes polarization detection according to claim 3, characterized in that, The full Stokes parameter recovery step also includes: After obtaining the reconstructed Mueller matrix, the polarized light of unknown polarization state is incident, and the focal intensity values ​​at each designed position are obtained to form the reconstructed light intensity matrix. The reconstructed Mueller matrix is ​​multiplied by the light intensity matrix and normalized to obtain the Stokes parameter matrix of the unknown polarization state. Then, the degree of polarization or polarization angle is calculated to obtain the polarization information of the object.

5. A method for recovering all-Stokes parameters using the design method of a metalens for all-Stokes polarization detection as described in claim 1, characterized in that, The Stokes parameter recovery method is as follows: The multifocal metalens has four focal points. First, X-polarized light, Y-polarized light, 45° linearly polarized light, 135° linearly polarized light, left-handed circularly polarized light (LCP), and right-handed circularly polarized light (RCP) with the same intensity are incident. At each incident point, the polarization focal point intensity value at each designed position is obtained. The focal point intensity value is taken as three times the full width at half maximum of the focal point. The intensity of each polarization focal point on the focusing plane is calculated and recorded. There are four designed polarization focal points, and a total of six different polarizations need to be incident. Finally, six sets of values ​​are calculated and obtained, which constitute a 4×6 light intensity matrix, called the reconstructed light intensity matrix. The theoretical Stokes parameters S0, S1, S2, and S3 for the corresponding incident polarized light are calculated, resulting in a total of six polarized light types, each with its own theoretical Stokes parameters. This forms a 4×6 known Stokes parameter matrix. Then, the pseudo-inverse matrix of the reconstructed light intensity matrix is ​​calculated, and the Stokes parameter matrix is ​​multiplied by the pseudo-inverse matrix to obtain a 4×4 numerical matrix, which is called the reconstructed Mueller matrix. The reconstruction aspect of the meta-lens is now complete. Subsequently, polarized light of unknown polarization state is incident, and the focal intensity values ​​at four designed positions are obtained, forming a 4×1 matrix called the light intensity matrix. Multiplying the reconstructed Mueller matrix by the light intensity matrix and normalizing it yields the Stokes parameters for the unknown polarization state. This allows the polarization degree or polarization angle to be calculated to obtain the polarization information of the object.

6. A metalens for all-Stokes polarization detection, fabricated using the design method of the metalens for all-Stokes polarization detection as described in claim 1, characterized in that, The metalens comprises a metalens substrate (3) and nanostructure units (2); The nanostructure units (2) are randomly and alternately arranged on the metalens substrate (3); The meta-lens is configured such that after a polychromatic light source (1) illuminates the meta-lens, multiple nanostructure units (2) focus polarized light of different polarization states to different positions, forming different focal points (5) on the focusing plane (4).

7. The metalens for all-Stokes polarization detection according to claim 6, characterized in that, The focusing points (5) include four points and are arranged in the focusing plane as follows: X-ray polarized light is focused to the upper left corner, Y-ray polarized light is focused to the upper right corner, 45° linearly polarized light is focused to the lower left corner, and left-handed circularly polarized light is focused to the lower right corner.

8. The metalens for all-Stokes polarization detection according to claim 6, characterized in that, The focusing points (5) include six points and are arranged in the focusing plane as follows: X-ray polarized light is focused to the upper left corner, Y-ray polarized light is focused to the upper left corner, 45° linear polarized light is focused to the upper middle position, 135° linear polarized light is focused to the lower middle position, left-handed circularly polarized light is focused to the upper right corner, and right-handed circularly polarized light is focused to the lower right corner.

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