Design method for realizing virtual polarization element

Abstract

The invention discloses a design method for realizing a virtual polarization element, relates to the field of optical device design, and aims to solve the problems of large size, difficulty in integration and limited regulation and control capability of a traditional polarization device. According to the method, a virtual polarization function (including a Jones matrix and an additional phase) is preset on a target plane, a plane wave weighting factor is solved through high-dimensional Fourier transform, and source plane light field distribution is generated through superposition. The metasurface is used as a platform, and accurate mapping from a source plane Jones matrix to a device structure is realized by adjusting geometric parameters of a nanostructure and combining a double-matrix holography. According to the design scheme, a polarization state with controllable spatial distribution can be generated as required in a two-dimensional plane at any propagation distance, and additional phase information can be flexibly superposed, so that the flexibility, precision and integration capability of light field regulation and control are remarkably improved, and technical support is provided for applications such as new-generation lens-free imaging, polarization coding communication, light field synthesis and the like.

Description

Technical Field

[0001] The present invention relates to the field of optical device design, and specifically to a design method for realizing virtual polarization elements based on wavefront modulation, which is applicable to fields such as optical communication, optical sensing, imaging technology, and quantum information science. Background Art

[0002] Polarization is one of the fundamental properties of light, used to describe the vibration characteristics of the electric field vector along the light propagation direction. Compared with traditional light intensity and phase information, polarization provides an additional degree of freedom for optical systems, thus significantly expanding the processing and transmission capabilities of optical information. This property is not only of great significance in theoretical research but also shows broad application prospects in fields such as optical communication, optical sensing, imaging technology, and quantum information science.

[0003] The precise control of the polarization state is usually achieved by changing the propagation characteristics of light in materials, such as adjusting the refractive index or absorption coefficient differences in different polarization directions. Traditionally, these control methods rely on anisotropic materials or optically active materials. However, due to the inherent limitations of solid materials, traditional polarization elements are usually large in size and difficult to meet the requirements of device miniaturization and integration, especially in non-contact applications. Therefore, researching polarization control methods that break through the limitations of solid materials and developing polarization elements with "virtual" characteristics have become an important direction in modern optical research. Summary of the Invention

[0004] The purpose of the present invention is to provide a design method for realizing virtual polarization elements based on high-dimensional weighted plane wave superposition and metasurface technology in view of the problems existing in the prior art that traditional polarization elements rely on anisotropic or optically active solid materials, resulting in large device size, difficulty in meeting the requirements of miniaturization and integration, and limited function realization especially in non-contact applications. This method realizes the functions equivalent to traditional polarization elements in the target plane through optical field control, breaks through the limitations of solid materials, and significantly improves the flexibility and precision of the control of the polarization state and phase distribution, providing a new path for the miniaturization, integration, and multi-functional design of optical elements.

[0005] To achieve the above-mentioned invention purpose, the present invention provides the following technical solutions.

[0006] The present invention provides a design method for realizing virtual polarization elements, including the following steps:

[0007] 1) Define the target polarization function: In a rectangular region of a two-dimensional target plane, describe the function of the virtual polarization element in the target plane through a complex matrix where the matrix is a Jones matrix for realizing polarization conversion, and is a phase modulation function;

[0008] 2) Solve the weighting factor by high-dimensional Fourier transform: According to the length L x and width L y of the target area, calculate the plane-wave weighting factor by high-dimensional Fourier transform;

[0009] 3) Construct the superposition light field of plane waves: Use the plane-wave weighting factor obtained in step 2) to superpose plane waves to generate the electric-field distribution of the target plane, making the electric-field distribution equivalent to the result after the incident light field passes through the Jones matrix and phase modulation, so as to achieve equivalent polarization control;

[0010] 4) Metasurface implementation platform: Use the metasurface as the implementation platform. Utilize its anisotropic characteristics. By adjusting the geometric parameters of the metasurface unit structure and double-matrix holography, convert the superposed electric-field distribution into a parameter combination that conforms to the form of the metasurface unit matrix, and complete the physical implementation of the virtual polarization element.

[0011] In step 1), specifically defining the target polarization function is to implement a virtual polarization optical element on the spatial plane (z = z0), and its function is described by the (2×2) complex matrix and is defined within a rectangular region L x ×L y ; where the matrices and represent the preset Jones matrix and phase modulation respectively. The Jones matrix is used to achieve the desired polarization conversion, and the phase modulation is used to control the phase; ~ represents a (2×2) matrix; the function of the virtual polarization element means that there is no polarization element at the target position, but the light field here is equivalent to the incident light field being affected by a polarization element described by the Jones matrix at this position; the function of the virtual polarization element on the target plane includes one or more combinations of a circular polarizer, a 45° linear polarizer, a half-wave plate, and a quarter-wave plate, and each function gives a different additional phase.

[0012] In step 2), calculating the plane-wave weighting factor by high-dimensional Fourier transform is as follows:

[0013]

[0014] where L x , L y are the length and width corresponding to the area range for realizing the polarization function , and are the wave numbers in the x and y directions respectively, u = -N1, -N1 + 1, … 0, … N1 - 1, N1; v = -N2, -N2 + 1, … 0, … N2 - 1, N2.

[0015] In step 3), the plane wave superposition light field is constructed. Specifically, the high-dimensional plane wave with the Jones matrix as the amplitude is superimposed on the z=0 plane:

[0016]

[0017] in is the wave number in the z direction, satisfying k = 2π / λ is the vacuum wave number.

[0018] In step 4), the metasurface adopts a TiO2 metasurface, and the metasurface unit structure adopts titanium dioxide nanobricks. By adjusting the aspect ratio and rotation angle of the titanium dioxide nanobricks, independent regulation of the amplitude and phase of the light field is achieved.

[0019] In step 4), the metasurface unit matrix satisfies the unitary matrix and symmetric matrix forms, and the target electric field distribution is converted into the standard form of the metasurface unit through double-matrix holography.

[0020] In step 4), the superimposed electric field distribution is converted into a parameter combination that conforms to the metasurface unit matrix form, which is determined by matching a preset nanostructure library, wherein the nanostructure library contains transmittance and phase delay characteristics corresponding to different aspect ratios and rotation angles, and the nanostructure library is solved by Get a device A virtual wave plate is realized on a spatial plane (z=z0).

[0021] The core concept of the present invention is to achieve precise control of the polarization state and phase distribution of the light field by assigning high-dimensional weighting factors to the superimposed plane waves. This method can realize customized virtual polarization function on a two-dimensional target plane at any distance behind the incident plane through the plane wave superposition of high-dimensional weighting factors. This design can not only generate specific polarization states according to needs, but also flexibly control the additional phase on this basis, thereby significantly improving the flexibility and accuracy of light field control.

[0022] The present invention is highly flexible and adjustable, and can accurately achieve diverse polarization states and phase distributions on the target plane without relying on traditional physical devices. This "virtual" polarization control strategy breaks through the limitations of physical materials and provides a new path for the design of multifunctional optical components. Compared with traditional polarization control methods, this technology no longer relies on specific physical material properties or physical devices, but achieves overall control of the light field through wavefront design. This innovative breakthrough in "virtual" polarization function provides a new design paradigm for the miniaturization, integration and multifunctional development of optical components, and shows broad application prospects in modern optical communications, imaging, information processing and other fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1Schematic diagram of the design of the main structure of the spatial virtual polarization element based on the metasurface in the embodiment of the present invention.

[0024] Figure 2 Schematic diagram of the structure of titanium oxide nanobricks and the characteristics of the nanolibrary in the embodiment of the present invention. Among them, (a) is the schematic diagram of the structure of titanium dioxide nanobricks; (b) is the schematic diagram of the transmittance and phase change of the titanium dioxide nanolibrary.

[0025] Figure 3 Schematic diagram of the design and response of the target plane polarization function in Embodiment 1 of the present invention. Among them, (a) is the design diagram of the target plane polarization function; (b) is the amplitude and phase response curves of the target plane to the incident linearly polarized light (polarization angle changing from 0° to 180°); (c) is the schematic diagram of the polarization response of the target plane to the incident light of four special polarization states.

[0026] Figure 4 Schematic diagram of the design and response of the target plane polarization function in Embodiment 2 of the present invention. Among them, (a) is the design diagram of the target plane polarization function; (b) is the amplitude (first row), phase (second row), and additional phase (third row) response curves of the target plane to the incident light (linearly polarized light rotating from 0° to 180°); (c) is the schematic diagram of the polarization response of the target plane to the incident light of four special polarization states.

[0027] Figure 5 Schematic diagram of the design and response of the target plane multi-functional polarization function in Embodiment 3 of the present invention. Among them, a) is the design diagram of the target plane polarization function; (b) is the amplitude (first row), phase (second row), and additional phase (third row) response curves of the target plane to the incident light (linearly polarized light rotating from 0° to 180°); (c) is the schematic diagram of the polarization response of the target plane to the incident light of four special polarization states.

[0028] Figure 6 Schematic diagram of the design and response of the target plane multi-functional polarization function in Embodiment 4 of the present invention. Among them, the first row is the design diagram of the target plane polarization function; it consists of a series of half-wave plates with the fast axis direction and additional phase changing with the spatial position, and the background color represents the phase change. The first column (m, l) = (1, 0), the second column (m, l) = (4, 0), the third column (m, l) = (4, 1), the fourth column, inner ring: (m, l) = (1, 0), outer ring: (m, l) = (-2, 1). The second to fourth rows: |E of the output electric field of the target plane out | 2Distribution of polarization states, incident polarization states: θ=0 (second row), θ=90° (third row) linearly polarized Gaussian light, left-handed circularly polarized Gaussian light (fourth row), the first column incident light half-waist w=10, the second and third columns w=40, the fourth column w=50. The light intensity is normalized to the incident light, the calculation area is (50um*50um), the white polarization ellipse represents the local polarization state, the arrow position represents the vibration phase, the gray inset represents the theoretical polarization state, and the scale bar is 10μm. DETAILED DESCRIPTION

[0029] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the following embodiments will further illustrate the present invention in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0030] The physical properties of the titanium dioxide nanobricks, the interaction between the units and the overall response characteristics of the metasurface in the present invention can be theoretically analyzed by solving Maxwell's equations and their corresponding boundary conditions, or obtained by numerical simulation calculations using electromagnetic field calculation software (such as the finite element method, the finite difference time domain method FDTD, etc.).

[0031] See also Figure 1 , showing the overall architecture of the metasurface realization platform, the present invention can realize customized polarization function on a two-dimensional plane at any distance behind the metasurface. By giving the light field a high-dimensional weighting factor, various virtual polarization optical elements can be approximately realized on a specified plane. When test light of different polarization states is incident on the metasurface, the corresponding polarization response characteristics will be presented on the specified plane.

[0032] The present invention realizes a virtual polarization optical element on a spatial plane (z=z0), and its function is represented by a (2×2) complex matrix Description, defined in a rectangular area L x ×L y In which the matrix and Respectively represent the preset Jones matrix and phase modulation, the former is used to achieve the desired polarization conversion, the latter is used to adjust the phase, and the present invention uses ~ to represent the (2×2) matrix. Here, virtual means that there is no polarization element at the target position, but the light field here is equivalent to the incident light field being subjected to a Jones matrix at this position. Describe the role of the polarization element. Once the polarization function Determine the corresponding matrix weighting factors through high-dimensional Fourier transform:

[0033]

[0034] Among them, L x ,Ly is to achieve the polarization function The length and width corresponding to the area range of and are the wave numbers in the x and y directions respectively (u = -N1, -N1 + 1, … 0, … N1 - 1, N1, v = -N2, -N2 + 1, … 0, … N2 - 1, N2). After the superposition of these (2N1 + 1)·(2N2 + 1) columns of high-dimensional plane waves with the Jones matrix as the amplitude on the z = 0 plane, there is:

[0035]

[0036] where is the wave number in the z direction, satisfying k = 2π / λ is the vacuum wave number. By solving a device is obtained to realize a virtual wave plate on the spatial plane (z = z0).

[0037] In a preferred embodiment, the present invention takes the TiO2 metasurface implementation platform as an example, and other implementation platforms can also be selected. This is mainly because titanium dioxide exhibits low optical loss in the visible light band and has excellent optical properties. With its anisotropic characteristics, the metasurface unit structure can support two different propagation modes, corresponding to different effective refractive indices and phase delays respectively, providing a physical basis for efficient optical field control. Specifically, by precisely designing and adjusting the geometric parameters (such as the aspect ratio) of titanium dioxide nanobricks and their rotation angles in the plane, independent control of the amplitude and phase of light can be achieved. This control mechanism enables the metasurface to flexibly meet the design requirements of optical elements. Since the standard form of the unit of the titanium dioxide metasurface is expressed as:

[0038]

[0039] Analysis shows that this matrix must satisfy the form of a unitary matrix and a symmetric matrix. To ensure that this expression conforms to the standard form of the metasurface unit, the present invention adopts double matrix holography (specifically, reference can be made to the literature Encoding Complex Fields by Using a Phase-Only Optical Element) to convert into a form that conforms to the standard of the metasurface unit matrix. Subsequently, by matching the corresponding dimensions in the titanium dioxide nanolibrary, the specific implementation is completed.

[0040] Figure 2Show the metasurface implementation platform of the present invention. This platform uses silica as the substrate, and by arranging titanium dioxide nanobricks with different sizes and rotation angles, the target polarization function is realized on the specified plane. By adjusting the aspect ratio of the titanium dioxide nanobricks, a titanium dioxide nanostructure library is constructed, and its height remains unchanged at 600 nm, providing a rich selection space for the design and function realization of the metasurface. Among them, Figure 2 In (a) is the schematic diagram of the titanium dioxide nanobrick structure. By adjusting the length and width (dx, dy) and rotation angle of the nanobrick Independent regulation of the amplitude and phase of the light field is achieved; Figure 2 In (b) is the schematic diagram of the transmittance (right figure) and phase change (left figure) of the titanium dioxide nanolibrary, showing the transmittance modulus value and phase delay characteristics corresponding to different geometric parameters, providing a parameter matching basis for the design of the metasurface unit structure.

[0041] The following gives specific embodiments:

[0042] Embodiment 1

[0043] A circular polarizer is set on the two-dimensional plane at z0 = 10 um behind the metasurface Define L in the plane at z0 = 10 um x = L y = 60 um rectangular area. The polarization function is distributed in the 10 um * 10 um square area at the center of the rectangle, and can be specifically expressed as Δ = 0.5 μm, see Figure 3 In (a). After determining the target polarization function, the corresponding matrix weighting factors are calculated using the high-dimensional Fourier transform (see Equation 1). These weighting factors are used to determine the superposition electric field distribution on the plane z = 0 (see Equation 2). At this time, the light field at each point in the plane is associated with a matrix transformation, thus providing a target transformation basis for the metasurface design.

[0044] The physical implementation platform is based on the titanium dioxide metasurface. The present invention uses double matrix holography to Convert it into a form that conforms to the metasurface unit matrix standard. Subsequently, the specific design and function realization of the metasurface unit are achieved by matching the closest size in the titanium dioxide nanolibrary.

[0045] To verify the accuracy of the design, the average amplitude and average phase difference responses of linearly polarized light when the polarization angle (θ°) changes from 0° to 180° are studied through simulation (the average amplitude and average phase difference refer to: the output light field within the range of 10 um * 10 um And The modulus value and phase difference are averaged, that is and to evaluate whether each metasurface achieves the expected polarization function. As can be seen from (b) in Figure 3 , the theoretical curve and the simulation curve are almost coincident. To further demonstrate the characteristics of the polarization device, for linearly polarized light, circularly polarized light, and elliptically polarized light with θ = 0° and θ = 135° respectively, the two-dimensional light intensity and polarization response of E on the target plane are plotted, see (c) in out . As can be seen from the figure, the theoretical calculation results and the full simulation results show a high degree of consistency at different incident polarization angles, indicating that the designed metasurface can stably generate the expected polarization response throughout the polarization angle range. Among them, Figure 3 , the modulus values of and are always close to 1, which conforms to the conversion characteristics of an ideal circular polarizer. In addition, the phase difference further verifies that the output optical field maintains a constant phase delay between two orthogonal components. In (c) in Figure 3 , the simulation results are in good agreement with the theoretical prediction (the lower right inset in (c) in Figure 3 ), verifying the accuracy and effectiveness of the present design method. Among them, when the incident light is left-handed circularly polarized, the output is almost completely extinguished, and the polarization state no longer has physical significance, so the theoretical prediction results in this case are not plotted.

[0046] Example 2

[0047] In Example 1, the present invention successfully realizes a circular polarizer. To further demonstrate the versatility of the design method, a half-wave plate is set on the two-dimensional plane at z0 = 10 μm behind the metasurface where L defined in the plane of z0 = 10 μm x = L y = 60 μm rectangular region, and the polarization function is distributed in a 10 μm * 10 μm square region at the center of the rectangle, which can be specifically expressed as Δ = 0.5 μm, see (a) in Figure 4 . Similarly, the amplitude and phase response curves of the target plane are calculated when the linearly polarized light changes at the polarization angle (θ°) from 0° to 180°, see (b) in Figure 4 , where the phase difference in the gray area is not well defined because the amplitude in these areas approaches zero and the phase has no practical significance; and for four typical incident polarization states (0° linearly polarized light, 135° linearly polarized light, left-handed circularly polarized light LCP, elliptically polarized light EP), the two-dimensional light intensity distribution and polarization response of the output optical field E out are plotted, see (c) in Figure 4 . As can be seen from the figure, whether it is Figure 4The amplitude and phase response curves of (b) in, or Figure 4 the two-dimensional light intensity and polarization response map of (c) in, the simulation results are in good agreement with the theoretical results.

[0048] Example 3

[0049] In Examples 1 and 2, the capabilities of the single-functional metasurface in specific polarization control are demonstrated respectively. To further verify the versatility of the proposed design method and the controllability of the additional phase, Example 3 is proposed, that is, the design and simulation verification of the multi-functional additional phase metasurface. This design aims to achieve the independent control ability of multiple polarization functions and their additional phases in the same plane. Specifically, in the four quadrants of the target plane z0 = 10um, four polarization devices are constructed respectively: a circular polarizer, a 45° linear polarizer, a half-wave plate, and a quarter-wave plate. The size of each device area is 10um * 10um, and they are distributed in the L x = L y = 60um rectangular area. Each device not only has a specific polarization function, but also introduces different additional phases. The complete target composite polarization function is defined as See details in Figure 5 (a) in. To evaluate the polarization control and additional phase regulation performance of this design, the output response of linearly polarized light during the process of the polarization angle (θ°) from 0° to 180° is simulated, mainly examining the output amplitude and phase response, including the polarization phase difference and the change of the additional phase. The results are as Figure 5 (b) shown; at the same time, the output two-dimensional light intensity and polarization state under four special incident polarized lights (such as linearly polarized light, circularly polarized light, etc.) are also analyzed, as Figure 5 (c) in shown. It can be seen from the figure that: Figure 5 In (b) in, the output amplitude and phase response curves corresponding to each device are highly consistent with the theoretical values throughout the polarization angle scanning range. Especially in terms of phase, in addition to maintaining the due polarization phase difference, the additional phase differences designed for different device areas are accurately presented, verifying the precise regulation ability of this metasurface for phase. Figure 5 (c) in shows the spatial images of the output light intensity and polarization distribution in each functional area under four typical polarized light incidences. It can be clearly observed that the output polarization states in different quadrants are consistent with the expected functions. For example, the output in the circular polarizer area is an approximately circular polarization ellipse, the 45° linear polarizer area shows a linear polarization distribution, and the wave plate area shows a typical phase delay effect. At the same time, the output light intensity distribution in each area is clear and the boundaries are distinct, without significant crosstalk, further indicating that this design has good spatial independence and multi-functional multiplexing ability. To sum up, Figure 5 (b) in and Figure 5The simulation results of (c) are highly consistent with the theoretical predictions, which not only proves the effectiveness of the designed metasurface in polarization control, but also demonstrates the ability to precisely control the additional phase in a unified platform for the first time, providing a new path for the joint control of complex polarization states and wavefront engineering.

[0050] Example 4

[0051] In order to demonstrate the flexibility and diversity of the method, a half-wave plate with an additional phase is further designed and arranged to construct a vortex wave plate with significant polarization dependence. The fast axis direction and additional phase change continuously with the spatial position, and the mathematical description is as follows: Where θ represents the fast axis direction of the wave plate, represents the additional phase. α is the azimuth angle, m is the topological charge of the vortex wave plate, θ0 is the fast axis direction when α=0; l represents the order of the phase, which determines the rate at which the phase changes along the azimuth angle. is the initial phase offset. Four different types of metasurface elements are designed and simulated, which respectively realize the following virtual half-wave plate functions on the z0=10um plane: (m,l)=(1,0) (first column), (m,l)=(4,0) (second column), (m,l)=(4,1) (third column) and dual-mode: inner ring: (m,l)=(1,0), outer ring: (m,l)=(-2,1) (fourth column), as shown in Figure 6 In all designs, the initial fast axis direction θ0 = 0, and the additional phase shift In order to further demonstrate the characteristics of the vortex wave plate, the E curves on the target plane are plotted for θ = 0°, θ = 90°, and left-handed Gaussian light. out Two-dimensional intensity and polarization response (see Figure 6 The second to fourth rows). It can be clearly seen from the figure that various virtual vortex wave plates have significant control effects on the incident polarization state: the first column (m,l) = (1,0): when the incident light is x-polarization (θ = 0°), the output light shows an obvious radial polarization distribution; when the incident light is y-polarization (θ = 90°), it is converted into an angularly polarized beam; when the incident light is left-handed circular polarization (LCP), an obvious dark spot is formed in the center, showing a phase singularity, and the circular polarization state is reversed, verifying the existence of the PB phase. The second column (m,l) = (4,0): the fast axis direction changes four times along the azimuth angle α, resulting in the output polarization having the same direction when α = 0°, 90°, 180°, 270°, and 360°; the output intensity diagram shows a spot structure with four-fold symmetry, verifying the realization of multiple polarization rotation control. The third column (m,l) = (4,1): an additional phase is introduced on the basis of the second column , so that the output optical field not only has multiple polarization controls but also superimposes a helical phase wavefront; it is clearly observed that the phase modulation causes changes in the polarization distribution in the directions of α = 90° and 270°, further illustrating the ability of phase control to regulate the polarization distribution. The fourth column shows a dual-mode structure: the inner and outer rings correspond to different combinations of (m, l) parameters respectively; different polarization distribution patterns of the double-ring structure are clearly visible in the image, verifying the feasibility of the multifunctional composite element; for example, under left-circular polarization (LCP) incidence, the central inner ring still retains the radial / azimuthal polarization characteristics, while the outer ring shows typical helical phase characteristics. These four vortex wave plates can generate vector polarization beams or vortex beams with helical phase wavefronts through precise control of the polarization state of the incident beam. Compared with the traditional vortex wave plates relying on liquid crystal polymer materials, the virtual vortex wave plate method proposed in this study significantly improves the miniaturization and integration levels of the device, and greatly expands the degrees of freedom of the optical field in terms of local polarization state and orbital angular momentum. This innovative scheme provides a new technical approach for achieving efficient and flexible optical field control.

[0052] The above embodiments are only preferred embodiments of the present invention and should not be considered as limiting the scope of implementation of the present invention. Any equivalent changes and improvements made within the scope of the application of the present invention should still fall within the scope covered by the patent of the present invention.

Claims

1. A design method for realizing a virtual polarization element, characterized in that The following steps are involved: 1) Define the target polarization function: In the rectangular area of ​​the two-dimensional target plane, through the complex matrix Describes the virtual polarization element function of the target plane, where the matrix is the Jones matrix, which is used to realize polarization conversion. is the phase modulation function; 2) High-dimensional Fourier transform to solve the weighting factor: according to the length and width L of the target area x , L y , plane wave weighting factors are calculated by high-dimensional Fourier transform; 3) constructing a plane wave superposition light field: using the plane wave weighting factor obtained in step 2) to superimpose the plane wave, generating an electric field distribution on the target plane, making the electric field distribution equivalent to the result of the incident light field after Jones matrix and phase modulation, and realizing equivalent polarization control; 4) Metasurface implementation platform: Taking the metasurface as the implementation platform and utilizing its anisotropic characteristics, by adjusting the geometric parameters of the metasurface unit structure and dual-matrix holography, the superimposed electric field distribution is converted into a parameter combination that conforms to the metasurface unit matrix form, thereby completing the physical implementation of the virtual polarization element.

2. A method for designing a virtual polarization element as claimed in claim 1, characterized in that In step 1), the definition of the target polarization function is to realize a virtual polarization optical element on the spatial plane (z=z0), whose function is represented by the (2×2) complex matrix Description, defined in a rectangular area L x ×L y In; the matrix and They represent the preset Jones matrix and phase modulation respectively. The Jones matrix is ​​used to achieve the desired polarization conversion, and the phase modulation is used to control the phase; ~ represents a (2×2) matrix.

3. A design method for realizing a virtual polarization element as claimed in claim 1, characterized in that In step 1), the virtual polarization element function means that there is no polarization element at the target position, but the light field here is equivalent to the incident light field being subjected to a Jones matrix at this position. Describe the role of the polarizing element.

4. A method for designing a virtual polarization element as claimed in claim 3, characterized in that The virtual polarization element function of the target plane includes one or more combinations of a circular polarizer, a 45° linear polarizer, a half wave plate, and a quarter wave plate, and each function imparts a different additional phase.

5. A design method for realizing a virtual polarization element as claimed in claim 1, characterized in that In step 2), the plane wave weighting factor is calculated by high-dimensional Fourier transform as follows: Among them, L x ,L y It realizes polarization function The length and width of the area range are and The wave numbers in the x and y directions are u = -N1, -N1+1, …0, …N1-1, N1; v = -N2, -N2+1, …0, …N2-1, N2.

6. A method for designing a virtual polarization element as claimed in claim 1, characterized in that In step 3), the plane wave superposition light field is constructed. Specifically, the electric field distribution of the high-dimensional plane wave with the Jones matrix as the amplitude after superposition on the z=0 plane is as follows: in, is the wave number in the z direction, satisfying k = 2π / λ is the vacuum wave number.

7. A design method for realizing a virtual polarization element as claimed in claim 1, characterized in that In step 4), the metasurface adopts a TiO2 metasurface, and the metasurface unit structure adopts titanium dioxide nanobricks. By adjusting the aspect ratio and rotation angle of the titanium dioxide nanobricks, independent regulation of the amplitude and phase of the light field is achieved.

8. A design method for realizing a virtual polarization element as claimed in claim 1, characterized in that In step 4), the metasurface unit matrix satisfies the unitary matrix and symmetric matrix forms, and the target electric field distribution is converted into the standard form of the metasurface unit through double-matrix holography.

9. A method for designing a virtual polarization element as claimed in claim 1, characterized in that In step 4), the superimposed electric field distribution is converted into a parameter combination that conforms to the metasurface unit matrix form, which is determined by matching a preset nanostructure library, wherein the nanostructure library contains transmittance and phase delay characteristics corresponding to different aspect ratios and rotation angles, and the superimposed electric field distribution is solved by Get a device A virtual wave plate is realized on a spatial plane (z=z0).

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