A Multi-Phase Metasurface Holographic Method Based on Wavelength and Polarization Decoupling

Abstract

The multi-phase metasurface holography method based on frequency and polarization decoupling belongs to the field of micro-nano holography. It includes the following steps: generating random phase holograms, multiplying them by a factor K to obtain n different K-fold phase holograms, calculating the mean square error of the output image and label, optimizing the phase of the random phase holograms using an adaptive moment estimation algorithm, multiplying the obtained basic phase by n factors K to obtain n optimized multi-phases, and matching the optimized multi-phases with frequency λ1 and a cross-circular polarization channel to obtain a phase φ; scanning the length and width of each nano-antenna column in the cross-circular polarization channel and the linear polarization channel with frequency λ2 to determine the complex amplitude modulation characteristics of the nano-antenna columns for different frequencies and polarizations, obtaining the corresponding phase distribution. This design of multi-phase metasurface holography based on frequency and polarization decoupling can improve energy conversion efficiency, and different combinations of polarization and frequency also enhance the flexibility of multi-phase holographic modulation.

Description

Technical Field

[0001] This invention relates to a multi-phase metasurface holographic method based on wavelength and polarization decoupling, belonging to the fields of micro-nano optics and holography. Background Technology

[0002] In recent years, metasurfaces, as a rapidly developing type of planar optical device for artificial intelligence, can achieve many functions through optimized design of nanostructures and arrays, finding applications in holographic displays, wavefront shaping, nonlinear optics, and high-capacity storage. They are gradually becoming the preferred approach for integrated and compact optical systems. Currently, most multi-phase holographic modulation schemes based on metasurfaces rely on nonlinear effects; however, multi-phase modulation based on nonlinear effects has low energy conversion efficiency and high experimental complexity. By designing multi-phase metasurface holograms based on wavelength and polarization decoupling, energy conversion efficiency can be improved. Different combinations of polarization and wavelength also enhance the flexibility of multi-phase holographic modulation. Summary of the Invention

[0003] This invention relates to a multi-phase metasurface holography method based on wavelength and polarization decoupling, belonging to the fields of micro-nano optics and holography. The invention generates a random phase hologram, multiplies the phase of the random phase hologram by n different factors K (K is any non-zero real number), obtaining n phase holograms of different factors K, and performs holographic reconstruction on the n phase holograms of different factors K to obtain output images. The mean square error of each of the n output images and their corresponding n labels is calculated. Based on the mean square error, the phase of the random phase hologram is optimized using an adaptive moment estimation algorithm to obtain the optimized basic phase. For the basic phase Multiplying by the corresponding n different multiples K, we get n optimized multiple phases. Recorded as Using a specific wavelength λ1 and a cross-circular polarization channel, a portion of the optimized multiple phase is used, such as Matching is performed to obtain a phase φ, where the cross-polarization channel is either left-handed circularly polarized (LCP) incident / transmitted to right-handed circularly polarized (RCP) or right-handed circularly polarized (RCP) incident / transmitted to left-handed circularly polarized (LCP). The remaining optimized multiple-phase metasurface is matched using another wavelength λ2 and a linear polarization channel. The multiple-phase metasurface used for wavelength and polarization decoupling is composed of multiple anisotropic nanoantenna columns with different geometries. To satisfy multiple-phase polarization decoupling at two wavelengths, the length and width of each nanoantenna column at a certain wavelength λ1 in the cross-circular polarization channel and at another wavelength λ2 in the linear polarization channel are scanned to determine the complex amplitude modulation characteristics of the nanoantenna columns for different wavelengths and polarizations, obtaining the corresponding phase distribution. The height H of the nanoantenna columns and the period P of the structural units are preset. The geometric dimensions (length and width) and rotation angle of the nanoantenna columns are determined, and the nanoantenna column array is arranged to form the metasurface. The nanoantenna column array is arranged according to the geometric dimensions and rotation angle of the nanoantenna columns to form the metasurface. The process involves generating a fabrication file and fabricating the material to obtain a solid metasurface structure. Designing a multi-phase metasurface hologram based on wavelength and polarization decoupling can improve energy conversion efficiency. Furthermore, different combinations of polarization and wavelength enhance the flexibility of multi-phase holographic modulation. This technology can provide new solutions for dynamic multi-phase beam directional refraction and excitation, orbital angular momentum communication, multi-phase holographic displays, optical encryption and camouflage, optical switching and shaping, and more.

[0004] In view of this, the purpose of this invention is to provide a multi-phase metasurface holographic method based on wavelength and polarization decoupling, the specific scheme of which is as follows:

[0005] In a first aspect, the multi-phase metasurface holography method based on wavelength and polarization decoupling disclosed in this invention includes the following steps:

[0006] Step 1: Generate a random phase hologram. Multiply the phase of the random phase hologram by n different factors K (K is any non-zero real number) to obtain n phase holograms with different K-fold multiplication factors. Perform holographic reconstruction on the n phase holograms with different K-fold multiplication factors to obtain the output image. Calculate the mean square error of each of the n output images and their corresponding n labels. Based on the mean square error, optimize the phase of the random phase hologram using an adaptive moment estimation algorithm to obtain the optimized basic phase. For the basic phase Multiplying by the corresponding n different multiples K, we get n optimized multiple phases. Recorded as

[0007] Step 2: Using a specific wavelength λ1 and a cross-circular polarization channel, the optimized multiple phase from Step 1 is applied as follows: Matching is performed to obtain a phase φ, wherein the cross-polarization channel is either left-handed circularly polarized (LCP) incident / transmitted to right-handed circularly polarized (RCP) or right-handed circularly polarized (RCP) incident / transmitted to left-handed circularly polarized (LCP); another wavelength λ2 and a linear polarization channel are used to optimize the remaining multiple phase from step one, such as... and Perform a match.

[0008] Step 3: The multi-phase metasurface used for wavelength and polarization decoupling is composed of multiple anisotropic nano-antenna columns with different geometric dimensions. To satisfy multi-phase polarization decoupling at two wavelengths, the length and width of each nano-antenna column corresponding to a certain wavelength λ1 in Step 2 are scanned in the cross-circular polarization channel and the linear polarization channel of another wavelength λ2. The complex amplitude modulation characteristics of the nano-antenna column for different wavelengths and polarizations are determined to obtain the corresponding phase distribution. The height H of the nano-antenna column and the period P of the structural unit are preset.

[0009] Step 4: Determine the geometric dimensions (length and width) and rotation angle of the nano-antenna pillars, and arrange the nano-antenna pillar array to form a metasurface.

[0010] Step 5: Arrange the nano-antenna pillar array according to the geometric dimensions and rotation angle of the nano-antenna pillars to form a metasurface; generate a processing file and process it to obtain a solid metasurface structure.

[0011] Optionally, step one can be implemented as follows:

[0012] A random phase hologram is generated. The phase of the random phase hologram is multiplied by n different factors K (K is any non-zero real number) to obtain n phase holograms of different factors K. Holographic reconstruction is performed on the n phase holograms of different factors K to obtain the output image. The holographic reconstruction is the reconstruction of the hologram to the object plane through Fourier transform. The mean square error (MSE) of the output image and the label is calculated based on the reference ground truth (target image) as the label. The mean square error Er(MSEs) of the reconstruction result and the label is:

[0013]

[0014] G represents the two-dimensional Fourier transform operation. n Indicates a label.

[0015] Based on the adaptive moment estimation algorithm, through the synchronous mean square error E r As a metric for optimizing the update in the loop phase, the random phase hologram is phase optimized to obtain the optimized basic phase.

[0016] For the basic phase Multiplying by the corresponding n different multiples K yields the optimized n multiple phases.

[0017]

[0018] Optionally, step two can be implemented as follows:

[0019] When light shines on the metasurface, the output light field E out This can be represented using a Jones matrix:

[0020] E out =J(θ)E in (2)

[0021] Among them, E in For the input light field incident through the circularly polarized channel, E in Represented as

[0022]

[0023] Polarization conversion is performed by determining the rotation angle (θ) of the metasurface nanoantenna pillar. The corresponding output light field E out Represented as:

[0024] E out =R -1 (θ)TR(θ)E in (4)

[0025] Where R(θ) represents the rotation matrix of the Jones matrix, and T represents the transmittance of the metasurface nanoantenna column, denoted as:

[0026]

[0027] and The eigenvectors of the metasurface nanoantenna pillars are represented in the x- and y-polarization channels; the transmittance T of the metasurface nanoantenna pillars can be expressed by inversely using Equation 4:

[0028]

[0029] In the decoupling of the cross-circular polarization channel, the RCP output and LCR output have completely independent phase distributions on the LCP and RCP incident channels, respectively.

[0030] When the output light field E out When the phase is determined to be multiple phases and In a cross-circular polarization channel at a certain wavelength λ1, the geometric phase under the cross-circular polarization is... It is a conjugate relationship, and the multiple phase is expressed as:

[0031]

[0032] Indicates the transmission phase. Indicates geometric phase, This represents the relationship between RCP incident and LCP output at a certain wavelength λ1. This represents the relationship between LCP incident and RCP output at a certain wavelength λ1. A simple derivation of Equation 7 yields the transmission phase. and the geometric phase Represented as:

[0033]

[0034] The phase φ is represented as:

[0035]

[0036] Optionally, step three can be implemented as follows:

[0037] Given the preset height H of the nanoantenna pillars and the period P of the structural unit, the length L and width W of each nanoantenna pillar are scanned at wavelengths λ1 and λ2, respectively, to determine the transmittance phase of the cross-circular polarization channel of nanoantenna pillars with different geometric dimensions at wavelength λ1. and the transmittance phase of the x-linear polarization channel at wavelength λ2 Transmittance phase of linearly polarized channel

[0038] Optionally, step four can be implemented as follows:

[0039] The geometric dimensions of the nano-antenna column are determined based on the minimum value of matrix L, where matrix L is:

[0040]

[0041] min represents the minimum value of the function, based on the geometric phase. The rotation angle θ of the nanoantenna column is determined, and the rotation angle θ of the nanoantenna column is the geometric phase. One-half of.

[0042] The nano-antenna pillars are arranged in an array according to their geometric dimensions and rotation angles to form a metasurface; a processing file is generated and processed to obtain a solid metasurface structure.

[0043] Beneficial effects:

[0044] This invention relates to a multi-phase metasurface holography method based on wavelength and polarization decoupling. This method can achieve multi-phase holography of metasurfaces without the need for nonlinear effects in structure and materials, greatly improving energy conversion efficiency and reducing experimental complexity. Furthermore, the combination of polarization and wavelength allows for convenient and effective multi-phase modulation, enhancing the flexibility of multi-phase holographic modulation. This technology can provide new solutions for dynamic multi-phase beam directional refraction and excitation, orbital angular momentum communication, holographic encryption / display, optical encryption and camouflage, optical switching and shaping, etc. Attached Figure Description

[0045] Figure 1 This is a flowchart of the multi-phase metasurface holographic method based on wavelength and polarization decoupling of the present invention.

[0046] Figure 2 This is a schematic diagram of a multi-phase metasurface holographic method based on wavelength and polarization decoupling, where K is the multiple.

[0047] Figure 3 This is a schematic diagram of the multi-phase hologram algorithm principle. FFT stands for Fourier transform.

[0048] Figure 4 These are schematic diagrams of the nanostructure units and transmission amplitude / phase of the metasurface. (a) Schematic diagram of a nanoantenna column. (bc) Cross-circular polarization intensity and phase diagrams of the scanning length and width at an incident wavelength of 800 nm. (de) X-linear polarization intensity and phase diagrams of the scanning length and width at an incident wavelength of 800 nm. (fg) X-linear polarization intensity and phase diagrams of the scanning length and width at an incident wavelength of 1000 nm.

[0049] Figure 5 This is a schematic diagram of the metasurface sample and optical path system. (a) SEM image of the metasurface, top view, scale bar: 1000 nm. (b) Broadband transmission efficiency curve of the circularly polarized channel (T rl ,T lr (c) Broadband transmission efficiency curve of the linearly polarized channel (T) xx ,T yy (d) Experimental optical setup: P: polarizer; λ / 4: quarter-wave plate; CMOS: complementary metal-oxide-semiconductor.

[0050] Figure 6 This is a schematic diagram of simulation and experimental results based on dual-wavelength polarized multiple-phase holograms. (a), (e) show cross-circular polarization at 800nm ​​wavelength (T rl (b) and (f) Simulation and experimental results of multi-phase (K=1) holographic reconstruction. lrSimulation and experimental results of multi-phase (K=3) holographic reconstruction at 1000nm wavelength. (c), (g) Linear polarization at 1000nm wavelength (T xx Simulation and experimental results of multi-phase (K=2) holographic reconstruction at 1000nm wavelength. (d), (h) y-linear polarization at 1000nm wavelength (T yy Simulation and experimental results of multi-phase (K=6) holographic reconstruction. Detailed Implementation

[0051] The method of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. The method flowchart is shown below. Figure 1 As shown, the method may include the following steps:

[0052] This embodiment selects wavelengths of λ1800nm ​​and λ21000nm, with multiple phase values. The multiples are K(1,2,3,6), the substrate material of the metasurface is silicon dioxide (SiO2), and the nanoantenna pillar material is silicon (Si). The nanoantenna pillars have a rectangular geometry. A schematic diagram of the multi-phase metasurface holographic method based on wavelength and polarization decoupling is shown below. Figure 2 As shown, multiple phase values ​​can be displayed when using a λ1800nm ​​cross-circular polarization channel. and The reconstructed holographic image, when viewed through a λ21000nm linear offset channel, can display multiple phase values. and The reconstructed holographic image is implemented as follows:

[0053] Step 1

[0054] The Adaptive Moment Estimation (Adam) algorithm plays a crucial role in the generation of multi-fold phase holograms. We developed an optimization algorithm based on Adaptive Moment Estimation for generating multi-fold phase holograms, as shown in Figure 3. First, a random phase hologram is generated. The phase of the random phase hologram is multiplied by a factor K (1, 2, 3, 6) to obtain four phase holograms with different K-fold values. Specifically, the different K-fold phase holograms are multiple folds and envelopes of the random phase hologram.

[0055] Holographic reconstruction is performed on the four phase holograms of different K-fold values ​​to obtain the output image. The holographic reconstruction is the reconstruction of the hologram to the object plane achieved through Fourier transform. The mean square error (MSE) of the output image and the label is calculated based on the reference true value as the label. The MSE of the reconstruction result and the label is:

[0056]

[0057] G represents the two-dimensional Fourier transform operation.n Indicates a label.

[0058] Based on the adaptive moment estimation algorithm, through the synchronous mean square error E r As a metric for optimizing the update in the loop phase, the random phase hologram is phase optimized to obtain the optimized basic phase. For the basic phase Multiplying by four different multiples K (1, 2, 3, 6) yields the optimized four-fold phase.

[0059] Step Two

[0060] When light shines on the metasurface, the output light field E out Represented using Jones matrix:

[0061] E out =J(θ)E in (2)

[0062] Among them, E in For the input light field incident through the circularly polarized channel, E in Represented as

[0063]

[0064] Polarization conversion is performed by determining the rotation angle (θ) of the metasurface nanoantenna pillar. Output light field E out Represented as:

[0065] E out =R -1 (θ)TR(θ)E in (4)

[0066] Where R(θ) represents the rotation matrix of the Jones matrix, and T represents the transmittance of the metasurface nanoantenna column, denoted as:

[0067]

[0068] and This represents the eigenvector of the metasurface nanoantenna column in the x- and y-polarization channels. The transmittance T of the metasurface nanoantenna column can be expressed by inversely using Equation 4:

[0069]

[0070] In the decoupling of the cross-circular polarization channel, the RCP output and LCR output have completely independent phase distributions on the LCP and RCP incident channels, respectively.

[0071] When the output light field Eout When the phase is determined to be multiple phases and In a cross-circular polarization channel at a wavelength of 800 nm, the geometric phase under the cross-circular polarization It is a conjugate relationship, and the multiple phase is expressed as:

[0072]

[0073] Indicates the transmission phase. T represents the geometric phase. rl800 This represents the RCP incident and LCP output at an incident wavelength of 800nm, T lr800 This represents the LCP incident and RCP output at an incident wavelength of 800 nm. A simple derivation of Equation 7 yields the transmission phase. and the geometric phase Represented as:

[0074]

[0075] The phase φ is represented as:

[0076]

[0077] Step 3

[0078] First, the height H of the nanoantenna column and the period P of the structural unit can be determined based on the finite-domain difference method. The period P of the structural unit is determined to be 450 nm, and the height H of the nanoantenna column is determined to be 1000 nm. To satisfy the multiple phase polarization decoupling at two wavelengths, the length L and width W of each nanoantenna column are scanned at wavelengths of 800 nm and 1000 nm, respectively. The complex amplitude modulation characteristics of nanoantenna columns with different geometric dimensions for different wavelengths and polarizations are determined, and the corresponding phase distribution is obtained. The nanoantenna column is as follows: Figure 4 As shown in (a). The length L of the scanned nanoantenna column ranges from 80 nm to 300 nm, and the width W ranges from 80 nm to 300 nm, with a scan step size of 10 nm. The cross-circular polarization conversion amplitude and phase diagram at an incident wavelength of 800 nm are shown below. Figure 4 As shown in (b)-(c), the amplitude and phase diagrams corresponding to the x-linear polarization at an incident wavelength of 800 nm are as follows. Figure 4 As shown in (d)-(e), the nanoantenna column has different transmittances at different incident wavelengths. The amplitude and phase diagrams of the x-linear polarization at an incident wavelength of 1000 nm are shown in Figure 1. Figure 4 As shown in (f)-(g).

[0079] Step 5

[0080] The geometric dimensions of the nano-antenna column are determined based on the minimum value of matrix L, where matrix L is:

[0081]

[0082] min represents the minimum value of the function, based on the geometric phase. The rotation angle θ of the nanoantenna column is determined, and the rotation angle θ of the nanoantenna column is the geometric phase. One-half of.

[0083] The nano-antenna pillars are arranged in an array according to their geometric dimensions and rotation angles to form a metasurface; a processing file is then generated.

[0084] Using the fabrication files of the obtained metasurface, metasurface samples were prepared on a quartz substrate through α-Si thin film deposition, electron beam lithography (EBL), Cr mask stripping and dry etching processes to obtain a solid metasurface structure. Figure 5 (a) is a top view of a scanning electron microscope (SEM).

[0085] Step Six

[0086] To verify the efficiency of the metasurface after processing, broadband transmittance curves of the metasurface were measured in cross-circular polarization channels at 800 nm and linear polarization channels at 1000 nm, as shown below. Figure 4 (bc). The fabricated metasurface is placed in the experimental optical path, and the optical experimental setup is as follows. Figure 5 As shown in (d), a supercontinuum laser (NKT Photonics SuperK) was used as the light source (wavelength selected 690-1100 nm). When the incident light wavelength was 800 nm, a combination of a linear polarizer and a quarter-wave plate generated circularly polarized light. This circularly polarized light then illuminated the metasurface, and a multi-phase holographic reconstructed image could be observed in the far field via Fourier transform. When the light wavelength was switched to 1000 nm, the quarter-wave plate was removed, and the linearly polarized channel was reconstructed in the far field.

[0087] Simulation and experimental reconstruction results of multi-fold holograms are as follows: Figure 6 As shown. When the illumination wavelength is 800 nm, the fencer's logo is reconstructed at the far-field RCP input LCP output channel. Figure 6 (a, (e), K = 1). Conversely, the rhythmic gymnastics logo is reconstructed using the far-field LCP input RCP output channel, ( Figure 6 (b), (f), K=3). The phase value of the rhythmic gymnastics hologram is three times that of the fencer. When the incident wavelength is 1000nm, at the horizontal (T xx ) and vertical (T) yyIn the linearly polarized channel, multiple holographic reconstructions are performed in the far field, such as... Figure 6 As shown in (c), (d), (g), and (h), holographic reconstructions of a water polo ball (K=2) and a ping-pong ball (K=6) were performed using the linear polarization channel. The phase value of the water polo hologram was twice that of the fencing athlete hologram, while the phase value of the ping-pong ball hologram was six times that of the fencing athlete hologram.

[0088] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A multi-phase metasurface holographic method based on wavelength and polarization decoupling, characterized in that, Includes the following steps: Step 1: Generate a random phase hologram. Multiply the phase of the random phase hologram by n different factors K (K is any non-zero real number) to obtain n phase holograms with different K-fold multiplication factors. Perform holographic reconstruction on the n phase holograms with different K-fold multiplication factors to obtain the output image. Calculate the mean square error of each of the n output images and their corresponding n labels. Based on the mean square error, optimize the phase of the random phase hologram using an adaptive moment estimation algorithm to obtain the optimized basic phase. For the basic phase Multiplying by the corresponding n different multiples K, we get n optimized multiple phases. Recorded as Step 2: Using a specific wavelength λ1 and a cross-circular polarization channel, the optimized multiple phase from Step 1 is applied as follows: Matching is performed to obtain a phase φ, wherein the cross polarization channel is left-handed circular polarization (LCP) incident / transmitted to right-handed circular polarization (RCP) or right-handed circular polarization (RCP) incident / transmitted to left-handed circular polarization (LCP); another wavelength λ2 and a linear polarization channel are used to match the remaining optimized multiple phase from step one. Step 3: The multi-phase metasurface used for wavelength and polarization decoupling is composed of multiple anisotropic nano-antenna columns with different geometric dimensions. To satisfy multi-phase polarization decoupling at two wavelengths, the length and width of each nano-antenna column corresponding to a certain wavelength λ1 in Step 2 are scanned in the cross-circular polarization channel and the linear polarization channel of another wavelength λ2. The complex amplitude modulation characteristics of the nano-antenna column for different wavelengths and polarizations are determined to obtain the corresponding phase distribution. The height H of the nano-antenna column and the period P of the structural unit are preset. Step 4: Determine the geometric dimensions (length and width) and rotation angle of the nano-antenna pillars, and arrange the nano-antenna pillar array to form a metasurface; Step 5: Arrange the nano-antenna pillar array according to the geometric dimensions and rotation angle of the nano-antenna pillars to form a metasurface; generate a processing file and process it to obtain a solid metasurface structure.

2. The method according to claim 1, characterized in that, The method for implementing step one is as follows: A random phase hologram is generated. The phase of the random phase hologram is multiplied by n different factors K (K is any non-zero real number) to obtain n phase holograms with different multiplication factors K. Holographic reconstruction is performed on the n phase holograms with different multiplication factors K to obtain an output image. The holographic reconstruction is the reconstruction of the hologram to the object plane through Fourier transform. The mean square error of the output image and the label is calculated based on the reference ground truth (target image) as the label. The mean square error E between the reconstruction result and the label is... r (MSEs) are: G represents the two-dimensional Fourier transform operation. n Indicates a label; Based on the adaptive moment estimation algorithm, through the synchronous mean square error E r As a metric for optimizing the update in the loop phase, the random phase hologram is phase optimized to obtain the optimized basic phase. For the basic phase Multiplying by the corresponding n different multiples K yields the optimized n multiple phases.

3. The method according to claim 1, characterized in that, If n=4, then the optimized multiple phase 4. The method according to claim 1, characterized in that, The method for implementing step two is as follows: When light shines on the metasurface, the output light field E out This can be represented using a Jones matrix: AND out =J(θ)E in (2) Among them, E in For the input light field incident through the circularly polarized channel, E in Represented as Polarization conversion is performed by determining the rotation angle (θ) of the metasurface nanoantenna column; the corresponding output light field E out Represented as: E out =R -1 (θ)TR(θ)E in (4) Where R(θ) represents the rotation matrix of the Jones matrix, and T represents the transmittance of the metasurface nanoantenna column, denoted as: and The eigenvectors of the metasurface nanoantenna pillars are represented in the x- and y-polarization channels; the transmittance T of the metasurface nanoantenna pillars can be expressed by inversely using Equation 4: In the decoupling of the cross-circular polarization channel, the RCP output and LCR output have completely independent phase distributions on the LCP and RCP incident channels, respectively. When the output light field E out When the phase is determined to be multiple phases and In a cross-circular polarization channel at a certain wavelength λ1, the geometric phase under the cross-circular polarization is... It is a conjugate relationship, and the multiple phase is expressed as: Indicates the transmission phase. Indicates geometric phase, This represents the relationship between RCP incident and LCP output at a certain wavelength λ1. This represents the relationship between LCP incident and RCP output at a certain wavelength λ1. A simple derivation of Equation 7 yields the transmission phase. and the geometric phase Represented as: The phase φ is represented as: 。 5. The method according to claim 1, characterized in that, The method for implementing step three is as follows: Given the preset height H of the nanoantenna pillars and the period P of the structural unit, the length L and width W of each nanoantenna pillar are scanned at wavelengths λ1 and λ2, respectively, to determine the transmittance phase of the cross-circular polarization channel of nanoantenna pillars with different geometric dimensions at wavelength λ1. and the transmittance phase of the x-linear polarization channel at wavelength λ2 Transmittance phase of the y-polarized channel 6. The method according to claim 1, characterized in that, The method for implementing step four is as follows: The geometric dimensions of the nano-antenna column are determined based on the minimum value of matrix L, where matrix L is: min represents the minimum value of the function, based on the geometric phase. The rotation angle θ of the nanoantenna column is determined, and the rotation angle θ of the nanoantenna column is the geometric phase. One-half of.

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