Multi-time phase metasurface holographic method based on wavelength and polarization decoupling

Abstract

The invention discloses a frequency and polarization decoupling-based multi-time phase metasurface holographic method, and belongs to the field of micro-nano holography. Comprising the following steps: generating a random phase hologram, multiplying the random phase hologram by a multiple K to obtain n different K-time phase holograms, calculating a mean square error of an output image and a label, performing phase optimization on the random phase hologram through an adaptive moment estimation algorithm, multiplying an obtained basic phase # imgabs0 # by n multiples K, and performing phase optimization on the obtained basic phase # imgabs0 #; n optimized multiple phases # imgabs 1 # are obtained, and the optimized multiple phases are matched through a frequency lambda 1 and a crossed circular polarization channel to obtain a phase phi; and scanning the length and width of each nano antenna column of the frequency lambda 1 in the crossed circular polarization channel and the frequency lambda 2 in the online polarization channel, determining complex amplitude modulation characteristics of the nano antenna columns for different frequencies and polarization, and obtaining corresponding phase distribution. Designing multiple phase metasurface holography based on frequency and polarization decoupling; the energy conversion efficiency can be improved, and the flexibility of multi-phase holographic modulation is also improved through different polarization and frequency combinations.

Description

Technical Field

[0001] The invention relates to a multiple phase metasurface holographic method based on wavelength and polarization decoupling, and belongs to the field of micro-nano optics and holography. Background Art

[0002] In recent years, metasurfaces, as a booming artificial intelligence planar optical device, can realize many functions through the optimization design of nanostructures and arrays, and are applied in the fields of holographic display, wavefront shaping, nonlinear optics, large-capacity storage, etc. It is gradually becoming the preferred path for integrated and compact optical systems. At present, the multiple phase holographic modulation schemes based on metasurfaces mostly rely on nonlinear effects. However, the energy conversion efficiency of multiple phase modulation of metasurfaces based on nonlinear effects is low and the experimental complexity is high. The energy conversion efficiency can be improved by designing multiple phase metasurface holography based on wavelength and polarization decoupling. Different polarization and wavelength combinations also improve the flexibility of multiple phase holographic modulation. Summary of the invention

[0003] The present invention relates to a multiple phase metasurface holographic method based on wavelength and polarization decoupling, and belongs to the field of micro-nano optics and holography. The present invention generates a random phase hologram, multiplies the phase of the random phase hologram by n different multiples K (K is any real number not equal to 0), obtains n phase holograms with different K multiples, holographically reconstructs the n phase holograms with different K multiples to obtain an output image, calculates the mean square error between the n output images and the corresponding n labels, optimizes the phase of the random phase hologram through an adaptive moment estimation algorithm according to the mean square error, and obtains the optimized basic phase For the basic phase Then multiply by the corresponding n different multiples K to obtain n optimized multiple phases Recorded as A wavelength λ1 and a cross circular polarization channel are used to optimize a part of the multiple phases such as Matching is performed to obtain a phase φ, and 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 of the other part. The multiple phase metasurface for wavelength and polarization decoupling is composed of multiple anisotropic nanoantenna column arrays of different geometric sizes. In order to meet the multiple phase polarization decoupling at two wavelengths, the length and width of each nanoantenna column of a certain wavelength λ1 in the cross-circular polarization channel and another wavelength λ2 in the linear polarization channel are scanned to determine the complex amplitude modulation characteristics of the nanoantenna column for different wavelengths and polarizations, and obtain the corresponding phase distribution. The height H of the nanoantenna column and the period P of the structural unit are preset. The geometric length and width of the nanoantenna column and the rotation angle are determined, and the nanoantenna column array is arranged to form a metasurface. The nanoantenna column array is arranged according to the geometric size and rotation angle of the nanoantenna column to form a metasurface. Generate processing files and process them to obtain a physical metasurface structure. Designing a multiple phase metasurface hologram based on wavelength and polarization decoupling can improve energy conversion efficiency. Different polarization and wavelength combinations also improve the flexibility of multiple phase holographic modulation. This technology can provide new solutions for dynamic multiple beam directional refraction and excitation, orbital angular momentum communication, multiple holographic display, optical encryption and camouflage, optical switching and shaping, etc.

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

[0005] In a first aspect, the multiple phase metasurface holographic method based on wavelength and polarization decoupling disclosed in the present invention comprises the following steps:

[0006] Step 1: Generate a random phase hologram, multiply the phase of the random phase hologram by n different multiples K (K is any real number not equal to 0) to obtain n phase holograms with different K multiples, perform holographic reconstruction on the n phase holograms with different K multiples to obtain an output image, calculate the mean square error between the n output images and the corresponding n labels, optimize the phase of the random phase hologram through an adaptive moment estimation algorithm according to the mean square error, and obtain the optimized basic phase For the basic phase Then multiply by the corresponding n different multiples K to obtain n optimized multiple phases Recorded as

[0007] Step 2: Use a wavelength λ1 and a cross circular polarization channel to optimize the multiple phase of a part of the step 1. 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 optimize the multiple phase of the other part remaining in step 1 as follows and to make a match.

[0008] Step 3: The multiple phase metasurface for wavelength and polarization decoupling is composed of multiple anisotropic nano-antenna column arrays of different geometric sizes. In order to satisfy the multiple phase polarization decoupling at two wavelengths, the length and width of each nano-antenna column at a wavelength λ1 corresponding to step 2 in the cross circular polarization channel and another wavelength λ2 in the linear polarization channel are scanned to determine the complex amplitude modulation characteristics of the nano-antenna column for different wavelengths and polarizations, and 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 length and width of the nano-antenna column and the rotation angle, and arrange the nano-antenna column array to form a metasurface.

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

[0011] Optionally, the implementation method of step 1 is:

[0012] Generate a random phase hologram, multiply the phase of the random phase hologram by n different multiples K (K is any real number not equal to 0), obtain n phase holograms with different K multiples, perform holographic reconstruction on the n phase holograms with different K multiples to obtain an output image, wherein the holographic reconstruction is the reconstruction of the hologram to the object plane through Fourier transform; and calculate the mean square error between the output image and the label according to the reference true value (target image) as the label, and the mean square error Er (MSEs) between the reconstruction result and the label is:

[0013]

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

[0015] Based on the adaptive moment estimation algorithm, the synchronous mean square error E r As a measure of the update of the optimization cycle stage, the phase of the random phase hologram is optimized to obtain the optimized basic phase

[0016] For the basic phase Multiply the corresponding n different multiples K to obtain the optimized n multiple phases

[0017]

[0018] Optionally, the implementation method of step 2 is:

[0019] When light hits the metasurface, the output light field E out It can be expressed as Jones matrix:

[0020] E out =J(θ)E in (2)

[0021] Among them, E in is the input light field of the circularly polarized channel, E in Expressed as

[0022]

[0023] Determine the rotation angle (θ) of the metasurface nanoantenna column to perform polarization conversion. The corresponding output light field E out It is expressed as:

[0024] E out =R -1 (θ)TR(θ)E in (4)

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

[0026]

[0027] and represents the eigenvector form of the metasurface nanoantenna column in the x-polarization channel and the y-polarization channel; the transmittance T of the metasurface nanoantenna column can be inversely expressed by formula 4 as follows:

[0028]

[0029] In the decoupling of the cross-circular polarization channels, 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 phase and Under a cross circular polarization channel of a certain wavelength λ1, the geometric phase under the cross circular polarization is a conjugate relationship, and the multiple phase is expressed as:

[0031]

[0032] represents the transmission phase, represents the geometric phase, It indicates the relationship between RCP incident and LCP output at a certain wavelength λ1. It represents the relationship between LCP incident and RCP output at a certain wavelength λ1. A simple derivation of formula 7 can derive the transmission phase and the geometric phase Expressed as:

[0033]

[0034] The phase φ is expressed as:

[0035]

[0036] Optionally, the implementation method of step three is:

[0037] The height H of the nano-antenna column and the period P of the structural unit are preset, and the length L and width W of each nano-antenna column are scanned at wavelength λ1 and wavelength λ2 respectively to determine the transmittance phase of the cross-circular polarization channel of nano-antenna columns of different geometric sizes at wavelength λ1. and the transmittance phase of the x-polarization channel at wavelength λ2 Transmittance phase of linearly polarized channel

[0038] Optionally, the implementation method of step 4 is:

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

[0040]

[0041] min represents the minimum value of the function, based on the geometric phase Determine the rotation angle θ of the nano-antenna column, the rotation angle θ of the nano-antenna column is the geometric phase One half of .

[0042] The nano-antenna column array is arranged according to the geometric size and rotation angle of the nano-antenna column to form a metasurface; a processing file is generated, and processing is performed to obtain a solid metasurface structure.

[0043] Beneficial effects:

[0044] The present invention relates to a multiple phase metasurface holographic method based on wavelength and polarization decoupling. The method can realize multiple phase holography of metasurface without the need for nonlinear effects of structure and material, greatly improve the energy conversion efficiency, and reduce the complexity of the experiment. In addition, multiple phase modulation can be conveniently and effectively realized by combining polarization and wavelength, and the flexibility of multiple phase holographic modulation is also improved. The technology can provide new solutions for dynamic multiple beam directional refraction and excitation, orbital angular momentum communication, holographic encryption / display, optical encryption and camouflage, optical switching and shaping, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a flow chart of the multiple phase metasurface holographic method based on wavelength and polarization decoupling of the present invention.

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

[0047] Figure 3 It is a schematic diagram of the principle of the multiple phase hologram algorithm, and FFT is Fourier transform.

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

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

[0050] Figure 6 Schematic diagram of simulation and experimental results based on dual-wavelength polarization multiple phase hologram. (a), (e) At 800nm ​​wavelength cross circular polarization (T rl ) The simulation and experimental multi-phase (K = 1) holographic reconstruction results. (b), (f) At 800nm ​​wavelength cross polarization (T lr) under the conditions of simulation and experiment multiple phase (K = 3) holographic reconstruction results. (c), (g) under the conditions of 1000nm wavelength x-linear polarization (T xx ) under the conditions of simulation and experiment multiple phase (K = 2) holographic reconstruction results. (d), (h) under the conditions of 1000nm wavelength y linear polarization (T yy ) simulation and experimental multiple phase (K=6) holographic reconstruction results under . DETAILED DESCRIPTION

[0051] The method of the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. The method flow chart is as follows Figure 1 As shown, the method may include the following steps:

[0052] In this embodiment, the wavelength λ1800nm ​​and the wavelength λ21000nm are selected, and the multiple phase The multiple of is K (1, 2, 3, 6), the substrate material of the metasurface is silicon dioxide (SiO2), and the material of the nanoantenna column is silicon (Si), the geometric shape of the nanoantenna column is rectangular, and the schematic diagram of the multiple phase metasurface holographic method based on wavelength and polarization decoupling is shown in Figure 2 As shown, when the λ1800nm ​​cross circular polarization channel is used, multiple phases can be displayed. and The reconstructed holographic image can show multiple phases when the λ21000nm line is biased to the channel. and The reconstructed holographic image is implemented as follows:

[0053] Step 1:

[0054] Adaptive moment estimation algorithm (Adam) plays a vital role in the generation of multiple phase holograms. We have developed an optimization algorithm based on adaptive moment estimation for generating multiple phase holograms, as shown in Figure 3. First, a random phase hologram is generated, and the phase of the random phase hologram is multiplied by K (1, 2, 3, 6) to obtain 4 phase holograms with different K times. Specifically, the phase holograms with different K times are multiple folding and envelopes of the random phase hologram.

[0055] The four phase holograms with different K times are holographically reconstructed to obtain an output image, wherein the holographic reconstruction is the reconstruction of the hologram to the object plane through Fourier transform; and the mean square error between the output image and the label is calculated based on the reference true value as the label, and the mean square error (MSEs) between the reconstruction result and the label is:

[0056]

[0057] represents the two-dimensional Fourier transform operation, Gn Indicates a label.

[0058] Based on the adaptive moment estimation algorithm, the synchronous mean square error E r As a measure of the update of the optimization cycle stage, the phase of the random phase hologram is optimized to obtain the optimized basic phase For the basic phase Multiply by 4 different multiples K (1, 2, 3, 6) to get the 4 optimized multiple phases

[0059] Step 2:

[0060] When light shines on the metasurface, the output light field E out It can be expressed as Jones matrix:

[0061] E out =J(θ)E in (2)

[0062] Among them, E in is the input light field of the circularly polarized channel, E in Expressed as

[0063]

[0064] Determine the rotation angle (θ) of the metasurface nanoantenna column to perform polarization conversion. Output light field E out It is expressed as:

[0065] E out =R -1 (θ)TR(θ)E in (4)

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

[0067]

[0068] and represents the eigenvector of the metasurface nano-antenna column in the x-polarization channel and the y-polarization channel. The transmittance T of the metasurface nano-antenna column can be inversely expressed by formula 4 as follows:

[0069]

[0070] In the decoupling of the cross circular polarization channels, the RCP output and the 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 phase and Under the cross circular polarization channel with a wavelength of 800nm, the geometric phase under the cross circular polarization is a conjugate relationship, and the multiple phase is expressed as:

[0072]

[0073] represents the transmission phase, represents the geometric phase, T rl800 It means RCP input and LCP output when the incident wavelength is 800nm, T lr800 It means that when the incident wavelength is 800nm, LCP is incident and RCP is output. A simple derivation of formula 7 can be obtained that the transmission phase and the geometric phase Expressed as:

[0074]

[0075] The phase φ is expressed as:

[0076]

[0077] Step 3:

[0078] First, the height H of the nano-antenna column and the period P of the structural unit can be determined based on the finite time-domain difference method. The period P of the structural unit is determined to be 450nm, and the height H of the nano-antenna column is determined to be 1000nm. In order to meet the multiple phase polarization decoupling at two wavelengths, the length L and width W of each nano-antenna column are scanned at a wavelength of 800nm ​​and a wavelength of 1000nm, respectively, and the complex amplitude modulation characteristics of nano-antenna columns of different geometric sizes for different wavelengths and polarizations are determined to obtain the corresponding phase distribution. The nano-antenna column is as follows: Figure 4 (a) is shown. The length L of the nanoantenna column is scanned in the range of 80nm to 300nm, the width W is in the range of 80nm to 300nm, and the scanning step is 10nm. The cross-circular polarization conversion amplitude and phase diagram at an incident wavelength of 800nm ​​are shown in Figure 4 The corresponding x-polarization amplitude and phase diagram at an incident wavelength of 800nm ​​is shown in (b)-(c). Figure 4 The nano antenna column has different transmittances at different incident wavelengths. The amplitude and phase diagram of the x-line polarization at an incident wavelength of 1000 nm are shown in FIG. Figure 4 As shown in (f)-(g).

[0079] Step 5:

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

[0081]

[0082] min represents the minimum value of the function, based on the geometric phase Determine the rotation angle θ of the nano-antenna column, the rotation angle θ of the nano-antenna column is the geometric phase One half of .

[0083] Arranging the nano-antenna column array according to the geometric size and rotation angle of the nano-antenna column to form a metasurface; generating a processing file.

[0084] Using the obtained processing files of the 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 6:

[0086] To verify the efficiency of the metasurface after processing, broadband transmittance curves of the metasurface in the cross-circular polarization channel at 800 nm and the linear polarization channel at 1000 nm were measured, as shown in FIG. Figure 4 The processed metasurface is placed in the experimental light path. The optical experimental configuration is as follows: Figure 5 (d) As shown. A supercontinuum laser (NKT Photonics SuperK) is used as the light source (wavelength selection 690-1100nm). When the wavelength of the incident light is 800nm, the linear polarizer is combined with the quarter-wave plate to produce circularly polarized light. Then, the circularly polarized light illuminates the metasurface, and the multi-fold phase holographic reconstructed image can be observed in the far field through Fourier transform. When the wavelength of the light is switched to 1000nm, the quarter-wave plate is removed, and the linear polarization channel is reconstructed in the far field.

[0087] The simulation and experimental reconstruction results of multiple holograms are shown in Figure 2. Figure 6 When the illumination wavelength is 800nm, the fencer logo is reconstructed in the far-field RCP input and LCP output channels ( Figure 6 (a, (e), K = 1). In contrast, the rhythmic gymnastics logo is reconstructed with the far-field LCP input and RCP output channels, ( 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 yy) linear polarization channel, multiple holographic reconstruction is performed in the far field, such as Figure 6 (c), (d), (g), (h). The water polo (K = 2) and table tennis (K = 6) are holographically reconstructed in the online polarization channel. The phase value of the water polo hologram is twice that of the fencer hologram. The phase value of the table tennis hologram is 6 times that of the fencer hologram.

[0088] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above 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 in the scope of protection of the present invention.

Claims

1. A multiple phase metasurface holographic method based on wavelength and polarization decoupling, characterized in that: The steps include: Step 1: Generate a random phase hologram, multiply the phase of the random phase hologram by n different multiples K (K is any real number not equal to 0) to obtain n phase holograms with different K multiples, perform holographic reconstruction on the n phase holograms with different K multiples to obtain an output image, calculate the mean square error between the n output images and the corresponding n labels, optimize the phase of the random phase hologram through an adaptive moment estimation algorithm according to the mean square error, and obtain the optimized basic phase For the basic phase Then multiply by the corresponding n different multiples K to obtain n optimized multiple phases Recorded as Step 2: Use a wavelength λ1 and a cross circular polarization channel to optimize the multiple phase of a part of the step 1. 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 other part of the optimized multiple phases remaining in step 1; Step 3: The multiple phase metasurface for wavelength and polarization decoupling is composed of multiple anisotropic nano-antenna column arrays of different geometric sizes. In order to satisfy the multiple phase polarization decoupling at two wavelengths, the length and width of each nano-antenna column at a wavelength λ1 corresponding to step 2 in the cross circular polarization channel and another wavelength λ2 in the linear polarization channel are scanned to determine the complex amplitude modulation characteristics of the nano-antenna column for different wavelengths and polarizations, and 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: determining the geometrical length and width of the nano-antenna column and the rotation angle, and arranging the nano-antenna column array to form a metasurface; Step 5: Arrange the nano-antenna column array according to the geometric size and rotation angle of the nano-antenna column 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 implementation method of step 1 is: Generate a random phase hologram, multiply the phase of the random phase hologram by n different multiples K (K is an arbitrary real number not equal to 0), obtain n phase holograms with different K multiples, perform holographic reconstruction on the n phase holograms with different K multiples to obtain an output image, wherein the holographic reconstruction is a reconstruction of the hologram to the object plane through Fourier transform; and calculate the mean square error between the output image and the label based on the reference true value (target image) as the label, and the mean square error E between the reconstruction result and the label is r (MSEs) are: represents the two-dimensional Fourier transform operation, G n Indicates a label; Based on the adaptive moment estimation algorithm, the synchronous mean square error E r As a measure of the update of the optimization cycle stage, the phase of the random phase hologram is optimized to obtain the optimized basic phase For the basic phase Multiply the corresponding n different multiples K to obtain the optimized n multiple phases 3. The method according to claim 1, characterized in that n=4, then the optimized multiple phase 4. The method according to claim 1, characterized in that The implementation method of step 2 is: When light hits the metasurface, the output light field E out It can be expressed as Jones matrix: AND out =J(θ)E in (2) Among them, E in is the input light field of the circularly polarized channel, E in Expressed as Determine the rotation angle (θ) of the metasurface nanoantenna column to perform polarization conversion. The corresponding output light field E out It is expressed as: E out =R -1 (θ)TR(θ)E in (4) Where R(θ) represents the rotation matrix of the Jones matrix, T represents the transmittance of the metasurface nanoantenna column, and T is expressed as: and represents the eigenvector form of the metasurface nanoantenna column in the x-polarization channel and the y-polarization channel; the transmittance T of the metasurface nanoantenna column can be inversely expressed by formula 4 as follows: In the decoupling of the cross-circular polarization channels, 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 phase and Under a cross circular polarization channel of a certain wavelength λ1, the geometric phase under the cross circular polarization is a conjugate relationship, and the multiple phase is expressed as: represents the transmission phase, represents the geometric phase, It indicates the relationship between RCP incident and LCP output at a certain wavelength λ1. It represents the relationship between LCP incident and RCP output at a certain wavelength λ1. A simple derivation of formula 7 can derive the transmission phase and the geometric phase Expressed as: The phase φ is expressed as:

5. The method according to claim 1, characterized in that The implementation method of step three is: The height H of the nano-antenna column and the period P of the structural unit are preset, and the length L and width W of each nano-antenna column are scanned at wavelength λ1 and wavelength λ2 respectively to determine the transmittance phase of the cross-circular polarization channel of nano-antenna columns of different geometric sizes at wavelength λ1. and the transmittance phase of the x-polarization channel at wavelength λ2 Transmittance phase of the y-polarization channel 6. The method according to claim 1, characterized in that The implementation method of step 4 is: The geometrical dimensions of the nano-antenna column are determined based on the minimum value of the matrix L, wherein the matrix L is: min represents the minimum value of the function, based on the geometric phase Determine the rotation angle θ of the nano-antenna column, the rotation angle θ of the nano-antenna column is the geometric phase One half of .

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