High-order mode vortex electromagnetic wave generation structure based on metasurface and design method

Abstract

The invention discloses a metasurface-based high-order vortex electromagnetic wave generation structure and a design method, the high-order mode vortex electromagnetic wave generation structure comprises a metasurface, the metasurface comprises a plurality of cellular structures, each cellular structure comprises a plurality of layers of plate-shaped structures, the first layer of the multi-layer platy structure is a metal patch layer, the second layer is a dielectric material layer, the third layer is a metal patch layer, the fourth layer is a dielectric material layer, and the fifth layer is a metal floor layer; the first metal patch layer comprises a square split ring unit, and the third metal patch layer comprises a cross unit. The high-modulus vortex wave beam can be flexibly adjusted through structures such as a metasurface, multi-direction and multi-angle wave beam control is achieved, and the antenna is suitable for a complex wireless communication environment. In addition to wireless communication, generation and control of high-modulus vortex waves, the system also shows a huge application prospect in the fields of radar, imaging and the like, and can improve the resolution and detection capability of the system.

Description

Technical Field

[0001] The present invention belongs to the technical field of artificial electromagnetic materials, and in particular relates to a high-order mode vortex electromagnetic wave generating structure based on a supersurface and a design method. Background Art

[0002] With the rapid update and iteration of wireless communication technology, traditional channel capacity enhancement technology faces huge challenges. In the microwave millimeter wave band, earlier methods of realizing vortex waves, such as spiral phase plates and circular antenna arrays, have great limitations in manufacturing process and working bandwidth. In recent years, metasurface structures have been used to achieve the generation of vortex waves. Their ability to modulate the electromagnetic wave front and their low-profile structure have extraordinary application prospects, but the related issues of using metasurfaces to generate high-order OAM vortex waves are still considered to be a field under preliminary exploration. Research on multifunctional vortex waves based on metasurfaces also mostly stays at the generation of dual-polarization vortex waves.

[0003] The use of metasurfaces to generate high-mode OAM vortex waves will cause undesirable side lobes between the two radiation peaks of the OAM vortex waves. At the same time, the radiation efficiency and mode purity of high-mode OAM vortex waves will decrease. In summary, it is necessary to find a structural combination and spatial allocation method to design a metasurface that is conducive to the generation of high-order mode vortex electromagnetic waves and can realize the free and independent regulation of the phases of multiple polarized electromagnetic waves under a unit aperture.

[0004] The existing patent CN115173071A provides a vortex wave generating structure and design method based on a multifunctional shared aperture metasurface, which cleverly combines the structural combination and spatial allocation methods to design a single-layer shared aperture multi-polarization multi-band reflective metasurface, thereby realizing independent phase control of different polarization reflected waves working in different wide frequency bands, but the mode number of the generated vortex wave beam is relatively low. Summary of the invention

[0005] The purpose of the present invention is to solve the problem of low mode number when using metasurface to generate vortex electromagnetic waves.

[0006] To achieve the above-mentioned object, the present invention provides a high-order mode vortex electromagnetic wave generating structure based on a metasurface, wherein the high-order mode vortex electromagnetic wave generating structure comprises a metasurface, the metasurface comprises a plurality of cellular structures, each of which comprises a multi-layer plate structure, wherein the first layer of the multi-layer plate structure is a metal patch layer, the second layer is a dielectric material layer, the third layer is a metal patch layer, the fourth layer is a dielectric material layer, and the fifth layer is a metal floor layer;

[0007] The first metal patch layer includes a square split ring unit for generating circularly polarized vortex electromagnetic waves;

[0008] The dielectric material of the second and fourth layers is F4B, and its phase dielectric constant ε r is 2.65, and the tangent loss angle is 0.0009;

[0009] The third metal patch layer includes a cross-shaped unit for generating a linearly polarized vortex electromagnetic wave under a linear polarization condition.

[0010] Furthermore, the unit period P of the cell x =P y =10°, the thickness of the dielectric material layer of the second layer is h=1, and the thickness of the dielectric material layer of the fourth layer is h=2.

[0011] The design method of high-order mode vortex electromagnetic waves of the metasurface includes the following steps:

[0012] S1. Construct the cell parameters. According to the requirements of the cell amplitude and phase for the reflected vortex wave, the rotation angle and slot width of the square split ring unit in the cell structure are used as optimization variables to optimize the size parameters of the square split ring unit structure. The slotted strip after rotation ɑ opens a slot with a width of g on the square resonant ring, thereby forming a square split ring. The rotation angle ranges from 0° to 180° at intervals of 5°. Different rotation angles correspond to the slot width required for the fixed resonant frequency, and a total of 37 basic states are obtained.

[0013] There are four basic states of the cross unit. Four cell styles are constructed based on the parameters of these four states. The parameters are:

[0014] w x =w y =0.3796; l x = l y =3.6657

[0015] w x =w y =0.4872; l x = l y =4.6389

[0016] w x =w y =0.4572; l x = l y =5.0891

[0017] w x =w y =0.4281; l x = l y =5.0891

[0018] Among them l x is the arm length of the metal bar in the horizontal direction, w xis the width of the metal strip in the horizontal direction, l y is the arm length of the metal strip in the vertical direction, w y is the width of the metal strip in the vertical direction;

[0019] S2. According to the Helmholtz equation of free space, the electric field expression of the vortex wave propagating along the direction of electromagnetic wave transmission is derived:

[0020]

[0021] Where i is the imaginary unit, is the azimuth in the cylindrical coordinate system, k is the longitudinal wave number, A is the amplitude of the beam, z is the height in the cylindrical coordinate system, r is the radial distance in the cylindrical coordinate system; l is the topological number, that is, the OAM mode number;

[0022] The theoretical phase distribution of the vortex wave carrying OAM in the transverse plane is: where l is the topological charge, is the angular coordinate, i is the imaginary sign; the vortex phase that needs to be introduced by the metasurface cell at the coordinate position (x, y) is:

[0023]

[0024] Since both the incident vertical polarization and horizontal polarization are spherical waves, cells at different positions need to compensate for the phase of the spherical wave. The relative position of the phase center of a selected feed source in space relative to the center point of the metasurface is The relative position of the cell with coordinates (x, y) on the hypersurface is Then the distance from the feed phase center to each cell is The feed compensation phase that needs to be introduced into the metasurface cell at the coordinate position (x, y) is:

[0025]

[0026] Where k is the wave number of the center frequency in vacuum, and λ is the wavelength corresponding to the center frequency.

[0027] Then for each cell of the metasurface, the metasurface compensation phase required for complete linear polarization is:

[0028]

[0029] S3. Phase compensation using metasurface in MATLAB The metasurface distribution of the calculation theory is calculated. The cross-cross unit is arranged using 2-bit coding. The square split ring adopts the PB phase rotation unit angle arrangement. The simulation modeling is performed using CST full-wave simulation software. The parameter variables of the cell in step S1 are scanned using full-wave numerical simulation to calculate the complex reflection coefficient of the unit under different parameters. According to the compensation phase The corresponding parameter value of each calculated cell is found in the scanning result to obtain the parameter setting value of the cell;

[0030] S4. Based on the parameter setting values ​​of each cell in the metasurface array obtained in MATLAB, the metasurface array is modeled using CST software.

[0031] Beneficial effects:

[0032] In this application, by optimizing the design of the metasurface unit structure, the generated vortex electromagnetic waves with high mode numbers maintain a high OAM mode purity, while keeping the SL0 of the side lobes between the radiation peak and the energy zero point at a low value. High-modulus vortex waves can carry more orbital angular momentum states, which means that higher-capacity information transmission can be achieved through vortex beams of different moduli. High-modulus vortex beams can be flexibly adjusted through structures such as metasurfaces to achieve multi-directional and multi-angle beam control, and are suitable for complex wireless communication environments. In addition to wireless communications, the generation and manipulation of high-modulus vortex waves also shows great application prospects in radar, imaging and other fields, which can improve the resolution and detection capabilities of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a schematic diagram of the overall structure of the cell of the metasurface of the high-order mode vortex electromagnetic wave provided by the present invention;

[0034] Figure 2 It is a top view of the first layer structure of the cell of the metasurface of the high-order mode vortex electromagnetic wave provided by the present invention;

[0035] Figure 3 It is a top view of the third-layer structure of the cell of the super surface of the high-order mode vortex electromagnetic wave provided by the present invention;

[0036] Figure 4 It is a top view of the fifth layer structure of the cell of the super surface of the high-order mode vortex electromagnetic wave provided by the present invention;

[0037] Figure 5 It is a result diagram of the co-polarization reflection coefficient and reflection phase performance of the cellular square split ring unit provided by the present invention;

[0038] Figure 6 It is a result diagram of the co-polarization reflection coefficient and reflection phase performance of the cellular square split ring unit provided by the present invention;

[0039] Figure 7 is a phase distribution diagram of the metasurface provided by the present invention;

[0040] Figure 8 is the rotation angle of the square split ring unit corresponding to the phase provided by the present invention;

[0041] Fig. 9 The distribution of four basic states of the cross-cross unit on the metasurface under X-polarization provided by the present invention;

[0042] Fig.10 The distribution of the four basic states of the cross-cross unit on the metasurface under Y polarization provided by the present invention;

[0043] Fig.11 It is a super surface diagram prepared by the PCB printed circuit board process provided by the present invention;

[0044] Fig.12 It is a simulation diagram of the near-field electric field strength provided by the present invention;

[0045] Fig.13 It is a simulation diagram of the near-field electric field phase distribution provided by the present invention;

[0046] Fig.14 It is the pattern purity diagram provided by the present invention. DETAILED DESCRIPTION

[0047] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. 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.

[0048] The application principle of the present invention is further described below in conjunction with the accompanying drawings and specific embodiments.

[0049] Embodiment 1:

[0050] like Figure 1-Figure 4 As shown, a high-order mode vortex electromagnetic wave generating structure based on a metasurface, the high-order mode vortex electromagnetic wave generating structure includes a metasurface, the metasurface includes multiple cellular structures, each of which includes a multi-layer plate structure, wherein the first layer of the multi-layer plate structure is a metal patch layer, the second layer is a dielectric material layer, the third layer is a metal patch layer, the fourth layer is a dielectric material layer, and the fifth layer is a metal floor layer, and the layers of the multi-layer plate structure are stacked in sequence.

[0051] The first metal patch layer of the cell includes a square split ring unit, where d o is the outer side length parameter of the square split ring, which is 6.139. iis the inner side length parameter of the square split ring, and its value is 5.404, and g is the crack width of the square split ring, and its value is 0.2. The square split ring unit is used to generate circularly polarized vortex electromagnetic waves, so it is also called a circularly polarized unit.

[0052] The dielectric layer material of the second and fourth layers of the cell is F4B (polytetrafluoroethylene glass fiber cloth ceramic film substrate), and its phase dielectric constant ε r The tangent loss angle is 2.65 and 0.0009. The metal patch of the first layer, the metal patch of the third layer and the metal floor of the fifth layer of the cell are all copper.

[0053] The third metal patch layer includes a cross-cross unit, which is used to generate linearly polarized vortex electromagnetic waves under linear polarization conditions, so it is also called a linear polarization unit.

[0054] This single-layer metasurface array antenna for generating vortex waves with high mode number and high mode purity can generate l=6 CP vortex waves, l=6 XLP vortex waves, and l=6 YLP vortex waves at an operating frequency of 12-18 GHz. The array antenna is square in shape and consists of 30×30 cells.

[0055] Cell parameters (unit: mm): unit period P x =P y =10°, the thickness of the dielectric material layer of the second layer is h=1, and the thickness of the dielectric material layer of the fourth layer is h=2.

[0056] A design method for high-order mode vortex electromagnetic waves based on metasurface:

[0057] S1. Construct the parameters of the cellular structure. According to the requirements of the amplitude and phase of the cellular structure for the reflected vortex wave, the rotation angle and slot width of the square split ring unit in the cellular structure are used as optimization variables to optimize the size parameters of the square split ring unit structure. The slotted strip after rotation ɑ opens a slot with a width of g on the square resonant ring, thereby forming a square split ring. The rotation angle ranges from 0° to 180° at intervals of 5°. Different rotation angles correspond to the slot width required for a fixed resonant frequency. A total of 37 basic states are obtained to realize the angle arrangement of the PB phase rotation unit. Angle (degrees) and corresponding g value: angle = 0°, g = 0.2000; angle = 5°, g = 0.2008; angle = 10°, g = 0.2031; angle = 15°, g = 0.2071; angle = 20°, g = 0.2128; angle = 25°, g = 0.2207; angle = 30°, g = 0.2309; angle = 35°, g = 0.2442; angle = 40°, g = 0.2611; Angle=45°, g=0.2828; Angle=50°, g=0.2611; Angle=55°, g=0.2442; Angle=60°, g=0.2309; Angle=65°, g=0.22 07; Angle=70°, g=0.2128; Angle=75°, g=0.2071; Angle=80°, g=0.2031; Angle=85°, g=0.2008; Angle=90°, g=0. 2000; angle = 95°, g = 0.2008; angle = 100°, g = 0.2031; angle = 105°, g = 0.2071; angle = 110°, g = 0.2128; angle = 11 5°, g=0.2207; angle=120°, g=0.2309; angle=125°, g=0.2442; angle=130°, g=0.2611; angle=135°, g=0.282 8; Angle=140°, g=0.2611; Angle=145°, g=0.2442; Angle=150°, g=0.2309; Angle=155°, g=0.2207; Angle=160° , g=0.2128; angle=165°, g=0.2071; angle=170°, g=0.2031; angle=175°, g=0.2008; angle=180°, g=0.2000.

[0058] The PB phase is twice the rotation angle of the cell, that is, the delay caused by the cell phase.

[0059] There are four basic states of the cross unit. Four cell styles are constructed based on the parameters of these four states. The parameters are:

[0060] w x =w y =0.3796; lx = l y =3.6657

[0061] w x =w y =0.4872; l x = l y =4.6389

[0062] w x =w y =0.4572; l x = l y =5.0891

[0063] w x =w y =0.4281; l x = l y =5.0891

[0064] Among them l x is the arm length of the metal bar in the horizontal direction, w x is the width of the metal strip in the horizontal direction, l y is the arm length of the metal strip in the vertical direction, w y is the width of the metal strip in the vertical direction.

[0065] S2. According to the Helmholtz equation of free space, the electric field expression of the vortex wave propagating along the direction of electromagnetic wave transmission is derived:

[0066]

[0067] Where i is the OAM mode number, is the azimuth in the cylindrical coordinate system, k is the longitudinal wave number, A is the complex amplitude of the beam, z is the height in the cylindrical coordinate system, r is the radial distance in the cylindrical coordinate system, and l is the topological number.

[0068] For the overall design of the metasurface, the cells of the metasurface are regarded as array units. Assuming that the coordinates of the unit in the rectangular coordinate system are (x, y), the actual coordinates of the corresponding unit center point are (m, n), where m = x·P x , n=y·P y , P x and P y are all unit periods; then the unit azimuth relative to the origin The range is 0 to 2π. The azimuth angle formula can be used to obtain the required phase at any position of the metasurface. The number of metasurface units in this design is 30×30, and the corresponding actual size is 320mm×320mm.

[0069] The theoretical phase distribution of the vortex wave carrying OAM in the transverse plane is: where l is the topological charge, is the angular coordinate, i is the imaginary sign. The vortex phase that needs to be introduced by the metasurface cell at the coordinate position (x, y) is:

[0070]

[0071] Since the incident vertical polarization and horizontal polarization are both spherical waves, cells at different positions need to compensate for the phase of the spherical wave. Assume that the relative position of the phase center of a selected feed source in space relative to the center point of the metasurface is The relative position of the cell with coordinates (x, y) on the hypersurface is Then the distance from the feed phase center to each cell is The feed compensation phase that needs to be introduced into the metasurface cell at the coordinate position (x, y) is:

[0072]

[0073] Where k is the wave number of the center frequency in vacuum, and λ is the wavelength corresponding to the center frequency.

[0074] Then for each cell of the metasurface, the metasurface compensation phase required for complete linear polarization is:

[0075]

[0076] S3. Phase compensation using metasurface in MATLAB The theoretical metasurface distribution is calculated. The cross-cross unit is arranged using 2-bit coding, and the square split ring is arranged using the PB phase rotation unit angle. The CST full-wave simulation software is used for simulation modeling. The full-wave numerical simulation method is used to simulate several parameter variables of the cell structure in step S1 (the slot width g of the square split ring unit, the rotation angle ɑ of the slotted strip, and the outer side length parameter d of the square split ring). o , the inner side length parameter d of the square split ring i , the arm length l of the horizontal metal strip of the cross unit x , the width of the metal strip in the horizontal direction w x , the arm length of the vertical metal strip l y , the width of the metal strip in the vertical direction w y ) is used to scan the parameters to calculate the complex reflection coefficient of the unit under different parameters, according to the compensation phase The corresponding parameter value of each calculated cell is found in the scanning result to obtain the parameter setting value of the cell.

[0077] S4. Simulate in CST microwave studio. According to the parameter setting values ​​of each cell in the metasurface array obtained in MATLAB. Model the metasurface array in CST software. Set the simulation working frequency band to 8-20 GHz, where the actual working frequency band of the metasurface is 10-18 GHz under circular polarization wave irradiation; under linear polarization wave irradiation, the actual working frequency band of the metasurface is 14.5-15.5 GHz. Select circular polarization wave, X polarization or Y polarization wave as the field source for simulation calculation, set the field source at 200 mm away from the metasurface, and make normal incidence on the metasurface. Set a sampling plane at 400 mm away from the metasurface, and obtain the electric field intensity diagram and phase distribution diagram of the high-order vortex electromagnetic wave generated by the reflection of the metasurface on the sampling plane to verify that the generated one is a high-order vortex electromagnetic wave.

[0078] Embodiment 2:

[0079] In order to study the radiation performance of the vortex electromagnetic wave reflection metasurface, a half-wavelength (10 mm) cell is used in this application, such as Figure 1-Figure 4 As shown. The cell is a symmetrical structure and is multi-polarized. The cell model consists of a square split ring, and the combination of multiple elements helps to achieve a multi-resonance structure. It is beneficial to achieve 360° phase coverage.

[0080] Please refer to Figure 5 , Figure 6 The CST microwave studio simulation software is used to analyze the amplitude curve and phase curve of the unit under specific periodic boundary conditions. In the range of 14.5 to 15.5 GHz for electromagnetic waves, the 2-bit coded cross unit is used to realize the vortex electromagnetic wave under linear polarization. The four basic states can achieve a 360° phase coverage range by changing the l between 3 mm and 6 mm. x , l y The CST simulation software is used to simulate the d of the square split ring unit. o ,d i After scanning the two parameters, the amplitude response curve and the phase response curve were analyzed to obtain the optimal parameters of the cell to achieve a 360° phase range at 10 to 18 GHz. The phase curves are quite linear and parallel to each other, which makes it suitable for broadband operation. Therefore, this cell structure can significantly improve the working bandwidth of vortex electromagnetic waves.

[0081] Embodiment 3:

[0082] The phase calculation formula required to generate a vortex electromagnetic wave reflecting each unit on the metasurface in a specified direction is as follows:

[0083]

[0084] in represents the phase compensation required for (m, n) units, Represents the azimuth corresponding to the (m, n) units. is the position vector of the feed irradiating the metasurface (the distance from the center of the metasurface to the center of the feed); is the position vector of the (m, n)th unit (the distance from the center of the metasurface to the (m, n)th unit), λ is the wavelength corresponding to the center frequency, and l is the topological number.

[0085] like Figure 7 , is the phase delay distribution corresponding to the 1=5 mode vortex electromagnetic wave generated by the metasurface.

[0086] Embodiment 4:

[0087] It is convenient to analyze the incident field and scattered field of a cell on the metasurface in the form of Jones matrix. The scattered field and the incident field can be linked through the reflection coefficient in the reflection Jones matrix.

[0088] r ll =0.5[(r xx -r yy )+i(r xy +r yx )] -i2α

[0089] r lr =0.5[(r xx +r yy )+i(r yx -r xy )]

[0090] r rl =0.5[(r xx +r yy )-i(r yx -r xy )]

[0091] r rr =0.5[(r xx -r yy )-i(r xy +r yx )]e i2α

[0092] Among them, r xx , r yy , r ll , r rr are the co-polarization reflection coefficients under normal incidence conditions of x-polarization, y-polarization, left-hand circular polarization, and right-hand circular polarization. xy , r yx , r lr , rrl is the corresponding cross-polarization reflection coefficient. α is the cell rotation angle, and i is the imaginary unit. It can be clearly seen from the formula that only the co-polarization reflection coefficient r ll and r rr ±2α phase is added, namely PB phase. The positive and negative signs indicate the conjugate phase of PB phase with RCP and LCP components, indicating r ll and r rr There is an inherent symmetric response between Figure 7 The phase distribution diagram shown has half the phase value. Figure 8 Rotation angle distribution of the square split ring unit.

[0093] The mode numbers of X-polarized and Y-polarized vortex electromagnetic waves generated by the metasurface constructed by the cross-unit are both 4, and the phase intervals corresponding to the four basic states are approximately 90°. Figure 7 The phase values ​​in the phase distribution diagram shown correspond to the dimension values ​​corresponding to the closest phase values ​​in the four basic states, and we can get Fig. 9 , Fig.10 The corresponding distribution of the four basic states of the cross-cross unit on the metasurface under X polarization and the distribution of the four basic states of the cross-cross unit on the metasurface under Y polarization.

[0094] Embodiment 5:

[0095] like Fig.11 In order to verify the effect of generating high-modulus vortex electromagnetic waves, a full-wave simulation based on CST was performed on a 300mm×300mm metasurface. A half-wavelength cell was used on the reflective metasurface to generate 1=5 mode vortex electromagnetic waves. Then, the mode purity corresponding to the generated vortex electromagnetic waves was calculated by simulating the phase distribution. A 300mm×300mm sampling plane was set in the near-field region 300mm away from the metasurface to obtain the e-field phase distribution. Fig.12 , Fig.13 It can be seen that the amplitude diagram of the electric field is donut-shaped, and the phase distribution diagram shows a typical spiral distribution. The phase distribution variation amplitude is 1800° (5×360°), which is an obvious feature of the OAM wave.

[0096] The purity of OAM can be obtained by decomposing the individual OAM modes through Fourier transform and then integrating them. l ) and sampling phase The relationship between:

[0097]

[0098] in is the function of the circular sampling field along the z-axis, i is the imaginary sign, is the kernel function of Fourier transform.

[0099] The modal purity of OAMVB is calculated by normalizing the spectrum of each OAMVB mode to the total spectrum of all OAMVBs modes, as shown in the following formula:

[0100]

[0101] Where l' represents the number of sampled modes. Here we consider OAM modes from l = -5 to l = 5, such as Fig.14 As shown, the mode purity for l=5 is 65%.

[0102] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A high-order mode vortex electromagnetic wave generating structure based on a metasurface, characterized in that: The high-order mode vortex electromagnetic wave generating structure includes a metasurface, the metasurface includes a plurality of cellular structures, each of which includes a multi-layer plate structure, the first layer of the multi-layer plate structure is a metal patch layer, the second layer is a dielectric material layer, the third layer is a metal patch layer, the fourth layer is a dielectric material layer, and the fifth layer is a metal floor layer; The first metal patch layer includes a square split ring unit for generating circularly polarized vortex electromagnetic waves; The dielectric material of the second and fourth layers is F4B, and its phase dielectric constant ε r is 2.65, and the tangent loss angle is 0.0009; The third metal patch layer includes a cross-shaped unit for generating a linearly polarized vortex electromagnetic wave under a linear polarization condition.

2. The high-order mode vortex electromagnetic wave generating structure based on a metasurface according to claim 1, characterized in that: The unit period of the cell is P x =P y =10°, the thickness of the dielectric material layer of the second layer is h=1, and the thickness of the dielectric material layer of the fourth layer is h=2.

3. A method for designing high-order mode vortex electromagnetic waves of the metasurface according to claim 1, characterized in that: Here are the steps: S1. Construct the cell parameters. According to the requirements of the cell amplitude and phase for the reflected vortex wave, the rotation angle and slot width of the square split ring unit in the cell structure are used as optimization variables to optimize the size parameters of the square split ring unit structure. The slotted strip after rotation ɑ opens a slot with a width of g on the square resonant ring, thereby forming a square split ring. The rotation angle ranges from 0° to 180° at intervals of 5°. Different rotation angles correspond to the slot width required for the fixed resonant frequency, and a total of 37 basic states are obtained. There are four basic states of the cross unit. Four cell styles are constructed based on the parameters of these four states. The parameters are: w x =w y =0.3796;l x =l y =3.6657 w x =w y =0.4872;l x =l y =4.6389 w x =w y =0.4572;l x =l y =5.0891 w x =w y =0.4281;l x =l y =5.0891 Among them l x is the arm length of the metal bar in the horizontal direction, w x is the width of the metal strip in the horizontal direction, l y is the arm length of the metal strip in the vertical direction, w y is the width of the metal strip in the vertical direction; S2. According to the Helmholtz equation of free space, the electric field expression of the vortex wave propagating along the direction of electromagnetic wave transmission is derived: Where i is the imaginary unit, is the azimuth in the cylindrical coordinate system, k is the longitudinal wave number, A is the amplitude of the beam, z is the height in the cylindrical coordinate system, r is the radial distance in the cylindrical coordinate system; l is the topological number, that is, the OAM mode number; The theoretical phase distribution of the vortex wave carrying OAM in the transverse plane is: where l is the topological charge, is the angular coordinate, i is the imaginary sign; the vortex phase that needs to be introduced by the metasurface cell at the coordinate position (x, y) is: Since both the incident vertical polarization and horizontal polarization are spherical waves, cells at different positions need to compensate for the phase of the spherical wave. The relative position of the phase center of a selected feed source in space relative to the center point of the metasurface is The relative position of the cell with coordinates (x, y) on the hypersurface is Then the distance from the feed phase center to each cell is The feed compensation phase that needs to be introduced into the metasurface cell at the coordinate position (x, y) is: Where k is the wave number of the center frequency in vacuum, and λ is the wavelength corresponding to the center frequency. Then for each cell of the metasurface, the metasurface compensation phase required for complete linear polarization is: S3. Phase compensation using metasurface in MATLAB The metasurface distribution of the calculation theory is calculated. The cross-cross unit is arranged using 2-bit coding. The square split ring adopts the PB phase rotation unit angle arrangement. The simulation modeling is performed using CST full-wave simulation software. The parameter variables of the cell in step S1 are scanned using full-wave numerical simulation to calculate the complex reflection coefficient of the unit under different parameters. According to the compensation phase The corresponding parameter value of each calculated cell is found in the scanning result to obtain the parameter setting value of the cell; S4. Based on the parameter setting values ​​of each cell in the metasurface array obtained in MATLAB, the metasurface array is modeled using CST software.

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