Phase-only electromagnetic metasurface design method based on two-phase method

Abstract

The application discloses a kind of phase electromagnetic metasurface design methods based on two-phase method, mainly solve the problem of electromagnetic metasurface structure complexity when existing technology electromagnetic metasurface is simultaneously regulated in amplitude phase.It is implementation scheme: initialization electromagnetic metasurface parameter;Electromagnetic metasurface unit required by two-phase method is calculated phase matrix;Design the electromagnetic metasurface unit including metal grating layer, two layers of dielectric layer and metal patch, and draw the phase table of the electromagnetic metasurface unit;According to the required phase of each unit of electromagnetic metasurface and the phase table of electromagnetic metasurface unit, the state of each unit of electromagnetic metasurface is adjusted to obtain adjusted electromagnetic metasurface;Feed horn is placed above adjusted electromagnetic metasurface, and radio frequency signal is added to feed horn, to generate required beam, complete phase electromagnetic metasurface design.The application can reduce the complexity of electromagnetic metasurface structure, improve the beam design capability of electromagnetic metasurface, and can be used for wireless transmission, communication system.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of electromagnetic super surface design, and further relates to a phase-only electromagnetic super surface design method based on a two-phase method, which can be used in wireless transmission and communication systems. BACKGROUND

[0002] A two-dimensional electromagnetic super surface can be regarded as a two-dimensional form of metamaterial, which is composed of sub-wavelength units arranged periodically or non-periodically. In recent years, electromagnetic super surfaces have a wide range of applications in electromagnetic polarization, amplitude and phase control due to their strong electromagnetic manipulation capabilities, and have become a candidate material for designing electromagnetic functional devices. Electromagnetic super surfaces can realize beam scanning and generation of special beams, and are applied to various scenarios such as wireless transmission and communication systems.

[0003] The patent document with the application number 202311019048.2 discloses a "spin direction independent amplitude and phase tuning method and reconfigurable multifunctional device", which designs an electromagnetic super surface unit with a metal structure layer, respectively an active adjustable circular arc metal resonator structure, a metal ground plate etched with a closed circular groove, a variable resistance diode and a switching diode. Although this method realizes the spin direction independent amplitude and phase tuning of the electromagnetic super surface unit, it adds many variable resistance diodes and switching diodes to the electromagnetic super surface unit in order to realize the simultaneous control of the amplitude and phase of the electromagnetic super surface unit, resulting in a very complex structure and high cost of the electromagnetic super surface.

[0004] The patent document with the application number 202211310414.5 discloses a "two-dimensional enhanced focusing Airy OAM beam phase control method", which generates an enhanced Airy OAM beam by superimposing the same direction of the Airy OAM phase and the near-field focusing phase of the electromagnetic super surface compensation phase. However, this method only compensates for the phase required for the Airy OAM beam, ignoring the amplitude information of the Airy OAM beam, which reduces the transmission efficiency of the electromagnetic super surface and affects the beam performance. SUMMARY

[0005] The purpose of the present application is to overcome the shortcomings of the prior art and provide a phase-only electromagnetic super surface design method based on a two-phase method, which reduces the design complexity of the electromagnetic super surface structure, simplifies the electromagnetic super surface design process and improves the beam design capability of the electromagnetic super surface.

[0006] The idea for achieving the object of the present application is to convert the amplitude and phase information required by the electromagnetic super surface into pure phase information, so that the electromagnetic super surface only needs to design a phase-adjustable unit to realize the ability of simultaneously regulating the amplitude and phase of the electromagnetic wave. By incorporating the amplitude information into the calculation of the pure phase information of the electromagnetic super surface, the near-field and far-field regulation of the electromagnetic super surface has better beam regulation effect, and the transmission efficiency of the electromagnetic super surface is improved.

[0007] According to the above idea, the technical scheme of the present application comprises the following steps:

[0008] (1) Initialization:

[0009] Set the working wavelength of the electromagnetic super surface as λ, and the electromagnetic super surface is composed of M rows and N columns of units; the row spacing between units is d M , and the column spacing is d N， , wherein N≥10, M≥10, d M ∈[0.3λ,0.7λ], d N ∈[0.3λ,0.7λ];

[0010] Set the coordinates of the feed horn as (0, 0, f z ) in the Cartesian coordinate system with the center of the electromagnetic super surface as the origin, wherein (M×d M )≤f z ≤(1.5N×d N );

[0011] Set the regulation amplitude matrix of the electromagnetic super surface unit as A and the compensation phase matrix as P, wherein the value range of each element of the A matrix is 0-1, the value range of each element of the P matrix is 0-360, and the size of the two matrices is M rows and N columns;

[0012] (2) According to the regulation amplitude matrix A and the compensation phase matrix P of the electromagnetic super surface unit, the unique phase matrix required by the electromagnetic super surface unit is calculated by using the double-phase method;

[0013] (3) Design the electromagnetic super surface unit, and draw the phase table of the electromagnetic super surface unit;

[0014] (4) According to the unique phase required by each unit of the electromagnetic super surface and the phase table of the electromagnetic super surface unit, adjust the state of each unit of the electromagnetic super surface to obtain the adjusted electromagnetic super surface;

[0015] (5) Place the feed horn above the adjusted electromagnetic super surface, and add a radio frequency signal to the feed horn to generate the required beam, thereby completing the design of the unique phase electromagnetic super surface.

[0016] Compared with the prior art, the present application has the following beneficial effects:

[0017] Firstly, the application converts the required amplitude information and compensation phase information of the electromagnetic metasurface into phase information only by the two-phase method, avoids the amplitude change of the electromagnetic metasurface unit, and makes the electromagnetic metasurface only need to design a phase-adjustable unit, greatly reduces the complexity and cost of the electromagnetic metasurface structure, and simplifies the design process of the electromagnetic metasurface.

[0018] Secondly, the amplitude information is integrated into the compensation calculation of the phase, compared with the traditional method of only compensating the required phase of the electromagnetic metasurface, the method can make the near-field and far-field regulation of the electromagnetic metasurface have better beam regulation effect, and improve the transmission efficiency of the electromagnetic metasurface. BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1 is a flowchart of the application;

[0020] Figure 2 is a schematic diagram of the electromagnetic metasurface unit designed in the embodiment of the application;

[0021] Figure 3 is a schematic diagram of the metal patch in the electromagnetic metasurface unit designed in the embodiment of the application;

[0022] Figure 4 is a schematic diagram of the compensation amplitude A and the compensation phase P of the electromagnetic metasurface for generating OAM modes l=+1 and l=+2 in the first group of parameters of the application;

[0023] Figure 5 is a schematic diagram of the phase-only matrix calculated in simulation experiment 1 of the application ;

[0024] Figure 6 is a schematic diagram of the electric field amplitude, electric field phase and OAM mode spectrum on the observation surface obtained in simulation experiment 2 of the application;

[0025] Figure 7 is a schematic diagram of the compensation amplitude A and the compensation phase P of the electromagnetic metasurface for generating beams with pitch angles of +40° and-40° at the same time in the second group of parameters of the application;

[0026] Figure 8 is a schematic diagram of the phase-only matrix calculated in simulation experiment 3 of the application ;

[0027] Figure 9 is a schematic diagram of the beam far-field pattern obtained in simulation experiment 4 of the application. DETAILED DESCRIPTION

[0028] The application will be further described in detail below in combination with the drawings and specific embodiments.

[0029] Referring to Figure 1 The implementation steps of the present embodiment include the following:

[0030] Step 1: Initialization:

[0031] 1.1) Set the working wavelength of the electromagnetic super surface, the size of the electromagnetic super surface, the spacing of the electromagnetic super surface units, and the position of the feed horn:

[0032] The present example sets the working wavelength of the electromagnetic super surface as λ = 10 mm, the size of the electromagnetic super surface as consisting of M rows and N columns of units, the row spacing between units as d M = 5 mm, and the column spacing as d N = 5 mm, where N ≥ 10, M ≥ 10, d M ∈ [0.3λ, 0.7λ], d N ∈ [0.3λ, 0.7λ]; and sets the coordinates of the feed horn as (0, 0, f z ) in the Cartesian coordinate system with the center of the electromagnetic super surface as the origin, where (M × d M ) ≤ f z ≤ (1.5N × d N ), the coordinates of the center of each unit of the electromagnetic super surface as (x m , y n ), 1 ≤ m ≤ (M + 1), 1 ≤ n ≤ (N + 1).

[0033] 1.2) Set the required modulation amplitude matrix A and compensation phase matrix P of the electromagnetic super surface units:

[0034] The present example sets the value range of each element in the modulation amplitude matrix A of the electromagnetic super surface units as 0-1, and the value range of each element in the P matrix as 0-360, and the size of both matrices is M rows and N columns.

[0035] Step 2: According to the modulation amplitude matrix A and the compensation phase matrix P of the electromagnetic super surface units, calculate the required unique phase matrix

[0036] 2.1) Encode the modulation amplitude matrix A and the compensation phase matrix P into two pure phase matrices:

[0037] θ(m, n) = P(m, n) + arccos(A(m, n) / max(A))

[0038] ω(m, n) = P(m, n) - arccos(A(m, n) / max(A))

[0039] wherein, θ(m, n) represents the element of the mth row and the nth column in the θ matrix, ω(m, n) represents the element of the mth row and the nth column in the ω matrix, 1≤m≤(M+1), 1≤n≤(N+1);

[0040] 2.2) Encode the θ matrix and the ω matrix by using the two-dimensional chessboard function to obtain the two encoded matrices:

[0041]

[0042]

[0043] wherein, U1(m, n) represents the element of the mth row and the nth column in the U1 matrix, U2(m, n) represents the element of the mth row and the nth column in the U2 matrix, 1≤m≤(M+1), 1≤n≤(N+1);

[0044] 2.3) Obtain the unique phase matrix required by the electromagnetic metasurface unit according to the U1 matrix and the U2 matrix

[0045]

[0046] wherein, represents the unique phase required by the mth row and the nth column unit in the electromagnetic metasurface, 1≤m≤(M+1), 1≤n≤(N+1).

[0047] Step 3: Design the electromagnetic metasurface unit and draw the phase table of the electromagnetic metasurface unit.

[0048] 3.1) Design the electromagnetic metasurface unit;

[0049] Referring to Figure 2 , the electromagnetic metasurface unit designed in the present example includes two layers of metal grating layers, two layers of dielectric layers and a metal patch, and the structure is: the first metal grating layer, the first dielectric layer, the metal patch, the second dielectric layer, and the second metal grating layer are sequentially linked;

[0050] The two dielectric layers are cuboids with equal volume and same shape, and in the present example, a cuboid with a length of 5 mm, a width of 5 mm and a height of 2 mm is selected but not limited to a F4B plate material with a relative dielectric constant of 2.2 and a loss tangent of 0.0015;

[0051] The first metal grating is composed of three square metal patches with same size and equal spacing arranged in parallel along the x-axis direction of the substrate, and the spacing between the two metal patches is 1 mm;

[0052] The second metal grating is composed of three square metal pieces of the same size and equal spacing arranged in parallel along the y-axis direction of the substrate, and the spacing between two metal pieces is 1mm; the two metal grating layers are respectively printed on the upper and lower ends of the first dielectric layer and the second dielectric layer;

[0053] The metal patch is printed between the first dielectric layer and the second dielectric layer, and the shape adopts an open I-shaped patch with an opening size of α and an angle of 45° between the center axis and the x-axis, as shown in Figure 3 The opening angle of the metal patch is used to control the transmission phase of the electromagnetic super surface unit, and the value range of α is [7°, 105°];

[0054] 3.2) Draw the phase table of the electromagnetic super surface unit;

[0055] By changing the opening angle α of the metal patch through simulation, the transmission phase corresponding to each value of the opening angle α of the metal patch is obtained, and each value of the opening angle α of the metal patch and the transmission phase corresponding thereto are drawn into a phase table.

[0056] In this example, when the opening angle α of the metal patch changes from 7° to 105°, the transmission phase of the electromagnetic super surface unit changes linearly from 136° to 334°, and when the metal patch rotates 90° around the z-axis, the transmission phase of the unit changes linearly from -44° to 158°, and the phase table of the opening angle α of the metal patch and the corresponding transmission phase is obtained.

[0057] Step 4, adjust the state of each unit of the electromagnetic super surface according to the unique phase required by each unit of the electromagnetic super surface and the phase table of the electromagnetic super surface unit, and obtain the adjusted electromagnetic super surface.

[0058] In this example, adjusting the state of each unit of the electromagnetic super surface means changing the opening angle α of the electromagnetic super surface unit, finding the opening angle α of the metal patch corresponding to the unique phase required by each unit of the electromagnetic super surface in the phase table of the electromagnetic super surface unit, and adjusting the opening angle α of the metal patch of each unit of the electromagnetic super surface according to this, and the value range of α is [7°, 105°];

[0059] Place the center of the adjusted electromagnetic super surface unit according to its rectangular coordinate position (x m ,y n ), and obtain the adjusted electromagnetic super surface with a scale of MxN, 1≤m≤(M+1), 1≤n≤(N+1).

[0060] Step 5, place the feed horn above the adjusted electromagnetic super surface, and add a radio frequency signal to the feed horn to generate the required beam, and complete the unique phase electromagnetic super surface design.

[0061] In the present example, a spatial coordinate system is constructed with the center of the electromagnetic super surface as the origin, the feed horn is placed at (0, 0, f z ) in the coordinate system, the feed horn is added with a radio frequency signal to generate the required beam.

[0062] The technical effects of the present application are further described below in combination with simulation experiments and analysis of sampling results.

[0063] 1. Simulation experiment conditions:

[0064] The hardware platform of the simulation experiment of the present application is: the processor is Intel(R) Core(TM) i7-10700 CPU, the main frequency is 2.90 GHz, and the memory is 16 GB.

[0065] The software platform of the simulation experiment of the present application is: Windows 10 operating system, Ansys HFSS2021 and MATLAB R2020b.

[0066] The data of the simulation experiment of the present application are set as two groups, wherein:

[0067] The first group of parameters is set as: the beam generated by the electromagnetic super surface is set as a multi-OAM modal vortex beam with OAM modal -1 and OAM modal -2, the electromagnetic super surface is located in the xoy plane of the Cartesian coordinate system, the working frequency of the electromagnetic super surface is f = 30 GHz, and the working wavelength is λ = 10 mm. The electromagnetic super surface is composed of 20 rows and 20 columns of units, the row spacing between every two units is 5 mm, the column spacing between every two units is 5 mm, and the coordinate of the feed horn in the Cartesian coordinate system is set as (0, 0, 120 mm). The electric field distribution of the beam can obtain the control amplitude matrix A of the electromagnetic super surface unit, as shown in Figure 4 (a), wherein the abscissa represents the position coordinate of the unit in the x direction, the ordinate represents the position coordinate of the unit in the y direction, and the amplitude distribution is between 0 and 1. The required compensation phase matrix P of the electromagnetic super surface unit of the beam is as shown in Figure 4 (b), wherein the abscissa represents the position coordinate of the unit in the x direction, the ordinate represents the position coordinate of the unit in the y direction, and the phase distribution is between 0° and 360°.

[0068] The second group of parameters is set as follows: the electromagnetic super surface is set to generate beams with a pitch angle of +40° and -40° and an azimuth angle of 0°, the electromagnetic super surface is located in the xoy plane of the Cartesian coordinate system, the working frequency of the electromagnetic super surface is f = 30 GHz, and the working wavelength is λ = 10 mm. The electromagnetic super surface is composed of 40 rows and 40 columns of units, the row spacing between every two units is 5 mm, the column spacing between every two units is 5 mm, and the coordinates of the feed horn in the Cartesian coordinate system are set as (0, 0, 150 mm). The amplitude matrix A required for the electromagnetic super surface units of the beam is set as shown in Figure 7 (a), where the abscissa represents the position coordinates of the units in the x direction, the ordinate represents the position coordinates of the units in the y direction, and the amplitude distribution is between 0 and 1. The compensation phase matrix P required for the electromagnetic super surface units of the beam is set as shown in Figure 7 (b), where the abscissa represents the position coordinates of the units in the x direction, the ordinate represents the position coordinates of the units in the y direction, and the phase distribution is between 0° and 360°.

[0069] 2. Simulation content and result analysis:

[0070] In simulation experiment 1, under the conditions of the first group of parameters described above, the unique phase matrix required for the electromagnetic super surface units is calculated by the simulation software MATLAB R2020b according to the set amplitude matrix A and the compensation phase matrix P by using the method of the present application. As shown in Figure 5 , where the abscissa represents the position coordinates of the units in the x direction, the ordinate represents the position coordinates of the units in the y direction, and the phase distribution is between 0° and 360°.

[0071] From Figure 5 , it can be seen that the unique phase matrix Figure 4 required for the electromagnetic super surface units can be obtained by the amplitude matrix A of Figure 4 (a) and the compensation phase matrix P of . According to the unique phase matrix , the electromagnetic super surface can be designed.

[0072] In simulation experiment 2, under the conditions of the first group of parameters described above, after the designed electromagnetic super surface is obtained, the feed horn is excited by the simulation software Ansys HFSS2021, a 200 mm x 200 mm observation surface is added at (0, 0, -200 m), and the electric field distribution and OAM mode distribution of the beam on the observation surface are simulated, as shown in Figure 6 . Wherein:

[0073] Figure 6 (a) is the electric field amplitude distribution, and the side axis represents the size of the electric field amplitude;

[0074] Figure 6 (b) is an electric field phase distribution, the side axis represents the phase value of the electric field;

[0075] Figure 6 (c) is an OAM mode spectrum distribution, the horizontal coordinate represents the OAM mode value, and the vertical coordinate represents the mode purity of the OAM.

[0076] From Figure 6 It can be seen that the electromagnetic metasurface designed by the application successfully generates OAM mode -1 and OAM mode -2 and multi-OAM mode vortex beams, and the generated beams present a hollow circular ring shape, and the near-field beam effect is good.

[0077] Simulation experiment 3, under the above second group of parameter conditions, using the method of the application, through the simulation software MATLAB R2020b, according to the set control amplitude matrix A and compensation phase matrix P, the unique phase matrix required by the electromagnetic metasurface unit is calculated As Figure 8 shown, wherein the horizontal coordinate represents the position coordinate of the unit in the x direction, the vertical coordinate represents the position coordinate of the unit in the y direction, and the phase distribution is between 0° and 360°.

[0078] From Figure 8 It can be seen that the unique phase matrix required by the electromagnetic metasurface unit can be obtained by the control amplitude matrix A of Figure 7 (a) and the compensation phase matrix P of Figure 7 (b). According to the unique phase matrix , the electromagnetic metasurface can be designed.

[0079] Simulation experiment 4, under the above second group of parameter conditions, after obtaining the designed electromagnetic metasurface, the simulation software Ansys HFSS2021 is used to perform radio frequency excitation on the feed horn, and the far-field pattern when the azimuth angle is 0° is simulated, as Figure 9 shown, wherein the vertical coordinate represents the gain of the beam, and the horizontal coordinate represents the elevation angle of the far field, and the elevation angle is between -180° and +180°.

[0080] From Figure 9 It can be seen that the electromagnetic metasurface designed by the application successfully generates beams with elevation angles of +40° and -40°, and the gains of the two beams are 23dB, and the difference between the gain of the side lobe and the gain of the main beam is 15dB, and good far-field beam performance is achieved.

[0081] The simulation results show that the electromagnetic metasurface designed by the application can realize the generation of near-field beams and far-field beams.

[0082] The above description is only one specific embodiment of the present application and does not constitute any limitation to the present application. It is obvious for those skilled in the art that, after understanding the content and principles of the present application, various modifications and changes in form and details can be made without departing from the principles and structures of the present application, and these modifications and changes based on the idea of the present application are still within the protection scope of the present application.

[0083] It should be noted that the step numbers in the present application specification and claims are only for clearly describing the embodiments of the present application and facilitating understanding, and the sequence of the numbers is not limited.

Claims

1. A phase-only electromagnetic metasurface design method based on two-phase method, characterized in that, The method comprises the following steps: (1) initialization: The working wavelength of the electromagnetic metasurface is set as The electromagnetic metasurface is composed of M rows and N columns of units; the row spacing between the units is d M The column spacing is d N , wherein N≥10, M≥10, , ; The coordinates of the feed horn are set as Cartesian coordinates with the center of the electromagnetic super surface as the origin where (M x d M ) ≤ (1.5N x d N ); Set the control amplitude matrix A and the compensation phase matrix P of the electromagnetic super surface unit, wherein the value range of each element of the matrix A is 0-1, the value range of each element of the matrix P is 0-360, and the size of the two matrices is M rows and N columns; (2) according to the control amplitude matrix A and the compensation phase matrix P of the electromagnetic super surface unit, the unique phase matrix required by the electromagnetic super surface unit is calculated by using the double-phase method; the implementation step comprises the following: 2a) encode the control amplitude matrix A and the compensation phase matrix P into two pure phase matrices: ； ； wherein denotes the element in the mth row and nth column of the matrix, denotes the element in the mth row and nth column of the matrix, , ; 2b) Using two-dimensional chessboard-like functions to... Matrix and The matrix is ​​encoded to obtain two encoded matrices: ； ； wherein denotes the element in the mth row and nth column of the matrix, denotes the element in the mth row and nth column of the matrix, , ; 2c) according to matrix and matrix, obtaining the required phase-only matrix for the electromagnetic metasurface unit : ； wherein, represents the required unique phase of the mth row and nth column cell in the electromagnetic metasurface, , ; (3) design an electromagnetic super surface unit comprising a metal grating layer, a dielectric layer and a metal patch, and draw a phase table of the electromagnetic super surface unit; (4) adjust the state of each unit of the electromagnetic super surface according to the unique phase required by each unit of the electromagnetic super surface and the phase table of the electromagnetic super surface unit, to obtain an adjusted electromagnetic super surface; (5) place a feed horn above the adjusted electromagnetic super surface, and add a radio frequency signal to the feed horn to generate a required beam, thereby completing the design of the unique phase electromagnetic super surface.

2. The method of claim 1, wherein, The control amplitude matrix A of the electromagnetic super surface unit set in step (1) is as follows: A(m, n) = mag(E(x m ,y n )) where A(m, n) represents the element in the mth row and the nth column of the A matrix, E(x m ,y n ) represents the required electric field distribution of the electromagnetic super surface at (x m ,y m ), and (x m ,y n ) represents the coordinates of the center of the mth row and the nth column unit of the electromagnetic super surface in the plane coordinate system as (x m ,y n ), , .

3. The method of claim 1, wherein, The compensation phase matrix P set in step (1) is as follows: P = arg(E(x m ,y n )) where P(m, n) represents an element of the P matrix in the mth row and the nth column, , .

4. The method of claim 1, wherein, The electromagnetic super surface unit designed in step (3) comprises two metal grating layers, two dielectric layers and a metal patch, and the structure is: first metal grating layer, second metal grating layer, metal patch, first dielectric layer, second dielectric layer; The two dielectric layers are cuboids with equal volume and same shape; The first metal grating is composed of three square metal pieces with same size and equal spacing arranged in parallel along the x-axis direction of the substrate; the second metal grating is composed of three square metal pieces with same size and equal spacing arranged in parallel along the y-axis direction of the substrate; the two metal grating layers are printed on the upper and lower ends of the first and second dielectric layers, respectively; The metal patch is printed between the first dielectric layer and the second dielectric layer, and the shape of the metal patch is any one of an open circular ring type and an I type, and the opening angle of the metal patch is used to control the transmission phase of the electromagnetic super surface unit.

5. The method of claim 1, wherein, In step (3), the phase table of the designed electromagnetic super surface unit is obtained by changing the opening angle of the metal patch to obtain the transmission phase corresponding to each value of the opening angle of the metal patch, and each value of the opening angle of the metal patch and the transmission phase corresponding thereto are drawn into a phase table.

6. The method of claim 1, wherein, In step (4), the state of each unit of the electromagnetic super surface is adjusted according to the unique phase required by each unit of the electromagnetic super surface and the phase table of the electromagnetic super surface unit, that is, the opening angle of the metal patch of each unit of the electromagnetic super surface is adjusted according to the opening angle of the metal patch corresponding to the unique phase of each unit of the electromagnetic super surface.

7. The method of claim 1, wherein, The step (5) of placing the feed horn above the adjusted electromagnetic super surface refers to constructing a space coordinate system with the center of the electromagnetic super surface as the origin, and the feed horn is placed at the place in the coordinate system.

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