A method for solving the transmission characteristics of a honeycomb frequency selective surface

Abstract

The present invention proposes a method for solving the transmission characteristics of a cellular frequency selective surface. The implementation steps include: constructing a unit geometric model of the cellular frequency selective surface; performing mesh division on the unit geometric model; calculating the direction vector of the polarized plane wave in OXYZ; calculating the incident field at the excitation port in different modes; constructing a finite element matrix equation; performing matrix element substitution on the matrix equation; and obtaining the transmission characteristics of the cellular frequency selective surface. By using two vector edges of the excitation port and transforming the three-dimensional coordinate system into a three-dimensional local coordinate system, and calculating the wave numbers of the polarized plane wave in the three axial directions of the three-dimensional local coordinate system, the present invention calculates the incident field at the excitation port in different modes, avoiding the defect in the prior art that the incident field at the excitation port cannot be calculated in a coordinate system with two vector edges of a regular hexagon as the coordinate axes by using the finite element method, and achieving high-precision solution of the transmission characteristics of the cellular frequency selective surface.

Description

Technical Field

[0001] The present invention belongs to the technical field of electromagnetic simulation, and relates to a method for solving the transmission characteristics of a cellular frequency selective surface, which can be applied to the design of the cellular frequency selective surface structure. Background Art

[0002] A frequency selective surface is a periodic array composed of units with the same material and shape arranged according to a specific rule. When designing the frequency selective surface structure, it is necessary to solve its transmission characteristics including the transmission coefficient and the reflection coefficient. The main solution methods include the method of moments, the finite difference time domain method, and the finite element method, etc. Compared with the method of moments and the finite difference time domain method, the finite element method has more advantages in the calculation of complex structures. By using tetrahedral meshes to divide structures such as curves, more accurate solution results can be obtained. And when calculating a periodic array using the finite element method, generally only one unit needs to be analyzed, which can better save memory, reduce the calculation time and resources.

[0003] When using the finite element method to solve the transmission characteristics of a frequency selective surface structure, it is necessary to establish its unit geometric model according to the object to be solved; perform mesh division on the unit geometric model to obtain multiple tetrahedrons; calculate the incident field of the excitation port in different modes by combining the wave number and direction vector of the polarized plane wave; construct the finite element matrix equation, and replace the elements of the matrix in the matrix equation according to the relationship of the period; solve the replaced matrix to obtain the total electric field; solve the transmission characteristics including the transmission coefficient and the reflection coefficient through the total electric field and the incident field.

[0004] When solving the transmission characteristics of a cellular frequency selective surface with a hexagonal prism as the unit geometric model, since the shapes of its excitation ports are all regular hexagons, and there are no two mutually orthogonal sides in a regular hexagon, when using the finite element method for solution, it is impossible to directly calculate the incident field of the excitation port in a coordinate system with two vector sides of the regular hexagon as the coordinate axes, and thus the transmission characteristics of the cellular frequency selective surface cannot be obtained. Summary of the Invention

[0005] The purpose of the present invention is to overcome the defects existing in the above-mentioned prior art, and propose a method for solving the transmission characteristics of a cellular frequency selective surface structure, which is used to solve the technical problem that the transmission characteristics of a cellular frequency selective surface cannot be solved by the finite element method in the prior art.

[0006] To achieve the above purpose, the technical solution adopted by the present invention includes the following steps:

[0007] (1) Construct the unit geometric model of the cellular frequency selective surface:

[0008] The unit structure for constructing a cellular frequency selective surface includes an air box in the shape of a regular hexagonal prism with its side parallel to the z-axis of the three-dimensional coordinate system OXYZ, a metal layer and a unit geometric model of R dielectric layers located in the air box. Any three adjacent sides of the air box are taken as the main sides, and the other three adjacent sides are taken as the secondary sides. The upper and lower regular hexagonal faces with an area of SUR are used as excitation ports. Among them, the relative permittivity and relative permeability of the r-th dielectric layer are ε r , μ r ;

[0009] (2) Mesh the unit geometric model:

[0010] Mesh the unit geometric model to obtain L tetrahedrons containing V edges and triangular faces. There are 2 degrees of freedom on each edge and triangular face, and H degrees of freedom in each tetrahedron. There are a total of 2V degrees of freedom in L tetrahedrons. The P degrees of freedom {λ1, λ2,..., λ p ,..., λ P} located on the main sides of the unit geometric model are taken as the main degrees of freedom, and the Q degrees of freedom {σ1, σ2,..., σ q ,..., σ Q} located on the secondary sides are taken as the secondary degrees of freedom;

[0011] (3) Calculate the direction vector of the polarized plane wave in OXYZ:

[0012] Through the angles θ between the polarized plane wave at infinity and the z-axis and x-axis in the three-dimensional coordinate system OXYZ, Calculate the direction vector of the polarized plane wave in OXYZ

[0013] (4) Calculate the incident fields at the excitation ports in different modes:

[0014] Transform the three-dimensional coordinate system OXYZ into a three-dimensional local coordinate system O′X′Y′Z′ through two vector edges a1 and a2 of the excitation port, and calculate the wave numbers k in the x′, y′, and z′ directions of the polarized plane wave in O′X′Y′Z′h at a frequency of f through the direction vector of the polarized plane wave in OXYZ x′mn , k y′mn and k z′mn . Then, according to k x′mn , k y′mn and k z′mn calculate the incident fields at the excitation ports in the TE nm , TM nm , TEM nm modes where n and m are respectively the number of half periods of the polarization plane wave varying along the x' and y' directions on O′X′Y′Z′;

[0015] (5) Construct the finite element matrix equation:

[0016] Construct a finite element system matrix D with dimension I×J and an excitation matrix b with dimension I×1, and construct a matrix equation Du = b for the electric field coefficient u through D and b, where D ij is the finite element system term related to the i-th degree of freedom and the j-th degree of freedom, and b i is the excitation term related to the i-th degree of freedom, and I = J = 2V;

[0017] (6) Perform matrix element substitution on the matrix equation:

[0018] Substitute the elements in the matrix D and the matrix b in the matrix equation to obtain the substituted matrix equation D′u = b′, where D′ and b′ are the substitution results of D and b respectively;

[0019] (7) Obtain the transmission characteristics of the honeycomb frequency selective surface:

[0020] Use a sparse matrix solver to solve the transformed matrix equation D′u = b′ to obtain the electric field coefficient u, and calculate the electric field E of each tetrahedron through u l Calculate the electric field E of the honeycomb frequency selective surface, then use a post-processor, and through E and the incident field at the excitation port obtained in step (4) Calculate the reflection coefficient S of the transmission characteristics of the honeycomb frequency selective surface 11 and the transmission coefficient S 21 .

[0021] Compared with the prior art, the present invention has the following advantages:

[0022] The present invention avoids the defect in the prior art that the incident field at the excitation port cannot be calculated in a coordinate system with two vector edges of a regular hexagon as the coordinate axes by using the finite element method. By two vector edges of the excitation port and transforming the three-dimensional coordinate system into a three-dimensional local coordinate system, and calculating the wave numbers of the polarization plane wave in the three axis directions of the three-dimensional local coordinate system and then calculating the incident field at the excitation port in different modes, the high-precision solution of the transmission characteristics of the honeycomb frequency selective surface is realized. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 is the implementation flowchart of the present invention;

[0024] Figure 2 is the structural schematic diagram of the unit geometric model of the present invention;

[0025] Figure 3 Structural schematic diagram of the perfect electric conductor PEC of the present invention;

[0026] Figure 4 Calculation result diagram of the transmission coefficient in the present invention;

[0027] Figure 5 Calculation result diagram of the reflection coefficient in the present invention. Specific implementation manners

[0028] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0029] Referring to Figure 1 , the present invention includes the following steps:

[0030] Step 1) Construct the unit geometric model of the honeycomb frequency selective surface:

[0031] Construct the unit structure of the honeycomb frequency selective surface, including the unit geometric model of the air box in the shape of a regular hexagonal prism with its side parallel to the z-axis of the three-dimensional coordinate system OXYZ, the metal layer located in the air box, and R dielectric layers. Any three adjacent sides of the air box are used as the main sides, and the other three adjacent sides are used as the secondary sides. The upper and lower two regular hexagonal faces with an area of SUR are used as the excitation ports. Among them, the relative permittivity and relative permeability of the r-th dielectric layer are ε r , μ r ;

[0032] Referring to Figure 2 , the unit geometric model of this embodiment includes an air box in the shape of a regular hexagonal prism with its side parallel to the z-axis of the three-dimensional coordinate system OXYZ, the metal layer is a perfect electric conductor PEC, and a regular hexagonal prism dielectric substrate with relative permittivity and relative permeability of 2.65 and 1 respectively. Sides 1, 2, and 3 of the air box are the main sides, and the other three sides are the secondary sides; the upper and lower two regular hexagons with an area SUR of 103.11 mm 2 are used as the excitation ports.

[0033] Among them, the center of the lower surface regular hexagon of the air box is located at the origin O of the three-dimensional coordinate system OXYZ; the perfect electric conductor PEC is printed on the upper surface of the dielectric substrate, and its structure is as Figure 3 shown, and R1, R2, R3, R4, R5, R6, R7 are 6.3 mm, 0.35 mm, 1.2 mm, 3.6 mm, 1.2 mm, 1.9 mm, 1.1 mm respectively; the thickness h of the dielectric substrate is 1 mm.

[0034] (2) Perform mesh division on the unit geometric model:

[0035] Mesh division of the geometric model is required for solving using the finite element method. ForFigure 2 The geometric model of the unit in this embodiment is meshed to obtain 3,130 tetrahedrons containing 11,141 edges and triangular faces. There are 2 degrees of freedom on each edge and triangular face, and 20 degrees of freedom in each tetrahedron. A total of 22,282 degrees of freedom exist in 3,130 tetrahedrons. The 1,842 degrees of freedom {λ1, λ2,..., λ 1842} on the main side of the unit geometric model are used as the main degrees of freedom, and the 1,798 degrees of freedom {σ1, σ2,..., σ 1798} on the slave side are used as the slave degrees of freedom; when the degree of freedom is on the edge where the main side and the slave side intersect, it is specified as the main degree of freedom.

[0036] (3) Calculate the direction vector of the polarized plane wave in OXYZ:

[0037] Through the angles θ between the polarized plane wave at infinity and the z-axis and x-axis in the three-dimensional coordinate system OXYZ, calculate the direction vector of the polarized plane wave in OXYZ

[0038]

[0039] where are the unit vectors in the x and y axis directions on OXYZ.

[0040] In this embodiment, θ, are 30° and 0° respectively, and the direction vector of the polarized plane wave in OXYZ

[0041] (4) Calculate the incident fields at the excitation ports in different modes:

[0042] The two vector edges a1 and a2 of the excitation port are as Figure 2 shown. The three-dimensional coordinate system OXYZ is transformed into the three-dimensional local coordinate system O′X′Y′Z′ as shown in Figure 2 through a1 and a2, and the wave numbers k in the x′, y′, and z′ directions of the polarized plane wave in O′X′Y′Z′ at frequency f are calculated through the direction vector of the polarized plane wave in OXYZ x′mn k y′mn and k z′mn , and then the incident fields x′mn k y′mn k z′mn at the excitation port in the TE nm , TM nm , TEM nm modes are calculated according to k where n and m are the numbers of half - periods of the polarization plane wave varying in the x' and y' directions along O′X′Y′Z′ respectively.

[0043] The relationships between the x', y', and z' axes of the three - dimensional local coordinate system O′X′Y′Z′ and the two vector edges a1 and a2 are as follows:

[0044]

[0045] k x′mn 、k y′mn and k z′mn , and The calculation formulas are as follows:

[0046]

[0047]

[0048]

[0049]

[0050]

[0051]

[0052]

[0053] where are the unit vectors in the x', y', and z' axis directions on O′X′Y′Z′, k0 is the free - space wave number, j is the imaginary unit, e is the natural constant, c is the speed of light, are the unit vectors of a1 and a2 respectively, a1 and a2 are the scalar values of a1 and a2 respectively, α is the angle between a1 and a2, μ0 is the vacuum permeability, and ε0 is the vacuum permittivity.

[0054] (5) Construct the finite - element matrix equation:

[0055] Construct a finite - element system matrix D with a dimension of 22282×22282 and an excitation matrix b with a dimension of 22282×1, and construct a matrix equation Du = b for the electric - field coefficient u through D and b, where; D ij is the finite - element coefficient term related to the i - th degree of freedom and the j - th degree of freedom, b i is the excitation term related to the i - th degree of freedom, and the calculation formulas are as follows:

[0056]

[0057]

[0058] Among them, W i is the basis function related to the i-th degree of freedom, Ω is the solution domain space, Γ is the surface of the solution domain space Ω, ▽ is the Hamiltonian operator, k0 is the free space wave number, is divided into the tensor form of ε r and μ r .

[0059] (6) Replace the matrix elements in the matrix equation:

[0060] Replace the elements in the matrix D and matrix b in the matrix equation to obtain the replaced matrix equation D′u = b′, where D′ and b′ are the replacement results of D and b respectively;

[0061] The specific method for replacing the elements in the matrix D and matrix b in the matrix equation is as follows:

[0062]

[0063]

[0064] D′ ij = 0 i ∈ {σ1, σ2,..., σ 1798} and j ∈ [1, 22282]

[0065] b′ i = 0 i ∈ {σ1, σ2,..., σ 1798}

[0066] D′ ij = 1 i = j ∈ {σ1, σ2,..., σ 1798}

[0067]

[0068]

[0069] Among them, ψ ij is the phase shift between the i-th degree of freedom and the j-th degree of freedom, k0 is the free space wave number, c i and c j are the position vectors of the i-th degree of freedom and the j-th degree of freedom respectively.

[0070] (7) Obtain the transmission characteristics of the honeycomb frequency selective surface:

[0071] Use a sparse matrix solver to solve the transformed matrix equation D′u = b′ to obtain the electric field coefficient u, and calculate the electric field E of each tetrahedron through u l Calculate the electric field E of the honeycomb frequency selective surface, then use a post-processor, and through E and the incident field at the excitation port obtained in step (4) Calculate the reflection coefficient S of the transmission characteristics of the cellular frequency selective surface 11 and the transmission coefficient S 21 .

[0072] Among them, the calculation formulas of E, S 11 and S 21 are as follows respectively:

[0073] E = {E 1 , E 2 ,..., E l ,..., E L}

[0074]

[0075]

[0076]

[0077] Among them, E l is the electric field of the l-th tetrahedron, is the h-th basis function in the l-th tetrahedron is 's electric field coefficient, is 's conjugate, Z is the impedance of the excitation port, mode ∈ {TE nm , TM nm , TEM nm}.

[0078] The technical effects of the present invention will be further described below in conjunction with the simulation results:

[0079] 1. Experimental conditions and content:

[0080] The hardware platform for the simulation experiment is: a cloud platform virtual machine, the processor is 1 six-core Intel(R) Xeon(R) Gold 6240 CPU, the main frequency is 2.60 GHz, and the memory is 32 GB. The software platform is: Windows 10 operating system and Fortran 90.

[0081] The transmission characteristics of the cellular frequency selective surface of the present invention are simulated, and the results are as Figure 4 , 5 shown.

[0082] 2. Analysis of experimental results:

[0083] Referring to Figure 4 , in the three modes TE 00 , TM 00 , TEM 00The transmission coefficients at the following calculated frequencies of 2.2 GHz, 2.4 GHz, 2.6 GHz, 2.8 GHz, 3.0 GHz, 3.2 GHz, 3.4 GHz, 3.6 GHz, 3.8 GHz, 4.0 GHz, 4.2 GHz, 4.4 GHz, 4.6 GHz, 4.8 GHz, 5 GHz are obtained, with the frequency on the vertical axis and the transmission coefficient S on the horizontal axis 11 to form a curve graph. The transmission coefficient S 11 in these three modes all reaches its maximum value at a frequency of 3.0 GHz, and the maximum value is 0.00 dB for all.

[0084] As Figure 4 (a) shows, when the mode is TE 00 , the calculated transmission coefficients at the above frequencies are -0.85 dB, -0.53 dB, -0.31 dB, -0.15 dB, -0.05 dB, 0.00 dB, -0.01 dB, -0.07 dB, -0.18 dB, -0.35 dB, -0.57 dB, -0.85 dB, -1.21 dB, -1.64 dB, -2.2 dB, -2.78 dB respectively;

[0085] As Figure 4 (b) shows, when the mode is TM 00 , the calculated transmission coefficients at the above frequencies are -1.73 dB, -1.12 dB, -0.65 dB, -0.30 dB, -0.09 dB, 0.00 dB, -0.05 dB, -0.24 dB, -0.56 dB, -1.00 dB, -1.58 dB, -2.28 dB, -3.11 dB, -4.06 dB, -5.16 dB, -6.42 dB respectively;

[0086] As Figure 4 (c) shows, when the mode is TEM 00 , the calculated transmission coefficients at the above frequencies are -1.05 dB, -0.67 dB, -0.38 dB, -0.18 dB, -0.06 dB, 0.00 dB, -0.02 dB, -0.10 dB, -0.25 dB, -0.46 dB, -0.74 dB, -1.09 dB, -1.51 dB, -2.01 dB, -2.59 dB, -3.27 dB respectively.

[0087] Referring to Figure 5 , in the three modes TE 00 , TM 00 , TEM 00The transmission coefficients at the following calculated frequencies: 2.2 GHz, 2.4 GHz, 2.6 GHz, 2.8 GHz, 3.0 GHz, 3.2 GHz, 3.4 GHz, 3.6 GHz, 3.8 GHz, 4.0 GHz, 4.2 GHz, 4.4 GHz, 4.6 GHz, 4.8 GHz, 5 GHz are used to obtain a curve graph with the frequency on the vertical axis and the reflection coefficient S on the horizontal axis. 21 For these three modes, the transmission coefficient S 21 all reaches its minimum value at a frequency of 3.0 GHz, and the maximum values are -31.86 dB, -30.27 dB, and -32.49 dB respectively.

[0088] As Figure 5 (a) shows, when the mode is TE 00 , the calculated reflection coefficients at the above frequencies are -7.53 dB, -9.36 dB, -11.68 dB, -14.83 dB, -19.74 dB, -31.86 dB, -25.80 dB, -17.80 dB, -13.87 dB, -11.15 dB, -9.118 dB, -7.49 dB, -6.16 dB, -5.03 dB, -4.08 dB, -3.25 dB respectively;

[0089] As Figure 5 (b) shows, when the mode is TE 00 , the calculated reflection coefficients at the above frequencies are -4.93 dB, -6.63 dB, -8.95 dB, -12.21 dB, -17.35 dB, -30.27 dB, -23.09 dB, -15.50 dB, -11.55 dB, -8.84 dB, -6.78 dB, -5.17 dB, -3.90 dB, -2.93 dB, -2.19 dB, -1.64 dB respectively;

[0090] As Figure 5 (c) shows, when the mode is TE 00 , the calculated reflection coefficients at the above frequencies are -6.66 dB, -8.45 dB, -10.76 dB, -13.93 dB, -19.00 dB, -32.49 dB, -23.90 dB, -16.48 dB, -12.61 dB, -10.01 dB, -8.07 dB, -6.55 dB, -5.33 dB, -4.32 dB, -3.47 dB, -2.77 dB respectively.

[0091] It can be seen from Figure 4 and Figure 5 that the present invention can use the finite element method to solve the transmission characteristics of the honeycomb frequency selective surface.

[0092] The above description of the embodiments is to enable those of ordinary skill in the art to understand and apply the technology of this case. It is obvious that those who are familiar with the technology in this field can easily make various modifications to these examples, and apply the general principles described herein to other embodiments without creative labor. Therefore, this case is not limited to the above embodiments, and the improvements and modifications made by those skilled in the art to this case based on the disclosure of this case should be within the protection scope of this case.

Claims

1. A method for solving the transmission characteristics of a cellular frequency selective surface, characterized in that Including the following steps: (1) Construct the unit geometric model of the cellular frequency selective surface: The unit structure for constructing a cellular frequency selective surface includes an air box in the shape of a regular hexagonal prism with its side parallel to the z-axis of the three-dimensional coordinate system OXYZ, a metal layer and a unit geometric model of R dielectric layers located in the air box. Any three adjacent sides of the air box are taken as the main sides, and the other three adjacent sides are taken as the secondary sides. The upper and lower regular hexagonal faces with an area of SUR are used as excitation ports. Among them, the relative permittivity and relative permeability of the r-th dielectric layer are ε r , μ r ; (2) Conduct mesh division on the unit geometric model: Mesh the unit geometric model to obtain L tetrahedrons containing V edges and triangular faces. There are 2 degrees of freedom on each edge and triangular face, and H degrees of freedom in each tetrahedron. There are a total of 2V degrees of freedom in L tetrahedrons. Let the P degrees of freedom {λ1, λ2,..., λ p ,..., λ P} on the main side of the unit geometric model be the main degrees of freedom, and the Q degrees of freedom {σ1, σ2,..., σ q ,..., σ Q} on the slave side be the slave degrees of freedom; (3) Calculate the direction vector of the polarized plane wave in OXYZ: By the angles θ between the polarization plane wave at infinity and the z-axis and the x-axis in the three-dimensional coordinate system OXYZ, calculate the direction vector of the polarization plane wave in OXYZ (4) Calculate the incident fields at the excitation ports in different modes: The three-dimensional coordinate system OXYZ is transformed into a three-dimensional local coordinate system O′X′Y′Z′ through two vector edges a1 and a2 of the excitation port, and the direction vector of the polarized plane wave in OXYZ is used to calculate the wave numbers k x′mn , k y′mn and k z′mn in the x′, y′, and z′ directions of the polarized plane wave in O′X′Y′Z′ at a frequency f. Then, based on k x′mn , k y′mn and k z′mn , the incident fields at the excitation port in the TE nm , TM nm , and TEM nm modes are calculated where n and m are the half-period numbers of the variation of the polarized plane wave along the x′ and y′ directions on O′X′Y′Z′, respectively; (5) Construct the finite element matrix equation: Construct a finite element system matrix D with dimensions I×J and an excitation matrix b with dimensions I×1, and construct a matrix equation Du = b for the electric field coefficient u through D and b, where D ij is a finite element system term related to the i-th degree of freedom and the j-th degree of freedom, and b i is an excitation term related to the i-th degree of freedom, and I = J = 2V; (6) Replace the elements in the matrix equation: Replace the elements in matrix D and matrix b in the matrix equation to obtain the replaced matrix equation D′u = b′, where D′ and b′ are the replacement results of D and b respectively; (7) Obtain the transmission characteristics of the cellular frequency selective surface: Solve the transformed matrix equation \(D'u = b'\) using a sparse matrix solver to obtain the electric field coefficients \(u\), and calculate the electric field \(E\) of each tetrahedron through \(u\). l Calculate the electric field \(E\) of the honeycomb frequency selective surface, then use a post-processor, and through \(E\) and the incident field at the excitation port obtained in step (4). Calculate the reflection coefficient \(S\) of the transmission characteristics of the honeycomb frequency selective surface. 11 And the transmission coefficient \(S\). 21 .

2. The method according to claim 1, characterized in that, The direction vector of the polarized plane wave in OXYZ described in step (3) The calculation formula is as follows: Among them, are unit vectors in the x and y axis directions on OXYZ.

3. The method according to claim 1, wherein For the three-dimensional local coordinate system O′X′Y′Z′ described in step (4), the relationships between its x′, y′, and z′ axes and the two vector edges a1 and a2 are as follows: x′ = a1 y′ = a2 - (a2·x′)x′ z′ = x′ × y′.

4. The method according to claim 1, wherein The wave number k of the polarized plane wave in the x′, y′ and z′ directions of O′X′Y′Z′ described in step (4) is x′mn , k y′mn and k z′mn , and in TE nm ,TM nm TEM nm The incident field at the excitation port in the mode The calculation formulas are: Wherein, are unit vectors in the x′, y′, and z′ axis directions on O′X′Y′Z′, k0 is the free space wave number, j is the imaginary unit, e is the natural constant, c is the speed of light, are the unit vectors of a1 and a2 respectively, a1 and a2 are the scalar values of a1 and a2 respectively, α is the angle between a1 and a2, μ0 is the vacuum permeability, and ε0 is the vacuum permittivity.

5. The method according to claim 1, wherein The finite element system terms D related to the ith degree of freedom and the jth degree of freedom described in step (5) ij and the excitation term b related to the ith degree of freedom i , and the calculation formulas are respectively: where, W i is the basis function related to the i-th degree of freedom, Ω is the solution domain space, Γ is the surface of the solution domain space Ω, is the Hamiltonian operator, k0 is the free space wave number, is divided into the tensor form of ε r , μ r .

6. The method according to claim 1, wherein The specific method for replacing the elements in matrix D and matrix b in the matrix equation described in step (6) is as follows: D′ ij = 0 for i ∈ {σ1, σ2,..., σ q ,..., σ Q}, j ∈ [1, J] b′ i = 0 for i ∈ {σ1, σ2,..., σ q ,..., σ Q} D′ ij = 1 when i = j ∈ {σ1, σ2,..., σ q ,..., σ Q} where, ψ ij is the phase shift between the i-th degree of freedom and the j-th degree of freedom, k0 is the free-space wave number, c i and c j are the position vectors of the i-th degree of freedom and the j-th degree of freedom, respectively.

7. The method according to claim 1, characterized in that, The electric field E of the honeycomb frequency selective surface and the reflection coefficient S and transmission coefficient S of the transmission characteristics of the honeycomb frequency selective surface described in step (7), and the calculation formulas are respectively: 11 and transmission coefficient S 21 , and the calculation formulas are respectively: E = {E 1 , E 2 ,..., E l ,..., E L} where, E l is the electric field of the l-th tetrahedron, is the h-th basis function in the l-th tetrahedron is the electric field coefficient of, is the conjugate of, Z is the impedance of the excitation port, mode ∈ {TE nm , TM nm , TEM nm}.

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