Method and device for constructing angle-stable FSS (frequency selective surface) based on high-order mode regulation and control

Abstract

The invention discloses a construction method and device of an angle-stable FSS based on high-order mode regulation and control, and the method specifically comprises the steps: decomposing the scattering of a structure into the superposition of different orthogonal characteristic modes, building a theoretical model of correlation structure reflection, transmission coefficients and modal behaviors, and converting the problem of eliminating the high-order resonance of the structure into the problem of regulating and controlling the high-order mode of the structure; obtaining a miniaturized FSS through joint simulation, and judging whether the structure has high-order resonance under the condition of oblique incidence; for a miniaturized structure with high-order resonance, CMA is analyzed through a characteristic mode, and a lumped element is loaded in the structure or the structure is adjusted to block characteristic current distribution to regulate and control a high-order mode, so that the influence of the high-order resonance on the angle stability of the FSS is eliminated; and finally determining a target structure of the angle-stable FSS by using a distributed capacitance-inductance equivalent lumped element. The high-efficiency structural design of the angle-stable FSS is realized by taking application requirements as guidance.

Description

Technical Field

[0001] The present invention belongs to the field of electromagnetic technology, and in particular to a method and device for constructing an angle-stabilized FSS based on high-order mode regulation. Background Art

[0002] Frequency Selective Surface (FSS) can effectively control the transmission and reflection of electromagnetic waves, and is used to achieve spatial filtering characteristics within a specified frequency band. It is widely used in the fields of antenna covers, absorbers, and electromagnetic interference. When electromagnetic waves are incident on the frequency selective surface, its frequency response characteristics are affected by many factors such as structural shape, unit size, incident direction, polarization mode, etc. Considering that electromagnetic waves will be incident on the structural surface at different angles in practical applications, the filtering characteristics of FSS are usually sensitive to the incident angle, which limits its application in complex electromagnetic environments. To solve this problem, designing FSS with angle stability has become a research hotspot to ensure that FSS can maintain stable filtering performance over a wide range of incident angles.

[0003] For the design of angle-stable FSS, a common method is to design a miniaturized structure so that the unit size is much smaller than the resonant wavelength, thereby reducing the sensitivity of the structure to the incident angle. Miniaturization technologies include interdigitation technology, bending technology, and technology of loading lumped elements in the structure. Reference 1 (S Ghosh and S Lim, “Fluidically Reconfigurable Multifunctional Frequency-Selective Surface With Miniaturization Characteristic,” IEEE Trans Microw Theory Techn, vol.66, no.8, pp.3857-3865, Aug.2018.) uses bending technology to design a unit size of The miniaturized FSS has rotational symmetry in the shape of the upper and lower layers of units, while ensuring the angular stability and polarization insensitivity of the structure; Reference 2 (J Liang, Q Cao, YWang, Z Wan, “A Multifunctional and Miniaturized Flexible Active FrequencySelective Surface,” IEEE Antennas Wirel Propag Lett, vol.20, no.12, pp.2549-2553, Oct.2021.) proposed a miniaturized flexible active FSS, which exhibits stable frequency response characteristics by loading PIN diodes in the structure. However, the existing design process and analysis methods of angle-stable FSS lack intuitive physical guidance. In addition, the design method based on miniaturization technology may also face the problem of high-order resonance under oblique incidence caused by unit coupling.

[0004] Theory of Characteristic Mode (TCM) provides an effective way to understand the inherent electromagnetic properties of a structure. The surface current excited by the incident wave on the structure can be expressed as a linear combination of the characteristic currents. Through Characteristic Mode Analysis (CMA), the modes at different resonant frequencies and the corresponding characteristic currents are analyzed, and the structure is analyzed and optimized in a targeted manner, thereby effectively guiding the design of FSS. Reference 3 (DZha, Z Cao, R Li, F He, K Si, J Dong, L Miao, S Bie, and J Jiang, “A physical insight into reconfigurable frequency selective surface using characteristic mode analysis,” IEEE Antennas Wireless Propag. Lett., vol. 20, no.10,pp.1863-1867, Oct.2021.) used TCM to explore the basic modal behavior of dipoles when designing a 2.1 GHz transmission / reflection RFSS. Reference 4 (T Li, R Wang, J Sun and W Dou, “Characteristic modes-inspired polarization twisting metasurface element for 1-bit foldedreflectarray,” IEEE Antennas Wireless Propag.Lett., vol.21, no.11, pp.2254-2258, Nov.2022.) Inspired by TCM, a dual-polarization FSS lens was proposed to improve the antenna aperture efficiency. Reference 5 (FA Dicandia and S Genovesi, “Characteristic modes analysis for circularlypolarized 1-bit dual-layer transmitarray design,” IEEE Open J AntennasPropag, vol 5, no 1, pp 112-123, Feb 2024.) realized a transmission polarization rotator for linearly polarized plane waves by exciting two modes with circularly polarized radiation fields.In addition, for FSS absorbers, reference 6 (ZH Ning, M Li, DZ Ding, X Ai, JQ Liu, and C.-F Wang, “A step-by-step design methodology for broadband tunable microwave metasurface absorbers using theory of characteristic modes,” IEEE Open J Antennas Propag., vol 5, no 4, pp 899-912, Aug 2024) developed a design framework based on characteristic modes. However, although TCM provides additional physical information to assist FSS design, there is currently no systematic study on the design of angle-stable FSS. Summary of the invention

[0005] The purpose of the present invention is to provide a method and device for constructing an angle-stable FSS based on high-order mode regulation, establish a theoretical model between reflection, transmission coefficient and modal behavior based on TCM, use joint simulation to construct a miniaturized FSS to improve the angle stability, and reduce the influence of high-order resonance on the angle stability of the structure by regulating high-order modes.

[0006] The technical solution to achieve the purpose of the present invention is: a method for constructing an angle-stabilized FSS based on high-order mode regulation, comprising the following steps:

[0007] Step 1: Decompose the scattering of the structure into the superposition of different orthogonal characteristic modes, formulate a theoretical model that relates the structural reflection, transmission coefficients and modal behavior, and transform the problem of eliminating high-order resonances of the structure into the problem of regulating high-order modes of the structure;

[0008] Step 2, obtain a miniaturized FSS structure through joint simulation, and determine whether the miniaturized FSS structure has high-order resonance under oblique incidence;

[0009] Step 3: For miniaturized FSS structures with high-order resonances, the high-order modes are regulated by loading lumped elements in the structure or adjusting the structure to block characteristic current distribution through characteristic mode analysis, thereby eliminating the influence of high-order resonances on the angular stability of the FSS;

[0010] Step 4: Use distributed capacitors and inductors equivalent to lumped elements to finally determine the target structure of the angle-stable FSS.

[0011] A device for constructing an angle-stable frequency selective surface, which is used to implement the method for constructing an angle-stable frequency selective surface, comprises a theoretical model formulation module, a miniaturized structure module, a high-order mode control module, and a structural optimization module of equivalent distributed parameters, wherein:

[0012] Theoretical model formulation module decomposes the scattering of the structure into the superposition of different orthogonal characteristic modes, formulates a theoretical model that correlates the reflection and transmission coefficients of the structure with the modal behavior, and transforms the problem of eliminating the high-order resonance of the structure into the problem of regulating the high-order modes of the structure;

[0013] Miniaturized structure module, obtains miniaturized FSS through joint simulation, and determines whether the structure has high-order resonance under oblique incidence;

[0014] High-order mode control module: For miniaturized structures with high-order resonance, high-order modes are controlled by CMA by loading lumped elements in the structure or adjusting the structure to block characteristic current distribution, thereby eliminating the influence of high-order resonance on the angular stability of FSS;

[0015] The structural optimization module of equivalent distributed parameters uses distributed capacitors and inductors equivalent to lumped elements to ultimately determine the target structure of the angle-stable FSS.

[0016] An angle-stable FSS, the structural parameters of which are determined according to the construction method of the angle-stable frequency selective surface.

[0017] Compared with the prior art, the present invention has the following significant advantages:

[0018] (1) A theoretical model between structural reflection, transmission coefficient and modal behavior is established, which can clearly enhance the design process of guiding angle-stable FSS;

[0019] (2) Co-simulation is used to realize miniaturization technology, and automatic modeling and simulation of complex curved structures are achieved. Based on the constructed objective function, the structure with small resonant frequency offset and working bandwidth change under oblique incidence is optimized;

[0020] (3) Under the guidance of TCM, we intuitively understand the inherent electromagnetic characteristics of FSS and use the method of regulating high-order modes to eliminate the high-order resonance of the structure under oblique incidence. This process clearly reveals the working mode and mechanism of the designed structure.

[0021] (4) Distributed capacitors and inductors are used to equal lumped components, reducing the processing cost and experimental error of subsequent structures;

[0022] (5) The design process is universal and can be used to construct an angle-stable FSS, which improves design efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a schematic diagram of the electromagnetic scattering system of the metal patch in the layered medium space in step 1 of the present invention.

[0024] Figure 2a It is a schematic diagram of the miniaturized bent FSS structure a obtained by the joint simulation in step 2 of the present invention.

[0025] Figure 2b yes Figure 2a Transmission coefficient curve corresponding to structure a.

[0026] Figure 2c It is a schematic diagram of the miniaturized bent FSS structure b obtained by the joint simulation in step 2 of the present invention.

[0027] Figure 2d yes Figure 2c Transmission coefficient curve corresponding to structure b.

[0028] Figure 2e It is a schematic diagram of the miniaturized bent FSS structure c obtained by the joint simulation in step 2 of the present invention.

[0029] Figure 2f yes Figure 2e Transmission coefficient curve corresponding to structure c.

[0030] Figure 2g It is a schematic diagram of the miniaturized bent FSS structure d obtained by the joint simulation in step 2 of the present invention.

[0031] Figure 2h yes Figure 2g Transmission coefficient curve corresponding to structure d.

[0032] Figure 3 It is a schematic diagram of the initial structure in step 3 of the present invention.

[0033] Figure 4a yes Figure 3 Pattern importance curve plot for the initial structure.

[0034] Figure 4b yes Figure 3 Plot of the mode weight coefficients of the initial structure at an incident angle of 0°.

[0035] Figure 4c yes Figure 3 Plot of the mode weight coefficient of the initial structure at an incident angle of 50°.

[0036] Figure 5a yes Figure 3 Characteristic current distribution diagram of the middle structure mode 1 at the resonant frequency.

[0037] Figure 5byes Figure 3 Characteristic current distribution diagram of the middle structure mode 3 at the resonant frequency.

[0038] Figure 5c yes Figure 3 Characteristic current distribution diagram of the middle structure mode 4 at the resonant frequency.

[0039] Figure 6 It is a schematic diagram of the structure of loading lumped elements in step 3 of the present invention.

[0040] Figure 7a yes Figure 6 Result plot of mode importance analysis of the structure after lumped elements are loaded.

[0041] Figure 7b yes Figure 6 Result diagram of the mode weight coefficient of the structure after loading the lumped elements at an incident angle of 0°.

[0042] Figure 7c yes Figure 6 MWC diagram of the mode weight coefficient of the structure after loading the lumped elements at an incident angle of 50°.

[0043] Figure 8a yes Figure 3 Comparison of the transmission coefficients of the initial structure at incident angles of 0° and 50°.

[0044] Figure 8b yes Figure 6 Comparison of transmission coefficients of the structure loaded with lumped elements at incident angles of 0° and 50°.

[0045] Figure 9a It is a unit structure diagram of the angle-stable FSS finally determined in step 4 of the present invention.

[0046] Figure 9b It is a top view of the angle-stable FSS finally determined in step 4 of the present invention.

[0047] Fig.9c It is a bottom view of the angle-stabilized FSS finally determined in step 4 of the present invention.

[0048] Fig.10a yes Figure 9a Result diagram of pattern importance analysis of target structure in .

[0049] Fig.10b yes Figure 9a Mode weight coefficient analysis results of the target structure at an incident angle of 0°.

[0050] Fig.10c yes Figure 9a Mode weight coefficient analysis results of the target structure at an incident angle of 50°.

[0051] Fig.11a yes Figure 9a Full-wave simulation transmission coefficient diagram of the target structure under TE polarization.

[0052] Fig.11b yes Figure 9a Full-wave simulation transmission coefficient diagram of the target structure in TM polarization.

[0053] Fig.12 It is a flow chart of the angle-stabilized FSS design method based on high-order mode regulation of the present invention. DETAILED DESCRIPTION

[0054] The present invention provides a method and device for constructing an angle-stable FSS based on high-order mode regulation. By establishing the relationship between structural reflection, transmission coefficient and modal behavior, the filtering characteristics are expanded into the modal space, so as to intuitively understand and deal with the problem of high-order resonance. Specifically, the scattering of the structure is decomposed into the superposition of different orthogonal characteristic modes, and a theoretical model of the associated structural reflection, transmission coefficient and modal behavior is formulated, and the problem of eliminating the high-order resonance of the structure is converted into the problem of regulating the high-order mode of the structure; a miniaturized FSS is obtained through joint simulation, and it is determined whether the structure has high-order resonance under oblique incidence; for a miniaturized structure with high-order resonance, a method of loading lumped elements in the structure or adjusting the structure to block the characteristic current distribution is used to regulate the high-order mode, so as to eliminate the influence of the high-order resonance on the angle stability of the FSS; and the target structure of the angle-stable FSS is finally determined by using the distributed capacitor and inductor equivalent lumped elements.

[0055] The present invention provides a method for constructing an angle-stable FSS based on high-order mode regulation, comprising the following steps:

[0056] Step 1: Decompose the scattering of the structure into the superposition of different orthogonal characteristic modes, formulate a theoretical model that relates the structural reflection, transmission coefficients and modal behavior, and transform the problem of eliminating high-order resonances of the structure into the problem of regulating high-order modes of the structure;

[0057] Step 2, obtain a miniaturized FSS structure through joint simulation, and determine whether the miniaturized FSS structure has high-order resonance under oblique incidence;

[0058] Step 3: For miniaturized FSS structures with high-order resonances, Characteristic Mode Analysis (CMA) is used to control the high-order modes by loading lumped elements in the structure or adjusting the structure to block the characteristic current distribution, thereby eliminating the influence of high-order resonances on the angular stability of the FSS.

[0059] Step 4: Use distributed capacitors and inductors equivalent to lumped elements to finally determine the target structure of the angle-stable FSS.

[0060] As a specific example, in step 1, the scattering of the structure is decomposed into the superposition of different orthogonal characteristic modes, and a theoretical model is formulated to associate the structural reflection, transmission coefficient and modal behavior, and the problem of eliminating the high-order resonance of the structure is transformed into the problem of regulating the high-order modes of the structure, as follows:

[0061] Step 1.1, when a plane wave is incident on the FSS surface, three different electromagnetic fields appear in the free space around the structure: the incident field generated by the excitation, the environmental field generated by the coupling between the dielectric layer and the adjacent units, and the scattered field caused by the current on the surface of the structure; combined with the law of conservation of energy, for the free space within the infinite closed surface surrounding the FSS, the external incident power is completely converted into output power; according to the physical meaning of the reflection coefficient and the transmission coefficient, the relationship between the reflection coefficient, the transmission coefficient and the output power of the FSS is established;

[0062] Step 1.2, solve the moment method impedance matrix of FSS to obtain the generalized characteristic equation; according to the orthogonality of the characteristic mode, the surface current of the structure is expressed as the linear superposition of each characteristic current, and the output power is expressed as the result of the orthogonal superposition of the mode power;

[0063] Step 1.3, based on the relationship between output power and reflection coefficient, transmission coefficient and characteristic mode physical quantity, establish a theoretical model that correlates structural reflection, transmission coefficient and modal behavior;

[0064] Step 1.4: Based on the established theoretical model, analyze the reasons why the FSS structure is sensitive to the incident angle and transform the problem of eliminating high-order resonances into the problem of regulating the high-order modes of the structure.

[0065] As a specific example, step 1.1 is as follows:

[0066] When a plane wave is incident on the FSS surface, three different electromagnetic fields appear in the free space around the structure: the incident field generated by the excitation , the environmental field generated by the coupling between the dielectric layer and the adjacent units and the scattered fields caused by the current on the surface of the structure ;in , F is the electromagnetic field, E and H represent the electric field and magnetic field respectively, and the superscripts inc, evn, and sca represent the incident field, the ambient field, and the scattered field respectively; combined with the law of conservation of energy, for the free space within the infinite closed surface surrounding the FSS, the external incident power All converted into output power ;

[0067] According to the physical meaning of reflection coefficient and transmission coefficient, the reflection coefficient of FSS is established , transmission coefficient With output power The relationship between

[0068] (1a)

[0069] (1b)

[0070] Among them, the reflected power and transmitted power Can be composed ,and , Respectively The real and imaginary parts are equal; Re( ) means taking the real part, Im( ) means taking the imaginary part, and are the components of the external input power in the upper half space and the lower half space bounded by the plane structure, respectively. Size and equal.

[0071] As a specific example, step 1.2 is as follows:

[0072] Solving the moment method impedance matrix Z of FSS, we obtain the generalized characteristic equation , where R and X are the Hermitian real and imaginary parts of the impedance matrix Z, respectively. and are characteristic current and characteristic value respectively, n represents the nth order mode; characteristic value Indicates the energy storage size. When it is 0, the nth-order mode is in resonance;

[0073] According to the orthogonality of the characteristic modes, the surface current J of the structure can be expressed as the linear superposition of the characteristic currents, that is, ,in is the mode weight coefficient, or MWC, which is used to measure the contribution of the characteristic current to the total current. If the number of selected modes is N, the output power Expressed as mode power The result of orthogonal superposition is

[0074] (2)

[0075] In formula (2), It is called mode importance or MS, and its value range is (0,1]; MS is only related to the structure itself and is not affected by external stimuli; when When the mode is φ, the radiation capacity of the mode reaches its highest and it is in a resonant state; therefore, MS can be used to reveal and evaluate the resonance of the mode.

[0076] As a specific example, the step 1.3 is as follows:

[0077] Combining equations (1a), (1b) and (2), according to the output power and reflection coefficient , transmission coefficient As well as the relationship between the physical quantities of the characteristic modes, a theoretical model is established to associate the structural reflection, transmission coefficients and modal behavior, which is specifically described as follows:

[0078] (3a)

[0079] (3b)

[0080] The above formula provides a deeper physical understanding of the FSS electromagnetic response based on the Theory of Characteristic Mode (TCM) and functional conservation. By mapping the structure's anti-transmission coefficient to the eigenvalue and mode weight coefficient The filtering characteristics are expanded into the modal space to intuitively understand and analyze the structure.

[0081] As a specific example, the step 1.4 is as follows:

[0082] For the FSS structure with unstable electromagnetic response under oblique incidence, the reason why the FSS structure is sensitive to the incident angle is analyzed based on the theoretical model of equations (3a) and (3b):

[0083] Through characteristic mode analysis, the working mode that contributes to the electromagnetic response of the structure within the designed working frequency band is identified. The criteria for judging the working mode include: whether the MS has a maximum value and whether the MWC is excited;

[0084] When a plane wave is incident at any angle, a part of the modes remain stable, which are called the main modes of the structure; while the other part of the modes are sensitive to the incident angle, and their MWC increases with the increase of the incident angle, which are called high-order modes.

[0085] Oblique incidence affects the high-order modes of the structure. The excitation of high-order modes corresponds to the generation of high-order resonances in the structure, making the electromagnetic response unstable. Therefore, when improving the angular stability of the FSS structure, the problem of eliminating high-order resonances is transformed into the problem of regulating the high-order modes of the structure.

[0086] As a specific example, in step 2, a miniaturized FSS structure is obtained through joint simulation, and it is determined whether the miniaturized FSS structure has high-order resonance under oblique incidence, as follows:

[0087] Step 2.1: Phase difference between units , where k is the wave number, is the unit size, is the angle between the incident wave and the normal line of the unit surface; under a given incident angle, as the unit size P increases, the phase difference between units also increases accordingly, causing the resonant frequency of the FSS to shift under oblique incidence. Therefore, the unit size P is one of the key factors affecting the angular stability of the structure. In order to improve the angular stability, the bending technology is used to achieve the miniaturization of the structure;

[0088] Step 2.2: Implement the bending technology in step 2.1 through joint simulation:

[0089] The unit size P and the metal bending shape are used as variables, and the metal bending shape of the unit is designed using binary coding; the unit array of the structure is discretized as small cells, where 1 and 0 represent whether the cell is metal or not. The whole process realizes automatic modeling and simulation, and the angular stability of the structure is judged according to the objective function shown in formula (4):

[0090] (4)

[0091] in, Represents the unit size The i-th miniaturized structure generated under represents the number of resonant frequencies of the structure, , They represent the jth resonant frequency and working bandwidth of the structure under vertical incidence of 0°, , Represents the structure at oblique incidence ° corresponding to the jth resonant frequency and working bandwidth;

[0092] The first part of the objective function represents the sum of the squares of the differences in the resonant frequencies of the structure at normal and oblique incidence, part 2 It represents the sum of squares of bandwidth differences under vertical incidence and oblique incidence. The entire objective function is adjusted by adjusting the first weight coefficient and the second weight coefficient To balance the requirements of resonant frequency and bandwidth consistency;

[0093] The miniaturized FSS structure obtained by the joint simulation method keeps the resonant frequency shift and operating bandwidth variation below the set value under oblique incidence;

[0094] Step 2.3: Determine whether the miniaturized FSS structure has high-order resonance.

[0095] This is because FSS cannot completely avoid the influence of the incident wave angle in practical applications. The bending technology based on the principle of miniaturization can reduce the offset of the resonant frequency at oblique incidence, but it is difficult to effectively suppress the unit coupling effect, resulting in high-order resonance of the structure, thus affecting the angle stability.

[0096] As a specific example, in step 3, for a miniaturized FSS structure with high-order resonance, the high-order mode is regulated by loading lumped elements in the structure or adjusting the structure to block the characteristic current distribution through characteristic mode analysis, thereby eliminating the influence of high-order resonance on the angular stability of the FSS, as follows:

[0097] For miniaturized FSS structures with high-order resonances, according to the corresponding relationship between high-order modes and high-order resonances, under the guidance of TCM, the angular stability of the miniaturized FSS structure is improved in the following two ways:

[0098] Method 1: Loading lumped elements in the structure to tune the higher-order modes;

[0099] Through characteristic mode analysis, the distribution of high-order mode characteristic current is observed: if an inductor is placed in the area where the current distribution is concentrated, the high-order mode resonance point can be moved to a low frequency and overlap with the main mode; if a capacitor is placed in the area where the current distribution is concentrated, the high-order mode resonance point can be moved to a high frequency and away from the working frequency band of the main mode; by tuning the high-order mode by loading lumped elements in this way, the resonant frequency of the high-order mode can be controlled, the high-order resonance corresponding to the high-order mode in the working frequency band can be eliminated, and the angular stability of the structure can be significantly improved.

[0100] Method 2: Adjust the structure to block the characteristic current flow and suppress the high-order mode;

[0101] Through characteristic mode analysis, the distribution of high-order mode characteristic current is observed: if the main mode current is only concentrated on a certain branch of the structure, and the characteristic current of the high-order mode is distributed throughout the entire structure, the two rotationally symmetrical branches of the structure are placed on the upper and lower sides of the dielectric layer respectively; this method effectively blocks the global flow of high-order mode current without affecting the distribution of the main mode current. The improved structure no longer has high-order modes within the working frequency band, and the high-order resonance of the structure is eliminated, thereby achieving the purpose of improving angular stability.

[0102] As a specific example, in step 4, the target structure of the angle-stable FSS is finally determined by using the distributed capacitor and inductor equivalent lumped elements, as follows:

[0103] In practical applications, loading too many lumped elements in the structure will significantly increase the processing cost and increase the experimental error. Therefore, distributed capacitors and inductors are used in the structural design. At the same time, according to the characteristic current distribution of the structure, the target structure is adjusted to achieve the best angle stability and the final target structure is output.

[0104] The present invention also provides a device for constructing an angle-stable frequency selective surface, which is used to implement the method for constructing the angle-stable frequency selective surface. The device includes a theoretical model formulation module, a miniaturized structure module, a high-order mode control module, and a structural optimization module of equivalent distributed parameters, wherein:

[0105] Theoretical model formulation module decomposes the scattering of the structure into the superposition of different orthogonal characteristic modes, formulates a theoretical model that correlates the reflection and transmission coefficients of the structure with the modal behavior, and transforms the problem of eliminating the high-order resonance of the structure into the problem of regulating the high-order modes of the structure;

[0106] Miniaturized structure module, obtains miniaturized FSS through joint simulation, and determines whether the structure has high-order resonance under oblique incidence;

[0107] High-order mode control module: For miniaturized structures with high-order resonance, high-order modes are controlled by CMA by loading lumped elements in the structure or adjusting the structure to block characteristic current distribution, thereby eliminating the influence of high-order resonance on the angular stability of FSS;

[0108] The structural optimization module of equivalent distributed parameters uses distributed capacitors and inductors equivalent to lumped elements to ultimately determine the target structure of the angle-stable FSS.

[0109] The present invention also provides an angle-stable FSS, the structural parameters of which are determined according to the construction method of the angle-stable frequency selective surface.

[0110] The present invention uses TCM as a theoretical support to establish a theoretical model between reflection, transmission coefficient and modal behavior, deeply explains the electromagnetic characteristics of FSS from a physical perspective, and eliminates the influence of high-order resonance on the angular stability of the structure based on high-order mode regulation. Guided by application needs, the efficient structural design of angle-stable FSS can be achieved.

[0111] The angle-stabilized FSS design method based on high-order mode regulation proposed by the present invention is further described in detail below in conjunction with the embodiments. Examples of the embodiments are shown in the accompanying drawings. The embodiments described with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and are not used to limit the present invention.

[0112] Example

[0113] The present embodiment provides a design method for an angle-stabilized FSS based on high-order mode control, comprising the following steps:

[0114] Step 1: Decompose the scattering of the structure into the superposition of different orthogonal characteristic modes, formulate a theoretical model that relates the structural reflection, transmission coefficients and modal behavior, and transform the problem of eliminating the high-order resonance of the structure into the problem of regulating the high-order modes of the structure, as follows:

[0115] Step 1.1. When a plane wave is incident on the FSS surface, three different electromagnetic fields appear in the free space around the structure, such as Figure 1 Shown: The incident field generated by the excitation , the environmental field generated by the coupling between the dielectric layer and the adjacent units and the scattered fields caused by the current on the surface of the structure .in , F is the electromagnetic field, E and H represent the electric field and magnetic field respectively, and the superscripts inc, evn, and sca represent the incident field, the ambient field, and the scattered field respectively. Combined with the law of conservation of energy, for the free space within the infinite closed surface surrounding the FSS, the external incident power All converted into system output power .

[0116] According to the physical meaning of reflection coefficient and transmission coefficient, the reflection coefficient of FSS is established , transmission coefficient With system output power The relationship between

[0117] (5a)

[0118] (5b)

[0119] Among them, the reflected power and transmitted power Can be composed , and respectively The real and imaginary parts are equal, Re( ) means taking the real part, and Im( ) means taking the imaginary part. and are the components of the external input power in the upper half space and the lower half space bounded by the plane structure, respectively. Size and equal.

[0120] Step 1.2: Solve the moment method impedance matrix Z of FSS to obtain the generalized characteristic equation , where R and X are the Hermitian real and imaginary parts of the impedance matrix Z, respectively. and are characteristic current and characteristic value respectively, n represents the nth order mode. It can be expressed as the energy storage size of the system. When it is 0, the nth-order mode is in resonance.

[0121] Due to the orthogonality of the characteristic modes, the surface current J of the structure can be expressed as the linear superposition of the characteristic currents, that is, .in, is the mode weight coefficient (MWC), which is used to measure the contribution of the characteristic current to the total current. If the number of selected modes is N, the output power of the structure Can be expressed as mode power The result of orthogonal superposition is

[0122] (6)

[0123] In formula (6), is called mode significance (MS), and its value range is (0,1). MS is only related to the structure itself and is not affected by external excitation. When the mode is at , the radiation capacity of the mode reaches its maximum and it is in a resonant state. Therefore, the resonant characteristics of the mode can be intuitively revealed and evaluated using MS.

[0124] Combining formula (5) and formula (6), according to the output power and reflection coefficient , transmission coefficient As well as the relationship between the above-mentioned characteristic mode physical quantities, a theoretical model of the correlation structure reflection, transmission coefficient and modal behavior is established, which is specifically expressed as follows

[0125] (7a)

[0126] (7b)

[0127] The above formula provides a deeper physical understanding of the FSS electromagnetic response based on TCM and functional conservation. By mapping the structure's anti-transmission coefficient to the eigenvalue and mode weight coefficient In general, expanding the filtering characteristics into the modal space can provide intuitive insight into and handle high-order resonance problems.

[0128] Therefore, for FSS structures with unstable electromagnetic response under oblique incidence, the reasons for their sensitivity to the incident angle can be analyzed based on the theoretical model of formula (7). Through CMA, the working mode that contributes to the electromagnetic response of the structure within the designed working frequency band is identified. The criteria for judging the working mode include: whether the MS has a maximum value (whether there is resonance in the mode) and whether the MWC is excited. When a plane wave is incident at any angle, some modes maintain a high stability, while other modes are sensitive to the incident angle, and their MWC increases with the increase of the incident angle. The former is called the main mode of the structure, and the latter is called the higher-order mode. Analysis shows that oblique incidence mainly affects the higher-order modes of the structure. The excitation of the higher-order modes corresponds to the generation of higher-order resonances in the structure, making the electromagnetic response of the structure unstable. In summary, when improving the angular stability of such structures, the problem of eliminating higher-order resonances can be transformed into the problem of regulating the higher-order modes of the structure.

[0129] Step 2: Get the miniaturized FSS through joint simulation and determine whether the structure has high-order resonance under oblique incidence, as follows:

[0130] Step 2.1: Phase difference between units It is known that (where k is the wave number, is the unit size, is the angle between the incident wave and the normal line of the unit surface). Under a given incident angle, as the unit size P increases, the phase difference between units will also increase accordingly, causing the resonant frequency of the FSS to shift under oblique incidence. Therefore, the unit size P is one of the key factors affecting the angular stability of the structure. To improve the angular stability, bending technology can be used to achieve miniaturization of the structure.

[0131] Step 2.2: Implement the bending technology in step 2.1 through joint simulation. In this process, the unit size P and the metal bending shape are used as variables, and the metal bending shape of the unit is designed using binary coding. The unit array of the structure is discretized as Small cells, where "1" and "0" represent whether the cell is metal or not. The whole process realizes automatic modeling and simulation, and the angular stability of the structure is judged according to the objective function shown in formula (8).

[0132] (8)

[0133] in, Represents the unit size The i-th miniaturized structure generated under represents the number of resonant frequencies of the structure, , , , Represents the structure at vertical incidence 0° and oblique incidence respectively ° corresponds to the jth resonant frequency and operating bandwidth. Therefore, the first part of the objective function represents the sum of the squares of the differences in the resonant frequencies of the structure at normal and oblique incidence, part 2 represents the sum of squares of the bandwidth differences between vertical incidence and oblique incidence. The entire objective function is adjusted by and Two weighting factors are used to balance the requirements of resonant frequency and bandwidth consistency.

[0134] In this example, the test results obtained by screening the objective function are as follows Figure 2a~Figure 2g As shown, all structural unit sizes do not exceed , meeting the requirements of miniaturized design. Figure 2a , Figure 2c , Figure 2e , Figure 2g The transmission coefficient variation curves of four different structures (structure a, structure b, structure c, structure d) at different incident angles are given. Figure 2a and Figure 2b is the structure a and the corresponding transmission coefficient curve obtained by joint simulation, Figure 2c and Figure 2d is the structure b and the corresponding transmission coefficient curve obtained by joint simulation, Figure 2e and Figure 2f is the structure c and the corresponding transmission coefficient curve obtained by joint simulation, Figure 2g and Figure 2h The structure d and the corresponding transmission coefficient curve obtained by joint simulation. The results show that the transmission coefficients of structures a and b at an incident angle of 50° are almost the same as those at vertical incidence, showing good angular stability; however, structures c and d produce high-order resonances at oblique incidence. This shows that in practical applications, the bending technology based on the principle of miniaturization can reduce the offset of the resonant frequency at oblique incidence, but it is difficult to effectively suppress the unit coupling effect, resulting in high-order resonances in the structure, thus affecting the angular stability.

[0135] This embodiment selects the structure d in the joint simulation as the initial structure, such as Figure 3 As shown, the unit size is 10 mm. The structure includes a bent metal patch 1 printed on a dielectric substrate 2. The dielectric constant of the dielectric substrate 2 is 4.3 and the thickness is 0.8 mm.

[0136] Step 3: For miniaturized structures with high-order resonances, the high-order modes are regulated by CMA by loading lumped elements in the structure or adjusting the structure to block the characteristic current distribution, thereby eliminating the influence of high-order resonances on the FSS angle stability, as follows:

[0137] For miniaturized FSS with high-order resonances, according to the corresponding relationship between high-order modes and high-order resonances, under the guidance of TCM, the angular stability of the structure can be improved in the following two ways:

[0138] Method 1: Load lumped elements in the structure to tune the higher-order modes. Through CMA, observe the distribution of the characteristic current of the higher-order modes: if an inductor is placed in the area where the current distribution is concentrated, the resonance point of the higher-order mode can be moved to a low frequency and overlap with the main mode; if a capacitor is placed in the area where the current distribution is concentrated, the resonance point of the higher-order mode can be moved to a high frequency and away from the operating frequency band of the main mode. This method of loading lumped elements to tune the higher-order modes can control the resonant frequency of the higher-order modes, eliminate the higher-order resonances corresponding to the higher-order modes in the operating frequency band of the structure, and significantly improve the angular stability of the structure.

[0139] Method 2: Adjust the structure to block the flow of characteristic current and suppress high-order modes. Through CMA, observe the distribution of high-order mode characteristic current: if the main mode current is only concentrated on a certain branch of the structure, and the characteristic current distribution of the high-order mode is throughout the entire structure, the two rotationally symmetrical branches of the structure can be placed on the upper and lower sides of the dielectric layer respectively. This method effectively blocks the global flow of high-order mode current without affecting the distribution of the main mode current. The improved structure no longer has high-order modes within the working frequency band, and eliminates the high-order resonance of the structure, thereby achieving the purpose of improving angular stability.

[0140] In this embodiment, we first use method 1 to perform CMA on the initial structure, and the result is as follows: Figure 4a~Figure 4c As shown, Figure 4a is the pattern importance of the initial structure, Figure 4b is the mode weight coefficient of the structure at 0° incidence angle, Figure 4c is the mode weight coefficient of the structure at an incident angle of 50°. Figure 4a It shows that in the frequency band of 6~11 GHz, the MS of the four modes are greater than , where mode 1 and mode 2 are a pair of degenerate modes. The frequency response characteristics of the degenerate modes are the same and the characteristic electric fields are orthogonal, so only mode 1 is discussed in the analysis. Figure 4b The MWC results at an incident angle of 0° are shown. In the case of TE polarization, only mode 1 is excited in the structure; Figure 4c The MWC results at an incident angle of 50° are shown. When , the MWC of mode 1 remains basically unchanged, while modes 3 and 4 are excited in the observed frequency band. The above analysis shows that mode 1 is the main mode of the structure, and modes 3 and 4 are higher-order modes. In the case of TM polarization, the excited state of the mode is similar to that of TE, except that the main mode changes from mode 1 to mode 2.

[0141] Figure 5a , Figure 5b , Figure 5c The characteristic current distributions of mode 1, mode 3 and mode 4 at the resonant frequency are shown respectively. Figure 5a The current in mode 1 is locally distributed on the structural branch and flows in the longitudinal direction, while Figure 5b and Figure 5c For modes 3 and 4, there are current distributions on the four branches of the structure. Therefore, according to the characteristic current distribution, inductors and capacitors are loaded in the structure to adjust the resonant frequency of the higher-order mode, so as to block the current distribution of the higher-order mode without affecting the mode current distribution of the main mode. The structure loaded with lumped elements is as follows Figure 6 As shown, , , , The CMA results of the structure are as follows Figure 7a , Figure 7b , Figure 7c As shown, Figure 7a is the mode importance of the structure after loading the lumped elements, Figure 7b is the mode weight coefficient of the structure at 0° incidence angle, Figure 7c is the mode weight coefficient MWC of the structure at an incident angle of 50°. Figure 7a The MS results show that within this frequency band, the resonant frequency of mode 3 is far away from the main mode operating frequency band, while the resonant frequency of mode 4 overlaps with the main mode and is covered within the operating bandwidth of the main mode. Figure 7b and Figure 7c The excitation of different modes is shown from the perspective of MWC. At an incident angle of 0°, only mode 1 is excited; at an incident angle of 50°, the MWC of mode 3 is always equal to 0, and the excitation range of MWC of mode 4 is covered by the MWC excitation range of mode 1, and the MWC value is much smaller than that of mode 1, thus effectively eliminating the influence of high-order modes on angle stability.

[0142] Full-wave simulation is performed on the structure before and after loading the lumped element, and the test results of the transmission coefficient curve are obtained, such as Figure 8a , Figure 8b As shown, Figure 8a and Figure 8b These are the transmission coefficient curves of the initial structure and the structure after loading the lumped elements at incident angles of 0° and 50°, Figure 8a The transmission coefficient curve of the initial structure is shown. It can be seen that the structure has only one resonant frequency under vertical incidence, while at an incident angle of 50°, two high-order resonances appear near the resonant frequency, which corresponds to Mode 3 and Mode 4 in the previous CMA results. Figure 8bThe transmission coefficient curve of the structure after loading the lumped element is shown. In this figure, the transmission coefficient at an incident angle of 50° is basically consistent with the transmission coefficient at vertical incidence. Only the resonant frequency corresponding to the main mode exists, and the high-order resonance has been effectively eliminated. This shows that the FSS structure after regulation shows good angular stability.

[0143] Step 4: Using the distributed capacitor and inductor equivalent lumped elements, the target structure of the angle-stable FSS is finally determined as follows:

[0144] In practical applications, loading too many lumped elements in the structure will significantly increase the processing cost and increase the experimental error. Therefore, in this embodiment, a bent metal strip equivalent distributed inductor is used. The bent metal strip can achieve the effect of inductance by extending the current path, and tune mode 3 to outside the working frequency band. At the same time, the second method in step 3 is adopted, and the two branches of the metal patch are placed on the upper and lower layers of the substrate respectively by utilizing the rotational symmetry of the structure to block the current path of mode 4. The schematic diagram of the final target structure is shown in FIG. Figure 9a , Figure 9b , Fig.9c As shown, Figure 9a It is a unit structure diagram. Figure 9b It is a top view. Fig.9c is the bottom view. The CMA results of the structure are as follows Fig.10a , Fig.10b , Fig.10c As shown, Fig.10a is the pattern importance of the target structure, Fig.10b is the mode weight coefficient of the structure at 0° incidence angle, Fig.10c is the mode weight coefficient of the structure at an incident angle of 50°. Fig.10a It shows that only mode 1 has resonance in the observed frequency band, while the MS of modes 3 and 4 is always 0. Fig.10b , Fig.10c The results show that only mode 1 is excited at both 0° and 50° incident angles, and the MWC of modes 3 and 4 is 0. Therefore, the high-order modes of the structure have been successfully suppressed. Next, a full-wave simulation is performed on the structure in the range of 0° to 70° incident angles. Fig.11a and Fig.11b The transmission coefficient curves of the target structure in the incident angle range of 0 to 70° under TE polarization and TM polarization respectively. Fig.11a represents the transmission coefficient diagram of the structure under TE polarization, Fig.11bThe transmission coefficient diagram under TM polarization is shown. The results show that under both polarizations, the transmission coefficient of the structure has almost no shift in the resonant frequency within the incident angle range of 0° to 70°, the frequency response characteristics are highly consistent, and the maximum relative frequency deviation does not exceed 1.18%. The results show that the structure can simultaneously maintain excellent angular stability and polarization insensitivity. So far, using the method of the present invention, as an example, an angle-stable FSS has been realized. The overall design process is as follows: Fig.12 shown.

[0145] In summary, the theoretical model of the associated structural reflection, transmission coefficient and modal behavior established in the present invention transforms the problem of eliminating high-order resonance of the structure into the problem of regulating high-order modes of the structure, and the theoretical model clearly reveals the working mode and mechanism of the designed structure; the present invention adopts joint simulation to realize bending technology, which can efficiently design and simulate miniaturized FSS; the present invention provides a method for eliminating high-order resonance by regulating high-order modes, and the method can clearly enhance the design process of guiding angle-stable FSS; the present invention provides a universal angle-stable FSS design process, according to which the angle-stable FSS design can be implemented in a targeted manner, thereby improving the design efficiency.

Claims

1. A method for constructing an angle-stabilized FSS based on high-order mode regulation, characterized in that: The following steps are involved: Step 1: Decompose the scattering of the structure into the superposition of different orthogonal characteristic modes, formulate a theoretical model that relates the structural reflection, transmission coefficients and modal behavior, and transform the problem of eliminating high-order resonances of the structure into the problem of regulating high-order modes of the structure; Step 2, obtain a miniaturized FSS structure through joint simulation, and determine whether the miniaturized FSS structure has high-order resonance under oblique incidence; Step 3: For miniaturized FSS structures with high-order resonances, the high-order modes are regulated by loading lumped elements in the structure or adjusting the structure to block characteristic current distribution through characteristic mode analysis, thereby eliminating the influence of high-order resonances on the angular stability of the FSS; Step 4: Use distributed capacitors and inductors equivalent to lumped elements to finally determine the target structure of the angle-stable FSS.

2. The method for constructing an angle-stable FSS based on high-order mode regulation according to claim 1, characterized in that: In step 1, the scattering of the structure is decomposed into the superposition of different orthogonal eigenmodes, and a theoretical model is formulated to correlate the structural reflection, transmission coefficients and modal behavior. The problem of eliminating the high-order resonance of the structure is transformed into the problem of regulating the high-order modes of the structure, as follows: Step 1.1, when a plane wave is incident on the FSS surface, three different electromagnetic fields appear in the free space around the structure: the incident field generated by the excitation, the environmental field generated by the coupling between the dielectric layer and the adjacent units, and the scattered field caused by the current on the surface of the structure; combined with the law of conservation of energy, for the free space within the infinite closed surface surrounding the FSS, the external incident power is completely converted into output power; according to the physical meaning of the reflection coefficient and the transmission coefficient, the relationship between the reflection coefficient, the transmission coefficient and the output power of the FSS is established; Step 1.2, solve the moment method impedance matrix of FSS to obtain the generalized characteristic equation; Depend on The orthogonality of the characteristic modes, the surface current of the structure is expressed as the linear superposition of each characteristic current, and the output power is expressed as the result of the orthogonal superposition of the mode powers; Step 1.3, based on the relationship between output power and reflection coefficient, transmission coefficient and characteristic mode physical quantity, establish a theoretical model that correlates structural reflection, transmission coefficient and modal behavior; Step 1.4: Based on the established theoretical model, analyze the reasons why the FSS structure is sensitive to the incident angle and transform the problem of eliminating high-order resonances into the problem of regulating the high-order modes of the structure.

3. The method for constructing an angle-stable FSS based on high-order mode regulation according to claim 2, characterized in that: The step 1.1 is specifically as follows: When a plane wave is incident on the FSS surface, three different electromagnetic fields appear in the free space around the structure: the incident field generated by the excitation , the environmental field generated by the coupling between the dielectric layer and the adjacent units and the scattered fields caused by the current on the surface of the structure ;in , F is the electromagnetic field, E and H represent the electric field and magnetic field respectively, and the superscripts inc, evn, and sca represent the incident field, the ambient field, and the scattered field respectively; combined with the law of conservation of energy, for the free space within the infinite closed surface surrounding the FSS, the external incident power All converted into output power ; According to the physical meaning of reflection coefficient and transmission coefficient, the reflection coefficient of FSS is established , transmission coefficient With output power The relationship between (1a) (1b) Among them, the reflected power and transmitted power Can be composed ,and , Respectively The real and imaginary parts are equal; Re( ) means taking the real part, Im( ) means taking the imaginary part, and are the components of the external input power in the upper half space and the lower half space bounded by the plane structure, respectively. Size and equal.

4. The method for constructing an angle-stable FSS based on high-order mode regulation according to claim 3 is characterized in that: The step 1.2 is specifically as follows: Solving the moment method impedance matrix Z of FSS, we obtain the generalized characteristic equation , where R and X are the Hermitian real and imaginary parts of the impedance matrix Z, respectively. and are characteristic current and characteristic value respectively, n represents the nth order mode; Eigenvalue Indicates the energy storage size. When it is 0, the nth-order mode is in resonance; According to the orthogonality of the characteristic modes, the surface current J of the structure can be expressed as the linear superposition of the characteristic currents, that is, ,in is the mode weight coefficient, or MWC, which is used to measure the contribution of the characteristic current to the total current. If the number of selected modes is N, the output power Expressed as mode power The result of orthogonal superposition is (2) In formula (2), It is called mode importance or MS, and its value range is (0,1]; MS is only related to the structure itself and is not affected by external stimuli; when When the mode is φ, the radiation capacity of the mode reaches its highest and it is in a resonant state; therefore, MS can be used to reveal and evaluate the resonance of the mode.

5. The method for constructing an angle-stable FSS based on high-order mode regulation according to claim 4, characterized in that: The step 1.3 is as follows: Combining equations (1a), (1b) and (2), according to the output power and reflection coefficient , transmission coefficient As well as the relationship between the physical quantities of the characteristic modes, a theoretical model is established to associate the structural reflection, transmission coefficients and modal behavior, which is specifically described as follows: (3a) (3b) By mapping the structure's reflectivity coefficient to the eigenvalue and mode weight coefficient The filtering characteristics are expanded into the modal space.

6. The method for constructing an angle-stabilized FSS based on high-order mode regulation according to claim 5, characterized in that: The step 1.4 is as follows: Based on the theoretical model of equations (3a) and (3b), the reason why the FSS structure is sensitive to the incident angle is analyzed: Through characteristic mode analysis, the working mode that contributes to the electromagnetic response of the structure within the designed working frequency band is identified. The criteria for judging the working mode include: whether the MS has a maximum value and whether the MWC is excited; When a plane wave is incident at any angle, a part of the modes remain stable, which are called the main modes of the structure; while the other part of the modes are sensitive to the incident angle, and the MWC increases with the increase of the incident angle, which are called high-order modes; Oblique incidence affects the high-order modes of the structure. The excitation of high-order modes corresponds to the generation of high-order resonances in the structure, making the electromagnetic response unstable. Therefore, when improving the angular stability of the FSS structure, the problem of eliminating high-order resonances is transformed into the problem of regulating the high-order modes of the structure.

7. The method for constructing an angle-stable FSS based on high-order mode regulation according to claim 6, characterized in that: In step 2, a miniaturized FSS structure is obtained through joint simulation, and it is determined whether the miniaturized FSS structure has high-order resonance under oblique incidence, as follows: Step 2.1: Phase difference between units , where k is the wave number, is the unit size, is the angle between the incident wave and the normal line of the unit surface; under a given incident angle, as the unit size P increases, the phase difference between units also increases accordingly, causing the resonant frequency of the FSS to shift under oblique incidence. The bending technology is used to achieve miniaturization of the structure; Step 2.2: Implement the bending technology in step 2.1 through joint simulation: The unit size P and the metal bending shape are used as variables, and the metal bending shape of the unit is designed using binary coding; the unit array of the structure is discretized as A small cell, where 1 and 0 respectively indicate whether the cell is metal or not; The angular stability of the structure is determined according to the objective function shown in formula (4): (4) in, Represents the unit size The i-th miniaturized structure generated under represents the number of resonant frequencies of the structure, , They represent the jth resonant frequency and working bandwidth of the structure under vertical incidence of 0°, , Represents the structure at oblique incidence ° corresponding to the jth resonant frequency and working bandwidth; The first part of the objective function represents the sum of the squares of the differences in the resonant frequencies of the structure at normal and oblique incidence, part 2 It represents the sum of squares of bandwidth differences under vertical incidence and oblique incidence. The entire objective function is adjusted by adjusting the first weight coefficient and the second weight coefficient To balance the requirements of resonant frequency and bandwidth consistency; The miniaturized FSS structure obtained by the joint simulation method keeps the resonant frequency shift and operating bandwidth variation below the set value under oblique incidence; Step 2.3: Determine whether the miniaturized FSS structure has high-order resonance.

8. The method for constructing an angle-stable FSS based on high-order mode regulation according to claim 7, characterized in that: In step 3, for miniaturized FSS structures with high-order resonances, the high-order modes are regulated by loading lumped elements in the structure or adjusting the structure to block the characteristic current distribution through characteristic mode analysis, thereby eliminating the influence of high-order resonances on the angular stability of the FSS, as follows: For miniaturized FSS structures with high-order resonances, according to the corresponding relationship between high-order modes and high-order resonances, under the guidance of TCM, the angular stability of the miniaturized FSS structure is improved in the following two ways: Method 1: Loading lumped elements in the structure to tune the higher-order modes; Through characteristic mode analysis, observe the distribution of high-order mode characteristic current: if an inductor is placed in the area where the current distribution is concentrated, the high-order mode resonance point can be moved to a low frequency and overlap with the main mode; If capacitors are placed in the area where current distribution is concentrated, the resonance point of the high-order mode can be moved to a high frequency, away from the working frequency band of the main mode. By tuning the high-order mode with this loading lumped element, the resonant frequency of the high-order mode can be controlled, and the high-order resonance corresponding to the high-order mode in the working frequency band can be eliminated. Method 2: Adjust the structure to block the characteristic current flow and suppress the high-order mode; Through characteristic mode analysis, observe the distribution of high-order mode characteristic current: if the main mode current is only concentrated on a certain branch of the structure, and the characteristic current of the high-order mode is distributed throughout the entire structure, then place the two rotationally symmetrical branches of the structure on the upper and lower sides of the dielectric layer respectively.

9. A device for constructing an angle-stabilized FSS based on high-order mode control, characterized in that: The device is used to implement the method for constructing an angle-stable FSS based on high-order mode regulation as described in any one of claims 1 to 8, and the device includes a theoretical model formulation module, a miniaturized structure module, a high-order mode regulation module, and a structural optimization module of equivalent distributed parameters, wherein: Theoretical model formulation module decomposes the scattering of the structure into the superposition of different orthogonal characteristic modes, formulates a theoretical model that correlates the reflection and transmission coefficients of the structure with the modal behavior, and transforms the problem of eliminating the high-order resonance of the structure into the problem of regulating the high-order modes of the structure; Miniaturized structure module, obtains miniaturized FSS through joint simulation, and determines whether the structure has high-order resonance under oblique incidence; High-order mode control module: For miniaturized structures with high-order resonance, high-order modes are controlled by CMA by loading lumped elements in the structure or adjusting the structure to block characteristic current distribution, thereby eliminating the influence of high-order resonance on the angular stability of FSS; The structural optimization module of equivalent distributed parameters uses distributed capacitors and inductors equivalent to lumped elements to ultimately determine the target structure of the angle-stable FSS.

10. An angle-stable FSS, characterized in that: The structural parameters of the FSS are determined according to the method for constructing an angle-stabilized FSS based on high-order mode regulation according to any one of claims 1 to 8.

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