Wave matrix based modeling and analysis method of electromagnetic transmission of cascaded metasurface and cascaded metasurface

Abstract

The application discloses a cascaded super surface electromagnetic transmission modeling and analysis method based on a wave matrix and a cascaded super surface, belongs to the technical field of high-frequency communication and artificial electromagnetic super surface, and takes the wave matrix theory as the core. The cascaded structure contains a dielectric partition and n sheet admittance layers, the total electric field is the sum of the forward and backward propagation fields, the magnetic field expression is obtained by combining a 90-degree rotation matrix, an equivalent four-port network is obtained, the wave matrix is associated with the scattering and transmission matrix, the total wave matrix is obtained by combining the wave matrix of each layer, the isolation medium is introduced for correction, and the modeling is completed by solving the parameters. The cascaded super surface electromagnetic transmission modeling and analysis method based on the wave matrix and the cascaded super surface can form a building surface signal enhancement system framework, improve the electromagnetic wave transmission efficiency through the glass curtain wall, reduce the deployment and maintenance cost, endow the super surface with mechanical adaptability, enhance the compatibility with the glass curtain wall, and support large-scale deployment in complex scenes.

Description

Technical Field

[0001] This invention belongs to the field of high-frequency communication and artificial electromagnetic metasurface technology, specifically involving a method for modeling and analyzing electromagnetic transmission of cascaded metasurfaces based on wave matrices and cascaded metasurfaces. Background Technology

[0002] Metasurface technology has undergone years of development, with its electromagnetic control capabilities continuously enhanced and its functional characteristics becoming increasingly diverse, making it an important research direction in the field of modern electromagnetic engineering. As an artificial electromagnetic structure with subwavelength thickness, compact structure, and easy fabrication and integration, metasurfaces can flexibly control key parameters such as the phase, amplitude, and polarization state of electromagnetic waves, exhibiting excellent performance in spatial beamforming, reflection control, and signal modulation. In the field of wireless communication, metasurface technology, due to its ability to effectively control the propagation path and waveform, provides a new path for improving signal quality and optimizing coverage, especially in scenarios such as indoor signal reconstruction and coverage blind spot compensation. In addition, with the advancement of research on sixth-generation mobile communication technology, communication frequency bands are expanding from traditional microwave bands to high-frequency microwave and millimeter-wave bands.

[0003] However, existing technologies have the following shortcomings: While existing metasurface technologies can suppress reflection under specific frequency bands and ideal conditions, they are insufficient to meet the requirements of "multi-angle, multi-medium, and multi-functional collaborative transmission" in complex scenarios, and have not formed a system design framework that is universal and adaptable to multiple scenarios; When electromagnetic wave signals pass through building facades such as glass curtain walls, the large difference in wave impedance between air and building materials generates strong reflection and shielding effects, resulting in low effective signal transmittance and affecting communication continuity and system capacity; Existing solutions that compensate for signal attenuation through "dense deployment of indoor repeaters and small base stations" have problems such as complex deployment, high cost, and heavy maintenance burden, which do not meet the development requirements of "lightweight and intelligent" communication infrastructure; Most metasurfaces do not consider the mechanical adaptability of building scenarios, lack flexible and low-profile designs, making it difficult to deploy on a large scale on complex building surfaces, and have not explored transparency characteristics to adapt to the appearance requirements of glass curtain walls, etc.

[0004] Therefore, a new method is urgently needed. Summary of the Invention

[0005] The purpose of this invention is to provide a method for modeling and analyzing electromagnetic transmission of cascaded metasurfaces based on wave matrices, and the cascaded metasurfaces themselves. This method achieves flexible control over a -3dB bandwidth and 0°-80° oblique incidence within the radio frequency, microwave, and millimeter wave bands, forming a framework for a cross-building surface signal enhancement system; it improves the transmission efficiency of electromagnetic waves through glass curtain walls, reduces deployment and maintenance costs; and it also endows metasurfaces with mechanical adaptability, enhances compatibility with glass curtain walls, and supports large-scale deployment in complex scenarios.

[0006] To achieve the above objectives, this invention provides a method for modeling and analyzing electromagnetic transmission in cascaded metasurfaces based on wave matrices, and a cascaded metasurface itself, specifically as follows:

[0007] The cascaded structure is defined as consisting of a dielectric partition and n thin admittance layers, with the total electric field in each region considered as a forward propagating field. With the back propagation field The sum is expressed as:

[0008] ;

[0009] ;

[0010] ;

[0011] in, It is the total electric field within the region. It is a region i The electric field propagating inwards is x Component of direction; It is a region i The electric field propagating inwards is y Component of direction; It is a region i Internal back-propagating electric field in x Component of direction; It is a region i Internal back-propagating electric field in y Component of direction;

[0012] By combining the 90° rotation matrix, the corresponding magnetic field expression is derived, and the mathematical relationship between the total electric field and magnetic field in region i is determined; expressed as:

[0013] ;

[0014] ;

[0015] in, It is a 90° rotation matrix; It is a region The electric field vector propagating inwards; It is a region The electric field vector propagating in the reverse direction within the interior; It is a region The inward-propagating magnetic field vector; It is a region The magnetic field vector propagating in the reverse direction within the interior; It is the intrinsic impedance;

[0016] The total magnetic field is represented as:

[0017] ;

[0018] in, It is a region The total magnetic field within;

[0019] The cascaded structure is equivalent to a four-port network, with ports located in region 1 and region n+1. Considering both x-polarization and y-polarization, a 4×4 microwave network parameter matrix is ​​constructed to establish the correlation between the incident wave and the reflected wave.

[0020] The wave matrix is ​​associated with the scattering matrix and the transmission matrix respectively. The scattering matrix is ​​associated with the incident wave and the reflected wave of region 1 and region n+1, the transmission matrix is ​​associated with the total electric field and magnetic field of region 1 and region n+1, and the wave matrix is ​​directly associated with the incident / reflected field of region 1 and the field of region n+1.

[0021] Define the wave matrix of the i-th interface and the dielectric separator. Based on the wave matrix definition, correlate the forward / backward propagation field of region i with the field of region i+1. Combine the wave matrices of n-1 dielectric separators and n thin-film admittance layers using matrix multiplication to obtain the total wave matrix of the cascaded structure. The total wave matrix of the cascaded structure is expressed as:

[0022] ;

[0023] in, It is the first n One interface wave matrix; It is the first n A medium delay wave matrix;

[0024] Derivation of the first based on boundary conditions i The wave matrix of the layer interface is derived for each component in different scenarios. Under the assumption of plane wave propagation inside the dielectric partition, the wave matrix of the dielectric plate is calculated.

[0025] An isolation medium is introduced after the last metasurface layer. The expressions for the total wave matrix and the associated scattering matrix of the cascaded structure are corrected. The interface wave matrix and the dielectric plate wave matrix are substituted into the corrected expressions to solve for the key parameters characterizing the electromagnetic response, thus completing the modeling.

[0026] Preferably, the scattering matrix S is expressed as:

[0027] ;

[0028] in, It is the electric field vector propagating in the backward direction in region 1; It is the electric field vector propagating forward in region n+1; It is the electric field vector propagating forward in region 1; It is the electric field vector propagating in the backward direction in region n+1; It is the scattering matrix, a parameter matrix used to describe the electromagnetic scattering characteristics of a four-port network.

[0029] Preferably, the transmission matrix ABCD is represented as:

[0030] ;

[0031] in, It is a transmission matrix, a parameter matrix used to describe the electromagnetic transmission characteristics of a four-port network.

[0032] Preferably, the wave matrix is ​​represented as:

[0033] ;

[0034] in, The wave matrix is ​​a parametric matrix used to describe the relationship between the forward and reverse electric field vectors in different regions of a cascaded metasurface electromagnetic structure.

[0035] Preferably, it also includes the transformation of traditional network parameters into wave matrices, specifically:

[0036] ;

[0037] ;

[0038] in, It is a block of the scattering matrix; It is the identity matrix; It is a zero matrix; It is the intrinsic impedance corresponding to region 1; It is the intrinsic impedance corresponding to region n+1.

[0039] Preferably, the wave matrix expressions for each component are derived for each scenario, specifically as follows:

[0040] Scenario 1: Considering only the electrical response and neglecting cross-polarization, the calculation formula, combined with the material interface transport matrix, is as follows:

[0041] ;

[0042] ;

[0043] in, It is a 2×2 transport matrix at the material interface; r Fresnel reflection coefficient; t It is the transmission coefficient; ; It is the 2×2 admittance value of the ideal electromagnetic response of the surface. ; It is the Kronecker product;

[0044] Scenario 2: Calculation of the identity matrix and the admittance value of the ideal electromagnetic response of the surface. The calculation formula is as follows:

[0045] ;

[0046] in, It is a matrix factor; It is the first i Surface impedance of each interface;

[0047] Scenario 3: Considering only the magnetic response, the calculation formula is derived through specific boundary conditions:

[0048] ;

[0049] in, Is with the first i The phase delay matrix associated with the dielectric separator.

[0050] Preferably, it also includes, when combined with an electrically responsive metasurface, i= At time 3, the total wave matrix of the cascaded structure is expressed as:

[0051] ;

[0052] in, It is the total wave matrix of the cascaded structure;

[0053] The scattering matrix S is associated with the total wave matrix of the cascaded structure, expressed as:

[0054] ;

[0055] Considering the cross-medium scenario, an isolation medium is introduced after the last metasurface layer. The correlation between the total wave matrix and the corresponding scattering matrix S of the cascaded structure is corrected and expressed as:

[0056] ;

[0057] ;

[0058] ;

[0059] ;

[0060] in, These are the 1st, 2nd, 3rd, and 4th interface wave matrices, respectively. These are the 2nd, 3rd, and 4th medium delay wave matrices, respectively. It is the phase delay matrix of the fourth dielectric separator; It is a transfer matrix block related to the fourth interface.

[0061] The present invention also provides a cascaded metasurface, which is designed based on the ideal admittance value of the "11" state, including three thin admittance layers and a dielectric separator, and uses flexible material PDMS as the substrate with a thickness of 0.058λ.

[0062] Preferably, the cascaded metasurface achieves impedance matching of the air-glass interface within a -3dB bandwidth in the radio frequency, microwave, and millimeter wave bands (e.g., a wide bandwidth of 5.75-8.15 GHz).

[0063] Therefore, by employing the aforementioned wave matrix-based cascaded metasurface electromagnetic transport modeling and analysis method and cascaded metasurface, the present invention offers the following advantages compared to existing technologies:

[0064] (1) This invention adopts the technical means of establishing a broadband equivalent coding state theoretical model and obtaining four 2-bit coding transmission states to overcome the technical problems of existing metasurfaces having a single control function, which makes it difficult to meet the multi-angle, multi-media, and multi-functional collaborative transmission requirements in complex scenarios, and lacking a systematic design framework. In this way, it realizes the flexible control of "broadband (5.75-8.15GHz-3dB bandwidth) + multi-angle (0°-80° oblique incidence still maintains good performance)", forming a systematic design framework for signal enhancement across building surfaces, and adapting to the technical effects of complex multi-scenario requirements.

[0065] (2) The present invention adopts the technical means of achieving conjugate impedance matching between air and glass based on wave matrix theory, which overcomes the technical problem that strong reflection is generated by the discontinuous wave impedance at the building interface, resulting in low transmission efficiency of electromagnetic wave signals and the existence of "glass shielding effect". In this way, the reflection loss is reduced from the root of the electromagnetic transmission mechanism, significantly improving the transmission efficiency of electromagnetic wave signals through the glass curtain wall and effectively alleviating the technical effect of "glass shielding effect".

[0066] (3) The present invention adopts the technical means of designing an ultra-thin (0.058λ, 2.5mm for example 5.75-8.15GHz-3dB bandwidth range) flexible metasurface and deploying it directly on the building surface. This overcomes the technical problems of traditional engineering compensation schemes that rely on additional repeaters or small base stations, which are complex to deploy, costly and have a heavy maintenance burden. In addition, no additional communication auxiliary equipment is needed, reducing deployment costs and maintenance burden. This is in line with the technical effect of the lightweight and intelligent development direction of communication infrastructure.

[0067] (4) This invention uses PDMS flexible substrate material and plans to explore the technical means of conformal deployment and application of transparent conductive materials. It overcomes the technical problems of existing metasurfaces lacking flexibility, low profile design, and insufficient mechanical adaptability and appearance compatibility with building surfaces such as glass curtain walls. In this way, it endows metasurfaces with mechanical adaptability, supports large-scale deployment on complex building surfaces, and enhances the technical effect of appearance and structural compatibility with glass curtain walls.

[0068] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0069] Figure 1 This is a schematic diagram illustrating the electromagnetic wave transmission characteristics of a cascaded metasurface based on the wave matrix electromagnetic transmission modeling and analysis method of the present invention and an embodiment of the cascaded metasurface.

[0070] Figure 2 This is a schematic diagram illustrating the design and parameters of the metasurface structure in the cascaded metasurface electromagnetic transmission modeling and analysis method based on wave matrices, and an embodiment of the cascaded metasurface, as described in this invention; wherein: Figure 2 In the diagram, (a) and (b) represent the three-dimensional structure decomposition diagram; Figure 2 (c) in the diagram is the planar dimension diagram of each layer unit;

[0071] Figure 3 This is a simulation diagram of the electric field distribution of each layer unit of the electromagnetic metasurface in the present invention, based on the wave matrix-based modeling and analysis method for electromagnetic transmission of cascaded metasurfaces and an embodiment of the cascaded metasurface.

[0072] Figure 4 This is a comparison diagram of the frequency response of the electromagnetic transmission characteristics of cascaded metasurfaces based on wave matrices and embodiments of the present invention.

[0073] Figure 5 The frequency response diagram of the electromagnetic transmission modeling and analysis method of cascaded metasurfaces based on wave matrices and the electromagnetic enhancement characteristics of metasurfaces in embodiments of cascaded metasurfaces is shown in the present invention.

[0074] Figure 6 This is a comparison diagram of the electromagnetic transmission modeling and analysis method of cascaded metasurfaces based on wave matrices and the oblique incidence transmission characteristics of cascaded metasurface embodiments of the present invention. Figure 6 In the figure (a), the curves showing the change of electromagnetic wave transmission coefficient with different incident angles when there is "without metasurface" are shown. Figure 6 (b) in the figure shows the transmission coefficient as a function of frequency at different incident angles when there is a metasurface.

[0075] Figure 7The angle-frequency response diagrams of the electromagnetic transmission modeling and analysis method of cascaded metasurfaces based on wave matrices and the electromagnetic enhancement characteristics of metasurfaces in embodiments of cascaded metasurfaces are presented in this invention. Detailed Implementation

[0076] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Unless otherwise defined, the technical or scientific terms used in the present invention should have the ordinary meaning understood by those skilled in the art.

[0077] Example 1

[0078] The present invention relates to a wave matrix-based method for modeling and analyzing electromagnetic transport in cascaded metasurfaces, and the cascaded metasurface itself, specifically as follows:

[0079] The cascaded structure is defined as consisting of a dielectric partition and n thin-film admittance layers. The total electric field in each region is defined as the sum of the forward propagation field and the reverse propagation field, where the forward propagation field is... The backpropagation field is , is represented as:

[0080] ;

[0081] in, It is a region The total electric field vector within, It is a region i The electric field propagating inwards is x Component of direction; It is a region i The electric field propagating inwards is y Component of direction; It is a region i Internal back-propagating electric field in x Component of direction; It is a region i Internal back-propagating electric field in y Component of direction;

[0082] At this point, the corresponding magnetic field expression is:

[0083] ;

[0084] ;

[0085] in, It is a 90° rotation matrix; It is a region The electric field vector propagating inwards; It is a region The electric field vector propagating in the reverse direction within the interior; It is a region The inward-propagating magnetic field vector; It is a region The magnetic field vector propagating in the reverse direction within the interior; It is the intrinsic impedance;

[0086] The total magnetic field is represented as:

[0087] ;

[0088] in, It is a region The total magnetic field within;

[0089] The cascaded structure is regarded as a four-port network (the ports are located in regions 1 and n+1, taking into account x and y polarization). A 4×4 matrix of microwave network parameters is constructed, and the relationships between the scattering matrix, transmission matrix, wave matrix and field quantities are established respectively.

[0090] The scattering matrix S is used to establish the relationship between the incident wave and the reflected waves in region 1 and region n+1, and is expressed as:

[0091] ;

[0092] in, It is the electric field vector propagating in the backward direction in region 1; It is the electric field vector propagating forward in region n+1; It is the electric field vector propagating forward in region 1; It is the electric field vector propagating in the backward direction in region n+1; It is the scattering matrix, a parameter matrix used to describe the electromagnetic scattering characteristics of a four-port network;

[0093] The transfer matrix ABCD is used to establish the relationship between the total electric and magnetic fields in region 1 and region n+1, and is expressed as:

[0094] ;

[0095] in, It is a transmission matrix, a parameter matrix used to describe the electromagnetic transmission characteristics of a four-port network;

[0096] The wave matrix is ​​used to establish the relationship between the incident / reflected field of region 1 and the field of region n+1, and is expressed as:

[0097] ;

[0098] in, The wave matrix is ​​a parametric matrix used to describe the relationship between forward and reverse electric field vectors in different regions of electromagnetic structures such as cascaded metasurfaces. It reflects the combined effect of electromagnetic signal propagation, scattering and other characteristics in the structure.

[0099] The relationships between the wave matrix and the scattering matrix S, and between the wave matrix and the transmission matrix ABCD, are further derived to realize the transformation of traditional network parameters into wave matrices, specifically as follows:

[0100] ;

[0101] ;

[0102] in, It is a block of the scattering matrix; It is the identity matrix; It is a zero matrix; It is the intrinsic impedance corresponding to region 1; It is the intrinsic impedance corresponding to region n+1;

[0103] Define the wave matrix (WMs) functions of the i-th interface and dielectric separator, correlate the forward / backward propagation fields of region i and region i+1, and based on the composition of n-1 dielectric separators and n sheet admittances, obtain the expression for the total wave matrix of the cascaded structure, and determine the logic for calculating the overall wave matrix by multiplying the wave matrices of each layer; the expression for the total wave matrix of the cascaded structure is:

[0104] ;

[0105] in, It is the first n One interface wave matrix; It is the first n A medium delay wave matrix;

[0106] Derivation of wave matrix expressions for each component under different scenarios;

[0107] Scenario 1: Considering only the electrical response and without cross-polarization, based on the boundary conditions, combined with the 2×2 transmission matrix of the material interface (including Fresnel reflection coefficient r and transmission coefficient t), the identity matrix, and the ideal electromagnetic response admittance of the surface, the interface wave matrix of the i-th layer is derived, and the calculation formula is as follows:

[0108] ;

[0109] ;

[0110] in, It is a 2×2 transport matrix at the material interface; r Fresnel reflection coefficient;t It is the transmission coefficient; ; It is the 2×2 admittance value of the ideal electromagnetic response of the surface. ; It is the Kronecker product;

[0111] Scenario 2: Considering only the magnetic response, derive the first... i The interfacial wave matrix is ​​calculated using the following formula:

[0112] ;

[0113] in, It is a matrix factor; It is the first i Surface impedance of each interface;

[0114] Scenario 3: Assuming plane wave propagation within a dielectric separator, and combining relevant parameters, derive the dielectric plate wave matrix using the following formula:

[0115] ;

[0116] in, Is with the first i A phase delay matrix related to a dielectric separator;

[0117] Taking an electrically responsive metasurface (i=3) as an example, substituting the expression for the interface and dielectric plate wave matrices, we obtain the total wave matrix of the cascaded structure, which is expressed as:

[0118] ;

[0119] in, It is the total wave matrix of the cascaded structure;

[0120] The scattering matrix S is associated with the total wave matrix of the cascaded structure, expressed as:

[0121] ;

[0122] Considering the cross-medium scenario, an isolation medium is introduced after the last metasurface layer. The correlation between the total wave matrix and the corresponding scattering matrix S of the cascaded structure is corrected and expressed as:

[0123] ;

[0124] ;

[0125] ;

[0126] ;

[0127] in, These are the 1st, 2nd, 3rd, and 4th interface wave matrices, respectively. These are the 2nd, 3rd, and 4th medium delay wave matrices, respectively. It is the phase delay matrix of the fourth dielectric separator; It is a transfer matrix block related to the fourth interface;

[0128] Substituting the interface wave matrix and the dielectric plate wave matrix into the corrected scattering matrix S correlation equation, the key parameters are solved. , and .

[0129] Meanwhile, the technical effects were verified through coding control (deriving the ideal admittance values ​​of four non-reflective broadband metasurface states using 2-bit coding), broadband impedance matching (achieving a -3dB bandwidth of 5.75-8.15GHz), and ultra-low profile design (thickness 0.058λ). Modeling and analysis verification were completed by combining simulation comparisons (transmission coefficient with and without metasurface, oblique incidence response, etc.).

[0130] like Figures 1-7 As shown, to achieve the mechanical flexibility of the metasurface, this embodiment selects the flexible polymer material PDMS as the dielectric substrate; in the simulation design stage, the metasurface pattern of each layer is modeled as an ideal electrical conductor (PEC) to ensure the feasibility of the design and the accuracy of the electromagnetic response;

[0131] The metasurface specifically adopts a three-layer cascaded metal pattern structure, where the PDMS substrate thickness between two adjacent metal patterns is 1 mm, and the outermost PDMS substrate thickness is 0.5 mm, thus controlling the overall metasurface thickness to 2.5 mm (corresponding to a wavelength of 0.058λ). At the same time, the metasurface unit size is set to 4 mm (corresponding to a wavelength of 0.093λ). This size design ensures that even with a small interlayer spacing, the electromagnetic waves incident on each metasurface layer can still be approximately plane waves, meeting the subsequent control requirements.

[0132] After obtaining the scattering parameters used to define the transmission field state, four transmission states with a phase difference of 90° can be obtained and defined as “00”, “01”, “10”, and “11” respectively. Subsequently, the cascaded structure is analyzed by the wave matrix model, and the ideal admittance values ​​of each layer of the metasurface under different transmission states can be calculated, providing a key basis for the design and optimization of each layer structure, and finally realizing the precise control of the incident electromagnetic wave.

[0133] Therefore, this invention employs the aforementioned wave matrix-based cascaded metasurface electromagnetic transmission modeling and analysis method and cascaded metasurface. This device achieves a 5.75-8.15 GHz-3 dB bandwidth and flexible control under 0°-80° oblique incidence, forming a cross-building surface signal enhancement system framework; it improves the transmission efficiency of electromagnetic waves through glass curtain walls, reduces deployment and maintenance costs; and it also endows the metasurface with mechanical adaptability, enhances compatibility with glass curtain walls, and supports large-scale deployment in complex scenarios.

[0134] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for modeling and analyzing electromagnetic transport in cascaded metasurfaces based on wave matrices, characterized in that, Includes the following steps: The cascaded structure is defined as consisting of a dielectric partition and n thin admittance layers, with the total electric field in each region considered as a forward propagating field. With the back propagation field The sum is expressed as: ； ； ； in, It is the total electric field within the region. It is a region i The electric field propagating inwards is x Component of direction; It is a region i The electric field propagating inwards is y Component of direction; It is a region i Internal back-propagating electric field in x Component of direction; It is a region i Internal back-propagating electric field in y Component of direction; By combining the 90° rotation matrix, the corresponding magnetic field expression is derived, and the mathematical relationship between the total electric field and magnetic field in region i is determined; expressed as: ； ； in, It is a 90° rotation matrix; It is a region The electric field vector propagating inwards; It is a region The electric field vector propagating in the reverse direction within the interior; It is a region The inward-propagating magnetic field vector; It is a region The magnetic field vector propagating in the reverse direction within the interior; It is the intrinsic impedance; The total magnetic field is represented as: ； in, It is a region The total magnetic field within; The cascaded structure is equivalent to a four-port network, with ports located in region 1 and region n+1. Considering both x-polarization and y-polarization, a 4×4 microwave network parameter matrix is ​​constructed to establish the correlation between the incident wave and the reflected wave. The wave matrix is ​​associated with the scattering matrix and the transmission matrix respectively. The scattering matrix is ​​associated with the incident wave and the reflected wave of region 1 and region n+1, the transmission matrix is ​​associated with the total electric field and magnetic field of region 1 and region n+1, and the wave matrix is ​​directly associated with the incident / reflected field of region 1 and the field of region n+1. Define the wave matrix of the i-th interface and the dielectric separator. Based on the wave matrix definition, correlate the forward / backward propagation field of region i with the field of region i+1. Combine the wave matrices of n-1 dielectric separators and n thin-film admittance layers using matrix multiplication to obtain the total wave matrix of the cascaded structure. The total wave matrix of the cascaded structure is expressed as: ； in, It is the first n One interface wave matrix; It is the first n A medium delay wave matrix; It is the electric field vector propagating forward in region n+1; It is the electric field vector propagating in the backward direction in region n+1; Derivation of the first based on boundary conditions i The wave matrix of the layer interface is derived for each component in different scenarios. Under the assumption of plane wave propagation inside the dielectric partition, the wave matrix of the dielectric plate is calculated. An isolation medium is introduced after the last metasurface layer. The expressions for the total wave matrix and the associated scattering matrix of the cascaded structure are corrected. The interface wave matrix and the dielectric plate wave matrix are substituted into the corrected expressions to solve for the key parameters characterizing the electromagnetic response, thus completing the modeling.

2. The method for modeling and analyzing electromagnetic transport in cascaded metasurfaces based on wave matrices according to claim 1, characterized in that, The scattering matrix S is expressed as: ； in, It is the electric field vector propagating in the backward direction in region 1; It is the electric field vector propagating forward in region 1; It is the scattering matrix, a parameter matrix used to describe the electromagnetic scattering characteristics of a four-port network.

3. The method for modeling and analyzing electromagnetic transport in cascaded metasurfaces based on wave matrices according to claim 1, characterized in that, The transfer matrix ABCD is represented as: ； in, It is a transmission matrix, a parameter matrix used to describe the electromagnetic transmission characteristics of a four-port network.

4. The method for modeling and analyzing electromagnetic transport in cascaded metasurfaces based on wave matrices according to claim 1, characterized in that, The wave matrix is ​​represented as: ； in, The wave matrix is ​​a parametric matrix used to describe the relationship between the forward and reverse electric field vectors in different regions of a cascaded metasurface electromagnetic structure.

5. The method for modeling and analyzing electromagnetic transport in cascaded metasurfaces based on wave matrices according to claim 1, characterized in that, It also includes the transformation of traditional network parameters into wave matrices, specifically: ； ； in, It is a block of the scattering matrix; It is the identity matrix; It is a zero matrix; It is the intrinsic impedance corresponding to region 1; It is the intrinsic impedance corresponding to region n+1.

6. The method for modeling and analyzing electromagnetic transport in cascaded metasurfaces based on wave matrices according to claim 1, characterized in that, The wave matrix expressions for each component are derived for each scenario, as follows: Scenario 1: Considering only the electrical response and neglecting cross-polarization, the calculation formula, combined with the material interface transport matrix, is as follows: ； ； in, It is a 2×2 transport matrix at the material interface; r Fresnel reflection coefficient; t It is the transmission coefficient; ; It is the 2×2 admittance value of the ideal electromagnetic response of the surface. ; It is the Kronecker product; Scenario 2: Calculation of the identity matrix and the admittance value of the ideal electromagnetic response of the surface. The calculation formula is as follows: ； in, It is a matrix factor; It is the first i Surface impedance of each interface; Scenario 3: Considering only the magnetic response, the calculation formula is derived through specific boundary conditions: ； in, Is with the first i The phase delay matrix associated with the dielectric separator.

7. The method for modeling and analyzing electromagnetic transport in cascaded metasurfaces based on wave matrices according to claim 1, characterized in that, It also includes, combined with electrically responsive metasurfaces, when i= At time 3, the total wave matrix of the cascaded structure is expressed as: ； in, It is the total wave matrix of the cascaded structure; The scattering matrix S is associated with the total wave matrix of the cascaded structure, expressed as: ； Considering the cross-medium scenario, an isolation medium is introduced after the last metasurface layer. The correlation between the total wave matrix and the corresponding scattering matrix S of the cascaded structure is corrected and expressed as: ； ； ； ； in, These are the 1st, 2nd, 3rd, and 4th interface wave matrices, respectively. These are the 2nd, 3rd, and 4th medium delay wave matrices, respectively. It is the phase delay matrix of the fourth dielectric separator; It is a transfer matrix block related to the fourth interface.

8. A cascaded metasurface designed using the method described in any one of claims 1-7, characterized in that, The cascaded metasurface is designed based on the ideal admittance value of the "11" state, and includes three thin admittance layers and a dielectric separator. It uses a dielectric material as the substrate with a thickness of 0.058λ.

9. The cascaded metasurface according to claim 8, characterized in that, The cascaded metasurface achieves impedance matching of the air-glass interface within a -3dB bandwidth in the radio frequency, microwave, and millimeter wave bands.

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