Electromagnetic metasurface irregular triangular mesh discretization and structure coding method

Abstract

The invention relates to an electromagnetic metasurface irregular triangular mesh discretization and structure coding method. Comprising the following steps: carrying out unstructured triangular mesh generation on a to-be-designed electromagnetic metasurface by utilizing a mesh generation algorithm and extracting all triangular meshes; clustering all the triangular meshes to obtain a plurality of common edges; designing a binary vector, coding the common edge according to the binary vector, and determining filling media of triangular meshes on two sides of the common edge according to coding values; when the triangular mesh filling media conflict due to coding, constraint integration is carried out by adopting an OR logic relation; and designing a multi-valued vector to encode the loading devices on the triangular grids on the two sides of the common edge, regulating and controlling the encoding values of the loading devices according to the encoding of the common edge, and combining the encoding values with the encoding values to realize the comprehensive structure encoding of the electromagnetic metasurface to be designed. The method is high in design flexibility, simple and efficient in coding form and better in simulation effect on a complex structure, and can improve the characterization and regulation capability of electromagnetic wave polarization characteristics.

Description

Technical Field

[0001] The present application relates to the technical field of electromagnetic metamaterials, and particularly to a method for discretizing irregular triangular meshes and encoding structures of an electromagnetic metasurface. Background Art

[0002] Electromagnetic metamaterials are a special type of artificial electromagnetic materials, which are usually composed of periodic array units. Through unique structural designs, they can achieve extraordinary electromagnetic characteristic parameters, generating various response characteristics such as reflection, scattering, and loss of electromagnetic waves, thereby realizing diversified regulation of the transmission characteristics of electromagnetic waves. In the actual application process, considering the conformal integration with the device form, two-dimensional electromagnetic metamaterials have always been a hot research direction in the field of electromagnetic metamaterials. Typical representatives include frequency selective surface (FSS), energy selective surface (FSS), etc. In the design of electromagnetic metasurfaces, the geometric structure design of array units is one of the core links, directly determining the response characteristics of the electromagnetic metasurface to electromagnetic waves. Early research mainly focused on the classical structures of metasurfaces, such as structures with fixed symmetries like cross-shaped, cylindrical, H-shaped, etc. Such structures are usually limited by preset geometric templates and can only achieve electromagnetic response characteristic regulation through limited adjustable parameters (such as arm length, spacing, etc.), with relatively low design freedom and relatively single regulation ability for electromagnetic waves. Later, with the in-depth research, scholars began to explore higher-degree-of-freedom topological configurations to break through the performance boundaries of traditional structures. Typical strategies include parametric deformation of the basic structure, rotation of unit orientations, or construction of composite resonant units, etc. However, these methods are still limited by the geometric constraints of the initial structure and it is difficult to achieve true topological free design. In recent years, the design method based on discrete grids has gradually become a research hotspot. By discretizing the design domain into binary or multi-valued pixel grids, it allows the geometric form of materials to freely evolve at the sub-wavelength scale. This free-form topological structure can provide a design space of dozens or even hundreds of dimensions, opening up new ways for the realization of various electromagnetic characteristics such as multi-modal, wide-band, and low-scattering.

[0003] Regarding the grid discretization and structure encoding methods of the design space, the existing technical means are mainly based on regular rectangular grids, and the encoding object is the rectangle grid itself, lacking flexibility in the design of special-shaped structures, and the polarization characteristic representation and regulation ability for electromagnetic waves are not significant enough. Summary of the Invention

[0004] Based on this, it is necessary to provide a method for discretizing irregular triangular meshes and encoding structures of an electromagnetic metasurface with high flexibility in the design of special-shaped structures, which can improve the representation and regulation ability for the polarization characteristics of electromagnetic waves, aiming at the above technical problems.

[0005] An irregular triangular grid discretization and structure encoding method for electromagnetic metasurfaces, the method comprising: Using a grid meshing algorithm to perform unstructured triangular grid meshing on the electromagnetic metasurface to be designed and extract all triangular grids; Clustering all triangular grids to obtain multiple common edges; designing a binary vector, encoding the common edges according to the binary vector, and determining the filling media of the triangular grids on both sides of the common edge according to the encoded values; when there is an encoding conflict in the filling media of the triangular grids, an OR logical relationship is used for constraint integration; Designing a multi-valued vector to encode the loading devices on the triangular grids on both sides of the common edge, and regulating the encoded values of the loading devices according to the encoding of the common edge, and the combination of the two realizes the comprehensive structure encoding of the electromagnetic metasurface to be designed The above-mentioned irregular triangular grid discretization and structure encoding method for electromagnetic metasurfaces first discretizes the design space using unstructured triangular grids. Compared with regular rectangular grids, the shape and layout of triangular grids are more flexible, and they can be adaptively meshed according to the complex shape and structure of the electromagnetic metasurface, so as to accurately simulate complex geometric configurations. For electromagnetic metasurfaces with curved, twisted or irregular boundaries, triangular grids can closely fit their shapes, greatly improving the design flexibility and overcoming the limitations of rectangular grids. Then, taking the common edge of each pair of triangular grids as the optimization encoding object, and controlling the filling media of the triangular grids on both sides of the common edge through a binary vector encoding, so as to realize the optimization control of the shape of the metal patches of the electromagnetic metasurface. Compared with rectangular grids, irregular triangular grids can achieve stronger characterization and regulation capabilities of the polarization characteristics of electromagnetic waves, effectively making up for the deficiencies of the regular grid encoding form. Finally, the state of the loading devices on the triangular grids on both sides of the common edge is controlled through a multi-valued vector encoding. The common edge encoding form based on the binary vector can perfectly accommodate the encoding design of device loading. The combination of the two can characterize physical features such as whether the device is loaded and the type of loaded device with only a simple one-dimensional vector. Compared with the traditional rectangular grid encoding that requires multiple encoding bits to achieve the same function, the encoding process is greatly simplified, and the encoding form is more concise and efficient. Description of the Drawings

[0006] Figure 1 Is a schematic flow chart of an irregular triangular grid discretization and structure encoding method for electromagnetic metasurfaces in an embodiment; Figure 2 Is a schematic diagram of the change in the spatial discretization method from a regular rectangular grid to an irregular triangular grid in an embodiment; wherein, Figure 2 (a) is a schematic diagram of a regular rectangular grid, Figure 2 (b) is a schematic diagram of an irregular triangular grid, Figure 2 (c) is a schematic diagram of grid symmetric mapping; Figure 3 Schematic diagram of structure encoding and device loading based on a common edge in an embodiment; Figure 4 Schematic diagram of the encoding form to be optimized for an electromagnetic protection metasurface in another embodiment. Detailed implementation manners

[0007] In order to make the objectives, technical solutions and advantages of the present application clearer and more understandable, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0008] In one embodiment, as Figure 1 shown, a method for discretizing and structurally encoding an irregular triangular grid of an electromagnetic metasurface is provided, including the following steps: Step 102, use a grid meshing algorithm to perform unstructured triangular grid meshing on the electromagnetic metasurface to be designed and extract all triangular grids.

[0009] In the existing publicly available technical means, for the discretization of the space to be designed, regular rectangular grids are mostly used, as Figure 2 (a) shown. Moreover, in order to reduce the number of variables to be optimized, local symmetric mapping processing is often performed on the discrete grid in actual operation.

[0010] In the present application, an unstructured triangular grid is proposed to discretize the design space, as Figure 2 (b) shown. Compared with regular rectangular grids, the shape and layout of triangular grids are more flexible. Moreover, triangular grids can be adaptively meshed according to the complex shape and structure of the electromagnetic metasurface, better simulating complex geometric configurations, which is crucial for solving the problem of low design flexibility. For an electromagnetic metasurface structure with curved, twisted or irregular boundaries, triangular grids can fit its shape more closely, while rectangular grids may have larger errors or situations that cannot be accurately described. In the actual application process, under the condition of limited computing power, symmetric mapping processing can also be performed on the design space based on irregular triangular grids to reduce the number of variables to be optimized, as Figure 2 (c) shown.

[0011] Step 104, cluster all triangular grids to obtain a plurality of common edges; design a binary vector, encode the common edges according to the binary vector, and determine the filling media of the triangular grids on both sides of the common edge according to the encoded value; when there is an encoding conflict in the filling media of the triangular grids, an OR logical relationship is used for constraint integration.

[0012] Cluster all the triangular meshes obtained in the previous step. Every two triangular meshes with a common edge can be grouped into a pair, and the common edge of these two triangular meshes is denoted as , N which is the total number of pairs of triangular meshes with common edges. These common edges are the subsequent coding objects, and according to the coding characteristics, they will determine the filling medium of the two triangular patches connected to the common edge. Considering the randomness of the spatial arrangement of irregular triangular meshes, each pair of triangular meshes controlled by a common edge can be characterized as a surface current element with a random polarization state. Therefore, triangular meshes with irregular spatial arrangement characteristics will have a relatively strong ability to characterize and regulate electromagnetic wave polarization characteristics. In contrast, the regularity of rectangular meshes results in relatively single characterization of electromagnetic wave polarization characteristics, and multiple meshes often need to cooperate to finely regulate complex electromagnetic wave polarization characteristics. In addition, for a specific triangular mesh, since there may be at most three common edges connected to it, this means that the filling medium of this triangular mesh may be affected by at most three encodings. When coding conflicts occur, an OR logic relationship is used for constraint integration, that is, among the three common edge encodings associated with it, as long as one is 1, then this triangular mesh is filled with metal. This constraint criterion can effectively solve the metal structure generation conflict brought by the coding method based on the common edges of triangular meshes, ensure the uniqueness and accuracy from structure coding to metal configuration generation, further improve the reliability and stability of the entire coding system, and enable the coding method based on the common edges of triangular meshes to be better applied to the actual design of electromagnetic metasurfaces.

[0013] Step 106: Design a multi-value vector to encode the loading devices on the triangular meshes on both sides of the common edge, and regulate the encoding value of the loading devices according to the encoding of the common edge. The combination of the two realizes the comprehensive structure coding of the electromagnetic metasurface to be designed. Based on the binary vector encoding of the common edge in the previous step, further design a multi-value vector to represent the state of the loading devices bridging a pair of triangular meshes. If the common edge encoding is 1, it means that the triangular meshes on both sides of the common edge are metal and device loading is allowed. If the common edge encoding is 0, device loading is not allowed. Therefore, this structure coding method based on triangular meshes for common edges can perfectly accommodate the coding design of device loading, and only one structure coding can represent physical characteristics such as whether a device is loaded and the type of loaded device. Compared with the traditional coding method for rectangular meshes, there is no need to design multiple complex encodings for different device loading characteristics, making the coding form more concise. In practical applications, if different types of devices need to be loaded on the electromagnetic metasurface, the coding method based on the common edges of triangular meshes can represent different loading situations through simple changes in a single-bit encoding value, while rectangular meshes may require combinations of multiple encoding bits to achieve the same function, resulting in complex coding and easy errors.

[0014] The above-mentioned electromagnetic metasurface irregular triangular grid discretization and structure encoding method first discretizes the design space using unstructured triangular grids. Compared with regular rectangular grids, the shape and layout of triangular grids are more flexible. They can be adaptively meshed according to the complex shape and structure of the electromagnetic metasurface, so as to accurately simulate complex geometric configurations. For electromagnetic metasurfaces with curved, twisted or irregular boundaries, triangular grids can closely fit their shapes, greatly improving the design flexibility and overcoming the limitations of rectangular grids. Then, the common edge of each pair of triangular grids is used as the optimization encoding object, and a binary vector encoding is used to control the media filled in the triangular grids on both sides of its common edge, so as to realize the optimization control of the shape of the electromagnetic metasurface metal patch. Compared with rectangular grids, the metal configuration generated based on irregular triangular grids can achieve a stronger characterization and regulation ability of the polarization characteristics of electromagnetic waves, effectively making up for the deficiencies of traditional methods. Finally, the state of the loading devices on the triangular grids on both sides of the common edge is controlled by a multi-value vector encoding. The common edge encoding form based on the binary vector can perfectly accommodate the encoding design of device loading. The combination of the two can characterize physical features such as whether the device is loaded and the type of loaded device with only a simple one-dimensional vector. Compared with the traditional rectangular grid encoding that requires multiple encoding bits to achieve the same function, the encoding process is greatly simplified, making the encoding form more concise and efficient.

[0015] In one embodiment, all the triangular grids are clustered to obtain multiple common edges, including: All the triangular grids are clustered. Every two triangular grids with a common edge are grouped into a pair, and the common edge of these two triangular grids is denoted as , N is the total number of pairs of all triangular grids with common edges, and these common edges are the subsequent encoding objects.

[0016] In one embodiment, a binary vector is designed to encode the common edge according to the binary vector, including: Design a 1×N-dimensional binary vector, that is, the value of each element in the vector is 0 or 1. Among them, "0" represents that the triangular grid patches on both sides of the common edge are filled with air, and "1" represents that they are filled with metal.

[0017] In a specific embodiment, for the obtained N common edges, design a 1× N -dimensional binary vector, that is, the value of each element in the vector is 0 or 1. Among them, "0" represents that the triangular grid patches on both sides of the common edge are filled with air, and "1" represents that they are filled with metal. Thus, the optimal design of the electromagnetic metasurface metal pattern is transformed into the optimal design of the structure encoding. As Figure 3As shown, the red line in the enlarged local view represents the common edge of two triangular meshes, and its coding determines the filling medium of the two triangular mesh patches connected to the common edge.

[0018] In one embodiment, during the filling process of the triangular mesh, theoretically each triangular mesh is associated with at most three common edges, that is, three codings. If there is a conflict between the three codings, an OR logical relationship is used for constraint integration, including: If among the multiple common edges of a triangular mesh, as long as one coding is 1, then the triangular mesh is filled with metal.

[0019] In a specific embodiment, based on the coding form of the common edge, there will be a situation where the same triangular mesh is affected by the codings of multiple common edges. Theoretically, the same triangular mesh may be affected by at most three codings. In this application, an "OR" logical relationship is used to constrain among the codings of multiple common edges that affect the same triangular mesh, that is, as long as one coding is 1, then the triangular mesh is filled with metal. For example, Figure 3 in the enlarged local view of, the middle triangular patch is theoretically determined by the codings of three common edges for its filling medium. It can be seen that as long as one of the three edges has a coding of 1, it means that the patch is filled with metal.

[0020] In one embodiment, a multi-valued vector is designed to code the loading devices on the triangular meshes on both sides of the common edge, and the coding value of the loading device is regulated according to the coding of the common edge. The two are combined to realize the comprehensive structure coding of the electromagnetic metasurface to be designed, including: Design a 1× N dimensional multi-valued vector to code the device loading states on the triangular meshes on both sides of the common edge. The value of each element in this coding vector is a positive integer between 0 and 4. "0" means no loading, "1" means loading a PIN diode, "2" means loading a capacitor, "3" means loading an inductor, and "4" means loading a resistor.

[0021] In a specific embodiment, the lumped element (resistor, inductor, capacitor, diode, etc.) loading is one of the core elements for the electromagnetic metasurface to achieve special electromagnetic regulation capabilities. In the actual design process, it can be considered that the size of the lumped element is much smaller than the structural size of the metal. Therefore, when it is loaded on the metal grid, it can be considered that it is bridged on both sides of a pair of common edges of the triangular meshes, and the meshes at both ends of the position landing point must be metal, such as Figure 3As shown in the enlarged partial view. In summary, regarding the loading of lumped elements, the present application is designed as a 1×N-dimensional multi-valued vector, and the value of each element in the coding vector is a positive integer between 0 and 4. Among them, "0" represents no loading, "1" represents loading PIN diodes, "2" represents loading capacitors, "3" represents loading inductors, "4" represents loading resistors, etc. In this way, only one-bit coding can characterize physical features such as the device loading state and device type on the electromagnetic metasurface, which will further expand the design boundary, realize the design of electromagnetic metasurfaces with more performance, and provide support for the design of multi-modal and multi-functional electromagnetic metasurfaces.

[0022] In one embodiment, the loading devices on the triangular meshes on both sides of the common edge are coded. Combining the coding of the common edge, the electromagnetic metasurface to be designed is discretized into a 2×N-dimensional coding vector. The first-row coding characterizes the structural form of the metal patch, and its value is 0 or 1; the second-row coding characterizes the loading condition of the lumped element, and its value range is an integer between 0 and 4. Among them, the coding value of the second row is constrained by the first row. Only when the coding of the first row is 1, the coding of the second row can take a non-zero value.

[0023] In a specific embodiment, after the above process, the design space to be optimized of the electromagnetic metasurface can be discretized into a 2×N-dimensional coding vector, as Figure 4 shown: The first-row coding characterizes the structural form of the metal patch, and its value is 0 or 1; the second-row coding characterizes the loading condition of the lumped element, and its value range is an integer between 0 and 4. It should be noted that the value of the second-row coding is not completely free and is affected by the first-row coding. Because on both sides where the lumped element is loaded, the triangular patches must be metal. That is to say, only when the coding of the first row is 1, the coding of the second row can take a non-zero value, which is also an inevitable requirement of physical feature constraints.

[0024] Finally, it should be pointed out that Figure 4The designed coding form and the triangular discrete grid of the design space are strongly correlated. The triangular discrete grid of the design space provides a physical carrier and a geometric basis for the coding. By performing unstructured triangular mesh dissection on the electromagnetic metasurface, a large number of triangular meshes are obtained. The distribution, shape, and connection relationships of these meshes constitute the basic structural framework of the electromagnetic metasurface. The coding is exactly based on these triangular meshes. For example, taking the common edge of each pair of triangular meshes as the coding object, the characteristics and distribution of the common edge directly determine the position and scope of the coding. Without this specific triangular mesh dissection method, the coding loses its clear object of action and cannot effectively describe and regulate the structure of the electromagnetic metasurface. By designing binary vectors and multi-valued vectors to encode the common edges of the triangular meshes and the loading states of the devices on both sides respectively, various physical characteristics of the electromagnetic metasurface, such as the geometric configuration of the metal patches and the device loading conditions, are transformed into computable and controllable digital codes. These codes can not only characterize the geometric features of the triangular meshes, but more importantly, can reflect the functional characteristics of the electromagnetic metasurface in the field of electromagnetics. For example, through coding, the responses of the electromagnetic metasurface to electromagnetic waves, such as reflection, scattering, and loss, can be precisely controlled, realizing diverse regulation of the electromagnetic wave transmission characteristics. Without the coding form, the triangular discrete grid is just a pile of meaningless geometric figures and cannot achieve the specific functions of the electromagnetic metasurface. It can be seen that the triangular discrete grid and the coding form are interdependent and indispensable. The unique structure of the triangular discrete grid enables the coding to have higher degrees of freedom and flexibility, and can make full use of the diverse polarization characteristics of the triangular meshes and the simulation advantages of complex structures to achieve richer electromagnetic response characteristics. The coding form endows the triangular discrete grid with practical physical meanings and functions. Through the design and optimization of the coding, the performance of the electromagnetic metasurface can be precisely regulated. The organic combination of the two, that is, the specific coding form based on the triangular discrete grid, breaks through the design limitations of the traditional rule-based rectangular grid, realizes the improvement of design flexibility, the enhancement of the ability to characterize the electromagnetic wave polarization characteristics, and the simplicity and efficiency of the coding, thus constituting the core innovation of this application.

[0025] It should be understood that although Figure 1 the steps in the flowchart of Figure 1 are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless there is a clear indication in this article, the execution of these steps has no strict order limit, and these steps can be executed in other orders. Moreover,

[0026] The technical features of the above embodiments can be combined arbitrarily. For the sake of concise description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope recorded in this specification.

[0027] The above-described embodiments merely represent several implementation manners of the present application. The description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the present application. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present application, several modifications and improvements can still be made, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the appended claims.

Claims

1. A method for discretizing and encoding irregular triangular grids of electromagnetic metasurfaces, characterized in that: The method comprises: Using a meshing algorithm to perform unstructured triangular meshing on the electromagnetic metasurface to be designed and extract all triangular meshes; Clustering all the triangular meshes to obtain a plurality of common edges; designing a binary vector, encoding the common edge according to the binary vector, and determining the filling medium of the triangular meshes on both sides of the common edge according to the encoding value; when the filling medium of the triangular mesh conflicts due to encoding, using an OR logical relationship to perform constraint integration; A multi-value vector is designed to encode the loading devices on the triangular meshes on both sides of the common edge, and the encoding value of the loading devices is adjusted according to the encoding of the common edge. The two are combined to realize the comprehensive structural encoding of the electromagnetic metasurface to be designed.

2. The method according to claim 1, characterized in that Clustering all the triangular meshes to obtain multiple common edges, including: Cluster all triangular meshes, and classify every two triangular meshes with common edges into a pair. The common edges of these two triangular meshes are recorded as , N It is the sum of the number of all triangle mesh pairs with common edges, which are the objects of subsequent encoding.

3. The method according to claim 1, characterized in that Designing a binary vector, and encoding the common edge according to the binary vector, comprising: Design a 1×N dimensional binary vector, that is, each element in the vector has a value of 0 or 1, where "0" represents that the triangular mesh faces on both sides of the common edge are filled with air, and "1" represents that they are filled with metal.

4. The method according to claim 3, characterized in that When the triangle mesh filling medium conflicts due to coding, the constraint integration is performed using OR logical relationships, including: If any one of the common edges of a triangle mesh is coded as 1, the triangle mesh is filled with metal.

5. The method according to claim 1, characterized in that A multi-value vector is designed to encode the loading devices on the triangular meshes on both sides of the common edge, and the encoding value of the loading device is adjusted according to the encoding of the common edge. The combination of the two realizes the comprehensive structural encoding of the electromagnetic metasurface to be designed, including: Design a 1× N dimensional multi-valued vector, encoding the loading devices on the triangular meshes on both sides of the common edge. Each element of the vector is a positive integer between 0 and 4, "0" means no loading, "1" means loading a PIN diode, "2" means loading a capacitor, "3" means loading an inductor, and "4" means loading a resistor.

6. The method according to claim 5, characterized in that The method further comprises: The loading devices on the triangular meshes on both sides of the common edge are encoded. Combined with the encoding of the common edge, the electromagnetic metasurface to be designed is discretized into a 2×N-dimensional encoding vector. The first row of encoding represents the structural form of the metal patch, and its value is 0 or 1; the second row of encoding represents the loading condition of the lumped element, and its value range is an integer between 0 and 4, among which the encoding value of the second row is constrained by the first row. Only when the encoding of the first row is 1, the encoding of the second row can take a non-zero value.

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