An electromagnetic metasurface irregular triangular grid discretization and structure encoding method

Abstract

This application relates to a discrete and structural encoding method for an electromagnetic metasurface with irregular triangular meshes. The method includes: performing unstructured triangular mesh division on the electromagnetic metasurface to be designed using a mesh division algorithm and extracting all triangular meshes; clustering all triangular meshes 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 meshes on both sides of the common edge according to the encoded values; when there are encoding conflicts in the filling media of the triangular meshes, using an OR logical relationship for constraint integration; designing a multi-valued vector to encode the loading devices on the triangular meshes 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 combining the two to achieve comprehensive structural encoding of the electromagnetic metasurface to be designed. Using this method, the design flexibility is high, the encoding form is concise and efficient, and the simulation effect on complex structures is better, which can improve the ability to characterize and regulate the polarization characteristics of electromagnetic waves.

Description

Technical Field

[0001] This application relates to the technical field of electromagnetic metamaterials, and in particular, to a method for discretizing irregular triangular grids 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 diverse 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 the regulation of electromagnetic response characteristics 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 are difficult to achieve truly free topological designs. 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. The encoding object is the rectangle grid itself, lacking flexibility in the design of irregular structures, and the ability to characterize and regulate the polarization characteristics of electromagnetic waves is not significant enough. Summary of the Invention

[0004] Based on this, it is necessary to provide a method for discretizing irregular triangular grids and encoding structures of an electromagnetic metasurface, which has high flexibility in the design of irregular structures and can improve the ability to characterize and regulate the polarization characteristics of electromagnetic waves for the above technical problems.

[0005] An irregular triangular grid discretization and structure encoding method for electromagnetic metasurfaces, the method comprising:

[0006] Using a grid meshing algorithm to perform unstructured triangular grid meshing on the electromagnetic metasurface to be designed and extract all triangular grids;

[0007] 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 medium 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 medium of the triangular grids, an OR logical relationship is used for constraint integration;

[0008] 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 value of the loading devices according to the encoding of the common edge, and combining the two to achieve the comprehensive structure encoding of the electromagnetic metasurface to be designed

[0009] The above-mentioned irregular triangular grid discretization and structure encoding method for electromagnetic metasurfaces first uses unstructured triangular grids to discretize the design space. Compared with regular rectangular grids, the shape and layout of triangular grids are more flexible, and 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 medium of the triangular grids on both sides of its 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 encoding forms of regular grids. Finally, the state of the loading devices on the triangular grids on both sides of the common edge is controlled by a multi-valued vector encoding. The common edge encoding form based on the binary vector can perfectly accommodate the encoding design of device loading. Combining the two, only a simple one-dimensional vector can represent physical characteristics such as whether the device is loaded and the type of loaded device. 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

[0010] Figure 1 It is a schematic flow chart of an irregular triangular grid discretization and structure encoding method for an electromagnetic metasurface in an embodiment;

[0011] Figure 2 It 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 and (c) is a schematic diagram of grid symmetric mapping;

[0012] Figure 3 is a schematic diagram of structure encoding and device loading based on a common edge in an embodiment;

[0013] Figure 4 is a schematic diagram of the encoding form to be optimized for an electromagnetic protection metasurface in another embodiment. Detailed implementation manners

[0014] In order to make the objectives, technical solutions and advantages of the present application clearer, 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.

[0015] 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:

[0016] Step 102, using a grid meshing algorithm to perform unstructured triangular meshing on the electromagnetic metasurface to be designed and extract all triangular grids.

[0017] In the existing publicly available technical means, for the discretization of the space to be designed, regular rectangular grids are mostly used, such 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.

[0018] In the present application, unstructured triangular grids are proposed to discretize the design space, such 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 the key to solving the problem of low design flexibility. For the electromagnetic metasurface structure with curved, twisted or irregular boundaries, triangular grids can fit its shape more closely, while rectangular grids may have large 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, such as Figure 2 (c) shown.

[0019] Step 104: Cluster all triangular meshes to obtain multiple common edges; design a binary vector, encode the common edges according to the binary vector, and determine the filling medium of the triangular meshes on both sides of the common edge according to the encoded value; when there is an encoding conflict in the filling medium of the triangular meshes, use the OR logical relationship for constraint integration.

[0020] 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 encoding objects, and the filling medium of the two triangular patches connected to the common edge will be determined according to the encoding characteristics. Considering the randomness of the spatial arrangement of irregular triangular meshes, a pair of triangular meshes controlled by each 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 a 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 there is an encoding conflict, use the OR logical relationship 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 caused by the encoding method based on the common edges of triangular meshes, ensure the uniqueness and accuracy from structure encoding to metal configuration generation, further improve the reliability and stability of the entire encoding system, and enable the encoding method based on the common edges of triangular meshes to be better applied to the actual design of electromagnetic metasurfaces.

[0021] 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 encoded values of the loading devices according to the encoding of the common edge. The combination of the two realizes the comprehensive structure encoding 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 characterize the states 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 metals, allowing device loading; if the common - edge encoding is 0, device loading is not allowed. Therefore, this structure - encoding method based on triangular meshes for the common edge can perfectly accommodate the encoding design of device loading, and only one structure encoding can characterize physical features such as whether a device is loaded and the type of the loaded device. Compared with the traditional encoding method for rectangular meshes, there is no need to design multiple complex encodings for the loading - feature states of different devices, making the encoding form more concise. In practical applications, if different types of devices need to be loaded on the electromagnetic metasurface, the encoding method based on the common edge of triangular meshes can represent different loading situations through a simple change in a single - bit encoding value, while rectangular meshes may require a combination of multiple encoding bits to achieve the same function, resulting in complex encoding and being error - prone.

[0022] The above - mentioned method for discretizing and structurally encoding the irregular triangular meshes of an electromagnetic metasurface first discretizes the design space using unstructured triangular meshes. Compared with regular rectangular meshes, the shape and layout of triangular meshes 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 an electromagnetic metasurface with curved, twisted, or irregular boundaries, triangular meshes can closely fit its shape, greatly improving the design flexibility and overcoming the limitations of rectangular meshes. Then, take the common edge of each pair of triangular meshes as the optimization - encoding object, and control the filling media of the triangular meshes on both sides of its common edge through a binary - vector encoding, thereby realizing the optimized control of the shape of the metal patches on the electromagnetic metasurface. Compared with rectangular meshes, the metal configurations generated based on irregular triangular meshes can achieve a stronger ability to characterize and regulate the polarization characteristics of electromagnetic waves, effectively making up for the deficiencies of traditional methods. Finally, control the states of the loading devices on the triangular meshes on both sides of the common edge through a multi - value - vector encoding. The encoding form based on the binary - vector common - edge can perfectly accommodate the encoding design of device loading. The combination of the two can characterize physical features such as whether a device is loaded and the type of the loaded device with only a simple one - dimensional vector. Compared with the traditional rectangular - mesh encoding that requires a combination of multiple encoding bits to achieve the same function, it greatly simplifies the encoding process and makes the encoding form more concise and efficient.

[0023] In one embodiment, cluster all the triangular meshes to obtain multiple common edges, including:

[0024] Cluster all triangular meshes. Every two triangular meshes with a common edge are grouped into a pair, and the common edge of these two triangular meshes is denoted as , N is the total number of pairs of triangular meshes with common edges, and these common edges are the subsequent coding objects.

[0025] In one embodiment, design a binary vector and encode the common edges according to the binary vector, including:

[0026] 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 mesh patches on both sides of the common edge are filled with air, and "1" represents that they are filled with metal.

[0027] 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 mesh 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 coding. As Figure 3 shown, the red line in the local enlarged 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.

[0028] In one embodiment, during the filling process of the triangular meshes, 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:

[0029] 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.

[0030] In a specific embodiment, based on the coding form of the common edges, 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. As Figure 3 shown in the local enlarged view, 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.

[0031] In one embodiment, a multi - value vector is designed to encode the loading devices on the triangular meshes on both sides of the common edge, and the encoded value of the loading device is regulated according to the encoding of the common edge. The combination of the two realizes the comprehensive structure encoding of the electromagnetic metasurface to be designed, including:

[0032] Design a 1× N N - dimensional multi - value vector to encode the device loading states on the triangular meshes on both sides of the common edge. The value of each element in this encoding vector is a positive integer between 0 and 4. "0" represents no loading, "1" represents loading a PIN diode, "2" represents loading a capacitor, "3" represents loading an inductor, and "4" represents loading a resistor.

[0033] 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 metal structure size. Therefore, when it is loaded on the metal grid, it can be considered that it is bridged across the common edge of a pair of triangular meshes, and the meshes at both ends of the position landing point must be metal, as shown in the Figure 3 local enlarged view. In summary, regarding whether the lumped element is loaded or not, this application designs it as a 1×N - dimensional multi - value vector. The value of each element in the encoding vector is a positive integer between 0 and 4. Among them, "0" represents no loading, "1" represents loading a PIN diode, "2" represents loading a capacitor, "3" represents loading an inductor, "4" represents loading a resistor, etc. In this way, only one - bit encoding 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 performances, and provide support for the design of multi - modal and multi - functional electromagnetic metasurfaces.

[0034] In one embodiment, the loading devices on the triangular meshes on both sides of the common edge are encoded. Combining 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 encoding characterizes the structural form of the metal patch, and its value is 0 or 1; the second - row encoding characterizes the loading situation of the lumped element, and its value range is an integer between 0 and 4. Among them, the encoded value of the second row is restricted 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.

[0035] In a specific embodiment, after the above - mentioned process, the design space to be optimized for the electromagnetic metasurface can be discretized into a 2×N - dimensional encoding vector, as shown in Figure 4Shown as follows: The first row of codes represents the structural form of the metal patch, and its value is 0 or 1; the second row of codes represents the loading condition of the lumped elements, and its value range is an integer between 0 and 4. It should be noted that the value of the second row of codes is not completely free and is affected by the first row of codes. Because on both sides where the lumped elements are loaded, the triangular patches must be metal. That is to say, only when the code in the first row is 1, the code in the second row can take a non-zero value, which is also an inevitable requirement of physical feature constraints.

[0036] Finally, it should be pointed out that Figure 4 The 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 division on the electromagnetic metasurface, a large number of triangular meshes are obtained. The distribution, shape, and connection relationship 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 range of the coding. Without this specific triangular mesh division 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 code 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 converted into computable and controllable digital codes. These codes can not only represent the geometric characteristics 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 for complex structures to achieve richer electromagnetic response characteristics. And the coding form endows the triangular discrete grid with actual physical meaning and functions. By designing and optimizing 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 regular 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.

[0037] It should be understood that although Figure 1The steps in the flowchart are sequentially shown according to the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise clearly stated in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. Moreover, Figure 1 At least some of the steps in Figure 1 may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed alternately or in turn with at least some of the sub-steps or stages of other steps or other steps.

[0038] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of 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 within the scope described in this specification.

[0039] 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. An electromagnetic metasurface irregular triangular grid discretization and structure encoding method, characterized in that The method includes: Performing unstructured triangular mesh division on the electromagnetic metasurface to be designed by using a mesh division algorithm and extracting all triangular meshes; Clustering all the triangular meshes 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 meshes 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 meshes, using an OR logic relationship for constraint integration; designing a binary vector, encoding the common edges according to the binary vector, including: Designing a 1×N-dimensional binary vector, that is, the value of each element in the vector is 0 or 1, where "0" represents that the triangular mesh patches on both sides of the common edge are filled with air, and "1" represents that they are filled with metal; Designing a multi-valued vector to encode the loading devices on the triangular meshes 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 combining the two to achieve the comprehensive structure encoding of the electromagnetic metasurface to be designed; Designing a multi-valued vector to encode the loading devices on the triangular meshes on both sides of the common edge, including; Design a 1× N dimensional multi-valued vector to encode the loading devices on the triangular meshes on both sides of the common edge. Each element of the vector takes a positive integer value 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.

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. Every two triangular meshes with a common edge are grouped into a pair, and the common edge of these two triangular meshes is denoted as l n , n = 1, 2, …, N , N where [total number] is the total number of pairs of triangular meshes with common edges, and these common edges are the subsequent coding objects.

3. The method according to claim 1, characterized in that When there is an encoding conflict in the filling media of the triangular meshes, using an OR logic relationship for constraint integration, including: If among the multiple common edges of a triangular mesh, as long as one encoding is 1, then the triangular mesh is filled with metal.

4. The method according to claim 1, wherein The method further includes: Encoding the loading devices on the triangular meshes on both sides of the common edge. Combining 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 characterizes the structural form of the metal patch, and its value is 0 or 1; the second row of encoding characterizes the loading situation of the lumped elements, and its value range is an integer between 0 and 4. Among them, 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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