A metasurface scattering behavior analysis method, device, equipment and storage medium

Abstract

The present application relates to the technical field of computational electromagnetics, and in particular to a metasurface scattering behavior analysis method, device, equipment and storage medium. The method comprises: tracking an incident wave incident into a metasurface based on geometric optics; for the tracked incident wave, determining a first relationship between an equivalent surface current and a scattering field based on physical optics; determining the equivalent surface current based on a generalized boundary condition and a surface polarizability model; and determining the scattering field by using Gordon integration in combination with the equivalent surface current and the first relationship. The metasurface scattering behavior analysis method provided by the present application can effectively analyze the scattering behavior of a metasurface target by combining the surface polarizability model with physical optics and geometric optics, while reducing the amount of calculation.

Description

Technical Field

[0001] This invention relates to the field of computational electromagnetics, specifically to a method, apparatus, device, and storage medium for analyzing metasurface scattering behavior. Background Technology

[0002] Currently, metasurfaces have been widely used in microwave systems and antennas, radar and satellite communications, and 5G mobile communication systems. Metasurfaces involve interface scattering composed of many discrete units. However, due to the large-scale characteristics of metasurfaces (spanning tens or more wavelengths) and the fact that metasurfaces are composed of non-uniformly arranged resonant particles with fine structures, the analysis of metasurfaces places a huge burden on limited computational resources and is a major challenge.

[0003] Currently, there are many techniques available for analyzing metasurfaces, which can be categorized into deterministic methods and parametric methods. Commonly used deterministic methods include: methods based on Periodic Boundary Condition (PBC) approximations, direct solvers with fast matrix solving algorithms, matrix reduction strategies, asymptotic methods, and array theory methods. In addition, combining parametric methods with traditional numerical methods is also an effective tool for metasurface analysis.

[0004] However, these methods face many challenges in practical applications when metasurfaces are part of larger scattering systems. Examples include frequency-selective surfaces mounted on antennas to reduce backscattering and reconfigurable smart metasurfaces on walls to enhance wireless signal propagation in built-up areas. The increasing complexity of field interactions necessitates multi-scale field methods and new analytical techniques, ranging from subwavelength unit-level to system-level approaches. Summary of the Invention

[0005] In view of this, the present invention provides a method, apparatus, device and storage medium for analyzing metasurface scattering behavior, in order to solve the problem that current techniques for analyzing metasurfaces are not applicable when metasurfaces are used in large scattering systems.

[0006] In a first aspect, the present invention provides a method for analyzing the scattering behavior of a metasurface, the method comprising: tracking an incident wave incident on the metasurface based on geometric optics; determining a first relationship between the equivalent surface current and the scattering field based on physical optics for the tracked incident wave; determining the equivalent surface current based on generalized boundary conditions and a surface polarizability model; and determining the scattering field by using Gordon integrals in combination with the equivalent surface current and the first relationship.

[0007] The metasurface scattering behavior analysis method provided in this invention combines the surface polarizability model with physical optics and geometric optics, which can effectively analyze the scattering behavior of metasurface targets while reducing the amount of computation.

[0008] In one alternative implementation, tracking an incident wave incident on a metasurface based on geometric optics includes: determining the propagation path of the incident wave in the metasurface based on geometric optics; and tracking the electric field within the metasurface based on the propagation path.

[0009] In this embodiment, when tracking the incident wave, the propagation path of the incident wave is first determined based on geometric optics, and then the electric field is tracked based on the propagation path, which provides a basis for subsequent analysis based on the tracked electric field.

[0010] In one alternative implementation, the electric field within the metasurface is tracked according to the propagation path, including: determining the intersection point between the incident wave and the metasurface as the wave propagates in the metasurface according to the propagation path; updating the electric field within the metasurface based on the intersection point, the electromagnetic wave propagation vector, the divergence factor, and the reflection coefficient, wherein the reflection coefficient is a function of the surface polarizability and is determined using a surface polarizability model.

[0011] In this embodiment, when tracking the electric field, the electric field is updated based on the intersection point of the incident wave with the metasurface each time and the relevant parameters, which ensures the accuracy of the electric field tracking.

[0012] In one alternative implementation, for the tracked incident wave, a first relationship between the equivalent surface current and the scattered field is determined based on physical optics, including: determining a second relationship between the radiation scattering field, electric field, and magnetic field of the metasurface using the Straton-Juran formula; and simplifying the second relationship between the radiation scattering field, electric field, and magnetic field based on the relationship between the magnetic field, surface current, and surface field, as well as the magnetic field discontinuity in the metasurface, to obtain the first relationship between the equivalent surface current and the scattered field.

[0013] In this embodiment, the first relationship is determined by analyzing and determining it using the Straton-Juran formula in physical optics, thus realizing the analysis of the incident wave by combining physical optics.

[0014] In one alternative implementation, the equivalent surface current is determined based on generalized boundary conditions and a surface polarizability model, including: determining a third relationship between the surface current and the surface polarizability model based on generalized boundary conditions; transforming the third relationship according to the characteristics of plane waves; and combining a fourth relationship between admittance and scattering parameters and a fifth relationship between electric field and scattering parameters to determine the equivalent surface current of the metasurface.

[0015] In this embodiment, the metasurface is modeled based on generalized boundary conditions, and the relationship between the corresponding surface polarizability model and the equivalent surface current is determined, providing a basis for determining the equivalent surface current.

[0016] In one optional implementation, determining the equivalent surface current based on generalized boundary conditions and a surface polarizability model further includes: when the incident wave is in a preset polarization mode, determining the admittance using a transformed third relation; substituting the determined admittance into a fourth relation to calculate the scattering parameters; and substituting the calculated scattering parameters into a fifth relation, combined with the fourth relation, to obtain the equivalent surface current.

[0017] In this embodiment, the incident wave under the preset polarization mode is analyzed, and the calculation method of the equivalent surface current under the preset polarization mode is determined, thus realizing the determination of the equivalent surface current under different conditions.

[0018] In an alternative implementation, the method further includes: calculating the bistatic radar cross section based on the scattered field.

[0019] In this embodiment, the calculation of the bistatic radar interface provides a data foundation for the analysis of applying metasurfaces to bistatic radar.

[0020] Secondly, the present invention provides a metasurface scattering behavior analysis device, the device comprising: a tracking module for tracking an incident wave incident on a metasurface based on geometric optics; a relationship determination module for determining a first relationship between the equivalent surface current and the scattering field for the tracked incident wave based on physical optics; a current determination module for determining the equivalent surface current based on generalized boundary conditions and a surface polarizability model; and a scattering field determination module for determining the scattering field by using Gordon integrals, combined with the equivalent surface current and the first relationship.

[0021] Thirdly, the present invention provides a computer device, comprising: a memory and a processor, wherein the memory and the processor are communicatively connected to each other, the memory stores computer instructions, and the processor executes the computer instructions to perform the metasurface scattering behavior analysis method of the first aspect or any corresponding embodiment described above.

[0022] Fourthly, the present invention provides a computer-readable storage medium storing computer instructions for causing a computer to execute the metasurface scattering behavior analysis method of the first aspect or any corresponding embodiment thereof. Attached Figure Description

[0023] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0024] Figure 1This is a schematic flowchart of a metasurface scattering behavior analysis method according to an embodiment of the present invention;

[0025] Figure 2 This is a schematic diagram of the possible path of a ray of light in the geometry of an embodiment of the present invention;

[0026] Figure 3 This is a schematic diagram of the vector direction in a closed surface according to an embodiment of the present invention;

[0027] Figure 4 This is a schematic diagram of the vectors involved in Gordon's integral in a triangular mesh according to an embodiment of the present invention;

[0028] Figure 5 This is a schematic diagram of the scattering unit configuration in a uniform array according to an embodiment of the present invention;

[0029] Figure 6 This is a schematic diagram of the bistatic RCS results of a uniform array under s (or TE) polarization according to an embodiment of the present invention.

[0030] Figure 7 This is a schematic diagram of the bistatic RCS results of a uniform array under p (or TM) polarization according to an embodiment of the present invention.

[0031] Figure 8 This is a schematic diagram of the scatterer configuration in a gradient array according to an embodiment of the present invention;

[0032] Figure 9 This is a schematic diagram of the bistatic RCS of a gradient array observed in the xoz plane according to an embodiment of the present invention;

[0033] Figure 10 This is a schematic diagram of the structure of a dihedral reflector according to an embodiment of the present invention;

[0034] Figure 11 This is a schematic diagram comparing the RCS value of the dihedral reflector according to an embodiment of the present invention with the value obtained by CST simulation;

[0035] Figure 12 This is a schematic diagram of a bistatic RCS with p (or TM) polarization according to an embodiment of the present invention;

[0036] Figure 13 This is a structural block diagram of a metasurface scattering behavior analysis device according to an embodiment of the present invention;

[0037] Figure 14 This is a schematic diagram of the hardware structure of a computer device according to an embodiment of the present invention. Detailed Implementation

[0038] 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. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0039] As mentioned in the background section, the increasing complexity of field interactions necessitates multi-scale field methods and new analytical techniques, ranging from subwavelength unit-level to system-level. Given the ability of combining geometrical optics (GO) and physical optics (PO) to perform rapid scattering analysis in complex environments, a method has emerged to analyze complex environments involving metasurfaces. This method combines the surface susceptibility model (SSM) with a unified asymptotic description of surface scattering from physical optics (PO). However, this method assumes that the surface susceptibility is a continuous mathematical function, which is inconsistent with the discrete distribution and unknown nature of SSM parameters in real metasurfaces.

[0040] According to an embodiment of the present invention, a method for analyzing metasurface scattering behavior is provided. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. Furthermore, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than that shown here.

[0041] This embodiment provides a method for analyzing the scattering behavior of metasurfaces, which can be used in electronic devices such as computers, mobile phones, and tablets. Figure 1 This is a flowchart of a metasurface scattering behavior analysis method according to an embodiment of the present invention, such as... Figure 1 As shown, the process includes the following steps:

[0042] Step S101: Track the incident wave into the metasurface based on geometric optics.

[0043] Specifically, a metasurface is an artificially layered material with a thickness less than the wavelength. Metasurfaces allow for flexible and effective control over the polarization, amplitude, phase, polarization, and propagation mode of electromagnetic waves. A metasurface can be considered a two-dimensional counterpart of a metamaterial. The incident wave entering a metasurface can be a ray emitted from a ray tube, which is also an electromagnetic wave. Therefore, when the ray propagates within the metasurface, it is modulated and altered by the metasurface.

[0044] Furthermore, when an incident wave propagates through a metasurface, it undergoes reflection, allowing for the tracking of the incident wave using geometrical optics. In geometrical optics, the object points that make up the surface are considered geometric points, and the beam of light emitted from it is seen as a collection of countless geometric rays, with the direction of the rays representing the direction of light energy propagation. Since light is also a type of electromagnetic wave, geometrical optics can be used to determine the propagation direction of the incident wave, thereby enabling its tracking.

[0045] Step S102: For the tracked incident wave, determine the first relationship between the equivalent surface current and the scattered field based on physical optics.

[0046] Since the incident wave is an electromagnetic wave, and electromagnetic waves are oscillating particle waves derived from in-phase and mutually perpendicular electric and magnetic fields emitted in space, propagating in wave form, the incident wave contains both electric and magnetic fields. Therefore, physical optics can be used to analyze the electric and magnetic fields in the incident wave. Physical optics considers light to be an electromagnetic wave with wave-particle duality. It uses physical theories such as the wave equation and Maxwell's equations to study the propagation, interference, and diffraction of light. Physical optics emphasizes the wave and electromagnetic properties of light, involving the propagation, diffraction, interference, and polarization of electromagnetic waves.

[0047] In this embodiment, the metasurface can be an electromagnetic metasurface used in antennas, radar, or microwave devices. This metasurface can be composed of scatterers to achieve scattering and manipulation of electromagnetic waves. Therefore, for electromagnetic waves incident on the metasurface, physical optics can be used to analyze them and determine the relationship between their electric and magnetic fields. Simultaneously, the relationship between the equivalent surface current and the scattered field (i.e., the first relationship) can be determined by linking the magnetic field and the surface current with the surface field.

[0048] Step S103: Determine the equivalent surface current based on the generalized boundary conditions and the surface polarizability model.

[0049] Generalized Sheet Transition Conditions (GSTCs) are a method applied to the analysis of electromagnetic field boundary conditions in ultrathin layer structures. Based on the derivative expansion of the Dirac distribution, they characterize the discontinuities on both sides of the ultrathin layer structure. Polarizability is used to represent the structure and electromagnetic parameters of the ultrathin layer, thus linking the "microscopic" structure with the macroscopic polarizability, and describing the overall electromagnetic properties of the ultrathin layer using an equivalent method. Therefore, GSTCs are used to model the metasurface in this embodiment. Then, the discrete surface polarizability parameters corresponding to the actual metasurface are combined with physical optics methods in the form of equivalent surface currents. That is, the relationship between the surface polarizability model and the equivalent surface current can be determined through generalized boundary conditions, and the equivalent surface current can be determined from this relationship.

[0050] Step S104: The Gordon integral is used to determine the scattered field by combining the equivalent surface current and the first relation. Specifically, substituting the obtained equivalent surface current into the first relation yields the scattered field, but this scattered field is in the form of a surface integral. Therefore, the Gordon integral can be used to transform the surface integral into a line integral, thereby determining the specific scattered field.

[0051] The metasurface scattering behavior analysis method provided in this invention combines the surface polarizability model with physical optics and geometric optics, which can effectively analyze the scattering behavior of metasurface targets while reducing the amount of computation.

[0052] This embodiment provides a method for analyzing the scattering behavior of metasurfaces, the process of which includes the following steps:

[0053] Step S201: Track the incident wave into the metasurface based on geometric optics.

[0054] Specifically, step S201 includes:

[0055] Step S2011: Determine the propagation path of the incident wave within the metasurface based on geometric optics; specifically, Figure 2 This demonstrates the possible path a ray of light can bounce off within the geometry. Specifically, E i (r j ) is one of the incident waves that enters the metasurface, enters the target, and is then reflected by the target, where r j It is the position vector of the intersection point I. The reflected ray tube becomes the new incident ray E. i (r j+1 ), fired into the other side of the target and located at r j+1 The rays intersect at point Q, and the new incident rays are reflected again until they leave the target.

[0056] Assuming the target is locally homogeneous, the direction of reflection can be determined using Snell's law. The calculation formula is:

[0057]

[0058] in It is position r j The incident direction, in this embodiment, is the normalized vector from the intersection point I to the starting point P. It is the direction of the normal to the intersecting plane. Assuming a1, a2, a3 are the vertices of an intersecting triangle arranged counter-clockwise, the normal vector in (1) can be calculated using the following formula:

[0059]

[0060] Therefore, when the target is a metasurface, the same method can be used to determine the propagation path of the incident wave in the metasurface, thereby achieving the tracking of the incident wave.

[0061] Step S2012: Track the electric field within the metasurface according to the propagation path.

[0062] In an optional implementation, step S2012 includes:

[0063] Step a1: Based on the propagation path, determine the intersection point between the incident wave and the metasurface during propagation; specifically, based on the propagation path determined in step S2011 above, the location information r of the intersection point between the incident wave and the metasurface can be determined. j .

[0064] Step a2: Update the electric field within the metasurface based on the intersection point, electromagnetic wave propagation vector, divergence factor, and reflection coefficient. The reflection coefficient is a function of the surface polarizability and is determined using the surface polarizability model.

[0065] In the process of tracking the incident wave, the field amplitude and phase can be tracked and recorded. Specifically, the amplitude, phase, and polarization of the electric field are updated using the following equations:

[0066]

[0067] Where e is the natural logarithm, k is the electromagnetic propagation vector, and DF j This is the divergence factor that controls the propagation of the ray tube. It applies to curved surfaces, and its value is 1 for planes. The center point is located at r jThe reflection coefficient of the intersecting triangular surfaces is typically -1 in the traditional GO / PO method. In this embodiment, it is a function of surface polarizability and is evaluated using the surface polarizability model (SSM).

[0068] The incident wave is tracked and updated according to the above process until it leaves the target or reaches the maximum number of intersections.

[0069] Step S202: For the tracked incident wave, determine the first relationship between the equivalent surface current and the scattered field based on physical optics.

[0070] Specifically, step S202 includes:

[0071] Step S2021 involves using the Stratton-Chu equation to determine the second relationship between the radiation scattering field, electric field, and magnetic field of the metasurface. Specifically, during the incident wave tracing process, when the incident wave intersects the metasurface, the physical optics equations can be executed within the intersection triangle to determine the scattering field. The principle of these physical optics equations comes from a special case of the Stratton-Chu equations, which are applicable to electric fields outside a bounded, source-free spatial region. The radiation scattering field of the surface can be expressed as follows:

[0072]

[0073] Formula (4) is the second relationship, where E is the electric field strength, H is the magnetic field strength, and η0 is the free space wave impedance. is the normal vector of the intersecting planes, and r is the vector from the intersection point to the observation point. Let S be the normalization direction of r. + +S - Forming a closed surface S, such as Figure 3 As shown.

[0074] Step S2022: Based on the relationship between magnetic field, surface current and surface field and the magnetic discontinuity in metasurface, the second relationship between radiation scattering field and electric field and magnetic field is simplified to obtain the first relationship between equivalent surface current and scattering field.

[0075] Specifically, by relating the magnetic field and surface current to the tangential component of the surface field, equation (4) is transformed into:

[0076]

[0077] J m It is the equivalent magnetic current, J e It is the equivalent current.

[0078] At the starting point, we only consider metasurfaces composed of a single layer or infinitely thin surfaces, where only magnetic field discontinuities exist. Equation (5) can then be simplified to:

[0079]

[0080] Formula (6) is the first relation.

[0081] Step S203: Determine the equivalent surface current based on generalized boundary conditions and the surface polarizability model; specifically, in this embodiment, the metasurface is composed of scatterers of isolated perfect electric conductors (PECs). Continuing to analyze this problem using the traditional PO equations would require a fine mesh to construct a detailed PEC model. Therefore, an SSM is used to evaluate the surface current.

[0082] Specifically, step S203 includes:

[0083] Step S2031: Determine the third relationship between the surface current and surface polarizability model based on generalized boundary conditions; specifically, the relationship between surface current and SSM is derived from GSTCs. When dealing with metasurfaces composed of PECs, the relationship can be expressed as follows: The equation can be expressed in matrix form as follows:

[0084]

[0085] Where x, y, and z are three directions in a rectangular coordinate system, and e and m represent the electric and magnetic fields, respectively. The SSM parameters of the electric field in the x-direction are given; ω is the angular momentum, ∈0 is the dielectric constant in air, ΔH represents the difference in electromagnetic fields across the two sides of the sheet, the subscript "av" indicates the mean field across the metasurface, and the subscript "∥" indicates... The horizontal component, Equal to surface current density J s , It is the surface polarization density, M z It is the surface magnetic polarization density.

[0086] Step S2032: Transform the third relationship according to the characteristics of plane waves, and combine the fourth relationship between admittance and scattering parameters and the fifth relationship between electric field and scattering parameters to determine the equivalent surface current of the metasurface.

[0087] Specifically, based on the characteristics of plane waves, namely (in (where η is the unit wave vector and η0 is the free space wave impedance), transforming equation (7) above into:

[0088]

[0089] Where k x and k y It is the transverse wavenumber. Let admittance be the denominator. Then, using the relationship between admittance and scattering parameters, the reflection and transmission coefficients can be expressed as:

[0090]

[0091]

[0092] Where (ab) = (xx,xy,yx,yy), The ratio of the tangential electric field to the magnetic field is called the wave impedance, which is derived from the wave impedance of a plane wave. (μ0 is the permeability of air) and the incident angle are determined. It should be noted that the scattering parameters are network parameters based on the relationship between the incident microwave and the reflected microwave. These scattering parameters include the reflection coefficient and the transmission coefficient. That is, the S-parameters are expressed in the form of complex amplitude (including amplitude and phase) to represent the reflection and transmission coefficients.

[0093] The average field in equation (8) can be calculated using the following formula, that is, the relationship between the electric field and the reflection coefficient and transmission coefficient in the scattering parameters can be expressed as:

[0094]

[0095] When calculating the equivalent surface current, equations (9a) and (9b) can be substituted into equation (10), and then equation (10) can be substituted into equation (8) to determine the equivalent surface current of the metasurface.

[0096] Furthermore, when the scatterer constituting the metasurface is symmetrical and the incident wave is s-polarized (or TE (transverse electric field)) or p-polarized (or TM (transverse magnetic field)), the admittance can be calculated using the above formula (8), and then the scattering parameters can be calculated using the calculated admittance, and the equivalent surface current can be further calculated. Specifically, taking the incident wave as s-polarized (or TE (transverse electric field)) as an example, the calculation process is explained as follows:

[0097] Step b1: When the incident wave is in a preset polarization mode, the admittance is determined by the transformed third relation. Specifically, when the incident wave is s-polarized (or TE (transverse electric field)), the admittance can be determined based on the characteristics of the incident wave and the above formula (8).

[0098] Step b2: Substitute the determined admittance into the fourth relation to calculate the scattering parameters; specifically, substitute the calculated admittance into equations (9a) and (9b) to obtain the reflection coefficient and transmission coefficient in the scattering parameters as shown in the following equations:

[0099]

[0100]

[0101] Step b3: Substitute the calculated scattering parameters into the fifth relation and combine them with the fourth relation to obtain the equivalent surface current. Specifically, substitute the calculated scattering parameters, i.e., equations (11a) and (11b), into equation (10), and then, guided by equations (9a) and (9b), obtain the final result of the equivalent surface current, as shown below:

[0102]

[0103] Where Z0=η0 / cos(θ) i ), θ i It is the angle of incidence.

[0104] Step S204: The Gordon integral is used to determine the scattering field by combining the equivalent surface current and the first relation. Specifically, the obtained equivalent surface current is substituted into the first relation, i.e., equation (6), where the integration region is specified as being within a single unit cell. The direction is assumed to be... The central ray of the ray tube hits point r0 and... Observe at a distance R along the direction (normalized direction of r) (e.g.) Figure 2 As shown), the phase of the electric field scattered from this intersecting aperture can be approximated as... This indicates that the vector operation in equation (6) can be extracted from the integral symbol. Therefore, substituting the equivalent surface current evaluated by SSM into equation (6) yields:

[0105]

[0106] It simplifies to, r ′ The field within the specified region has the same amplitude as the field associated with the central ray, and there is a linear phase change throughout the region. Then, the surface integral in equation (13) can be simplified to a closed-form expression that does not involve integration, according to the Gordon method. The Gordon method can transform the surface integral into a line integral. Furthermore, this method has no requirements on the size and shape of the integration region; the scattering object can be approximated by a mesh of any shape and size. For example, a triangular mesh... Figure 4 The vectors involved in Gordon's integral are given. Let the vertices of the triangle be a1, a2, a3 arranged counterclockwise, and define... for The projection onto the triangle, and let According to Gordon's method, the surface integral in equation (13) can be calculated using the following formula:

[0107]

[0108] in,

[0109]

[0110] Δa n =a n+1 -a n n = 1, 2, 3 (16)

[0111] And set a4 = a1.

[0112] If the incident wave is perpendicular to the triangle, then w = 0. In this case, the integral equals the area of ​​the triangle, that is:

[0113]

[0114] At this point, the physical optical integral resulting from the intersection of the triangular ray tube and the target can be efficiently calculated using the Gordon method. Furthermore, the mesh can be of various shapes. If the mesh is square, the integral can be calculated in a similar manner:

[0115]

[0116] The number of edges changes from 3 to 4. Because many metasurfaces are constructed using square lattice cells, a square grid is chosen in this embodiment to analyze the non-uniform array. Thus, the scattering field is obtained.

[0117] This embodiment provides a method for analyzing the scattering behavior of metasurfaces, which includes the following steps:

[0118] Step S301: Track the incident wave incident on the metasurface based on geometric optics; for details, please refer to [link to relevant documentation]. Figure 1 Step S101 of the illustrated embodiment will not be described again here.

[0119] Step S302: For the tracked incident wave, determine the first relationship between the equivalent surface current and the scattered field based on physical optics; see [link to details] for more information. Figure 1 Step S102 of the illustrated embodiment will not be described again here.

[0120] Step S303: Determine the equivalent surface current based on the generalized boundary conditions and the surface polarizability model; for details, please refer to [link to relevant documentation]. Figure 1 Step S103 of the illustrated embodiment will not be described again here.

[0121] Step S304: The scattering field is determined using Gordon integration, combined with the equivalent surface current and the first relation. For details, please refer to [link to relevant documentation]. Figure 1 Step S104 of the illustrated embodiment will not be described again here.

[0122] Step S305: Calculate the bistatic radar cross section based on the scattered field. Specifically, when this metasurface is applied to radar, in order to gain a deeper understanding of the scattering characteristics, the bistatic radar cross section (RCS) can also be calculated based on the following formula:

[0123]

[0124] Bistatic radar can be defined as a radar where the transmitter and receiver are located in different positions. From the perspective of radar target detection, the bistatic radar interface reflects whether the target is easily detected by the radar. Therefore, the characteristics of bistatic radar are analyzed through the calculated bistatic radar interface.

[0125] To address the multi-scale scattering problem of metasurfaces, this invention proposes a method for analyzing the scattering behavior of metasurfaces. This method utilizes the polarizability tensor parameters of homogeneous surfaces. The analysis is performed in conjunction with PO / GO. Specifically, this method first extracts the homogeneous surface polarizability tensor parameters from the metasurface and models the metasurface based on generalized sheet transition conditions (GSTCs). Then, the discrete surface polarizability parameters corresponding to the actual metasurface are combined with the PO method in the form of equivalent surface currents, allowing the calculation of the metasurface scattering field using physical optics (PO) surface integrals (calculated using the Gordon method), followed by evaluation of multiple reflections using geometrical optics (GO). This improves the efficiency of metasurface scattering analysis, especially in complex environments.

[0126] The metasurface scattering behavior analysis method provided in this embodiment begins by emitting a ray tube and determining whether the ray intersects with the target. After intersection, the equivalent surface current is calculated using the SSM (Surface-Side Array Model) and then integrated into the PO (Poisson-Oxley) equation. The scattered field is calculated using the Gordon method. Subsequently, the direction, amplitude, and phase of the ray are updated using the GO (Gross-Oriented Array) technique. These steps are iterated until the ray leaves the target or reaches the maximum number of intersection points.

[0127] To demonstrate the accuracy, efficiency, and versatility of the proposed method, uniform arrays, gradient arrays, and dihedrals composed of two perpendicular metasurfaces were analyzed and validated. For validation, the results were compared with brute-force simulations performed using the commercial software CST (Computer Simulation Technology). The CST simulation was executed on a workstation with 128 GB of RAM, while the PO+GO+SSM simulation (the method used in this embodiment) was executed on a standard personal computer.

[0128] (1) Uniform Array Analysis

[0129] First, we verified a uniform planar array composed of identical unit cells. These physical arrays were replaced by SSMs. Electro-liquid crystal scatterers (Electric-LCs) are known for their resonant properties and are commonly used as unit cells in metasurfaces. Therefore, we chose to construct a uniform array using Electric-LC scatterers for analysis.

[0130] like Figure 5 As shown, the array consists of 50×50 scattering elements, with each grid having an area of ​​0.1λ×0.1λ (λ being the free-space wavelength) arranged on the xoy plane. yoz is the incident surface, with an incident angle of 135°.

[0131] We analyze the s (or TE) polarization and p (or TM) polarization separately to thoroughly validate our algorithm. Due to consistency, the integration path of PO with the Gordon integral is not limited by size or shape in this case. Considering the widespread use of triangular meshes, a triangular mesh is employed to describe the target in this example. We scan in the yoz plane and observe the RCS results at f = 12 GHz, as this frequency closely coincides with the resonant frequency of the scatterer.

[0132] Figure 6 Showing Figure 5 The bistatic RCS results of the array under s (or TE) polarization are shown. The RCS results calculated by PO+GO+SSM are compared with those of CST. It can be seen that the RCS is symmetrical with respect to the horizontal plane due to the infinitely thin target. The main lobe is at 225° and 315°, and because the array is uniform, the reflection angle is equal to the incident angle.

[0133] A comparison between PO+GO+SSM and CST shows good consistency in most regions, validating the accuracy of the proposed algorithm. The high accuracy achieved indicates that the PO+GO+SSM method is significantly more efficient than the brute-force simulation in CST and outperforms the traditional PO+GO method. However, slight differences still exist near 90° and 270°. These differences mainly stem from the lack of consideration for edge diffraction, a factor that can be addressed by incorporating Physical Theory of Diffraction (PTD) and its extensions.

[0134] Similarly, the case of p (or TM) polarization is handled in a similar manner. Figure 7 The bistatic RCS data with p (or TM) polarization are shown. The RCS results obtained by the PO+GO+SSM method show strong agreement with the CST results, providing further validation of the effectiveness of the proposed algorithm.

[0135] (2) Gradual Display Analysis

[0136] Figure 8 An example gradient array is shown, with a total size of 3λ × 2λ (λ is the free-space wavelength), consisting of cross-shaped scatterers of size 0.5λ × 0.5λ. It was chosen for its geometric simplicity.

[0137] Figure 9 This shows what is observed in the xoz plane. Figure 8 The bistatic RCS of the array. This mode indicates that the main lobe is oriented in a specific direction, such as... Figure 11 The dashed lines in the diagram highlight the discrepancy. However, the small lobe calculated by the PO+GO+SSM method does not align with the CST results in end-fire. This discrepancy can be attributed to the neglect of edge diffraction and the fact that the SSM used is derived from a simulation with periodic boundary conditions without considering edge effects. Essentially, while each scatterer emits radiation in all directions, the SSM used only considers one of those directions.

[0138] (3) Metasurface Dihedron

[0139] To evaluate the effectiveness of the proposed PO+GO+SSM method in scenarios involving multiple scattering, a dihedral reflector with an interior angle of 90° was further investigated. Compared to a conventional dihedral reflector composed of two PEC plates, the dihedral reflector analyzed in this study was created using two annular LC scatterer arrays. The specific structure is as follows... Figure 10 As shown. The period of each array forming the reflector is 0.1λ (10 GHz), and the side length of each array is 5λ.

[0140] One of the incident ray tubes, representing the incident plane wave, strikes one surface of a dihedral reflector, causing scattering. The resulting scattered ray tube is then directed toward the opposite surface, undergoes another scattering, and eventually exits the dihedral reflector. The PO integral is calculated at each intersection, and the scattered field is calculated by combining the PO integrals of all ray tubes. The incident angle is 135°, and both s (or TE) and p (or TM) polarizations are considered. Since the triangular mesh is uniform in this case, it is used to describe the target. The RCS results are scanned in the yoz plane and observed at f = 12 (GHz), as this frequency is close to the resonant frequency of the scatterer.

[0141] First, the PO+GO+SSM algorithm using s-polarization is applied, meaning the electric field vector is parallel to the latitudinal axis of the dihedral reflector. The bistatic RCS is determined as a function of the elevation angle in a plane perpendicular to the dihedral latitudinal axis. Then, the calculated RCS value of the dihedral reflector is compared with the value obtained from CST simulations, such as... Figure 11 As shown. The PO+GO+SSM results (shown by dashed lines) and CST results (depicted by solid lines) show acceptable agreement. The observed differences can be attributed to edge diffraction caused by inhomogeneities or “edge” currents near each edge.

[0142] Similarly, Figure 12 The bistatic RCS with p (or TM) polarization is shown, where the electric field vector is parallel to the longitudinal plane of the dihedral reflector. Scanning the bistatic RCS on the yoz plane, the PO+GO+SSM results show good agreement with the CST results. Figure 11 and 12 The results presented here serve as conclusive evidence of the accuracy of the proposed method in scenarios involving multiple scattering.

[0143] This embodiment also provides a metasurface scattering behavior analysis device, which is used to implement the above embodiments and preferred embodiments; details already described will not be repeated. As used below, the term "module" can refer to a combination of software and / or hardware that performs a predetermined function. Although the device described in the following embodiments is preferably implemented in software, hardware implementation, or a combination of software and hardware, is also possible and contemplated.

[0144] This embodiment provides a device for analyzing metasurface scattering behavior, such as... Figure 13 As shown, it includes:

[0145] The tracking module is used to track incident waves that have entered the metasurface based on geometric optics.

[0146] The relationship determination module is used to determine the first relationship between the equivalent surface current and the scattered field based on physical optics for the tracked incident wave;

[0147] The current determination module is used to determine the equivalent surface current based on generalized boundary conditions and the surface polarizability model.

[0148] The scattering field determination module is used to determine the scattering field by employing Gordon integrals, combined with the equivalent surface current and the first relation.

[0149] In one optional implementation, the tracking module includes: a path determination module for determining the propagation path of an incident wave into the metasurface based on geometric optics; and a tracking submodule for tracking the electric field within the metasurface according to the propagation path.

[0150] In one alternative implementation, the tracking submodule is specifically used to: determine the intersection point between the incident wave and the metasurface as the wave propagates in the metasurface, based on the propagation path; and update the electric field within the metasurface based on the intersection point, the electromagnetic wave propagation vector, the divergence factor, and the reflection coefficient, wherein the reflection coefficient is a function of the surface polarizability and is determined using a surface polarizability model.

[0151] In one alternative implementation, the relationship determination module is specifically used to: determine the second relationship between the radiation scattering field, electric field, and magnetic field of the metasurface using the Straton-Juran formula; and simplify the second relationship between the radiation scattering field, electric field, and magnetic field based on the relationship between the magnetic field, surface current, and surface field, as well as the magnetic field discontinuity in the metasurface, to obtain the first relationship between the equivalent surface current and the scattering field.

[0152] In one alternative implementation, the current determination module is specifically used to: determine the third relationship between the surface current and the surface polarizability model based on the generalized boundary conditions; transform the third relationship according to the characteristics of the plane wave, and combine the fourth relationship between admittance and scattering parameters and the fifth relationship between electric field and scattering parameters to determine the equivalent surface current of the metasurface.

[0153] In an optional implementation, the current determination module is further configured to: determine the admittance using the transformed third relation when the incident wave is in a preset polarization mode; substitute the determined admittance into the fourth relation to calculate the scattering parameters; substitute the calculated scattering parameters into the fifth relation and combine them with the fourth relation to obtain the equivalent surface current.

[0154] In an alternative implementation, the method further includes a cross-section calculation module for calculating the bistatic radar cross-section based on the scattered field.

[0155] Further functional descriptions of the above modules are the same as those in the corresponding embodiments described above, and will not be repeated here.

[0156] This invention also provides a computer device having the above-described features. Figure 13The apparatus shown is for analyzing metasurface scattering behavior.

[0157] Please see Figure 14 , Figure 14 This is a schematic diagram of the structure of a computer device provided in an optional embodiment of the present invention, such as... Figure 14 As shown, the computer device includes one or more processors 10, memory 20, and interfaces for connecting the components, including high-speed interfaces and low-speed interfaces. The components communicate with each other via different buses and can be mounted on a common motherboard or otherwise installed as needed. The processors can process instructions executed within the computer device, including instructions stored in or on memory to display graphical information of a GUI on external input / output devices (such as display devices coupled to the interfaces). In some alternative implementations, multiple processors and / or multiple buses can be used with multiple memories and multiple memory modules, if desired. Similarly, multiple computer devices can be connected, each providing some of the necessary operations (e.g., as a server array, a group of blade servers, or a multiprocessor system). Figure 14 Take a processor 10 as an example.

[0158] Processor 10 may be a central processing unit, a network processor, or a combination thereof. Processor 10 may further include a hardware chip. The hardware chip may be an application-specific integrated circuit (ASIC), a programmable logic device (PLD), or a combination thereof. The programmable logic device may be a complex programmable logic device (CAMP), a field-programmable gate array (FPGA), a general-purpose array logic (GDA), or any combination thereof.

[0159] The memory 20 stores instructions executable by at least one processor 10 to cause at least one processor 10 to perform the method shown in the above embodiments.

[0160] The memory 20 may include a program storage area and a data storage area. The program storage area may store the operating system and applications required for at least one function; the data storage area may store data created based on the use of the computer device as shown by a landing page for an app. Furthermore, the memory 20 may include high-speed random access memory and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some alternative embodiments, the memory 20 may optionally include memory remotely located relative to the processor 10, which can be connected to the computer device via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0161] The memory 20 may include volatile memory, such as random access memory; the memory may also include non-volatile memory, such as flash memory, hard disk or solid-state drive; the memory 20 may also include a combination of the above types of memory.

[0162] The computer device also includes a communication interface 30 for communicating with other devices or communication networks.

[0163] This invention also provides a computer-readable storage medium. The methods described above according to embodiments of the invention can be implemented in hardware or firmware, or implemented as computer code that can be recorded on a storage medium, or implemented as computer code downloaded via a network and originally stored on a remote storage medium or a non-transitory machine-readable storage medium and then stored on a local storage medium. Thus, the methods described herein can be processed by software stored on a storage medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware. The storage medium can be a magnetic disk, optical disk, read-only memory, random access memory, flash memory, hard disk, or solid-state drive, etc.; further, the storage medium can also include combinations of the above types of memory. It is understood that computers, processors, microprocessor controllers, or programmable hardware include storage components capable of storing or receiving software or computer code, which, when accessed and executed by the computer, processor, or hardware, implements the methods shown in the above embodiments.

[0164] A portion of this invention can be applied as a computer program product, such as computer program instructions, which, when executed by a computer, can invoke or provide the methods and / or technical solutions according to the invention through the operation of the computer. Those skilled in the art will understand that the forms in which computer program instructions exist in a computer-readable medium include, but are not limited to, source files, executable files, installation package files, etc. Correspondingly, the ways in which computer program instructions are executed by a computer include, but are not limited to: the computer directly executing the instructions, or the computer compiling the instructions and then executing the corresponding compiled program, or the computer reading and executing the instructions, or the computer reading and installing the instructions and then executing the corresponding installed program. Here, the computer-readable medium can be any available computer-readable storage medium or communication medium accessible to a computer.

[0165] Although embodiments of the invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the invention, and such modifications and variations all fall within the scope defined by the appended claims.

Claims

1. A method for analyzing the scattering behavior of metasurfaces, characterized in that, The method includes: Step S101: Track the incident wave into the metasurface based on geometric optics; The method of tracking incident waves incident on a metasurface based on geometric optics includes: Determine the propagation path of the incident wave in the metasurface based on geometric optics; The electric field within the metasurface is tracked according to the propagation path. The step of tracking the electric field within the metasurface based on the propagation path includes: Based on the propagation path, determine the intersection point between the incident wave and the metasurface as the wave propagates in the metasurface; The electric field within the metasurface is updated based on the intersection point, electromagnetic wave propagation vector, divergence factor, and reflection coefficient. The reflection coefficient is a function of the surface polarizability and is determined using a surface polarizability model. Step S102: For the tracked incident wave, determine the first relationship between the equivalent surface current and the scattered field based on physical optics; The determination of the first relationship between the equivalent surface current and the scattered field based on physical optics for the tracked incident wave includes: The second relationship between the radiation scattering field, electric field, and magnetic field of the metasurface was determined using the Straton-Juran formula; Based on the relationship between magnetic field, surface current and surface field, and the magnetic field discontinuity in metasurface, the second relationship between radiation scattering field and electric field and magnetic field is simplified to obtain the first relationship between equivalent surface current and scattering field; Step S103: Determine the equivalent surface current based on the generalized boundary conditions and the surface polarizability model; The determination of the equivalent surface current based on generalized boundary conditions and the surface polarizability model includes: The third relationship between the surface current and surface polarizability models is determined based on generalized boundary conditions; The third relationship is transformed based on the characteristics of plane waves, and the equivalent surface current of the metasurface is determined by combining the fourth relationship between admittance and scattering parameters and the fifth relationship between electric field and scattering parameters. Step S104: Use Gordon integral to determine the scattering field by combining the equivalent surface current and the first relationship.

2. The method according to claim 1, characterized in that, Determining the equivalent surface current based on generalized boundary conditions and surface polarizability models also includes: When the incident wave is in a preset polarization mode, the admittance is determined by the transformed third relation; Substituting the determined admittance into the fourth relationship, the scattering parameters are calculated; Substituting the calculated scattering parameters into the fifth relation and combining it with the fourth relation, the equivalent surface current is obtained.

3. The method according to claim 1, characterized in that, The method further includes: The bistatic radar cross section is calculated based on the scattered field.

4. A metasurface scattering behavior analysis apparatus, used to perform a metasurface scattering behavior analysis method as described in any one of claims 1 to 3, characterized in that, The device includes: The tracking module is used to track incident waves that have entered the metasurface based on geometric optics. The relationship determination module is used to determine the first relationship between the equivalent surface current and the scattered field based on physical optics for the tracked incident wave; The current determination module is used to determine the equivalent surface current based on generalized boundary conditions and the surface polarizability model. The scattering field determination module is used to determine the scattering field by employing Gordon integration, combining the equivalent surface current and the first relationship.

5. A computer device, characterized in that, include: A memory and a processor are communicatively connected, the memory stores computer instructions, and the processor executes the computer instructions to perform a metasurface scattering behavior analysis method according to any one of claims 1 to 3.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions for causing a computer to execute a metasurface scattering behavior analysis method according to any one of claims 1 to 3.

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