Metasurface scattering behavior analysis method, device and equipment and storage medium

Abstract

The invention relates to the technical field of computational electromagnetism, in particular to a metasurface scattering behavior analysis method and device, equipment and a storage medium. The method comprises the following steps: tracking an incident wave emitted into the metasurface based on geometrical optics; for the tracked incident wave, determining a first relationship between the equivalent surface current and the scattered field based on physical optics; determining an equivalent surface current based on the generalized boundary condition and a surface polarizability model; and determining a scattering field by combining the equivalent surface current and the first relationship by adopting Gordon integral. According to the metasurface scattering behavior analysis method provided by the embodiment of the invention, the surface polarizability model is combined with physical optics and geometrical optics, so that the scattering behavior related to the metasurface target can be effectively analyzed, and meanwhile, the calculation amount is reduced.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of computational electromagnetics, and particularly relates to a metasurface scattering behavior analysis method, device, equipment and storage medium. BACKGROUND

[0002] At present, metasurfaces have been widely applied in the fields of microwave systems and antennas, radars and satellite communications, and 5G mobile communication systems. Metasurfaces involve interface scattering composed of many discrete units. However, because of the large-scale characteristics (spanning tens or more wavelengths) of metasurfaces and the fact that metasurfaces are composed of resonant particles with fine structures arranged non-uniformly, the analysis problem of metasurfaces brings a huge burden to limited computing resources and is a major challenge.

[0003] Now, there are many techniques for analyzing metasurfaces, which can be divided into deterministic methods and parametric methods. Common deterministic methods include: methods based on Periodic Boundary Condition (PBC) approximation, direct solvers with fast matrix solution algorithms, matrix reduction strategies, asymptotic methods, and array theory methods; in addition, parametric methods combined with traditional numerical methods are also effective tools for metasurface analysis.

[0004] However, when metasurfaces are part of larger scattering systems, these methods face many challenges in practical applications. For example, frequency-selective surfaces installed on antennas to reduce backscattering and reconfigurable intelligent metasurfaces on walls to enhance wireless signal propagation in building areas. The increase in complexity of field interactions requires multi-scale field methods and new analysis techniques from the subwavelength unit level to the system level. SUMMARY

[0005] Therefore, the present application provides a metasurface scattering behavior analysis method, device, equipment and storage medium to solve the problem that current metasurface analysis techniques are not applicable when metasurfaces are used in larger scattering systems.

[0006] In a first aspect, the present application provides a metasurface scattering behavior analysis method, which comprises: tracking an incident wave incident into a metasurface based on geometric optics; determining a first relationship between an equivalent surface current and a scattering field for the tracked incident wave 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 based on Gordon integration, in combination with the equivalent surface current and the first relationship.

[0007] The metasurface scattering behavior analysis method provided by the embodiments of the present application can effectively analyze the scattering behavior of metasurface targets by combining the surface polarizability model with physical optics and geometric optics, while reducing the amount of calculation.

[0008] In an optional implementation, the tracking of the incident wave into the metasurface based on geometric optics comprises: determining a propagation path of the incident wave into the metasurface in the metasurface based on geometric optics; and tracking the electric field in the metasurface according to 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 tracking of the electric field is realized based on the propagation path, thereby providing a basis for subsequent analysis based on the tracked electric field.

[0010] In an optional implementation, the tracking of the electric field in the metasurface according to the propagation path comprises: determining an intersection point of the incident wave and the metasurface when the incident wave propagates in the metasurface according to the propagation path; and updating the electric field in the metasurface based on the intersection point, an electromagnetic wave propagation vector, a divergence factor, and a reflection coefficient, the reflection coefficient being a function of a surface polarizability, and the reflection coefficient being 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 and the metasurface each time the incident wave intersects the metasurface and related parameters, thereby ensuring the accuracy of the tracking of the electric field.

[0012] In an optional implementation, for the tracked incident wave, a first relationship between an equivalent surface current and a scattering field is determined based on physical optics, comprising: determining a second relationship between a radiative scattering field and electric and magnetic fields of the metasurface using a Stratton-Chu formula; simplifying the second relationship between the radiative scattering field and the electric and magnetic fields based on a relationship among the magnetic field, the surface current, and the surface field and a magnetic field discontinuity in the metasurface, to obtain the first relationship between the equivalent surface current and the scattering field.

[0013] In this embodiment, when determining the first relationship, the analysis and determination are performed by using the Stratton-Chu formula in physical optics, thereby realizing the analysis of the incident wave in combination with physical optics.

[0014] In an optional implementation, the equivalent surface current is determined based on a generalized boundary condition and a surface polarizability model, comprising: determining a third relationship between the surface current and the surface polarizability model based on the generalized boundary condition; transforming the third relationship according to a characteristic of a plane wave, and determining the equivalent surface current of the metasurface in combination with a fourth relationship between an admittance and a scattering parameter and a fifth relationship between the electric field and the scattering parameter.

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

[0016] In an optional implementation, the determining the equivalent surface current based on the generalized boundary condition and the surface polarizability model further comprises: when the incident wave is a preset polarization mode, determining the admittance by using the third relationship after transformation; substituting the determined admittance into a fourth relationship to calculate the scattering parameter; and substituting the calculated scattering parameter into a fifth relationship to obtain the equivalent surface current in combination with the fourth relationship.

[0017] In the embodiment, the calculation manner of the equivalent surface current under the preset polarization mode is determined by analyzing the incident wave under the preset polarization mode, and the determination of the equivalent surface current under different conditions is realized.

[0018] In an optional implementation, the method further comprises: calculating the bistatic radar cross section based on the scattering field.

[0019] In the embodiment, the data basis for analyzing the application of the metasurface to the bistatic radar is provided by calculating the bistatic radar interface.

[0020] In a second aspect, the present application provides a metasurface scattering behavior analysis device, the device comprising: a tracking module configured to track an incident wave incident on a metasurface based on geometric optics; a relationship determining module configured to determine a first relationship between an equivalent surface current and a scattering field based on physical optics for the tracked incident wave; a current determining module configured to determine the equivalent surface current based on a generalized boundary condition and a surface polarizability model; and a scattering field determining module configured to determine the scattering field by using Gordon integration in combination with the equivalent surface current and the first relationship.

[0021] In a third aspect, the present application provides a computer device, comprising: a memory and a processor, which are communicatively connected to each other, and the memory stores computer instructions; the processor executes the computer instructions to perform the metasurface scattering behavior analysis method of the first aspect or any of the corresponding embodiments thereof.

[0022] In a fourth aspect, the present application provides a computer readable storage medium, which stores computer instructions for causing a computer to perform the metasurface scattering behavior analysis method of the first aspect or any of the corresponding embodiments thereof. BRIEF DESCRIPTION OF DRAWINGS

[0023] In order to more clearly illustrate the specific embodiments of the present application or the technical solutions in the prior art, the following will briefly introduce the drawings needed to be used in the description of the specific embodiments or the prior art. Obviously, the drawings described below are some embodiments of the present application, and those skilled in the art can obtain other drawings according to these drawings without creative labor.

[0024] Figure 1is a flowchart of a method for analyzing scattering behavior of a metasurface according to an embodiment of the present application;

[0025] Figure 2 is a schematic diagram of a possible path of a light ray in a geometric body according to an embodiment of the present application;

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

[0027] Figure 4 is a schematic diagram of vectors involved in Gordon integration in a triangular mesh according to an embodiment of the present application;

[0028] Figure 5 is a schematic diagram of scattering elements in a uniform array according to an embodiment of the present application;

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

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

[0031] Figure 8 is a schematic diagram of scattering elements in a tapered array according to an embodiment of the present application;

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

[0033] Figure 10 is a schematic diagram of a dihedral corner reflector according to an embodiment of the present application;

[0034] Figure 11 is a schematic diagram of a comparison of RCS values of a dihedral corner reflector with values obtained by CST simulation according to an embodiment of the present application;

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

[0036] Figure 13 is a block diagram of a device for analyzing scattering behavior of a metasurface according to an embodiment of the present application;

[0037] Figure 14 is a schematic diagram of a hardware structure of a computer device according to an embodiment of the present application. DETAILED DESCRIPTION

[0038] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the following will clearly and completely describe the technical solutions in the embodiments of the present application with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some but not all of the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the protection scope of the present application.

[0039] As in the background, the current increase in the complexity of field interaction requires multi-scale field methods and new analysis techniques from sub-wavelength unit level to system level. And in view of the ability of the combination of physics optics (GO) and geometrical optics (PO) to quickly analyze scattering in a complex environment, an analysis method for a complex environment containing a super surface is proposed, which combines a surface susceptibility model (SSM) with a unified asymptotic description of physical optics (PO) surface scattering. However, this method assumes that the surface susceptibility is a continuous mathematical function, which is inconsistent with the actual super surface having a discrete distribution of SSM parameters and the unknown nature of SSM parameters.

[0040] According to the embodiments of the present application, a super surface scattering behavior analysis method embodiment is provided. It should be noted that the steps shown in the flowchart of the drawings can be executed in a computer system such as a set of computer executable instructions, and although the logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0041] In the present embodiment, a super surface scattering behavior analysis method is provided, which can be used in electronic devices such as computers, mobile phones, tablet computers, etc. Figure 1 The flowchart of the super surface scattering behavior analysis method according to the embodiments of the present application is shown in FIG. 1, which includes the following steps: Figure 1 As shown in FIG. 1, the flowchart includes the following steps:

[0042] In step S101, the incident wave incident into the super surface is tracked based on geometrical optics.

[0043] Specifically, the super surface refers to an artificial layered material with a thickness less than the wavelength. The super surface can realize flexible and effective regulation of the polarization, amplitude, phase, polarization mode, propagation mode and other characteristics of electromagnetic waves. The super surface can be regarded as a two-dimensional counterpart of metamaterial. The incident wave incident into the super surface can be a ray emitted by a ray tube, which is also an electromagnetic wave. Therefore, when the ray is transmitted in the super surface, it will be regulated and changed by the super surface.

[0044] In addition, when the incident wave is transmitted in the metasurface, reflection occurs, and thus the incident wave can be tracked by using geometric optics. In geometric optics, an object point constituting an object is regarded as a geometric point, and a light beam emitted by the object point is regarded as a collection of infinite geometric rays, and the direction of the rays represents the propagation direction of light energy. The rays are also electromagnetic waves, and thus the propagation direction of the incident wave can be determined by using geometric optics to track the incident wave.

[0045] In step S102, for the tracked incident wave, a first relationship between the equivalent surface current and the scattering field is determined based on physical optics.

[0046] In the formula, since the incident wave is an electromagnetic wave, the electromagnetic wave is an oscillation particle wave derived from an electric field and a magnetic field that are in phase and perpendicular to each other and are transmitted in space in a wave form, that is, the incident wave includes an electric field and a magnetic field. Therefore, the electric field and the magnetic field in the incident wave can be analyzed by using physical optics. Physical optics considers that light is an electromagnetic wave and has wave-particle duality. Physical optics uses physical theories such as wave equations and Maxwell equations to study the linearity of light propagation, interference, diffraction, and the like. Physical optics emphasizes the wave nature and electromagnetic properties of light and involves the propagation, diffraction, interference, and polarization of electromagnetic waves.

[0047] The metasurface in the embodiment can be an electromagnetic metasurface applied in an antenna, a radar, or a microwave device. The metasurface can be composed of scatterers to achieve scattering regulation of electromagnetic waves. Therefore, for the electromagnetic wave incident in the metasurface, the electromagnetic wave can be analyzed by using physical optics to determine the relationship between the electric field and the magnetic field. Meanwhile, the relationship between the equivalent surface current and the scattering field, that is, the first relationship, can be determined by the relationship between the magnetic field and the surface current and the surface field.

[0048] In step S103, the equivalent surface current is determined based on a generalized boundary condition and a surface polarizability model.

[0049] The generalized sheet transition conditions (GSTCs) are a method applied to the analysis of ultra-thin layer structures (boundary conditions for electromagnetic fields). The discontinuity on both sides of the ultra-thin layer structure is characterized based on the derivative expansion form of the Dirac distribution, and the structure and electromagnetic parameters of the ultra-thin layer are represented by the polarizability, so as to link the microstructure with the macroscopic polarizability and describe the overall electromagnetic properties of the ultra-thin layer by an equivalent method. Therefore, the GSTCs are used to model the metasurface in the embodiment. Then, the discrete surface polarizability parameters corresponding to the actual metasurface are combined with the physical optics method in the form of equivalent surface current, that is, the relationship between the surface polarizability model and the equivalent surface current is determined by the generalized boundary conditions, and the equivalent surface current is determined from the relationship.

[0050] In step S104, the scattering field is determined by combining the equivalent surface current and the first relationship by using Gordon integration. Specifically, the obtained equivalent surface current is substituted into the first relationship to obtain the scattering field, but the obtained scattering field is in the form of an area integral, and therefore, the Gordon integration can be used to convert the area integral into a line integral, so as to determine the specific scattering field.

[0051] The metasurface scattering behavior analysis method provided in the embodiment can effectively analyze the scattering behavior of the metasurface target by combining the surface polarizability model with the physical optics and the geometrical optics, while reducing the calculation amount.

[0052] In the embodiment, a metasurface scattering behavior analysis method is provided, and the flow includes the following steps:

[0053] In step S201, the incident wave incident on the metasurface is tracked based on the geometrical optics.

[0054] Specifically, step S201 includes the following steps.

[0055] In step S2011, the propagation path of the incident wave incident on the metasurface in the metasurface is determined based on the geometrical optics. Specifically, Figure 2 The path on which a light ray in a geometric body can bounce is shown. Specifically, E i (r j ) is one of the incident waves incident on the metasurface, which enters the target and is then reflected by the target, where r j is the position vector of the intersection point I. The reflected ray becomes a new incident ray E i (r j+1 ), which enters the other side of the target and intersects with the Q point located at r j+1 . The new incident ray is reflected again until it leaves the target.

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

[0057]

[0058] Wherein is the incident direction at position r j , which is the normalized vector from intersection point I to starting point P in this embodiment, is the normal direction of the intersection plane. Assuming that a1, a2, a3 are the vertices of the intersection triangle arranged in a counterclockwise direction, the normal vector in (1) can be calculated as follows:

[0059]

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

[0061] Step S2012, according to the propagation path, tracking the electric field in the metasurface.

[0062] In an optional embodiment, the above step S2012 comprises:

[0063] Step a1, according to the propagation path, determining the intersection point of the incident wave and the metasurface when the incident wave propagates in the metasurface; specifically, according to the transmission path determined in the above step S2011, the position information r j of the intersection point of the incident wave and the metasurface can be determined.

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

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

[0066]

[0067] Wherein, e is the natural logarithm, k is the electromagnetic wave propagation scalar, DF j is the divergence factor controlling the propagation of the ray tube, which is applicable to curved surfaces, and the value of the plane is 1, is the central point located at r jthe reflection coefficient of the intersecting triangular surface, which is taken as -1 in the traditional GO / PO method. In the present embodiment, it is a function of the surface susceptibility, which is evaluated by a surface susceptibility model (SSM), i.e.

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

[0069] At step S202, for the tracked incident wave, a first relationship between the equivalent surface current and the scattered field is determined based on physical optics.

[0070] Specifically, the above step S202 comprises:

[0071] At step S2021, a second relationship between the radiated scattered field and the electric and magnetic fields of the super surface is determined using the Stratton-Chu formula; wherein, in the process of tracking the incident wave, when the incident wave intersects with the super surface, the scattered field can be determined by performing a physical optics equation within the intersecting triangle. The principle of this physical optics equation comes from a special case of the Stratton-Chu formula, which is applicable to the electric field outside a bounded passive space region, and can express the radiated scattered field of the surface as the following formula:

[0072]

[0073] wherein the formula (4) is the second relationship, in which E is the electric field intensity, H is the magnetic field intensity, η0 is the wave impedance of free space, is the normal vector of the intersecting plane, r is the intersecting point pointing to the observation point vector, is the normalized direction of r, S + + S - composes a closed surface S, as shown in Figure 3

[0074] At step S2022, the second relationship between the radiated scattered field and the electric and magnetic fields of the super surface is simplified based on the relationship between the magnetic field, the surface current and the surface field and the magnetic discontinuity in the super surface, to obtain the first relationship between the equivalent surface current and the scattered field.

[0075] Specifically, the tangential components of the magnetic field, the surface current and the surface field are related, and the formula (4) is transformed into:

[0076]

[0077] wherein J m is the equivalent magnetic current, J e is the equivalent electric current. ​

[0078] At the starting point, only single-layer or infinitely thin metasurfaces are considered, where only magnetic field discontinuity exists. Then, equation (5) can be simplified as:

[0079]

[0080] wherein equation (6) is the first relationship.

[0081] At step S203, the equivalent surface current is determined based on the generalized boundary condition and the surface polarizability model; specifically, the metasurface in this embodiment is composed of scatterers of isolated perfect electric conductors (PEC). Continuing to use the traditional PO equation to analyze this problem will require a fine grid to construct a detailed PEC model. Therefore, SSM is used to evaluate the surface current.

[0082] Specifically, the above step S203 includes:

[0083] At step S2031, a third relationship between the surface current and the surface polarizability model is determined based on the generalized boundary condition; specifically, the relationship between the surface current and the SSM is derived from the GSTCs. When dealing with metasurfaces composed of PEC, the relationship therebetween can be expressed as The display matrix form of the equation is as follows:

[0084]

[0085] wherein x, y and z are three directions in a rectangular coordinate system, e and m represent electric field and magnetic field respectively, for example represents the SSM parameter of the electric field in the x direction; ω is the angular momentum, ∈0 is the dielectric constant in air, ΔH represents the difference of electromagnetic field on both sides of the sheet, subscript "av" represents the average field on both sides of the metasurface, and subscript "∥" represents the transverse component of is equal to the surface current density J s , is the surface electric polarization density, M z is the surface magnetic polarization density.

[0086] At step S2032, the third relationship is transformed according to the characteristics of the plane wave, and the equivalent surface current of the metasurface is determined in combination with the fourth relationship between the admittance and the scattering parameter and the fifth relationship between the electric field and the scattering parameter.

[0087] Specifically, according to the characteristics of the plane wave, i.e. (wherein is the unit wave vector, and η0 is the wave impedance in free space), the above equation (7) is transformed as:

[0088]

[0089] where k x and k y is the transverse wave number, represent the admittance. Then, by using the relationship between the admittance and the scattering parameters, the reflection and transmission coefficients can be expressed as:

[0090]

[0091]

[0092] where (ab) = (xx, xy, yx, yy), is the ratio of the tangential electric field to the magnetic field, i.e., the wave impedance, which is determined by the wave impedance of the plane wave (μ0is the magnetic permeability in air) and the incident angle. It should be noted that the scattering parameters are network parameters based on the relationship between the incident microwave and the reflected microwave, and the scattering parameters include the reflection and transmission coefficients, i.e., the S parameters are in the form of complex amplitudes (including amplitudes and phases) to represent the reflection and transmission coefficients.

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

[0094]

[0095] where, in the calculation of the equivalent surface current, equation (9a) and equation (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 super surface.

[0096] In addition, when the scatterers constituting the super surface are symmetrical and the incident wave is s-polarized (or TE (transverse electric)) or p-polarized (or TM (transverse magnetic)), 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 s-polarized (or TE (transverse electric)) incident wave as an example, the calculation process is described as follows:

[0097] Step b1, when the incident wave is a preset polarization mode, the admittance is determined using the transformed third relationship; specifically, when the incident wave is s-polarized (or TE (transverse electric)), the admittance can be determined based on the characteristics of the incident wave and based on the above formula (8).

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

[0099]

[0100]

[0101] Step b3, the calculated scattering parameters are substituted into the fifth relationship to obtain the equivalent surface current in combination with the fourth relationship. Specifically, the calculated scattering parameters, i.e. formula (11a) and formula (11b), are substituted into formula (10), and then under the guidance of formula (9a) and formula (9b), the final result of the equivalent surface current can be obtained as shown below:

[0102]

[0103] wherein Z0=η0 / cos(θ i ), θ i is the incident angle.

[0104] Step S204, the Gordon integral is used to determine the scattering field in combination with the equivalent surface current and the first relationship. Specifically, the obtained equivalent surface current is substituted into the first relationship, i.e. formula (6), wherein the integral region is specified to be within a single unit cell. It is assumed that the central ray of the ray tube in the direction hits the r0point, and is observed at a distance R in the direction (the normalized direction of r) (as shown in ). The phase of the electric field scattered from the intersection aperture can be approximated as This shows that the vector operation in formula (6) can be taken out of the integral sign. Therefore, the equivalent surface current evaluated by the SSM is substituted into formula (6) to obtain:

[0105]

[0106] which is simplified as, r ′ The field in the specified region of the r Figure 2 point has the same amplitude as the field related to the central ray, and there is a linear phase change throughout the region. Then, the surface integral in formula (13) can be simplified to a closed-form expression not involving integration according to the Gordon method. The Gordon method can convert the surface integral into a line integral. In addition, this method has no requirements for the size and shape of the integral region, and the scattering object can be approximated by a grid of any shape and size. Taking a triangular grid as an example, Figure 4 the vectors involved in the Gordon integral are given. Let the vertices of the triangle be arranged counterclockwise as a1, a2, a3, and define as The projection on the triangle, and set According to the method of Gordon, the surface integral in formula (13) can be calculated by the following formula:

[0107]

[0108] Wherein,

[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 is equal to the area of the triangle, that is:

[0113]

[0114] So far, the physical optical integral of the intersection of the triangular ray tube and the target can be effectively calculated using the Gordon method. In addition, the grid can be of various shapes. If the grid is square, the integral can be calculated in a similar manner as follows:

[0115]

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

[0117] In this embodiment, a method for analyzing the scattering behavior of a metasurface is provided, which comprises the following steps:

[0118] Step S301, based on geometric optics, the incident wave incident on the metasurface is tracked; for details, please refer to Figure 1 The step S101 of the embodiment shown in the figure will not be repeated here.

[0119] Step S302, for the tracked incident wave, based on physical optics, determine the first relationship between the equivalent surface current and the scattering field; for details, please refer to Figure 1 The step S102 of the embodiment shown in the figure will not be repeated here.

[0120] Step S303, based on the generalized boundary condition and the surface polarizability model, determine the equivalent surface current; for details, please refer to Figure 1 The step S103 of the embodiment shown in the figure will not be repeated here.

[0121] Step S304, the scattering field is determined by combining the equivalent surface current and the first relationship using Gordon integration. For details, please refer to Figure 1 Step S104 of the embodiment shown will not be described here.

[0122] Step S305, based on the scattering field, the bistatic radar cross section is calculated. Specifically, when the metasurface is applied to radar, in order to deeply understand the scattering characteristics, the bistatic radar cross section (Radar Cross Section, RCS) can also be calculated based on the following formula:

[0123]

[0124] Wherein, the bistatic radar can be defined as a radar in which the transmitter and receiver are located at different positions. From the perspective of radar target detection, the bistatic radar interface reflects whether the target is easy to be detected by the radar. Therefore, the bistatic radar interface obtained by calculation is analyzed for the characteristics of the bistatic radar.

[0125] For the multi-scale scattering problem of the metasurface, the present application provides a metasurface scattering behavior analysis method, which extracts the homogeneous surface polarization tensor parameter Combined with PO / GO for analysis. Specifically, this method first extracts the homogeneous surface polarization tensor parameter from the metasurface, and models the metasurface based on the generalized sheet transition conditions (Generalized Sheet Transition Conditions, GSTCs). Then, the discrete surface polarization parameter corresponding to the actual metasurface is combined with the PO method in the form of equivalent surface current, thereby allowing the use of physical optics (PO) surface integral (calculated using the Gordon method) to calculate the metasurface scattering field, and then using geometric optics (GO) to evaluate multiple reflections. In this way, the efficiency of metasurface scattering analysis is improved, especially in complex environments.

[0126] The metasurface scattering behavior analysis method provided by the embodiment starts from emitting a ray tube and determining whether the ray intersects the target; after intersection, the equivalent surface current is calculated using SSM, and then integrated into the PO equation. The scattering field is calculated by the Gordon method. Subsequently, the direction, amplitude and phase of the light ray are updated using GO technology. These steps are iterated until the ray exits 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 an incident plane wave hits one surface of the dihedral reflector, resulting in a scattering. Then, the resulting scattered ray tube is directed towards the opposite surface, experiences another scattering, and finally exits the dihedral reflector. The PO integrals are computed at each intersection point, and the scattered field is computed by combining each PO integral of all ray tubes. The incident angle is 135°, while both s (or TE) and p (or TM) polarizations are considered. Since the triangular mesh is uniform in this case, it is adopted to describe the target. The RCS results are observed in the yoz plane and at f = 12 (GHz), since this frequency is close to the resonant frequency of the scatterer.

[0141] First, the PO+GO+SSM algorithm using s-polarized field is applied, which means that the electric field vector is parallel to the dihedral reflector's latitude axis. The bistatic RCS is determined as a function of the elevation angle in the plane perpendicular to the dihedral latitude axis. The computed RCS values of the dihedral reflector are then compared with the values obtained from the CST simulation, as shown in Figure 11 The PO+GO+SSM results (indicated with dashed lines) exhibit an acceptable agreement with the CST results (depicted by solid lines). The observed differences can be attributed to the edge diffraction caused by the non-uniform 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 dihedral reflector's longitudinal axis. The bistatic RCS is scanned over the yoz plane, and the PO+GO+SSM results exhibit a good agreement with the CST results. Figure 11 and 12 The results presented in and serve as a decisive evidence of the accuracy of the proposed method in scenarios involving multiple scattering.

[0143] There is also provided in the present embodiment a metasurface scattering behavior analysis apparatus for implementing the above-described embodiments and preferred embodiments, which have been described above. As used below, the term "module" can be a combination of software and / or hardware that implements a predetermined function. Although the apparatus described in the following embodiments is preferably implemented in software, implementation of hardware, or a combination of software and hardware, is also possible and contemplated.

[0144] The present embodiment provides a metasurface scattering behavior analysis apparatus, as shown in Figure 13 comprises:

[0145] a tracing module configured to trace, based on geometric optics, an incident wave impinging on the metasurface;

[0146] a relationship determining module configured to determine, for the traced incident wave, a first relationship between an equivalent surface current and a scattered field based on physical optics;

[0147] a current determination module configured to determine an equivalent surface current based on the generalized boundary condition and the surface polarizability model;

[0148] a scattering field determination module configured to determine a scattering field by employing a Gordon integration in combination with the equivalent surface current and the first relationship.

[0149] In an alternative implementation, the tracking module comprises: a path determination module configured to determine a propagation path of the incident wave in the metasurface based on geometric optics; and a tracking sub-module configured to track the electric field in the metasurface according to the propagation path.

[0150] In an alternative implementation, the tracking sub-module is specifically configured to: determine an intersection of the incident wave with the metasurface during propagation of the incident wave in the metasurface according to the propagation path; and update the electric field in the metasurface based on the intersection, the electromagnetic wave propagation vector, the divergence factor and a reflection coefficient, the reflection coefficient being a function of the surface polarizability, the reflection coefficient being determined by the surface polarizability model.

[0151] In an alternative implementation, the relationship determination module is specifically configured to: determine a second relationship between the radiative scattering field and the electric field and the magnetic field of the metasurface by employing a Stratton-Chu formulation; and simplify the second relationship between the radiative scattering field and the electric field and the magnetic field of the metasurface based on a relationship between the magnetic field, the surface current and the surface field and a magnetic field discontinuity in the metasurface, to obtain the first relationship between the equivalent surface current and the scattering field.

[0152] In an alternative implementation, the current determination module is specifically configured to: determine a third relationship between the surface current and the surface polarizability model based on the generalized boundary condition; transform the third relationship according to a characteristic of the plane wave, in combination with a fourth relationship between the admittance and the scattering parameter and a fifth relationship between the electric field and the scattering parameter, to determine the equivalent surface current of the metasurface.

[0153] In an alternative implementation, the current determination module is further configured to: determine the admittance by employing the transformed third relationship when the incident wave is of a preset polarization mode; substitute the determined admittance into the fourth relationship to calculate the scattering parameter; and substitute the calculated scattering parameter into the fifth relationship, in combination with the fourth relationship, to obtain the equivalent surface current.

[0154] In an alternative implementation, the method further comprises: a cross section calculation module configured to calculate a bistatic radar cross section based on the scattering field.

[0155] Further function descriptions of the above modules are the same as those of the above corresponding embodiments, which are not repeated here.

[0156] The embodiment of the present application further provides a computer device having the above Figure 13The illustrated metasurface scattering behavior analysis device.

[0157] See Figure 14 , Figure 14 is a structural schematic diagram of a computer device provided by an optional embodiment of the present application, as Figure 14 shown, the computer device includes one or more processors 10, a memory 20, and interfaces for connecting various components, including high-speed interfaces and low-speed interfaces. Various components are communicatively connected using different buses, and can be mounted on a common main board or otherwise mounted as needed. The processor can process instructions executed within the computer device, including instructions stored in the memory or on the memory to display graphical information of a GUI on an external input / output device, such as a display device coupled to the interface. In some optional embodiments, multiple processors and / or multiple buses can be used with multiple memories and multiple memory, if desired. Also, multiple computer devices can be connected, each device providing part of the necessary operations (e.g., as a server array, a group of blade servers, or a multi-processor system). Figure 14 The processor 10 is taken as an example in the figure.

[0158] The processor 10 can be a central processor, a network processor, or a combination thereof. The processor 10 can further include a hardware chip. The hardware chip can be an application specific integrated circuit, a programmable logic device, or a combination thereof. The programmable logic device can be a complex programmable logic device, a field programmable logic gate array, a generic array logic, or any combination thereof.

[0159] The memory 20 stores instructions executable by the at least one processor 10 to cause the at least one processor 10 to perform the methods implemented by the above-mentioned embodiments.

[0160] The memory 20 can include a program storage area and a data storage area. The program storage area can store an operating system, application programs required by at least one function; and the data storage area can store data created by use of the computer device according to the display of a small program landing page, and the like. In addition, the memory 20 can include a high-speed random access memory, and can also include a non-transitory memory, such as at least one magnetic disk storage device, a flash memory device, or other non-transitory solid-state memory device. In some optional embodiments, the memory 20 can optionally include a memory disposed remotely with respect to the processor 10, and these remote memories can be connected to the computer device through a network. Examples of the network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and a combination thereof.

[0161] The memory 20 can include a volatile memory, such as a random access memory, and / or a non-volatile memory, such as a flash memory, a hard disk, or a solid state disk. The memory 20 can also include a combination of the above-mentioned types of memories.

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

[0163] The embodiments of the present application also provide a computer readable storage medium, and the method according to the embodiments of the present application can be implemented in hardware, firmware, or recorded in a storage medium, or stored in a remote storage medium or a non-transitory machine readable storage medium and downloaded to a local storage medium through network, so that the method described herein can be processed by such software on a storage medium using a general purpose computer, a special purpose processor, or programmable or special purpose hardware. The storage medium can be a disk, an optical disk, a read-only memory, a random access memory, a flash memory, a hard disk, or a solid state disk, etc. Further, the storage medium can also include a combination of the above-mentioned types of memories. It can be understood that the computer, the processor, the microprocessor controller, or the programmable hardware includes a storage component that can store or receive software or computer code, when the software or computer code is accessed and executed by the computer, the processor, or the hardware, the method shown in the above embodiments is implemented.

[0164] Part of the present application can be applied as a computer program product, for example, computer program instructions, when executed by a computer, through the operation of the computer, the method and / or technical solutions according to the present application can be invoked or provided. Those skilled in the art should understand that the form of computer program instructions in a computer readable medium includes but is not limited to source files, executable files, installation package files, etc. Correspondingly, the way of computer program instructions executed by computer includes but is not limited to: the computer directly executes the instructions, or the computer compiles the instructions and then executes the corresponding compiled program, or the computer reads and executes the instructions, or the computer reads and installs the instructions and then executes the corresponding installed program. Here, the computer readable medium can be any available computer readable storage medium or communication medium accessible to the computer.

[0165] Although the embodiments of the present application are described in conjunction with the accompanying drawings, various modifications and changes can be made by those skilled in the art without departing from the spirit and scope of the present application, and such modifications and changes fall within the scope defined by the appended claims.

Claims

1. A metasurface scattering behavior analysis method, characterized in that, The method comprises: tracking, based on geometric optics, an incident wave entering a metasurface; determining, based on physical optics, a first relationship between an equivalent surface current and a scattering field for the tracked incident wave; determining the equivalent surface current based on a generalized boundary condition and a surface polarizability model; determining the scattering field by combining the equivalent surface current and the first relationship using Gordon integration.

2. The method of claim 1, wherein, The tracking, based on geometric optics, an incident wave entering a metasurface comprises: determining, based on geometric optics, a propagation path of the incident wave entering the metasurface in the metasurface; tracking, according to the propagation path, an electric field in the metasurface.

3. The method of claim 2, wherein, The tracking, according to the propagation path, an electric field in the metasurface comprises: determining, according to the propagation path, a point of intersection between the incident wave and the metasurface during the propagation of the incident wave in the metasurface; updating, based on the point of intersection, an electromagnetic wave propagation vector, a divergence factor, and a reflection coefficient, the electric field in the metasurface, the reflection coefficient being a function of the surface polarizability, the reflection coefficient being determined using a surface polarizability model.

4. The method of claim 2, wherein, The determining, based on physical optics, a first relationship between an equivalent surface current and a scattering field for the tracked incident wave comprises: determining, using Stratton-Chu formula, a second relationship between a radiative scattering field and electric field and magnetic field of the metasurface; simplifying the second relationship between the radiative scattering field and electric field and magnetic field based on a relationship between the magnetic field, the surface current, and the surface field and a magnetic field discontinuity in the metasurface, to obtain the first relationship between the equivalent surface current and the scattering field.

5. The method of claim 1, wherein, The determining the equivalent surface current based on a generalized boundary condition and a surface polarizability model comprises: determining, based on the generalized boundary condition, a third relationship between the surface current and the surface polarizability model; transforming the third relationship according to a characteristic of a plane wave, combining a fourth relationship between an admittance and a scattering parameter and a fifth relationship between the electric field and the scattering parameter, to determine the equivalent surface current of the metasurface.

6. The method of claim 5, wherein, The determining the equivalent surface current based on a generalized boundary condition and a surface polarizability model further comprises: when the incident wave is of a preset polarization mode, determining the admittance using the transformed third relationship; substituting the determined admittance into the fourth relationship to calculate the scattering parameter; substituting the calculated scattering parameter into the fifth relationship, combining the fourth relationship, to obtain the equivalent surface current.

7. The method of claim 1, wherein, The method further comprises: calculating a bistatic radar cross section based on the scattering field.

8. An ultrametrix scattering behavior analysis apparatus, characterized by, The apparatus comprises: a tracking module configured to track, based on geometric optics, an incident wave entering a metasurface; a relationship determining module configured to determine, based on physical optics, a first relationship between an equivalent surface current and a scattering field for the tracked incident wave; a current determining module configured to determine the equivalent surface current based on a generalized boundary condition and a surface polarizability model; a scattering field determining module configured to determine the scattering field by combining the equivalent surface current and the first relationship using Gordon integration.

9. A computer device, comprising: comprise: a memory and a processor in communication connection with each other, the memory storing computer instructions, and the processor executing the computer instructions to perform the method for analyzing scattering behavior of a metasurface according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer readable storage medium has stored thereon computer instructions for causing a computer to perform the metasurface scattering behavior analysis method of any one of claims 1 to 7.

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