A fast acquisition method of large-scale conformal reflective metasurface scattering field

Abstract

A kind of fast acquisition method of large-scale conformal reflective metasurface scattering field, its steps are: large-scale conformal reflective metasurface array is divided into regions, selects subarray and obtains scattering field in each unit array of subarray;Local coordinate system and global coordinate system are established at the geometric center of each unit of subarray, and position coordinates and rotation angle are obtained;Field in each unit array of subarray is transformed to normal local coordinate system;Subarray is extrapolated and equivalent to large-scale conformal reflective metasurface array;Field in each unit array of large-scale conformal reflective metasurface array is transformed to global coordinate system;Total scattering field is obtained by field superposition;The present application uses scattering field data in each unit array of subarray, realizes equivalent construction to large-scale conformal reflective metasurface array by space coordinate rotation method, solves the problem of low calculation efficiency and large amount of calculation resources required when obtaining large-scale conformal reflective metasurface scattering field in prior art, has the advantages of accurate, fast and efficient.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic technology, and specifically relates to a method for rapidly acquiring large-scale conformal reflective metasurface scattering fields. Background Technology

[0002] Reflective metasurfaces can manipulate incident electromagnetic waves without significantly affecting the basic structure of the carrier. The analysis of scattering characteristics based on conformal reflective metasurfaces has attracted widespread attention in many applications. Currently, research on the scattering characteristics of reflective metasurfaces mainly relies on numerical simulation algorithms such as the finite element method, the method of moments, and the finite-difference time-domain method. However, the application of these methods is often severely limited by computational resources and time, and may even be impossible to complete. Researching efficient analysis methods for the scattering fields of large-scale conformal reflective metasurfaces is of great significance for solving the problems of high time and resource consumption in scattering characteristic analysis in scenarios such as electromagnetic stealth, radar systems, wireless communication, and autonomous driving.

[0003] To address the analysis of the scattering properties of reflective metasurfaces, traditional commercial simulation software and electromagnetic calculation methods are used to obtain the scattering field of large-scale conformal metasurfaces. However, the complex multilayered media of large-scale conformal reflective metasurfaces introduce a large number of computational unknowns. Current accurate full-wave analysis methods are computationally resource-intensive and inefficient, while high-frequency calculation methods have poor accuracy and cannot meet engineering requirements. Another approach is to utilize periodic Green's functions and domain Green's functions based on Floquet's theorem, but the different orientations and relative positions of the elements in large-scale conformal reflective metasurfaces render methods for calculating the electromagnetic properties of conventional periodic arrays inapplicable. Therefore, researching a rapid method for obtaining the scattering field of large-scale conformal reflective metasurfaces is of great significance for solving the problem of slow scattering analysis in practical engineering applications.

[0004] Patent application CN110737873A, entitled "A Method and System for Determining the Scattered Field of a Frequency-Selective Surface Structure," discloses a method and system for determining the scattered field of a frequency-selective surface structure. This method treats each array element of a finite-sized frequency-selective surface structure as one of an infinite-sized array element, using local incident conditions as the illumination conditions for that infinite-sized array element. The resulting surface current is used as the basic surface current distribution for that array element. This avoids complex mutual coupling calculations between array elements and solves the computational complexity problem of methods for analyzing the basic scattered field of selected surface electrical properties. However, this method treats each array element as one of an infinite-sized curved surface array element and uses a periodic method for calculation, neglecting the edge effects of the finite-periodic structure for elements at the edges. Furthermore, this method calculates each element of the entire finite-sized frequency-selective surface structure sequentially, thus its computational load cannot escape the constraint of the large number of array elements, resulting in significant computation time requirements and impacting evaluation efficiency. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, the present invention aims to propose a rapid method for obtaining the scattering field of a large-scale conformal reflective metasurface. This method involves dividing the large-scale conformal reflective metasurface array into regions, selecting subarrays, and obtaining the scattering field in each element of the subarray. Local and global coordinate systems are established at the geometric center of each element of the subarray, and their position coordinates and rotation angles are obtained. The field of each element of the subarray is transformed to the normal local coordinate system. The subarray is extrapolated to be equivalent to a large-scale conformal reflective metasurface array. The field of each element of the large-scale conformal reflective metasurface array is transformed to the global coordinate system. The fields are superimposed to obtain the total scattering field. This invention uses the scattering field data from each element of the subarray and employs a spatial coordinate rotation method to achieve an equivalent construction of the large-scale conformal reflective metasurface array. This method has the advantages of accuracy, speed, and efficiency, reducing computational resources, shortening computation time, and improving the evaluation efficiency of large-scale conformal reflective metasurface structures.

[0006] To achieve the above technical objectives, the present invention adopts the following technical solution:

[0007] A rapid method for acquiring the scattering field of a large-scale conformal reflective metasurface includes the following steps:

[0008] Step 1: Divide the large-scale conformal reflective metasurface array structure into regions, select a small conformal reflective metasurface subarray for equivalent replacement (referred to as subarray), and obtain the coordinates of each element of this small conformal reflective metasurface subarray in the global coordinate system. In-array scattering field ;

[0009] Step 2: Establish a local coordinate system with the geometric center of each element of the small conformal reflective metasurface subarray as the origin. and normal local coordinate system Obtain the polar coordinates of the geometric centers of each element in the global coordinate system of a small conformal reflective metasurface subarray. and the coordinate axes of the local coordinate system normal to each element , , Rotation angle relative to the local coordinate system , , ;

[0010] Step 3: Transform the scattered field of each element in the small conformal reflective metasurface subarray from the global coordinate system to the local coordinate system to obtain the scattered field of each element in the small conformal reflective metasurface subarray in the local coordinate system. Then transform the scattered field from the local coordinate system to the normal local coordinate system. ;

[0011] Step 4: Establish a local coordinate system with the geometric center of each unit of the large-scale conformal reflective metasurface array as the origin. and normal local coordinate system Obtain the spherical coordinates of the geometric centers of each element in a large-scale conformal reflective metasurface array in the global coordinate system. and the coordinate axes of the local coordinate system of each element of a large-scale conformal reflective metasurface array , , Compared to the local coordinate system of each element in a large-scale conformal reflective metasurface array rotation angle , , ;

[0012] Step 5: Extrapolate the small conformal reflective metasurface subarray to construct an equivalent large-scale conformal reflective metasurface array, and obtain the scattering field of each element of the large-scale conformal reflective metasurface array in the normal local coordinate system. ;

[0013] Step 6: Transform the scattered field in each element of the large-scale conformal reflective metasurface array from the normal local coordinate system to the local coordinate system to obtain the scattered field of each element in the local coordinate system of the large-scale conformal reflective metasurface array. Then, by transforming from the local coordinate system to the global coordinate system, we obtain the units of the large-scale conformal reflective metasurface array in the global coordinate system. Scattering field under ;

[0014] Step 7: Obtain the total scattering field of a large-scale conformal reflective metasurface array based on the principle of field superposition. :

[0015]

[0016] Large-scale conformal reflective metasurface arrays are of the following size: OK List.

[0017] Step 1 involves dividing the large-scale conformal reflective metasurface array structure into regions and selecting a small conformal reflective metasurface subarray for equivalent replacement. The method is as follows:

[0018] 1.1. Treat a metasurface of one period length as a whole, and take the phase gradient dimension of the metasurface array to be solved as columns and the vertical phase gradient dimension as rows;

[0019] 1.2. Calculate the least common multiple of the metasurface period length and the incident wave wavelength, and use it as the standard for dividing the phase gradient dimension length;

[0020] 1.3. Calculate the least common multiple of the metasurface unit length and the incident wave wavelength, and use it as the standard for dividing the vertical phase gradient dimension length;

[0021] 1.4. Based on the partitioning criteria in steps 1.2 and 1.3, the metasurface array to be solved is re-partitioned, and each partitioned region is regarded as a whole as a unit for a large-scale conformal reflective metasurface array and a unit for subsequent composition of a small conformal reflective metasurface subarray.

[0022] 1.5. For elements whose phase gradient dimension or vertical phase gradient dimension length does not meet the corresponding partitioning length standard after step 1.4, the elements whose closest phase gradient dimension and vertical phase gradient dimension length both meet the corresponding partitioning length standard are merged. This ensures that all elements in the large-scale conformal reflective metasurface array have phase gradient dimension and vertical phase gradient dimension lengths greater than or equal to their corresponding partitioning length standard. At this point, the scale of the large-scale conformal reflective metasurface array is... OK List;

[0023] 1.6. Select a surface from the large-scale conformal reflective metasurface array divided in step 1.5 that contains both its central and edge position elements. OK A small conformal reflective metasurface subarray.

[0024] Step 1 involves obtaining the elements of the small conformal reflective metasurface subarray in the global coordinate system. In-array scattering field It is expressed as follows:

[0025]

[0026] in, , To measure the pitch angle in a spatial rectangular coordinate system, , The number of sampling points for pitch angle. To measure the azimuth angle in a spatial rectangular coordinate system, , This represents the number of azimuth sampling points. , , These are the scattering fields of each element of a small conformal reflective metasurface subarray in the global coordinate system. exist , , Components in direction.

[0027] Step 2 describes establishing a local coordinate system with the geometric center of each unit of the small conformal reflective metasurface subarray as the origin. and normal local coordinate system The method is as follows:

[0028] 2.1. Specify the first... The geometric center of each unit is the origin of the local coordinate system. Local coordinate system coordinate axes , , The positive directions are all aligned with the coordinate axes of the global coordinate system. , , Establish a local coordinate system with the same positive direction. ;

[0029] 2.2. Specify the first... The geometric center of each element is the origin of the local normal coordinate system. Local coordinate system The positive axis direction is the direction of the outer normal to the element. Establish a normal local coordinate system along the positive axis direction of the phase gradient. .

[0030] The scattering field of each element of the small conformal reflective metasurface subarray in the local coordinate system described in step 3 It is expressed as follows:

[0031]

[0032] in, It is the symbol for imaginary numbers. For wave number.

[0033] Step 3 describes the transformation from the local coordinate system to the normal local coordinate system to obtain the scattering field of each element of the subarray in the normal local coordinate system. The method is as follows:

[0034] 3.1. The components of the normal local coordinate system are represented by three Euler matrices. and local coordinate system components When linked together, it can be represented as follows:

[0035]

[0036] in, To bypass Rotate the axis counterclockwise The Euler rotation matrix corresponding to the angle. To bypass Rotate the axis counterclockwise The Euler rotation matrix corresponding to the angle. To bypass Rotate the axis counterclockwise The Euler rotation matrix corresponding to the angle. , , It is expressed as follows:

[0037]

[0038]

[0039] ;

[0040] 3.2. Calculation and The correspondence between them is expressed as follows:

[0041]

[0042]

[0043] ;

[0044] 3.3. Calculate the scattering field of each element of the small conformal reflective metasurface subarray in the normal local coordinate system according to steps 3.1 and 3.2. , means as follows:

[0045]

[0046] in, , , These are the scattering fields of each element of a small conformal reflective metasurface subarray in the normal local coordinate system. exist , , Components in direction, , , These are the scattering fields of each element of a small conformal reflective metasurface subarray in the local coordinate system. exist , , Components in direction.

[0047] Step 4 describes establishing a local coordinate system with the geometric center of each unit of the large-scale conformal reflective metasurface array as the origin. and normal local coordinate system The method is as follows:

[0048] 4.1. Large-scale conformal reflective metasurface arrays The geometric center of each unit is the origin of the local coordinate system. Local coordinate system coordinate axes , , The positive directions are all aligned with the coordinate axes of the global coordinate system. , , Establish a local coordinate system with the same positive direction. ;

[0049] 4.2. Large-scale conformal reflective metasurface arrays The geometric center of each element is the origin of the local normal coordinate system. Local coordinate system The positive axis direction is the direction of the outer normal to the element. Establish a normal local coordinate system along the positive axis direction of the phase gradient. .

[0050] Step 5 describes the extrapolation of the small conformal reflective metasurface subarray to equivalently construct a large-scale conformal reflective metasurface array, thereby obtaining the scattering field of each element of the large-scale conformal reflective metasurface array in the normal local coordinate system. ,in The implementation is as follows:

[0051] 5.1. Perform row equivalents on small conformal reflective metasurface subarrays, and... OK The equivalent construction of the subarray is as follows OK Column array:

[0052] The first row to the second row of the small conformal reflective metasurface subarray The row unit is equivalent to OK The first row to the second row of the column array Row cells, which will be the first row of a small conformal reflective metasurface subarray. Row unit equivalent to OK The first column array Arriving at the Row cells, which will be the first row of a small conformal reflective metasurface subarray. Arriving at the Row unit equivalent to OK The first column array Arriving at the row unit, to obtain OK The array scattering field of each element in the column array in the normal local coordinate system;

[0053] 5.2. Regarding OK Perform column equivalence on column arrays, OK Column arrays are equivalently constructed as OK Large-scale conformal reflective metasurface arrays:

[0054] Will OK The first column to the second column of the column array Column cells are equivalent to OK The first column to the second column of the column array Column cells, OK Column array Column cells are equivalent to OK Column array Listed to number Column cells, OK The first column array Listed to number Column cells are equivalent to OK The first column array To the column cells, to obtain OK In-array scattering field of each element in a large-scale conformal reflective metasurface array in the normal local coordinate system .

[0055] Step 6 describes the transformation from the normal local coordinate system to the local coordinate system to obtain the scattering field of each element of the large-scale conformal reflective metasurface array in the local coordinate system. The implementation is as follows:

[0056] 6.1. Using three Euler matrices to represent the components of the local coordinate system and normal local coordinate system components When linked together, it can be represented as follows:

[0057]

[0058] in, Represents the inverse matrix. To bypass Rotate the axis counterclockwise The Euler rotation matrix corresponding to the angle. To bypass Rotate the axis counterclockwise The Euler rotation matrix corresponding to the angle. To bypass Rotate the axis counterclockwise The Euler rotation matrix corresponding to the angle. , , It is expressed as follows:

[0059]

[0060]

[0061] ;

[0062] 6.2. Calculation and The correspondence between them is expressed as follows:

[0063]

[0064]

[0065] ;

[0066] 6.3. Calculate the scattering field of each element of the large-scale conformal reflective metasurface array in the local coordinate system according to steps 6.1 and 6.2. , means as follows:

[0067]

[0068] in, , , These represent the scattering fields of each element in a large-scale conformal reflective metasurface array in the local coordinate system. exist , , Components in direction, , , These represent the scattering fields of each element in a large-scale conformal reflective metasurface array in the normal local coordinate system. exist , , Components in direction.

[0069] The scattering field of each element of the large-scale conformal reflective metasurface array in the global coordinate system described in step 6 It is expressed as follows:

[0070]

[0071] in, It is the symbol for imaginary numbers. For wave number.

[0072] Compared with the prior art, the present invention has the following advantages:

[0073] First, the present invention divides the large-scale conformal reflective metasurface into regions, making the scattered fields in the unit array of the middle part more consistent, and then selects the subarray for equivalent construction based on the array element similarity theory, thereby improving the computational efficiency.

[0074] Second, by introducing a spatial coordinate rotation method, the present invention transforms the scattering field of each unit to the normal local coordinate system, thereby realizing the equivalent scattering field of each unit in the subarray to the scattering field of each unit in a large-scale conformal reflective metasurface array, thus accelerating the calculation speed.

[0075] Third, this invention simplifies the calculation problem of the scattering field of a large-scale conformal reflective metasurface into the calculation problem of the scattering field of a subarray, thus shortening the calculation time. It is applicable to conformal metasurface arrays of different sizes, and the calculation time does not increase significantly with the increase of array size.

[0076] In summary, this invention has the advantages of high computational efficiency, short computation time, and wide applicability. Attached Figure Description

[0077] Figure 1 This is a flowchart illustrating the implementation of the present invention.

[0078] Figure 2 This is a schematic diagram of a large-scale conformal reflective metasurface array for which the scattered field is to be acquired in this invention.

[0079] Figure 3 This is a schematic diagram of the region division of the large-scale conformal reflective metasurface array in this invention.

[0080] Figure 4 for Figure 2 The diagram shows a subarray of a large-scale conformal reflective metasurface array.

[0081] Figure 5 This is a schematic diagram illustrating the establishment of a local coordinate system and a normal local coordinate system in this invention.

[0082] Figure 6 This is a schematic diagram illustrating the row and column equivalence of the subarrays in this invention; wherein, Figure 6 (a) is a diagram illustrating the row equivalent. Figure 6 (b) is a schematic diagram of the column equivalent.

[0083] Figure 7 This is a comparison chart of the calculation results of this invention and the full-wave simulation results when a horizontally polarized plane wave is incident.

[0084] Figure 8 This is a comparison chart of the calculation results of this invention and the full-wave simulation results when a vertically polarized plane wave is incident. Detailed Implementation

[0085] To more clearly describe the technical solution and effects of the present invention, the following description is provided in conjunction with specific embodiments and accompanying drawings.

[0086] Reference Figure 1 The implementation steps of this invention are as follows:

[0087] Step 1: Construct a large-scale conformal reflective metasurface array and divide the region to select a small conformal reflective metasurface subarray for equivalent replacement, and collect the array scattering field of each element of the subarray in the global coordinate system.

[0088] 1.1) Reference Figure 2 This example uses FEKO simulation software to model and simulate the large-scale conformal reflective metasurface array to be solved. The reflective metasurface used is in... The angular domain can enhance the target monostation RCS. The metasurface element length is 7.8 mm, and the period length is 15.6 mm, in the global Cartesian coordinate system. A cylindrical conformal reflective metasurface array with 20 periods in the phase gradient dimension and 40 elements in the vertical phase gradient dimension is established as the large-scale conformal reflective metasurface array to be solved. The phase gradient is along the radial direction of the cylinder, the cylinder radius is 148.97 mm, and the element rotation angle is [missing information]. The incident wave is selected as a plane wave with a frequency of 10 GHz, and the incident angle is set. The range is , The range is The intervals are all ;

[0089] 1.2) Divide the large-scale conformal reflective metasurface array structure into regions and select small conformal reflective metasurface subarrays for equivalent replacement;

[0090] 1.2.1) Treat a metasurface of one period length as a whole, and use the phase gradient dimension as the column and the vertical phase gradient dimension as the row of the metasurface array to be solved;

[0091] 1.2.2) The least common multiple of the metasurface period length and the incident wave wavelength is approximately 30 mm, which is used as the standard for dividing the phase gradient dimension length;

[0092] 1.2.3) The least common multiple of the metasurface unit length and the incident wave wavelength is approximately 30 mm, which is used as the standard for dividing the vertical phase gradient dimension length;

[0093] 1.2.4) Based on the partitioning criteria of 1.2.2) and 1.2.3), the metasurface array to be solved is repartitioned, and each partitioned region is regarded as a whole as a unit for a large-scale conformal reflective metasurface array and a unit for subsequent composition of a small conformal reflective metasurface subarray;

[0094] 1.2.5) For elements whose phase gradient dimension or vertical phase gradient dimension lengths at the edge positions after partitioning in 1.2.4) do not meet their corresponding partitioning length criteria, the elements whose closest phase gradient dimension and vertical phase gradient dimension lengths both meet their corresponding partitioning length criteria are merged, so that each element has phase gradient dimension and vertical phase gradient dimension lengths greater than or equal to its corresponding partitioning length criteria. At this point, the large array size is 10 rows and 10 columns, such as... Figure 3 As shown;

[0095] 1.2.6) Based on the element similarity theory, elements are selected from the middle and edge parts of the divided large-scale conformal reflective metasurface array to form an equivalent 5x5 small conformal reflective metasurface subarray, such as... Figure 4 As shown;

[0096] 1.3) Set the incident angle The range is , The range is The intervals are all Obtain the values ​​of each element of a small conformal reflective metasurface subarray in the global coordinate system. In-array scattering field It is expressed as follows:

[0097]

[0098] in, , To measure the pitch angle in a spatial rectangular coordinate system, , To measure the azimuth angle in a spatial rectangular coordinate system, , , , These are the scattering fields of each element of a small conformal reflective metasurface subarray in the global coordinate system. exist , , Components in direction.

[0099] Step Two: Refer to Figure 5 A local coordinate system is established with the geometric center of each unit of the small conformal reflective metasurface subarray as the origin. and normal local coordinate system Obtain the polar coordinates of the geometric center of each element in the global coordinate system. and the coordinate axes of the local coordinate system normal to each element , , Rotation angle relative to the local coordinate system , , .

[0100] 2.1) Specify the first... The geometric center of each unit is the origin of the local coordinate system. Local coordinate system coordinate axes , , The positive directions are all aligned with the coordinate axes of the global coordinate system. , , Establish a local coordinate system with the same positive direction. ;

[0101] 2.2) Specify the first... The geometric center of each element is the origin of the local normal coordinate system. Local coordinate system The positive axis direction is the direction of the outer normal to the element. Establish a local coordinate system with the positive axis perpendicularly downwards along the cylinder axis. ;

[0102] 2.3) Obtain the polar coordinates of the geometric center of each element in the global coordinate system. and the coordinate axes of the local coordinate system normal to each element , , Rotation angle relative to the local coordinate system , , ;

[0103] Step 3: Transform the scattered field in each element of the small conformal reflective metasurface subarray from the global coordinate system to the local coordinate system to obtain the scattered field of each element in the local coordinate system. Then, by transforming from the local coordinate system to the normal local coordinate system, the scattered field of each element in the normal local coordinate system can be obtained. .

[0104] 3.1) Transform the scattered field of each element in the small conformal reflective metasurface subarray from the global coordinate system to the local coordinate system to obtain the scattered field of each element in the local coordinate system. , means as follows:

[0105]

[0106] in, It is the symbol for imaginary numbers. Wave number;

[0107] 3.2) Transform the scattered field in each element of the small conformal reflective metasurface subarray from the local coordinate system to the normal local coordinate system to obtain the scattered field of each element in the normal local coordinate system. ;

[0108] 3.2.1) The components of the normal local coordinate system are represented by three Euler matrices. and local coordinate system components When linked together, it can be represented as follows:

[0109]

[0110] in, To bypass Rotate the axis counterclockwise The Euler rotation matrix corresponding to the angle. To bypass Rotate the axis counterclockwise The Euler rotation matrix corresponding to the angle, where To bypass Rotate the axis counterclockwise The Euler rotation matrix corresponding to the angle. , , It is expressed as follows:

[0111]

[0112]

[0113] ;

[0114] 3.2.2) Calculation and The correspondence between them is expressed as follows:

[0115]

[0116]

[0117] ;

[0118] 3.2.3) Calculate the scattering field of each element of the small conformal reflective metasurface subarray in the normal local coordinate system based on the results of 3.2.1) and 3.2.2). , means as follows:

[0119]

[0120] in, , , These are the scattering fields of each element of a small conformal reflective metasurface subarray in the normal local coordinate system. exist , , Components in direction, , , These are the scattering fields of each element of a small conformal reflective metasurface subarray in the local coordinate system. exist , , Components in direction.

[0121] Step Four: Refer to Figure 5 A local coordinate system is established with the geometric center of each unit of the large-scale conformal reflective metasurface array as the origin. and normal local coordinate system Obtain the spherical coordinates of the geometric centers of each element in the global coordinate system. and the coordinate axes of the local coordinate system normal to each element , , Rotation angle relative to the local coordinate system , , ;

[0122] 4.1) Specify the first large-scale conformal reflective metasurface array The geometric center of each unit is the origin of the local coordinate system. Local coordinate system coordinate axes , , The positive directions are all aligned with the coordinate axes of the global coordinate system. , , Establish a local coordinate system with the same positive direction. ;

[0123] 4.2) Specify the first large-scale conformal reflective metasurface array The geometric center of each element is the origin of the local normal coordinate system. Local coordinate system The positive axis direction is the direction of the outer normal to the element. Establish a normal local coordinate system along the positive axis direction of the phase gradient. ;

[0124] 4.3) Obtain the spherical coordinates of the geometric center of each element in the global coordinate system. and the coordinate axes of the local coordinate system normal to each element , , Rotation angle relative to the local coordinate system , , .

[0125] Step 5: Extrapolate the small conformal reflective metasurface subarray to construct an equivalent large-scale conformal reflective metasurface array, and obtain the scattering field of each element of the large-scale conformal reflective metasurface array in the normal local coordinate system. ,in .

[0126] 5.1) Perform row equivalence on the small conformal reflective metasurface subarray, transforming the 5x5 small conformal reflective metasurface subarray into a 10x5 array, such as... Figure 6 As shown in (a), the first and second rows of the small conformal reflective metasurface subarray are equivalent to the first and second rows of a 10x5 array, the third row of the small conformal reflective metasurface subarray is equivalent to the third to eighth rows of a 10x5 array, and the fourth and fifth rows of the small conformal reflective metasurface subarray are equivalent to the ninth to tenth rows of a 10x5 array, thus obtaining the array scattering field of each element of the 10x5 array in the normal local coordinate system;

[0127] 5.2) Perform column equivalence on the 10x5 array, effectively constructing it as a large-scale conformal reflective metasurface array of 10x10 columns, such as... Figure 6As shown in (b), the first and second columns of the 10x5 array are equivalent to the first and second columns of the 10x10 array, the third column of the 10x5 array is equivalent to the third to eighth columns of the 10x10 array, and the fourth and fifth columns of the 10x5 array are equivalent to the ninth and tenth columns of the 10x10 array. This yields the in-array scattering field of each element of the 10x10 large-scale conformal reflective metasurface array in the normal local coordinate system. .

[0128] Step 6: Transform the scattered field in each element of the large-scale conformal reflective metasurface array from the normal local coordinate system to the local coordinate system to obtain the scattered field of each element in the local coordinate system. Then, the scattering field of each element in the global coordinate system is obtained by transforming from the local coordinate system to the global coordinate system. .

[0129] 6.1) Transform the scattered field of each element in a large-scale conformal reflective metasurface array from the normal local coordinate system to the local coordinate system to obtain the scattered field of each element in the local coordinate system. ;

[0130] The components of the local coordinate system are represented by three Euler matrices. and normal local coordinate system components When linked together, it can be represented as follows:

[0131]

[0132] in, Represents the inverse matrix. To bypass Rotate the axis counterclockwise The Euler rotation matrix corresponding to the angle. To bypass Rotate the axis counterclockwise The Euler rotation matrix corresponding to the angle. To bypass Rotate the axis counterclockwise The Euler rotation matrix corresponding to the angle. , , It is expressed as follows:

[0133]

[0134]

[0135] ;

[0136] 6.2) Calculation and The correspondence between them is expressed as follows:

[0137]

[0138]

[0139] ;

[0140] 6.3) Based on the results of 6.1) and 6.2), calculate the scattering field of each element of the large-scale conformal reflective metasurface array in the local coordinate system. , means as follows:

[0141]

[0142] in, , , These represent the scattering fields of each element in a large-scale conformal reflective metasurface array in the local coordinate system. exist , , Components in direction, , , These represent the scattering fields of each element in a large-scale conformal reflective metasurface array in the normal local coordinate system. exist , , Components in direction.

[0143] The scattered fields in each element of a large-scale conformal reflective metasurface array are transformed from the local coordinate system to the global coordinate system to obtain the scattered field of each element in the global coordinate system. , means as follows:

[0144]

[0145] in, It is the symbol for imaginary numbers. For wave number.

[0146] Step 7: Superimpose the scattered fields of each element in the large-scale conformal reflective metasurface array to obtain the total scattered field. :

[0147] .

[0148] The effects of this invention can be further illustrated by the following simulation experiments:

[0149] I. Simulation Experiment Conditions

[0150] The FEKO simulation software was used to model and simulate the large-scale conformal reflective metasurface array to be solved. The reflective metasurface used was in... The angular domain can enhance the target monostation RCS. The metasurface element length is 7.8 mm, and the period length is 15.6 mm, in the global Cartesian coordinate system. A cylindrical conformal reflective metasurface array with 20 periods in the phase gradient dimension and 40 elements in the vertical phase gradient dimension is established as the large-scale conformal reflective metasurface array to be solved. The phase gradient is along the radial direction of the cylinder, the cylinder radius is 148.97 mm, and the element rotation angle is [missing information]. The incident wave is selected as a plane wave with a frequency of 10 GHz, and the incident angle is set. The range is , The range is The intervals are all To obtain total single-station scattering field data for a large-scale conformal reflective metasurface array, the large-scale conformal reflective metasurface array was divided into regions, and regions with the same arrangement as the large-scale conformal reflective metasurface array were selected. The metasurface array is used as a small conformal reflective metasurface subarray, and the scattered field data of each element of the small conformal reflective metasurface subarray in the monostation array in the global coordinate system are obtained.

[0151] II. Simulation Experiment Content

[0152] Simulation Experiment 1: Under the above experimental conditions, the method of this invention utilizes the scattering field data of each unit of a small conformal reflective metasurface subarray when horizontally polarized plane waves are incident to obtain the total scattering field of a large-scale conformal reflective metasurface array when horizontally polarized plane waves are incident. This is compared with the results obtained by directly simulating a large-scale conformal reflective metasurface array using FEKO. The results are as follows: Figure 7 As shown.

[0153] from Figure 7 It can be seen that the total scattering field of a large-scale conformal reflective metasurface array at a single station calculated by this invention when a horizontally polarized plane wave is incident is similar to the FEKO simulation results. The error is basically consistent within the angular domain, while in other angular domains the error shows a small increasing trend with angular deviation, indicating that the present invention can realize the acquisition of large-scale conformal reflective metasurface scattering fields.

[0154] Simulation Experiment 2: Under the above experimental conditions, the method of this invention utilizes the scattered field data from each unit of a small conformal reflective metasurface subarray when a vertically polarized plane wave is incident to obtain the total scattered field of a large-scale conformal reflective metasurface array when a vertically polarized plane wave is incident. This is compared with the results obtained by directly simulating a large-scale conformal reflective metasurface array using FEKO. The results are as follows: Figure 8 As shown.

[0155] from Figure 8 As can be seen, the total scattering field of a single station of a large-scale conformal reflective metasurface array calculated by the present invention when a vertically polarized plane wave is incident is basically consistent with the FEKO simulation results, and the degree of agreement is good, indicating that the present invention can realize the acquisition of the scattering field of a large-scale conformal reflective metasurface.

Claims

1. A method for rapidly acquiring the scattering field of a large-scale conformal reflective metasurface, characterized in that: include: Step 1: Divide the large-scale conformal reflective metasurface array structure into regions, select a small conformal reflective metasurface subarray for equivalent replacement (referred to as subarray), and obtain the coordinates of each element of this small conformal reflective metasurface subarray in the global coordinate system. In-array scattering field ; Step 2: Establish a local coordinate system with the geometric center of each element of the small conformal reflective metasurface subarray as the origin. and normal local coordinate system Obtain the polar coordinates of the geometric centers of each element in the global coordinate system of a small conformal reflective metasurface subarray. and the coordinate axes of the local coordinate system normal to each element , , Rotation angle relative to the local coordinate system , , ; Step 3: Transform the scattered field of each element in the small conformal reflective metasurface subarray from the global coordinate system to the local coordinate system to obtain the scattered field of each element in the small conformal reflective metasurface subarray in the local coordinate system. Then transform the scattered field from the local coordinate system to the normal local coordinate system. ; Step 4: Establish a local coordinate system with the geometric center of each unit of the large-scale conformal reflective metasurface array as the origin. and normal local coordinate system Obtain the spherical coordinates of the geometric centers of each element in a large-scale conformal reflective metasurface array in the global coordinate system. and the coordinate axes of the local coordinate system of each element of a large-scale conformal reflective metasurface array , , Compared to the local coordinate system of each element in a large-scale conformal reflective metasurface array rotation angle , , ; Step 5: Extrapolate the small conformal reflective metasurface subarray to construct an equivalent large-scale conformal reflective metasurface array, and obtain the scattering field of each element of the large-scale conformal reflective metasurface array in the normal local coordinate system. ; Step 6: Transform the scattered field in each element of the large-scale conformal reflective metasurface array from the normal local coordinate system to the local coordinate system to obtain the scattered field of each element in the local coordinate system of the large-scale conformal reflective metasurface array. Then, by transforming from the local coordinate system to the global coordinate system, we obtain the units of the large-scale conformal reflective metasurface array in the global coordinate system. Scattering field under ; Step 7: Obtain the total scattering field of a large-scale conformal reflective metasurface array based on the principle of field superposition. : Large-scale conformal reflective metasurface arrays are of the following size: OK List.

2. The method for rapidly acquiring the scattering field of a large-scale conformal reflective metasurface according to claim 1, characterized in that, Step 1 involves dividing the large-scale conformal reflective metasurface array structure into regions and selecting a small conformal reflective metasurface subarray for equivalent replacement. The method is as follows: 1.

1. Treat a metasurface of one period length as a whole, and take the phase gradient dimension of the metasurface array to be solved as columns and the vertical phase gradient dimension as rows; 1.

2. Calculate the least common multiple of the metasurface period length and the incident wave wavelength, and use it as the standard for dividing the phase gradient dimension length; 1.

3. Calculate the least common multiple of the metasurface unit length and the incident wave wavelength, and use it as the standard for dividing the vertical phase gradient dimension length; 1.

4. Based on the partitioning criteria in steps 1.2 and 1.3, the metasurface array to be solved is re-partitioned, and each partitioned region is regarded as a whole as a unit for a large-scale conformal reflective metasurface array and a unit for subsequent composition of a small conformal reflective metasurface subarray. 1.

5. For elements whose phase gradient dimension or vertical phase gradient dimension length does not meet the corresponding partitioning length standard after step 1.4, the elements whose closest phase gradient dimension and vertical phase gradient dimension length both meet the corresponding partitioning length standard are merged. This ensures that all elements in the large-scale conformal reflective metasurface array have phase gradient dimension and vertical phase gradient dimension lengths greater than or equal to their corresponding partitioning length standard. At this point, the scale of the large-scale conformal reflective metasurface array is... OK List; 1.

6. Select a surface from the large-scale conformal reflective metasurface array divided in step 1.5 that contains both its central and edge position elements. OK A small conformal reflective metasurface subarray.

3. The method for rapidly acquiring the scattering field of a large-scale conformal reflective metasurface according to claim 1, characterized in that, Step 1 involves obtaining the elements of the small conformal reflective metasurface subarray in the global coordinate system. In-array scattering field It is expressed as follows: in, , To measure the pitch angle in a spatial rectangular coordinate system, , The number of sampling points for pitch angle. To measure the azimuth angle in a spatial rectangular coordinate system, , This represents the number of azimuth sampling points. , , These are the scattering fields of each element of a small conformal reflective metasurface subarray in the global coordinate system. exist , , Components in direction.

4. The method for rapidly acquiring the scattering field of a large-scale conformal reflective metasurface according to claim 1, characterized in that, Step 2 describes establishing a local coordinate system with the geometric center of each unit of the small conformal reflective metasurface subarray as the origin. and normal local coordinate system The method is as follows: 2.

1. Specify the first... The geometric center of each unit is the origin of the local coordinate system. Local coordinate system coordinate axes , , The positive directions are all aligned with the coordinate axes of the global coordinate system. , , Establish a local coordinate system with the same positive direction. ; 2.

2. Specify the first... The geometric center of each element is the origin of the local normal coordinate system. Local coordinate system The positive axis direction is the direction of the outer normal to the element. Establish a normal local coordinate system along the positive axis direction of the phase gradient. .

5. The method for rapidly acquiring the scattering field of a large-scale conformal reflective metasurface according to claim 1, characterized in that, The scattering field of each element of the small conformal reflective metasurface subarray in the local coordinate system described in step 3 It is expressed as follows: in, It is the symbol for imaginary numbers. For wave number.

6. The method for rapidly acquiring the scattering field of a large-scale conformal reflective metasurface according to claim 1, characterized in that, Step 3 describes the transformation from the local coordinate system to the normal local coordinate system to obtain the scattering field of each element of the subarray in the normal local coordinate system. The method is as follows: 3.

1. The components of the normal local coordinate system are represented by three Euler matrices. and local coordinate system components When linked together, it can be represented as follows: in, To bypass Rotate the axis counterclockwise The Euler rotation matrix corresponding to the angle. To bypass Rotate the axis counterclockwise The Euler rotation matrix corresponding to the angle. To bypass Rotate the axis counterclockwise The Euler rotation matrix corresponding to the angle. , , It is expressed as follows: ； 3.

2. Calculation and The correspondence between them is expressed as follows: ； 3.

3. Calculate the scattering field of each element of the small conformal reflective metasurface subarray in the normal local coordinate system according to steps 3.1 and 3.

2. , means as follows: in, , , These are the scattering fields of each element of a small conformal reflective metasurface subarray in the normal local coordinate system. exist , , Components in direction, , , These are the scattering fields of each element of a small conformal reflective metasurface subarray in the local coordinate system. exist , , Components in direction.

7. The method for rapidly acquiring the scattering field of a large-scale conformal reflective metasurface according to claim 1, wherein step 4 establishes a local coordinate system with the geometric center of each unit of the large-scale conformal reflective metasurface array as the origin. and normal local coordinate system The method is as follows: 4.

1. Large-scale conformal reflective metasurface arrays The geometric center of each unit is the origin of the local coordinate system. Local coordinate system coordinate axes , , The positive directions are all aligned with the coordinate axes of the global coordinate system. , , Establish a local coordinate system with the same positive direction. ; 4.

2. Large-scale conformal reflective metasurface arrays The geometric center of each element is the origin of the local normal coordinate system. Local coordinate system The positive axis direction is the direction of the outer normal to the element. Establish a normal local coordinate system along the positive axis direction of the phase gradient. .

8. The method for rapidly acquiring the scattering field of a large-scale conformal reflective metasurface according to claim 1, characterized in that, Step 5 describes the extrapolation of the small conformal reflective metasurface subarray to equivalently construct a large-scale conformal reflective metasurface array, thereby obtaining the scattering field of each element of the large-scale conformal reflective metasurface array in the normal local coordinate system. ,in The implementation is as follows: 5.

1. Perform row equivalents on small conformal reflective metasurface subarrays, and... OK The equivalent construction of the subarray is as follows OK Column array: The first row to the second row of the small conformal reflective metasurface subarray The row unit is equivalent to OK The first row to the second row of the column array Row cells, which will be the first row of a small conformal reflective metasurface subarray. Row unit equivalent to OK The first column array Arriving at the Row cells, which will be the first row of a small conformal reflective metasurface subarray. Arriving at the Row unit equivalent to OK The first column array Arriving at the row unit, to obtain OK The array scattering field of each element in the column array in the normal local coordinate system; 5.

2. Regarding OK Perform column equivalence on column arrays, OK Column arrays are equivalently constructed as OK Large-scale conformal reflective metasurface arrays: Will OK The first column to the second column of the column array Column cells are equivalent to OK The first column to the second column of the column array Column cells, OK Column array Column cells are equivalent to OK Column array Listed to number Column cells, OK The first column array Listed to number Column cells are equivalent to OK The first column array To the column cells, to obtain OK In-array scattering field of each element in a large-scale conformal reflective metasurface array in the normal local coordinate system .

9. The method for rapidly obtaining the scattering field of a large-scale conformal reflective metasurface according to claim 1, wherein step 6 involves transforming from the normal local coordinate system to the local coordinate system to obtain the scattering field of each unit of the large-scale conformal reflective metasurface array in the local coordinate system. The implementation is as follows: 6.

1. Using three Euler matrices to represent the components of the local coordinate system and normal local coordinate system components When linked together, it can be represented as follows: in, Represents the inverse matrix. To bypass Rotate the axis counterclockwise The Euler rotation matrix corresponding to the angle. To bypass Rotate the axis counterclockwise The Euler rotation matrix corresponding to the angle. To bypass Rotate the axis counterclockwise The Euler rotation matrix corresponding to the angle. , , It is expressed as follows: ； 6.

2. Calculation and The correspondence between them is expressed as follows: ； 6.

3. Calculate the scattering field of each element of the large-scale conformal reflective metasurface array in the local coordinate system according to steps 6.1 and 6.

2. , means as follows: in, , , These represent the scattering fields of each element in a large-scale conformal reflective metasurface array in the local coordinate system. exist , , Components in direction, , , These represent the scattering fields of each element in a large-scale conformal reflective metasurface array in the normal local coordinate system. exist , , Components in direction.

10. The method for rapidly acquiring the scattering field of a large-scale conformal reflective metasurface according to claim 1, characterized in that, The scattering field of each element of the large-scale conformal reflective metasurface array in the global coordinate system described in step 6 It is expressed as follows: in, It is the symbol for imaginary numbers. For wave number.

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