Rapid acquisition method for large-scale conformal reflection type metasurface scattered field

Abstract

The invention relates to a method for quickly acquiring a large-scale conformal reflection type metasurface scattered field, which comprises the following steps of: carrying out region division on a large-scale conformal reflection type metasurface array, selecting a sub-array and acquiring a scattered field in each unit array of the sub-array; establishing a local coordinate system and a global coordinate system at the geometric center of each unit of the subarray, and obtaining position coordinates and corners; field transformation is carried out on each unit array of the sub-array to a normal local coordinate system; the subarray extrapolation is equivalent to a large-scale conformal reflection type metasurface array; performing field transformation on each unit array of the large-scale conformal reflection type metasurface array to a global coordinate system; performing field superposition to obtain a total scattering field; the large-scale conformal reflection type metasurface array is equivalently constructed by using the scattered field data in each unit array of the sub-array through a space coordinate rotation method, so that the problems of low calculation efficiency and large calculation resource demand when the large-scale conformal reflection type metasurface scattered field is obtained in the prior art are solved, and the calculation efficiency of the large-scale conformal reflection type metasurface array is improved. The method has the advantages of accuracy, rapidness and high efficiency.

Description

Technical Field

[0001] The present invention belongs to the field of electromagnetic technology, and particularly relates to a method for rapidly obtaining the scattering field of a large-scale conformal reflective metasurface. Background Art

[0002] The reflective metasurface can regulate the incident electromagnetic wave without significantly affecting the basic structure of the carrier. The analysis of the scattering characteristics based on the conformal reflective metasurface has received extensive attention in many applications. At present, the research on the scattering characteristics of the reflective metasurface 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 greatly limited by computing resources and time, and even cannot be completed. Studying an efficient analysis method for the scattering field of a large-scale conformal reflective metasurface is of great significance for solving the problem of large consumption of scattering analysis time and resources in scenarios such as electromagnetic stealth, radar systems, wireless communication, and unmanned driving.

[0003] Regarding the analysis problem of the scattering characteristics of the reflective metasurface, on the one hand, the scattering field of the large-scale conformal metasurface is obtained through traditional commercial simulation software and electromagnetic calculation methods. However, the complex multi-layer medium of the large-scale conformal reflective metasurface brings a huge number of unknowns to be calculated. The current accurate full-wave analysis method requires a large amount of computing resources and has low computing efficiency, while the high-frequency calculation method has poor calculation accuracy and cannot meet the engineering requirements. On the other hand, according to its periodic nature, the periodic Green's function and the domain Green's function based on the Floquet theorem are used. However, the large-scale conformal reflective metasurface has different orientations and relative positions between its units, and the electromagnetic characteristic calculation methods for conventional periodic arrays are no longer applicable. Studying a method for rapidly obtaining the scattering field of a large-scale conformal reflective metasurface is of great significance for solving the problem of slow scattering analysis speed in practical engineering applications.

[0004] The patent application with the publication number CN110737873A and the title "A method and system for determining the scattering field of a frequency selective surface structure" discloses a method and system for determining the scattering field of a frequency selective surface structure. In this method, each array unit of the finite-sized curved frequency selective surface structure is regarded as one of the array units of an infinite-sized curved surface, and the local incident condition is used as the irradiation condition for solving this infinite-sized curved surface array unit. The surface current obtained by solving is used as the basic surface current distribution of this array unit, which can avoid complex mutual coupling calculations between array units and solve the problem of complex calculations in the basic-scattering field analysis method for solving the electrical properties of the selective surface. However, in this method, each array unit is regarded as one of the infinite-sized curved surface array units and then calculated using the periodic method, ignoring the edge effect of the finite periodic structure for the units at the edge position. Moreover, this method calculates each unit of the entire finite-sized frequency selective structure of the curved surface in sequence, so its calculation amount cannot get rid of the constraint of the large number of array units, and the demand for calculation time is still large, affecting the evaluation efficiency. Summary of the Invention

[0005] In order to overcome the defects of the above-mentioned prior art, the purpose of the present invention is to propose a method for quickly obtaining the scattering field of a large-scale conformal reflective metasurface, which divides the large-scale conformal reflective metasurface array into regions, selects sub-arrays and obtains the scattering fields in each unit array of the sub-arrays; establishes a local coordinate system and a global coordinate system at the geometric center of each unit of the sub-array and obtains the position coordinates and rotation angles; transforms the fields in each unit array of the sub-array to the normal local coordinate system; extrapolates the sub-array to be equivalent to the large-scale conformal reflective metasurface array; transforms the fields in each unit array of the large-scale conformal reflective metasurface array to the global coordinate system; and superimposes the fields to obtain the total scattering field. The present invention uses the scattering field data in each unit array of the sub-array and realizes the equivalent construction of the large-scale conformal reflective metasurface array through the spatial coordinate rotation method, which has the advantages of accuracy, speed and efficiency to reduce the computing resources, shorten the computing time and improve the evaluation efficiency of the large-scale conformal reflective metasurface structure.

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

[0007] A method for quickly obtaining the scattering field of a large-scale conformal reflective metasurface, the specific steps include:

[0008] Step 1: Divide the structure of the large-scale conformal reflective metasurface array into regions, select a small conformal reflective metasurface sub-array for equivalent replacement, abbreviated as sub-array, and obtain the in-array scattering fields of each unit of the small conformal reflective metasurface sub-array in the global coordinate system o-xyz

[0009] Step 2: Establish a local coordinate system with the geometric center of each unit of the small conformal reflective metasurface sub-array as the origin and the normal local coordinate system Obtain the polar coordinates (R n , θ n , φ n ) of the geometric center of each unit of the small conformal reflective metasurface subarray in the global coordinate system and the coordinate axes of the normal local coordinate system of each unit and the rotation angles α n , β n , γ n ;

[0010] Step 3: Transform the scattered field in the center of each unit of the small conformal reflective metasurface subarray from the global coordinate system to the local coordinate system to obtain the scattered field of each unit of the small conformal reflective metasurface subarray in the local coordinate system and then transform it to the scattered field in the normal local coordinate system

[0011] Step 4: Establish a local coordinate system and the normal local coordinate system with the geometric center of each unit of the large-scale conformal reflective metasurface array as the origin, and obtain the spherical coordinates (R m , θ m , φ m ) of the geometric center of each unit of the large-scale conformal reflective metasurface array in the global coordinate system and the coordinate axes of the normal local coordinate system of each unit of the large-scale conformal reflective metasurface array with respect to the local coordinate system of each unit of the large-scale conformal reflective metasurface array and the rotation angles α m , β m , γ m ;

[0012] Step 5: Extrapolate and equivalently construct the small conformal reflective metasurface subarray into a large-scale conformal reflective metasurface array to obtain the scattered field of each unit of the large-scale conformal reflective metasurface array in the normal local coordinate system

[0013] Step 6: Transform the scattered field in the center of each unit 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 unit of the large-scale conformal reflective metasurface array in the local coordinate system and then transform it from the local coordinate system to the global coordinate system to obtain the scattered field of each unit of the large-scale conformal reflective metasurface array in the global coordinate system o-xyz

[0014] Step 7: According to the field superposition principle, obtain the total scattered field of the large-scale conformal reflective metasurface array

[0015]

[0016] For the regional division of the large-scale conformal reflective metasurface array structure in Step 1, a small conformal reflective metasurface subarray for equivalent replacement is selected as follows:

[0017] 1.1. Consider the metasurface with a period length as a whole. For the metasurface array to be solved, the phase gradient dimension is regarded as columns, and the dimension perpendicular to the phase gradient is regarded as rows.

[0018] 1.2. Calculate the least common multiple of the metasurface period length and the incident wave wavelength, and use it as the length division standard for the phase gradient dimension.

[0019] 1.3. Calculate the least common multiple of the metasurface unit length and the incident wave wavelength, and use it as the length division standard for the dimension perpendicular to the phase gradient.

[0020] 1.4. According to the division standards in Steps 1.2 and 1.3, re-divide the metasurface array to be solved, and regard each divided region as a whole as the unit of the large-scale conformal reflective metasurface array and the unit for subsequently forming the small conformal reflective metasurface subarray.

[0021] 1.5. For the units at the edge positions in the phase gradient dimension or the dimension perpendicular to the phase gradient whose lengths do not meet their corresponding division length standards after the division in Step 1.4, merge them with the units whose phase gradient dimension and dimension perpendicular to the phase gradient lengths closest to them both meet their corresponding length division standards, so that the lengths of all units of the large-scale conformal reflective metasurface array in the phase gradient dimension and the dimension perpendicular to the phase gradient are greater than or equal to their corresponding division length standards. At this time, the scale of the large-scale conformal reflective metasurface array is A rows and B columns.

[0022] 1.6. Select a small conformal reflective metasurface subarray with a rows and b columns from the large-scale conformal reflective metasurface array after the division in Step 1.5, which includes the units at its middle position and edge positions.

[0023] In Step 1, obtain the in-array scattering fields of each unit of the small conformal reflective metasurface subarray in the global coordinate system o-xyz which is expressed as follows:

[0024]

[0025] where n = 1, 2, … b, b + 1, …, a·b, θ is the elevation angle in the measurement space rectangular coordinate system, p = 1, 2,..., P, P is the number of elevation angle sampling points, φ is the azimuth angle in the measurement space rectangular coordinate system, q = 1, 2, …, Q, Q is the number of azimuth angle sampling points. The scattered fields of each unit of the small conformal reflective metasurface subarray in the global coordinate system, respectively Components in the x, y, and z directions.

[0026] The local coordinate system and the normal local coordinate system established with the geometric center of each unit of the small conformal reflective metasurface subarray as the origin as described in step 2 And the normal local coordinate system The method is as follows:

[0027] 2.1. It is stipulated that the geometric center of the nth unit of the small conformal reflective metasurface subarray is the origin o of the local coordinate system n , and the coordinate axes of the local coordinate system The positive directions are the same as the positive directions of the coordinate axes x, y, and z of the global coordinate system, and the local coordinate system is established

[0028] 2.2. It is stipulated that the geometric center of the nth unit of the small conformal reflective metasurface subarray is the origin o of the normal local coordinate system n , and the normal local coordinate system The positive direction of the axis is the unit outer normal direction, The positive direction of the axis is along the phase gradient direction, and the normal local coordinate system is established

[0029] The scattered fields of each unit of the small conformal reflective metasurface subarray in the local coordinate system as described in step 3 Are expressed as follows:

[0030]

[0031] Where j is the imaginary symbol, Is the wave number.

[0032] The method of obtaining the scattered fields of each unit of the subarray in the normal local coordinate system by transforming from the local coordinate system to the normal local coordinate system as described in step 3 Is as follows:

[0033] 3.1. The components of the normal local coordinate system And the components of the local coordinate system Are related through three Euler matrices and are expressed as follows:

[0034]

[0035] Where I 1n Is the Euler rotation matrix corresponding to a counterclockwise rotation of γ Angles about the n Axis, and I 2n Is the Euler rotation matrix corresponding to a counterclockwise rotation of α Angles about the nEuler rotation matrix corresponding to the angle, I 3n is the Euler rotation matrix corresponding to a counterclockwise rotation of β radians about the n axis, I 1n , I 2n , I 3n are expressed as follows:

[0036]

[0037] 3.2. Calculation The correspondence between is expressed as follows:

[0038]

[0039] 3.3. Calculate the scattering field of each unit of the small conformal reflective metasurface subarray in the normal local coordinate system according to Steps 3.1 and 3.2 which is expressed as follows:

[0040]

[0041] where are the components of the scattering field of each unit of the small conformal reflective metasurface subarray in the normal local coordinate system in the direction, and are the components of the scattering field of each unit of the small conformal reflective metasurface subarray in the local coordinate system in the direction.

[0042] The method for establishing the local coordinate system and the normal local coordinate system with the geometric center of each unit of the large-scale conformal reflective metasurface array as the origin described in Step 4 is as follows:

[0043] 4.1. The geometric center of the m-th unit of the large-scale conformal reflective metasurface array is the origin o of the local coordinate system m , and the positive directions of the coordinate axes of the local coordinate system are the same as the positive directions of the coordinate axes x, y, and z of the global coordinate system, and the local coordinate system

[0044] 4.2. The geometric center of the m-th unit of the large-scale conformal reflective metasurface array is the origin o of the normal local coordinate system m , the positive direction of the axis of the normal local coordinate system is the unit outer normal direction, and the positive direction of the axis is along the phase gradient direction, and the normal local coordinate system

[0045] The extrapolation and equivalent construction of the small conformal reflective metasurface subarray into a large-scale conformal reflective metasurface array as described in step 5, obtaining the scattering fields of each unit of the large-scale conformal reflective metasurface array in the normal local coordinate system where m = 1, 2, … B, B + 1, …, A·B, and the implementation is as follows:

[0046] 5.1. Perform row equivalence on the small conformal reflective metasurface subarray, and equivalently construct the a-row b-column subarray into an A-row b-column array:

[0047] Equivalent the units in the first row to the [(a - 1) / 2]-th row of the small conformal reflective metasurface subarray to the units in the first row to the [(a - 1) / 2]-th row of the A-row b-column array. Equivalent the unit in the [(a - 1) / 2]+1-th row of the small conformal reflective metasurface subarray to the units in the [(a - 1) / 2]+1-th row to the A - (a - 1) / 2-th row of the A-row b-column array. Equivalent the units in the [(a - 1) / 2]+2-th row to the a-th row of the small conformal reflective metasurface subarray to the units in the A - (a - 1) / 2+1-th row to the A-th row of the A-row b-column array, obtaining the in-array scattering fields of each unit of the A-row b-column array in the normal local coordinate system;

[0048] 5.2. Perform column equivalence on the A-row b-column array, and equivalently construct the A-row b-column array into a large-scale conformal reflective metasurface array of A rows and B columns:

[0049] Equivalent the units in the first column to the [(b - 1) / 2]-th column of the A-row b-column array to the units in the first column to the [(b - 1) / 2]-th column of the A-row B-column array. Equivalent the unit in the [(b - 1) / 2]+1-th column of the A-row b-column array to the units in the [(b - 1) / 2]+1-th column to the B - (b - 1) / 2-th column of the A-row B-column array. Equivalent the units in the [(b - 1) / 2]+2-th column to the b-th column of the A-row b-column array to the units in the B - (b - 1) / 2+1-th to the B-th column of the A-row B-column array, obtaining the in-array scattering fields of each unit of the A-row B-column large-scale conformal reflective metasurface array in the normal local coordinate system

[0050] The transformation from the normal local coordinate system to the local coordinate system as described in step 6 to obtain the scattering fields of each unit of the large-scale conformal reflective metasurface array in the local coordinate system The implementation is as follows:

[0051] 6.1. Connect the local coordinate system components and the normal local coordinate system components through three Euler matrices, and the representation is as follows:

[0052]

[0053] Among them, -1 represents the inverse matrix, I 1m is the Euler rotation matrix corresponding to a counterclockwise rotation of γ degrees about the m axis, I 2m is the Euler rotation matrix corresponding to a counterclockwise rotation of α degrees about the m axis, I 3m is the Euler rotation matrix corresponding to a counterclockwise rotation of β degrees about the m axis, I 1m , I 2m , I 3m are represented as follows:

[0054]

[0055] 6.2. Calculate and The correspondence between them is represented as follows:

[0056]

[0057] 6.3. Calculate the scattering fields of each unit of the large-scale conformal reflective metasurface array in the local coordinate system according to Steps 6.1 and 6.2 are represented as follows:

[0058]

[0059] Among them, are the components of the scattering fields of each unit of the large-scale conformal reflective metasurface array in the local coordinate system in the direction, are the components of the scattering fields of each unit of the large-scale conformal reflective metasurface array in the normal local coordinate system in the direction.

[0060] The scattering fields of each unit of the large-scale conformal reflective metasurface array described in Step 6 in the global coordinate system are represented as follows:

[0061]

[0062] Among them, j is the imaginary symbol, is the wave number.

[0063] Compared with the prior art, the present invention has the following advantages:

[0064] First, the present invention divides the large-scale conformal reflective metasurface into regions, making the scattered fields in the unit array in the middle part tend to be consistent. Then, according to the element similarity theory, a sub-array for equivalent construction is selected, improving the calculation efficiency.

[0065] Second, the present invention introduces the spatial coordinate rotation method to transform the scattered fields of each unit into the normal local coordinate system, realizing the equivalence of the scattered fields in each unit array of the sub-array to the scattered fields in each unit array of the large-scale conformal reflective metasurface array, and accelerating the calculation speed.

[0066] Third, the present invention simplifies the calculation problem of the scattered field of the large-scale conformal reflective metasurface into the calculation problem of the scattered field of a sub-array, shortening the calculation time. It is applicable to conformal metasurface arrays of different scales, and the calculation time will not increase significantly with the increase of the array scale.

[0067] In summary, the present invention has the advantages of high calculation efficiency, short calculation time consumption, and wide application range. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 is the implementation flowchart of the present invention.

[0069] Figure 2 is the schematic diagram of the large-scale conformal reflective metasurface array for which the scattered field is to be obtained in the present invention.

[0070] Figure 3 is the schematic diagram of the region division of the large-scale conformal reflective metasurface array in the present invention.

[0071] Figure 4 is Figure 2 the schematic diagram of the sub-array of the large-scale conformal reflective metasurface array shown.

[0072] Figure 5 is the schematic diagram of establishing the local coordinate system and the normal local coordinate system in the present invention.

[0073] Figure 6 is the schematic diagram of performing row equivalence and column equivalence on the sub-array respectively in the present invention; among them, Figure 6 (a) is the schematic diagram of row equivalence, Figure 6 (b) is the schematic diagram of column equivalence.

[0074] Figure 7 is the comparison diagram of the calculation result of the present invention and the full-wave simulation result when a horizontally polarized plane wave is incident.

[0075] Figure 8 is the comparison diagram of the calculation result of the present invention and the full-wave simulation result when a vertically polarized plane wave is incident. DETAILED DESCRIPTION OF THE INVENTION

[0076] To more clearly describe the technical solution and effects of the present invention, the following will be described in conjunction with specific embodiments and the accompanying drawings.

[0077] Refer to Figure 1 , the implementation steps of the present invention are as follows:

[0078] Step 1: Construct a large-scale conformal reflective metasurface array, perform regional division to select a small conformal reflective metasurface subarray for equivalent replacement, and collect the in-array scattering fields of each unit of this subarray in the global coordinate system.

[0079] 1.1) Refer to Figure 2 , in this example, the FEKO simulation software is used to model and simulate the large-scale conformal reflective metasurface array to be solved. The reflective metasurface used can enhance the target monostatic RCS in the angular range of 62.5° to 77.5°. The length of the metasurface unit is 7.8 mm, and the period length is 15.6 mm. A cylindrical conformal reflective metasurface array with 20 periods in the phase gradient dimension and 40 units in the vertical phase gradient dimension is established in the global rectangular coordinate system o-xyz as the large-scale conformal reflective metasurface array to be solved. The phase gradient is along the radial direction of the cylinder, the radius of the cylinder is 148.97 mm, the unit rotation angle is 3°, the incident wave is selected as a plane wave with a frequency of 10 GHz, the incident angle θ range is set to 0° to 180°, and the φ range is 0° to 360°, with an interval of 1° for both;

[0080] 1.2) Perform regional division on the structure of the large-scale conformal reflective metasurface array, and select a small conformal reflective metasurface subarray for equivalent replacement;

[0081] 1.2.1) Regard one period length of the metasurface as a whole. The metasurface array to be solved is regarded as columns along the phase gradient dimension and rows along the vertical phase gradient dimension;

[0082] 1.2.2) Calculate that the least common multiple of the metasurface period length and the incident wave wavelength is approximately 30 mm, and use it as the length division standard for the phase gradient dimension;

[0083] 1.2.3) Calculate that the least common multiple of the metasurface unit length and the incident wave wavelength is approximately 30 mm, and use it as the length division standard for the vertical phase gradient dimension;

[0084] 1.2.4) Re-divide the metasurface array to be solved according to the division standards in 1.2.2) and 1.2.3), and regard each divided region as a whole as the unit of the large-scale conformal reflective metasurface array and the unit for subsequently forming the small conformal reflective metasurface subarray;

[0085] 1.2.5) For the cells whose lengths of the phase gradient dimension or the vertical phase gradient dimension after the division in 1.2.4) do not meet their corresponding division length criteria, they are merged with the cells whose lengths of both the closest phase gradient dimension and the vertical phase gradient dimension meet their corresponding length division criteria, so that the length of each cell in both the phase gradient dimension and the vertical phase gradient dimension is greater than or equal to its corresponding division length criterion. At this time, the scale of the large array is 10 rows and 10 columns, as Figure 3 shown;

[0086] 1.2.6) According to the theory of array element similarity, cells are respectively selected from the middle part and the edge part of the divided large-scale conformal reflective metasurface array to form a 5-row and 5-column small conformal reflective metasurface sub-array for equivalence, as Figure 4 shown;

[0087] 1.3) Set the range of the incident angle θ to be 0° to 180°, and the range of φ to be 0° to 360°, with an interval of 1° each, and obtain the in-array scattering field of each cell of the small conformal reflective metasurface sub-array in the global coordinate system o-xyz which is expressed as follows:

[0088]

[0089] where n = 1, 2,... 9, θ is the pitch angle in the measured space rectangular coordinate system, p = 1, 2,..., 181, φ is the azimuth angle in the measured space rectangular coordinate system, q = 1, 2,..., 361, are respectively the scattering fields of each cell of the small conformal reflective metasurface sub-array in the global coordinate system in the x, y, and z directions.

[0090] Step 2: Refer to Figure 5 , and establish a local coordinate system and a normal local coordinate system with the geometric center of each cell of the small conformal reflective metasurface sub-array as the origin, and obtain the polar coordinates (R n , θ n , φ n ) of the geometric center of each cell in the global coordinate system and the rotation angles α of the coordinate axes of each cell's normal local coordinate system relative to the local coordinate system n , β n , γ n .

[0091] 2.1) It is stipulated that the geometric center of the nth cell of the small conformal reflective metasurface sub-array is the origin o n of the local coordinate system, and the coordinate axes of the local coordinate system The positive directions are the same as the positive directions of the coordinate axes x, y, and z of the global coordinate system, and a local coordinate system is established

[0092] 2.2) It is stipulated that the geometric center of the nth unit of the small conformal reflective metasurface subarray is the origin o of the normal local coordinate system n , the normal local coordinate system The positive direction of the axis is the unit outer normal direction, The positive direction of the axis is vertically downward along the cylindrical axis, and a normal local coordinate system is established

[0093] 2.3) Obtain the polar coordinates (R n , θ n , φ n ) of the geometric center of each unit in the global coordinate system and the axes of the normal local coordinate system of each unit The rotation angles α n , β n , γ n ;

[0094] Step 3: Transform the scattered fields at the centers of each unit of the small conformal reflective metasurface subarray from the global coordinate system to the local coordinate system to obtain the scattered fields of each unit in the local coordinate system Then transform from the local coordinate system to the normal local coordinate system to obtain the scattered fields of each unit in the normal local coordinate system

[0095] 3.1) Transform the scattered fields at the centers of each unit of the small conformal reflective metasurface subarray from the global coordinate system to the local coordinate system to obtain the scattered fields of each unit in the local coordinate system It is expressed as follows:

[0096]

[0097] Among them, j is the imaginary symbol, is the wave number;

[0098] 3.2) Transform the scattered fields at the centers of each unit of the small conformal reflective metasurface subarray from the local coordinate system to the normal local coordinate system to obtain the scattered fields of each unit in the normal local coordinate system

[0099] 3.2.1) Connect the components of the normal local coordinate system and the components of the local coordinate system through three Euler matrices, and it is expressed as follows:

[0100]

[0101] Among them, I 1n is the rotation around The axis rotates counterclockwise by γ n The Euler rotation matrix corresponding to the angle, I 2n is for rotation around the axis counterclockwise by α n The Euler rotation matrix corresponding to the angle, where I 3n is for rotation around the axis counterclockwise by β n The Euler rotation matrix corresponding to the angle, I 1n , I 2n , I 3n are expressed as follows:

[0102]

[0103] 3.2.2) Calculate and The corresponding relationship between them is expressed as follows:

[0104]

[0105] 3.2.3) Calculate the scattering field of each unit of the small conformal reflective metasurface subarray in the normal local coordinate system according to the results of 3.2.1) and 3.2.2) is expressed as follows:

[0106]

[0107] Among them, are respectively the scattering fields of each unit of the small conformal reflective metasurface subarray in the normal local coordinate system in the direction components, are respectively the scattering fields of each unit of the small conformal reflective metasurface subarray in the local coordinate system in the direction components.

[0108] Step Four: Refer to Figure 5 and establish a local coordinate system and a normal local coordinate system with the geometric center of each unit of the large-scale conformal reflective metasurface array as the origin, and obtain the spherical coordinates (R m , θ m , φ m ) of the geometric center of each unit in the global coordinate system and the rotation angles α of the axes m of the normal local coordinate system of each unit relative to the local coordinate system, β m , γ m ;

[0109] 4.1) Define the geometric center of the m-th unit of the large-scale conformal reflective metasurface array as the origin o of the local coordinate system. m , and the positive directions of the coordinate axes of the local coordinate system are the same as the positive directions of the coordinate axes x, y, and z of the global coordinate system, and establish the local coordinate system

[0110] 4.2) Define the geometric center of the m-th unit of the large-scale conformal reflective metasurface array as the origin o of the normal local coordinate system. m , and the normal local coordinate system The positive direction of the axis is the unit outer normal direction, The positive direction of the axis is along the phase gradient direction, and establish the normal local coordinate system

[0111] 4.3) Obtain the spherical coordinates (R m , θ m , φ m ) of the geometric center of each unit in the global coordinate system and the rotation angles α of the coordinate axes of the normal local coordinate system of each unit relative to the local coordinate system m , β m , γ m .

[0112] Step Five: Extrapolate and equivalently construct the small conformal reflective metasurface subarray into a large-scale conformal reflective metasurface array, and obtain the scattering fields of each unit of the large-scale conformal reflective metasurface array in the normal local coordinate system where m = 1, 2,... 100.

[0113] 5.1) Perform row equivalence on the small conformal reflective metasurface subarray, and equivalently construct the 5×5 small conformal reflective metasurface subarray into a 10×5 array. As shown in Figure 6 (a), the units in the first row to the second row of the small conformal reflective metasurface subarray are equivalent to the units in the first row to the second row of the 10×5 array, the units in the third row of the small conformal reflective metasurface subarray are equivalent to the units in the third row to the eighth row of the 10×5 array, and the units in the fourth row to the fifth row of the small conformal reflective metasurface subarray are equivalent to the units in the ninth row to the tenth row of the 10×5 array, and obtain the in-array scattering fields of each unit of the 10×5 array in the normal local coordinate system;

[0114] 5.2) Perform column equivalence on the 10×5 array, and equivalently construct the 10×5 array into a 10×10 large-scale conformal reflective metasurface array, as shown in Figure 6As shown in (b), the units in the 1st to 2nd columns of the 10-row and 5-column array are equivalent to the units in the 1st to 2nd columns of the 10-row and 10-column array, the units in the 3rd column of the 10-row and 5-column array are equivalent to the units in the 3rd to 8th columns of the 10-row and 10-column array, and the units in the 4th to 5th columns of the 10-row and 5-column array are equivalent to the units in the 9th to 10th columns of the 10-row and 10-column array, obtaining the in-array scattering fields of each unit of the large-scale conformal reflective metasurface array with 10 rows and 10 columns in the normal local coordinate system

[0115] Step 6: Transform the in-array scattering fields of each unit of the large-scale conformal reflective metasurface array from the normal local coordinate system to the local coordinate system to obtain the scattering fields of each unit in the local coordinate system Then transform from the local coordinate system to the global coordinate system to obtain the scattering fields of each unit in the global coordinate system

[0116] 6.1) Transform the in-array scattering fields of each unit of the large-scale conformal reflective metasurface array from the normal local coordinate system to the local coordinate system to obtain the scattering fields of each unit in the local coordinate system

[0117] Relate the local coordinate system components and the normal local coordinate system components through three Euler matrices, expressed as follows:

[0118]

[0119] where, -1 represents the inverse matrix, I 1m is the Euler rotation matrix corresponding to a counterclockwise rotation of γ angle about the m axis, I 2m is the Euler rotation matrix corresponding to a counterclockwise rotation of α angle about the m axis, I 3m is the Euler rotation matrix corresponding to a counterclockwise rotation of β angle about the m axis, I 1m 、I 2m 、I 3m are expressed as follows:

[0120]

[0121] 6.2) Calculate the corresponding relationship between and , expressed as follows:

[0122]

[0123] 6.3) Calculate the scattering fields of each unit of the large-scale conformal reflective metasurface array in the local coordinate system according to the results of 6.1) and 6.2). It is expressed as follows:

[0124]

[0125] Where, are respectively the scattering fields of each unit of the large-scale conformal reflective metasurface array in the local coordinate system in the direction, are respectively the scattering fields of each unit of the large-scale conformal reflective metasurface array in the normal local coordinate system in the direction.

[0126] Transform the scattering fields of each unit in the large-scale conformal reflective metasurface array from the local coordinate system to the global coordinate system to obtain the scattering fields of each unit in the global coordinate system It is expressed as follows:

[0127]

[0128] Where, j is the imaginary symbol, is the wave number.

[0129] Step 7: Perform long addition on the scattering fields of each unit of the large-scale conformal reflective metasurface array to obtain the total scattering field

[0130]

[0131] The effects of the present invention can be further illustrated by the following simulation experiments:

[0132] I. Simulation experiment conditions

[0133] The large-scale conformal reflective metasurface array to be solved is modeled and simulated using the FEKO simulation software. The reflective metasurface used can enhance the target monostatic RCS in the angular range of 62.5° to 77.5°. The length of the metasurface unit is 7.8 mm, and the period length is 15.6 mm. A cylindrical conformal reflective metasurface array with 20 periods in the phase gradient dimension and 40 units in the vertical phase gradient dimension is established in the global rectangular coordinate system o-xyz as the large-scale conformal reflective metasurface array to be solved. The phase gradient is along the radial direction of the cylinder, the radius of the cylinder is 148.97 mm, the unit rotation angle is 3°, the incident wave is a plane wave with a frequency of 10 GHz, the incident angle θ range is set to 0° to 180°, and the φ range is 0° to 360°, with an interval of 1° for both. The total monostatic scattering field data of the large-scale conformal reflective metasurface array is obtained. The large-scale conformal reflective metasurface array is divided into regions, and a 5×5 element metasurface array with the same arrangement as the large-scale conformal reflective metasurface array is selected as the small conformal reflective metasurface sub-array, and the monostatic in-array scattering field data of each unit of the small conformal reflective metasurface sub-array in the global coordinate system is obtained.

[0134] II. Simulation Experiment Contents

[0135] Simulation Experiment 1: Under the above experimental conditions, the method of the present invention uses the monostatic in-array scattering field data of each unit of the small conformal reflective metasurface sub-array when a horizontally polarized plane wave is incident to obtain the monostatic total scattering field of the large-scale conformal reflective metasurface array when a horizontally polarized plane wave is incident, and compares it with the result obtained by directly simulating the large-scale conformal reflective metasurface array using FEKO. The results are as Figure 7 shown.

[0136] As can be seen from Figure 7 it, when a horizontally polarized plane wave is incident, the monostatic total scattering field of the large-scale conformal reflective metasurface array calculated by the present invention is basically consistent with the FEKO simulation result in the angular range of 60° to 120°, and the error in other angular ranges shows a slightly increasing trend as the angle deviates, indicating that the present invention can achieve the acquisition of the scattering field of the large-scale conformal reflective metasurface.

[0137] Simulation Experiment 2: Under the above experimental conditions, the method of the present invention uses the monostatic in-array scattering field data of each unit of the small conformal reflective metasurface sub-array when a vertically polarized plane wave is incident to obtain the monostatic total scattering field of the large-scale conformal reflective metasurface array when a vertically polarized plane wave is incident, and compares it with the result obtained by directly simulating the large-scale conformal reflective metasurface array using FEKO. The results are as Figure 8 shown.

[0138] As can be seen from Figure 8It can be seen that when a vertically polarized plane wave is incident, the total monostatic scattering field of the large-scale conformal reflective metasurface array calculated by the present invention is basically consistent with the FEKO simulation results, and the degree of coincidence is good, indicating that the present invention can achieve the acquisition of the scattering field of the large-scale conformal reflective metasurface.

Claims

1. A method for rapidly acquiring a large-scale conformal reflective metasurface scattering field, 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 a subarray, and obtain the scattering field of each unit of the small conformal reflective metasurface subarray in the global coordinate system o-xyz Step 2: Establish 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 Obtain the polar coordinates (R n ,θ n ,φ n ) and the local coordinate system axes of each element normal The rotation angle α relative to the local coordinate system n , β n , γ n ; Step 3: transform the scattered field in each unit array of the small conformal reflective metasurface subarray from the global coordinate system to the local coordinate system to obtain the scattered field of each unit of the small conformal reflective metasurface subarray in the local coordinate system. Then transform from the local coordinate system to the scattered field in 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 (R m ,θ m ,φ m ) and the normal local coordinate system axes of each unit of the large-scale conformal reflective metasurface array Relative to the local coordinate system of each unit of the large-scale conformal reflective metasurface array The rotation angle α m , β m , γ m ; Step 5: Extrapolate the small conformal reflective metasurface subarray into a large-scale conformal reflective metasurface array to obtain the scattering field of each unit of the large-scale conformal reflective metasurface array in the normal local coordinate system. Step 6: Transform the scattered field in each unit array 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 unit of the large-scale conformal reflective metasurface array in the local coordinate system. Then transform from the local coordinate system to the global coordinate system to obtain the scattering field of each unit of the large-scale conformal reflective metasurface array in the global coordinate system o-xyz Step 7: Obtain the total scattered field of a large-scale conformal reflective metasurface array based on the field superposition principle 2. The method for rapidly acquiring a large-scale conformal reflective metasurface scattering field according to claim 1, characterized in that: In step 1, the large-scale conformal reflective metasurface array structure is divided into regions, and a small conformal reflective metasurface sub-array for equivalent replacement is selected, and the method is as follows: 1.

1. Consider a metasurface of one period length as a whole, and the metasurface array to be solved along the phase gradient dimension as the column and the perpendicular phase gradient dimension as the row; 1.

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

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

4. According to the division criteria of step 1.2 and step 1.3, the metasurface array to be solved is re-divided, and each divided area is regarded as a whole as a unit of a large-scale conformal reflective metasurface array and a unit used to form a small conformal reflective metasurface sub-array in the future; 1.

5. For the units whose edge position phase gradient dimension or vertical phase gradient dimension length does not meet the corresponding division length standard after the division in step 1.4, the units whose phase gradient dimension and vertical phase gradient dimension length meet the corresponding length division standard are merged, so that the phase gradient dimension and vertical phase gradient dimension length of all units in the large-scale conformal reflective metasurface array are greater than or equal to the corresponding division length standard. At this time, the scale of the large-scale conformal reflective metasurface array is A rows and B columns; 1.

6. Select a small conformal reflective metasurface sub-array with a rows and b columns containing middle position units and edge position units from the large-scale conformal reflective metasurface array divided in step 1.

5.

3. The method for rapidly acquiring a large-scale conformal reflective metasurface scattering field according to claim 1, characterized in that: In step 1, the scattered field of each unit of the small conformal reflective metasurface subarray in the global coordinate system o-xyz is obtained. It is expressed as follows: Wherein, n=1,2,...b,b+1,...,a·b, θ is the pitch angle in the rectangular coordinate system of the measurement space, p=1,2,...,P, P is the number of sampling points for the pitch angle, φ is the azimuth angle in the rectangular coordinate system of the measurement space, q=1,2,...,Q, Q is the number of sampling points for the azimuth angle, The scattering fields of each unit of the small conformal reflective metasurface subarray in the global coordinate system are Components in the x, y, and z directions.

4. The method for rapidly acquiring a large-scale conformal reflective metasurface scattering field according to claim 1, characterized in that: Step 2: Establish 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 Here’s how: 2.

1. Define the geometric center of the nth unit of the small conformal reflective metasurface subarray as the origin of the local coordinate system o n , local coordinate system axes The positive directions are the same as the positive directions of the coordinate axes x, y, and z of the global coordinate system, and a local coordinate system is established. 2.

2. Define the geometric center of the nth unit of the small conformal reflective metasurface subarray as the origin o of the normal local coordinate system n , normal local coordinate system The positive direction of the axis is the direction of the unit's external normal. The positive direction of the axis is along the phase gradient direction, and the normal local coordinate system is established 5. The method for rapidly acquiring a large-scale conformal reflective metasurface scattering field according to claim 1, characterized in that: Scattering field of each unit of the small conformal reflective metasurface subarray in the local coordinate system in step 3 It is expressed as follows: Where j is the imaginary number symbol, is the wave number.

6. The method for rapidly acquiring a large-scale conformal reflective metasurface scattering field according to claim 1, characterized in that: Step 3: Transform 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. Here’s how: 3.

1. Transform the normal local coordinate system components through three Euler matrices and the local coordinate system components In connection, it is expressed as follows: Among them, I 1n For around Axis rotates counterclockwiseγ n The Euler rotation matrix corresponding to the angle, I 2n For around Axis rotates counterclockwise α n The Euler rotation matrix corresponding to the angle, I 3n For around Axis rotates counterclockwise β n The Euler rotation matrix corresponding to the angle, I 1n ,I 2n ,I 3n It is expressed as follows: 3.

2. Calculation and The corresponding relationship between them is expressed as follows: 3.

3. Calculate the scattering field of each unit of the small conformal reflective metasurface subarray in the normal local coordinate system according to steps 3.1 and 3.2 It is expressed as follows: in, The scattering fields of each unit of the small conformal reflective metasurface subarray in the normal local coordinate system are exist The weight in direction, The scattering fields of each unit of the small conformal reflective metasurface subarray in the local coordinate system are exist Directional weight.

7. According to the method for rapidly acquiring the scattering field of a large-scale conformal reflective metasurface according to claim 1, in step 4, 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 Here’s how: 4.

1. The geometric center of the mth unit of the large-scale conformal reflective metasurface array is the origin of the local coordinate system o m , local coordinate system axes The positive directions are the same as the positive directions of the coordinate axes x, y, and z of the global coordinate system, and a local coordinate system is established. 4.

2. The geometric center of the mth unit of the large-scale conformal reflective metasurface array is the origin of the normal local coordinate system o m , normal local coordinate system The positive direction of the axis is the direction of the unit's external normal. The positive direction of the axis is along the phase gradient direction, and the normal local coordinate system is established 8. The method for rapidly acquiring a large-scale conformal reflective metasurface scattering field according to claim 1, characterized in that: In step 5, the small conformal reflective metasurface subarray is extrapolated and equivalently constructed into a large-scale conformal reflective metasurface array, and the scattering field of each unit of the large-scale conformal reflective metasurface array in the normal local coordinate system is obtained. Where m = 1, 2, ... B, B + 1, ..., A·B, and is implemented as follows: 5.

1. Perform row equivalence on the small conformal reflective metasurface subarray, and construct the a-row and b-column subarray equivalently into an A-row and b-column array: The units from the 1st to (a-1) / 2th rows of the small conformal reflective metasurface subarray are equivalent to the units from the 1st to (a-1) / 2th rows of the A row and b column array, the units from the [(a-1) / 2]+1th row of the small conformal reflective metasurface subarray are equivalent to the units from the [(a-1) / 2]+1th row to the A-(a-1) / 2th row of the A row and b column array, and the units from the [(a-1) / 2]+2th row to the ath row of the small conformal reflective metasurface subarray are equivalent to the units from the A-(a-1) / 2+1th row to the Ath row of the A row and b column array, and the scattered field in the array of each unit of the A row and b column array in the normal local coordinate system is obtained; 5.

2. Perform column equivalence on the A-row and B-column array, and construct the A-row and B-column array equivalently into a large-scale conformal reflective metasurface array with A-row and B-column: The units from the 1st to the (b-1) / 2th columns of the A-row and b-column array are equivalent to the units from the 1st to the (b-1) / 2th columns of the A-row and B-column array, the units from the [(b-1) / 2]+1th column of the A-row and b-column array are equivalent to the units from the [(b-1) / 2]+1th column to the B-(b-1) / 2th column of the A-row and B-column array, and the units from the [(b-1) / 2]+2th column to the b-column of the A-row and b-column array are equivalent to the units from the B-(b-1) / 2+1th column to the B-column of the A-row and B-column array. The scattering field of each unit of the A-row and B-column large-scale conformal reflective metasurface array in the normal local coordinate system is obtained.

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

1. Transform the local coordinate system components through three Euler matrices and the normal local coordinate system component In connection, it is expressed as follows: in, [] -1 represents the inverse matrix, I 1m For around Axis rotates counterclockwise γ m The Euler rotation matrix corresponding to the angle, I 2m For around Axis rotates counterclockwise α m The Euler rotation matrix corresponding to the angle, I 3m For around Axis rotates counterclockwise β m The Euler rotation matrix corresponding to the angle, I 1m ,I 2m ,I 3m It is expressed as follows: 6.

2. Calculation and The corresponding relationship between them is expressed as follows: 6.

3. Calculate the scattering field of each unit of the large-scale conformal reflective metasurface array in the local coordinate system according to steps 6.1 and 6.2 It is expressed as follows: in, The scattering fields of each unit of the large-scale conformal reflective metasurface array in the local coordinate system are exist The weight in direction, They are the scattering fields of each unit of the large-scale conformal reflective metasurface array in the normal local coordinate system. exist Directional weight.

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

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