A method for characterizing target scattering characteristics based on electromagnetic vortex polarization joint scattering matrix

Abstract

The present invention provides a method for characterizing target scattering characteristics based on an electromagnetic vortex polarization joint scattering matrix, and belongs to the technical field of radar target scattering characteristics. From the two dimensions of electromagnetic wave orbital angular momentum (OAM) and spin angular momentum (SAM), while utilizing the orthogonal characteristics of the OAM electromagnetic vortex mode and the orthogonal characteristics of the electromagnetic wave SAM polarization mode, an electromagnetic vortex polarization joint scattering matrix is ​​established to characterize the target scattering characteristics including all angular momentum characteristics of the electromagnetic wave, and to comprehensively describe the target scattering characteristics under the irradiation of electromagnetic vortex waves of different modes and polarization modes. The present invention integrates the electromagnetic vortex scattering matrix and the polarization scattering matrix to construct a three-dimensional matrix that characterizes the target scattering characteristics, and realizes a multi-dimensional and refined description of the target scattering characteristics under the irradiation of complex electromagnetic waves.

Description

Technical Field

[0001] The invention belongs to the technical field of radar target scattering characteristics, and in particular relates to a target scattering characteristic characterization method based on an electromagnetic vortex polarization joint scattering matrix. Background Art

[0002] According to classical electromagnetic theory, the momentum carried by electromagnetic waves can be divided into linear momentum and angular momentum, and angular momentum can be decomposed into spin angular momentum. (Spin Angular Momentum, SAM) and orbital angular momentum (Orbital Angular Momentum, OAM), spin angular momentum is related to the polarization state of the electromagnetic wave, and orbital angular momentum is related to the phase space distribution of the electromagnetic wave front. The expression is:

[0003] Electromagnetic vortex waves are electromagnetic waves that carry information in both SAM and OAM dimensions. Compared with traditional plane waves, the wave function of electromagnetic vortex waves contains a phase term related to the spatial azimuth. ,Right now:

[0004] ,

[0005] in, represents the imaginary unit, represents the exponential function, Represents the position vector from a point in the electromagnetic field space to the beam axis, represents the amplitude of a conventional electromagnetic wave, represents the orbital angular momentum mode number, It indicates the azimuth angle around the beam axis. From the above formula, we can see that the phase distribution of the electromagnetic vortex wave is related to the modal value, and the isophase surface advances in a spiral.

[0006] The phase distribution of different modes of electromagnetic vortex waves is different, so when electromagnetic waves are irradiated on the same target, their scattering characteristics will be different. Different modes are orthogonal to each other, and any mode can form a pair of orthogonal bases. Based on the above theory, the electromagnetic vortex scattering matrix is ​​constructed, using the symbol It is used to describe the target scattering characteristics based on the single dimension of electromagnetic vortex wave OAM. The matrix form of electromagnetic vortex scattering matrix is ​​as follows: Figure 1 As shown. Electromagnetic vortex scattering matrix Under any combination of different transmission and reception modes, it can be divided into four sizes: Submatrix of , which is used to describe the scattering characteristics of electromagnetic vortex targets under different mode combinations. For a submatrix , when a contains When an electromagnetic vortex wave with an OAM mode value is incident on the target, the backscattered field is expressed as:

[0007]

[0008] Among them, the superscript denotes the incident field, the superscript represents the scattered field, that is is the incident vortex electric field, is the scattered vortex electric field. Each element in Indicates that the subscript represents the modal value of the incident wave orbital angular momentum, represents the modal value of the orbital angular momentum of the scattered wave, , each element is a complex number, and each complex value depends on the sign state of the electromagnetic wave receiving and transmitting mode value. According to the sign state of the receiving and transmitting mode value, each submatrix It is defined as the vortex scattering sub-matrix corresponding to the four transmitting and receiving states. The specific corresponding relationship is shown in Table 1.

[0009] Table 1

[0010]

[0011] The scattered waves formed after the incident wave irradiates the target contain a variety of different SAM polarization components. According to the SAM polarization characteristics of electromagnetic scattering, for most targets, the polarization of the scattered field will change compared to the polarization of the incident field, which is called depolarization or cross-polarization. The SAM polarization scattering characteristics of the target refer to the co-polarization and depolarization effects of the target on various polarized electromagnetic waves.

[0012] The SAM polarization scattering matrix is ​​related to the polarization basis. The polarization basis consists of two orthogonal polarization vectors forming a column vector. Commonly used polarization bases include horizontal-vertical polarization bases. , Rotational Linear Polarization Basis and left-right circular polarization basis The superscript T represents the transpose of the matrix. The three polarization bases can be expressed by coordinate transformation. The polarization scattering matrix of the same target is different under different polarization bases. The polarization scattering field expressions under different polarization bases are as follows:

[0013]

[0014]

[0015]

[0016] Among them, the superscript represents the incident field, represents the scattered field, that is represents the incident electric field vector, represents the electric field vector of the scattered field. Corresponding to the three polarization bases mentioned above, namely , , represents the incident electric field vector under three orthogonal polarization combinations, represents the three polarization scattering matrices, They represent the SAM polarization scattering coefficients of the above three orthogonal polarization combinations. Each element is a complex number, and each complex value depends on the polarization state of the electromagnetic wave. From the above formula, we can see that the SAM polarization scattering matrix consists of a size of The matrix fully reflects the relationship between the incident field and the scattered field in the SAM dimension, contains rich information such as target shape, size, structure, and posture, and can effectively characterize the target scattering characteristics.

[0017] In the field of radar detection, the target scattering characteristics presented by electromagnetic vortex waves will include the angular momentum characteristics of SAM and OAM. If a characterization method that can fully describe the target scattering characteristics reflected by electromagnetic vortex waves SAM and OAM is constructed, it will have potential application value in many application fields such as target characteristic measurement and extraction, target classification and recognition, super-resolution imaging, and rotational Doppler extraction. Summary of the invention

[0018] In order to solve the above technical problems, the present invention provides a method for characterizing target scattering characteristics based on an electromagnetic vortex polarization joint scattering matrix. Based on the orthogonal characteristics between the electromagnetic vortex wave OAM modes and the orthogonal characteristics of the SAM polarization modes, a three-dimensional matrix is ​​used to simultaneously describe the target scattering characteristics of multi-modal electromagnetic vortex waves SAM and OAM.

[0019] To achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0020] A method for characterizing target scattering characteristics based on an electromagnetic vortex polarization joint scattering matrix comprises the following steps:

[0021] Step 1, construct the electromagnetic vortex polarization joint scattering matrix: establish a three-dimensional rectangular coordinate system in space, and the three coordinate axes of the coordinate system are the incident wave OAM mode value, the scattered wave OAM mode value and the SAM polarization combination mode; regard the same SAM polarization combination mode as a state of transmitting and receiving angular momentum, that is, the target scattering coefficients of the same SAM polarization combination mode constitute a planar electromagnetic vortex scattering matrix. In the direction of the coordinate axis of the SAM polarization combination mode, the planar electromagnetic vortex scattering matrix is ​​expanded to a scale of The three-dimensional matrix is ​​defined as the electromagnetic vortex polarization joint scattering matrix, using the symbol Indicates that when a After the electromagnetic vortex wave with an OAM mode value is incident and irradiates the target, the backscattered field is expressed as:

[0022] ,

[0023] ,

[0024] In the formula, the superscript denotes the incident field, the superscript represents the scattered field, the superscript indicates the polarization direction of the incident wave, and the superscript Indicates the polarization direction of the scattered wave and the polarization direction of the incident wave , scattered wave polarization direction Take the average or , H represents horizontal polarization, V represents vertical polarization; subscript represents the incident wave OAM mode value, subscript represents the OAM mode value of the scattered wave, ; E represents the vortex electric field, that is Indicates that the SAM polarization combination is When the incident wave OAM mode value is m, the incident vortex electric field The SAM polarization combination is represented by When the scattered wave OAM mode value is n, the scattered vortex electric field Indicates that the SAM polarization combination is The electromagnetic vortex polarization joint scattering matrix at time , each element is recorded as a complex number , indicating that the SAM polarization combination is The electromagnetic vortex scattering coefficient when the incident wave OAM mode value is m and the scattered wave OAM mode value is n;

[0025] Step 2, define the degradation of the electromagnetic vortex polarization joint scattering matrix: observe the electromagnetic vortex polarization joint scattering matrix longitudinally. When the OAM modal values ​​of the incident wave and the scattered wave of the electromagnetic vortex wave are both fixed values, the electromagnetic vortex polarization joint scattering matrix degenerates into the polarization scattering matrix corresponding to the electromagnetic vortex wave with the incident wave OAM modal value m and the scattered wave OAM modal value n; when the OAM modal values ​​of the incident wave and the scattered wave of the electromagnetic vortex wave are both 0, the electromagnetic wave morphology degenerates into a plane wave.

[0026] The beneficial effects of the present invention are:

[0027] Compared with the electromagnetic vortex scattering matrix, the electromagnetic vortex polarization joint scattering matrix describes the target characteristics from two dimensions: orbital angular momentum and spin angular momentum of the electromagnetic vortex wave angular momentum. It contains more comprehensive target scattering characteristic information, further improving the radar system's ability to extract and classify target characteristics. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a schematic diagram of the expression of electromagnetic vortex scattering matrix in the prior art;

[0029] Figure 2 It is a schematic diagram of the expression of the electromagnetic vortex polarization joint scattering matrix of the present invention;

[0030] Figure 3 This is a schematic diagram of the SAM polarization scattering matrix corresponding to a single modal value after the electromagnetic vortex polarization joint scattering matrix is ​​degraded. DETAILED DESCRIPTION

[0031] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0032] The present invention takes the orbital angular momentum modal value as As an example, the electromagnetic vortex wave is used as the incident wave. After irradiating the target, the orbital angular momentum modal value is The electromagnetic vortex wave SAM takes the horizontal-vertical polarization basis as an example, that is, the electromagnetic vortex wave is decomposed into horizontal polarization (H) and vertical polarization (V), and the corresponding electromagnetic vortex angular momentum scattering matrix is ​​defined to characterize the target scattering characteristics. On the basis of the electromagnetic vortex scattering matrix, the electromagnetic vortex polarization joint scattering matrix adds the dimension of characterizing the electromagnetic vortex wave SAM to form a three-dimensional matrix, thereby providing a more complete description of the target angular momentum scattering characteristics.

[0033] A three-dimensional rectangular coordinate system is established with the incident wave orbital angular momentum modal value, scattered wave orbital angular momentum modal value and SAM polarization combination as three mutually perpendicular coordinate axes. Among them, the SAM polarization combination includes four combinations: incident wave horizontal polarization, scattered wave horizontal polarization, incident wave horizontal polarization, scattered wave vertical polarization, incident wave vertical polarization, scattered wave horizontal polarization, incident wave vertical polarization, scattered wave vertical polarization, and so on. They are represented by symbols express.

[0034] For the convenience of description, the same SAM polarization combination is regarded as a state of transmitting and receiving angular momentum, that is, the target scattering coefficient of the same SAM polarization combination constitutes a plane matrix, which is a plane matrix with a scale of In the direction of the SAM polarization combination coordinate axis, the electromagnetic vortex scattering matrix is ​​expanded to a scale of The three-dimensional matrix is ​​defined as the electromagnetic vortex polarization joint scattering matrix, using the symbol Indicates. In the SAM polarization combination hour, Both are acceptable or , when a contains After the electromagnetic vortex wave with orbital angular momentum modal value is incident and irradiates the target, the corresponding electromagnetic vortex polarization joint scattering matrix is ​​expressed as:

[0035]

[0036] Among them, the superscript consists of two parts, one of which is represents the incident field, represents the scattered field; secondly, represents the polarization direction of the incident wave, Indicates the polarization direction of the scattered wave. Left-hand circular polarization, right-hand circular polarization or other polarization orthogonal bases can also be used. The subscript contains two parts, one of which is represents the OAM modal value of the incident wave; secondly, represents the OAM mode value of the scattered wave, . E represents the vortex electric field, that is The SAM polarization combination is When , the incident vortex electric field with OAM mode value m is as follows: represents the incident vortex electromagnetic field with an OAM mode value of +1 under SAM HH polarization; The SAM polarization combination is When , the scattered vortex electric field with OAM mode value n is as follows: Represents the scattered vortex electromagnetic field with an OAM mode value of -1 under SAM VH polarization. The SAM polarization combination is , describing the electromagnetic vortex polarization joint scattering matrix in the OAM dimension, where each element is expressed as express. are all complex numbers, and their complex values ​​indicate that the SAM polarization combination is The electromagnetic vortex scattering coefficient when the OAM mode value of the incident wave is m and the OAM mode value of the scattered wave is n.

[0037] Under the same SAM polarization mode, different modes of electromagnetic vortex waves are orthogonal to each other, and the orbital angular momentum mode value is The electromagnetic vortex waves of the four combinations of transmitting and receiving modes include There are different combinations of orthogonal bases, that is, the matrix contains The present invention takes the horizontal-vertical polarization basis as a pair of orthogonal basis as an example. Without loss of generality, the polarization orthogonal basis can also be selected as other polarization forms, such as left-hand circular polarization-right-hand circular polarization or other mutually orthogonal oblique polarizations, elliptical polarizations. Each SAM polarization combination contains the same number of orthogonal basis. Therefore, looking at all SAM polarization combinations, the number of orthogonal basis for transmitting and receiving electromagnetic vortex waves is There are different combinations of orthogonal bases, that is, the matrix contains The meaning of each element in the matrix is ​​the scattering coefficient corresponding to any pair of combinations of multi-mode electromagnetic vortex incident waves and scattered waves under a certain SAM polarization combination.

[0038] Example

[0039] The present invention provides a method for characterizing target scattering characteristics based on an electromagnetic vortex polarization joint scattering matrix, which specifically includes the following steps:

[0040] Step 1: Construct the electromagnetic vortex polarization joint scattering matrix. Figure 2 As shown in Figure 1, first, a three-dimensional rectangular coordinate system is established. The three coordinate axes of the coordinate system are the incident wave OAM mode value, the scattered wave OAM mode value and the SAM polarization combination mode. The values ​​of the incident wave OAM mode value axis and the scattered wave OAM mode value axis are both , Z represents an integer. The values ​​of the SAM polarization axes are , the above four values ​​respectively indicate that both the incident wave and the scattered wave are horizontally polarized waves, the incident wave is horizontally polarized wave and the scattered wave is vertically polarized wave, the incident wave is vertically polarized wave and the scattered wave is horizontally polarized wave, and both the incident wave and the scattered wave are vertically polarized waves.

[0041] The target scattering coefficients of the same SAM polarization combination form a plane matrix, which is the electromagnetic vortex scattering matrix; Figure 2 For the convenience of description, the same SAM polarization mode is regarded as a whole. The four SAM polarization combinations can divide the three-dimensional matrix into four plane sub-matrices, which are represented as , , and , each plane corresponds to the corresponding SAM transmit and receive polarization combination.

[0042] Each element in the electromagnetic vortex polarization joint scattering matrix represents a characterization of the target scattering characteristics of any pair of orthogonal basis combinations in each OAM mode value of the electromagnetic vortex wave under a certain SAM polarization combination. Indicates that the superscript represents the SAM polarization combination of the current element, Both are acceptable or , subscript represents the incident wave OAM mode value, represents the OAM mode value of the scattered wave, .

[0043] Step 2, define the degenerate problem of the electromagnetic vortex polarization joint scattering matrix. Observe the matrix longitudinally. When the modal values ​​of the electromagnetic vortex wave incident wave and the scattered wave are fixed values, the matrix contains only four coefficients, corresponding to the four SAM polarization combinations, such as Figure 3 According to the meaning of the coefficients of the electromagnetic vortex polarization joint scattering matrix, these four coefficients can be formed into a matrix form similar to the traditional polarization scattering matrix, and the matrix size is That is, the electromagnetic vortex polarization joint scattering matrix will degenerate into the polarization scattering matrix corresponding to the electromagnetic vortex wave with incident wave mode m and scattered wave mode n (that is, the SAM polarization scattering matrix when the incident wave mode value is +1 and the scattered wave mode value is +1 as shown in the figure) ), the polarization scattering matrix describes the target scattering characteristics when the electromagnetic vortex wave is a specific mode value.

[0044] The OAM mode of a plane wave is 0. In particular, when the values ​​of the electromagnetic vortex wave transmission and reception modes are all degenerated to 0, its electromagnetic wave form will degenerate into a plane wave. At this time, the electromagnetic vortex polarization joint scattering matrix will degenerate into the traditional plane wave polarization scattering matrix used to describe the scattering characteristics of a plane wave target .

[0045] The specific embodiments described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for characterizing target scattering characteristics based on an electromagnetic vortex polarization joint scattering matrix, characterized in that: The steps include: Step 1: Construct an electromagnetic vortex polarization joint scattering matrix: establish a three-dimensional rectangular coordinate system in space, where the three coordinate axes are the incident wave OAM mode value, the scattered wave OAM mode value and the SAM polarization combination mode; Step 2, define the degradation of the electromagnetic vortex polarization joint scattering matrix: observe the electromagnetic vortex polarization joint scattering matrix longitudinally. When the OAM modal values ​​of the incident wave and the scattered wave of the electromagnetic vortex wave are both fixed values, the electromagnetic vortex polarization joint scattering matrix degenerates into the polarization scattering matrix corresponding to the electromagnetic vortex wave with the incident wave OAM modal value m and the scattered wave OAM modal value n; when the OAM modal values ​​of the incident wave and the scattered wave of the electromagnetic vortex wave are both 0, the electromagnetic wave morphology degenerates into a plane wave.

2. The target scattering characteristic characterization method based on the electromagnetic vortex polarization joint scattering matrix according to claim 1 is characterized in that: The step 1 includes treating the same SAM polarization combination mode as a state of transmitting and receiving angular momentum, that is, the target scattering coefficients of the same SAM polarization combination mode constitute a plane electromagnetic vortex scattering matrix, and in the coordinate axis direction of the SAM polarization combination mode, the plane electromagnetic vortex scattering matrix is ​​expanded to a scale of The three-dimensional matrix is ​​defined as the electromagnetic vortex polarization joint scattering matrix, using the symbol Indicates that when a After the electromagnetic vortex wave with an OAM mode value is incident and irradiates the target, the backscattered field is expressed as: ， ， In the formula, the superscript denotes the incident field, the superscript represents the scattered field, the superscript indicates the polarization direction of the incident wave, and the superscript Indicates the polarization direction of the scattered wave and the polarization direction of the incident wave , scattered wave polarization direction Take the average or , H represents horizontal polarization, V represents vertical polarization; subscript represents the incident wave OAM mode value, subscript represents the OAM mode value of the scattered wave, ; E represents the vortex electric field, that is Indicates that the SAM polarization combination is When, the incident vortex electric field with the incident wave OAM mode value m; The SAM polarization combination is represented by When, the scattered vortex electric field with the scattered wave OAM mode value n; Indicates that the SAM polarization combination is The electromagnetic vortex polarization joint scattering matrix at time , each element is recorded as a complex number , indicating that the SAM polarization combination is The electromagnetic vortex scattering coefficient when the OAM mode value of the incident wave is m and the OAM mode value of the scattered wave is n.

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