A two-dimensional scanning design method for directional vortex electromagnetic beams

Abstract

The application discloses a two-dimensional scanning design method of a directive vortex electromagnetic beam, adopts a multi-ring circular array as an array surface structure, and preselects a candidate OAM mode set arranged continuously from a low-order mode; for a given target elevation angle, OAM modes are introduced in order of mode orders, the effective aperture of the array surface is divided into continuous radial partitions along the radial direction, the effective OAM mode set actually participating in superposition and the corresponding partition radius are determined through partition radius optimization, the amplitude weight of each order of OAM mode is optimized, and the array element amplitude excitation configuration corresponding to the target elevation angle is obtained; for a given target azimuth angle, a uniform phase bias is loaded on the basis of the original spiral phase of each order of OAM mode, so that each order of OAM mode satisfies the in-phase superposition condition in the target azimuth angle direction, and the array element phase excitation configuration is generated. The application can realize the scanning of the directive vortex electromagnetic beam in the two-dimensional angle domain, and improve the pointing accuracy and main lobe gain in the target direction.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication and array antenna beam control technology, specifically relating to a two-dimensional scanning design method for a directional vortex electromagnetic beam. Background Technology

[0002] In modern wireless communication, radar detection, and millimeter-wave / terahertz systems, beam scanning technology is a crucial means of achieving directional radiation, spatial coverage, target search, and target tracking. Vortex electromagnetic waves carrying orbital angular momentum (OAM) possess helical phase wavefronts, and different OAM modes are theoretically orthogonal, providing new degrees of freedom for electromagnetic wave manipulation and spatial multiplexing. Therefore, OAM-based vortex beams have significant application value in areas such as enhancing wireless communication capacity, anti-jamming communication, and secure communication.

[0003] In the prior art, Professor Huang Shanguo's team at Beijing University of Posts and Telecommunications disclosed a two-dimensional beam control method for radio frequency OAM based on optical control technology in their paper "2D Optically Controlled Radio Frequency Orbital Angular Momentum Beam Steering System Based on a Dual-Parallel Mach–Zehnder Modulator" (Optics Letters, 2019, 44(2): 255–258). This method drives a circular antenna array by connecting a parallel Mach-Zehnder modulator and a fiber true time delay network, simultaneously loading a spiral phase distribution and a linear phase gradient on the array surface to achieve the deflection of a few OAM mode vortex beams in the two-dimensional angular domain. However, this method mainly focuses on beam adjustment for a few OAM modes and has not yet established a unified two-dimensional scanning design method to address the problem of inconsistent divergence angles of different OAM modes under multi-mode superposition conditions.

[0004] In their paper "Realization of Beam Steering Based on Plane Spiral Orbital Angular Momentum Wave" (IEEE Transactions on Antennas and Propagation, 2018, 66(3): 1352–1358), Professor Zheng Shilie's team at Zhejiang University proposed a method for controlling multimode planar vortex electromagnetic beams based on Plane Spiral OAM (PSOAM). This method constructs different combinations of PSOAM modes as mode groups and applies a phase offset to each mode group as a whole to achieve beam scanning in the azimuth dimension. However, the beam scanning of this method is mainly concentrated in the azimuth direction, and a two-dimensional scanning design framework for multimode directional vortex beams has not yet been given.

[0005] In summary, existing OAM vortex beam scanning methods primarily target single-mode or a few-mode beam deflection, or mainly achieve azimuth scanning under multi-mode superposition conditions. For directional vortex electromagnetic beams involving the superposition of multiple OAM modes, direct superposition easily leads to main lobe energy dispersion, elevation pointing offset, and unstable radiation pattern due to differences in divergence angles and radial energy distributions among different modes. Therefore, how to simultaneously achieve effective scanning in both elevation and azimuth dimensions on the same array surface, and improve the main lobe energy concentration and pointing accuracy in the target direction, remains a problem that existing technologies need to solve. Summary of the Invention

[0006] To overcome the shortcomings of the existing technology, this invention provides a two-dimensional scanning design method for a directional vortex electromagnetic beam. This method features independent adjustment of the pitch and azimuth directions, high beam gain, and high pointing accuracy.

[0007] To achieve the above objectives, the present invention adopts the following technical solution.

[0008] A two-dimensional scanning design method for a directional vortex electromagnetic beam includes the following steps: Step 1: Determine the multi-ring circular array as the array surface structure, and pre-select a set of candidate OAM modes arranged continuously starting from the lower-order modes. This serves as the initial mode pool for subsequent step-by-step introduction and partition radius optimization. Step 2: Establish a two-dimensional scanning mechanism in which the pitch and azimuth directions are independent of each other. The pitch response of the OAM mode is determined by its mode order and radial action range, while the azimuth response is determined by the OAM spiral phase and unified phase offset. Step 3: For a given target pitch angle, select from the candidate OAM mode set OAM modes are introduced step by step from low to high according to modal order. The effective aperture of the plane is radially partitioned, and the effective set of OAM modes participating in the superposition and the corresponding partition radius are determined by optimizing the partition radius. Step 4: Based on the effective OAM mode set and partition radius determined in Step 3, optimize the amplitude weights of each OAM mode to obtain the array element amplitude excitation configuration corresponding to the target pitch angle; Step 5: For a given target azimuth angle, add a uniform phase offset to the original spiral phase of each OAM mode so that each OAM mode satisfies the in-phase superposition condition in the target azimuth angle direction, and generate the array element phase excitation configuration corresponding to the target azimuth angle. Step 6: Repeat steps 3 and 4 for different target elevation angles, and step 5 for different target azimuth angles to obtain the array element amplitude and phase excitation configuration covering the two-dimensional angular domain, thereby realizing the two-dimensional scanning of the directional vortex electromagnetic beam.

[0009] The multi-ring circular array in step 1 consists of multiple physically concentric rings with the geometric center of the same array surface as the center. Multiple radiation elements capable of independently loading amplitude and phase are arranged on each physically concentric ring. The radiation elements on the same physically concentric ring are evenly distributed along the azimuth direction. When performing radial partitioning, one or more adjacent physically concentric rings are assigned to the same radial partition, and an OAM mode is configured in each radial partition.

[0010] In step 2, let the first... The first OAM mode is configured in the radial action region. Within this order, the single-mode array factor of the OAM mode is expressed as: in, For spatial pitch angle, It is the spatial azimuth angle. To characterize the first OAM mode in radial action region The pitch response formed within the single mode.

[0011] For the case where multiple OAM modes participate in the superposition, the multimode synthesis array factor is expressed as: in, For an effective OAM mode set, For the first Amplitude weights of the first-order OAM mode; by adjusting the radial action range. and magnitude weight The pitch direction of the synthesized main lobe is controlled by a uniform phase offset, and the azimuth direction of the synthesized main lobe is controlled by a uniform phase offset.

[0012] In step 3, regarding the currently introduced The current mode set consisting of OAM modes The effective aperture of the multi-ring circular array is divided radially into... There are three consecutive radial partitions, each consisting of one or more adjacent physically concentric rings, and each partition corresponds to an OAM mode. Let the partition radius vector be: No. The radial partitions are: And with the objective of minimizing the deviation between the main lobe pitch angle of each OAM mode's single-mode radiation pattern and the target pitch angle, a partition radius optimization objective function is constructed: in, For the target pitch angle, For the first OAM mode in radial partition The pitch angle of the main lobe of the single-mode radiation pattern when the array element is configured internally.

[0013] The optimization of the partition radius satisfies the following constraints: in, The maximum usable radius of the array. The minimum radial partition width is defined. If the current mode set satisfies the constraints, higher-order OAM modes are introduced. If no feasible partitioning result is obtained after introducing higher-order OAM modes, mode introduction is stopped, and the last mode set that satisfies the constraints is determined as the valid OAM mode set. .

[0014] In step 4, let the effective OAM mode set be... The magnitude weight vector is With the pitch angle of the main lobe of the multi-mode synthesized radiation pattern approaching the target pitch angle as the main objective, and combining modal coordination terms and weight regularization terms, an amplitude weight optimization objective function is constructed: in, Alignment with the main lobe. For modal cooperation terms, For weight regularization terms, and The weighting factor is: The main lobe alignment term is: in, Weight vector The pitch angle corresponding to the main lobe of the multimode synthesis pattern under the action. For the target pitch angle; the first The normalized effective contribution of the OAM mode at the target pitch angle is: The modal cooperation term is: in, This is a vector composed of the normalized effective contributions of each order of OAM mode; the weight regularization term is: The magnitude weight optimization satisfies the following constraints: .

[0015] In step 5, the target azimuth angle is set as... For those located at the th Within the radial partition, the first Each array element corresponds to an OAM mode order of . The azimuth of the formation is Then the phase excitation of the array element is: The complex excitation of this array element is: This allows each OAM mode to be positioned at the target azimuth angle. The direction satisfies the in-phase superposition condition and makes the multimode synthesized main lobe point to the target azimuth angle.

[0016] In step 6, the modal radial partitioning parameters and multimode superposition amplitude excitation determined in steps 3 and 4 are kept unchanged, and only the unified phase offset parameters are used. As an azimuth scan control variable, among which For the corresponding target azimuth angle, for the first Within the radial annular region, the first Phase excitation applied to array elements of the OAM mode ,in The azimuth angle of the array element is changed by altering... Each OAM mode relative to the original spiral phase Synchronous introduction The initial phase offset causes the main lobe of the multimode superposition pattern to rotate as a whole in the azimuth direction. The specified target azimuth angle enables the scanning design of the vortex electromagnetic beam in the azimuth direction.

[0017] An application of a two-dimensional scanning design method for directional vortex electromagnetic beams is disclosed. This method is applied to two-dimensional scanning and high-precision pointing control of vortex electromagnetic beams in electromagnetic wave systems for millimeter-wave communication and radar detection. In millimeter-wave communication systems, it is used for OAM mode directional transmission, beam alignment, and user direction tracking; in radar detection systems, it is used for target search, angular domain scanning, and target tracking; and in spatial multiplexing transmission and reconfigurable array antenna systems, it is used for pointing control and two-dimensional scanning of multimode vortex beams.

[0018] The beneficial effects of this invention are: (1) This invention achieves two-dimensional angular domain scanning of a directional vortex electromagnetic beam by combining adaptive updating of mode configuration corresponding to the target elevation angle with unified phase offset loading corresponding to the target azimuth angle. In the elevation direction, the effective OAM mode set, partition radius, and mode amplitude weight are updated for different target elevation angles to make the multimode synthesized main lobe point towards the target elevation direction; in the azimuth direction, the azimuth phase relationship of each OAM mode is adjusted by unified phase offset to make each mode satisfy the coherent superposition condition in the target azimuth direction. Thus, this invention separates the design variables of elevation scanning and azimuth scanning, and has the advantages of clear scanning mechanism, simple implementation method, and easy engineering implementation.

[0019] (2) This invention introduces partition radius optimization and modal amplitude weight optimization under multi-mode superposition conditions. Since the pitch response of different OAM modes is related to the modal order and radial action range, direct superposition may lead to inconsistent main lobe pointing of each mode, thus affecting the pointing accuracy and gain of the synthesized main lobe. This invention adjusts the radial action range of each OAM mode through partition radius optimization, so that the main lobe of each OAM mode participating in the superposition is aligned with the target pitch angle as much as possible; and balances the effective contribution of each OAM mode in the target pitch direction through modal amplitude weight optimization, so that the multi-mode synthesized main lobe is stably formed in the target pitch direction. Thus, the influence of inconsistent divergence characteristics of each OAM mode on the synthesized pattern can be reduced, and the main lobe gain and pointing accuracy during two-dimensional scanning can be improved. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the overall process of the two-dimensional scanning design method for directional vortex electromagnetic beams of the present invention.

[0021] Figure 2 This is a schematic diagram of the multi-ring circular array surface structure in an embodiment of the present invention.

[0022] Figure 3 This is a schematic diagram of array amplitude excitation in Embodiment 1 of the present invention.

[0023] Figure 4 This is a schematic diagram of array phase excitation in Embodiment 1 of the present invention.

[0024] Figure 5 This is the far-field 3D radiation pattern of Embodiment 1 of the present invention.

[0025] Figure 6 This is the far-field 2D radiation pattern of Embodiment 1 of the present invention.

[0026] Figure 7 This is a schematic diagram of array amplitude excitation in Embodiment 2 of the present invention.

[0027] Figure 8 This is a schematic diagram of array phase excitation in Embodiment 2 of the present invention.

[0028] Figure 9 This is the far-field 3D radiation pattern of Embodiment 2 of the present invention.

[0029] Figure 10 This is the far-field 2D radiation pattern of Embodiment 2 of the present invention.

[0030] Figure 11 This is a schematic diagram of the pitch angle scanning of the present invention.

[0031] Figure 12 This is a schematic diagram of the azimuth scanning of the present invention. Detailed Implementation

[0032] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0033] A two-dimensional scanning design method for a directional vortex electromagnetic beam includes the following steps: Step 1: Determine the array structure and candidate OAM mode set A multi-ring circular array with radial division capability is used as the array surface structure to realize two-dimensional scanning of directional vortex electromagnetic beams. The multi-ring circular array is composed of multiple concentric circular ring arrays with the geometric center of the same array surface as the center. Several radiation elements that can be independently loaded with amplitude and phase are arranged on each ring. Adjacent rings are arranged at a preset spacing in the radial direction, and the radiation elements on the same ring are evenly distributed along the azimuth direction.

[0034] Let the target operating frequency be The corresponding operating wavelength is ,in, The speed of light. Establish a polar coordinate system with the geometric center of the array as the origin, and denote the first... The radial distance of each array element is azimuth angle is Its re-excitation is Under the far-field approximation, the fundamental array factor of a multi-ring circular array can be expressed as: in, The total number of array elements, For spatial pitch angle, It is the spatial azimuth angle.

[0035] For topological charge number The OAM mode, whose element excitation includes a spiral phase term varying along the azimuth direction, can be expressed as: in, For the first The amplitude coefficients of the array elements corresponding to the OAM mode of order. The ring is the first Spiral phase term of the OAM mode.

[0036] Based on system requirements, select a continuous set of candidate OAM modes. ,in, This represents the number of candidate modes. The set of candidate OAM modes serves as the initial mode pool for subsequent radial partitioning optimization. In subsequent steps, modes are selected from the candidate OAM mode set in ascending order of modal order. OAM modes are introduced sequentially, and the effective set of OAM modes participating in multi-mode superposition is determined based on the feasibility of partition optimization. .

[0037] Step 2: Establish a pitch-azimuth independent two-dimensional scanning mechanism In step 1, the first Substituting the element excitations of the first-order OAM mode into the basic array factor of the multi-ring circular array, we can obtain the single-mode array factor corresponding to that order OAM mode. Let the first-order OAM mode be... The first OAM mode is configured in the radial action region. Within a given circle, when the array elements on the same ring are uniformly distributed along the azimuth direction and the number of array elements is sufficient, a discrete circular ring array can be approximated as a continuous circular ring. For a radius of... A continuous circular ring, loaded with the first After the OAM spiral phase is applied, its pitch response can be approximated as follows: in, For the first The first-order Bessel function. From the above expression, we can see that the first... The pitch response of the OAM mode and its modal order and radial position Related. For the radial action zone consisting of one or more concentric rings. The composite response of each ring in the pitch direction within this interval can be denoted as... Therefore, the first The single-mode array factor of the OAM mode can be approximated as: For the case where multiple OAM modes participate in the superposition, the multimode synthesis array factor can be expressed as: in, For the first Amplitude weights of the OAM mode. As shown in the above expression, the position of the main lobe in the pitch direction is mainly affected by the radial action range. and modal amplitude weights Impact: Azimuth scanning can be achieved by introducing a phase offset controlled by unified parameters on the basis of the original spiral phase of each OAM mode. Therefore, this invention separates the design variables of pitch scanning and azimuth scanning, forming a two-dimensional independent scanning mechanism.

[0038] Step 3: OAM Modal Partition Radius Optimization For a given target pitch angle Candidate OAM modes are selected from the modal order in ascending order. OAM modes are introduced sequentially. Let the number of OAM modes currently introduced be... The current modality set is For the current modality set The effective aperture of the array is divided radially outward from the center of the array into three parts. Let there be three consecutive concentric ring regions, with each concentric ring region corresponding to a single OAM mode. Let the radial partition boundary vector be... No. Each concentric annular region is represented as Set the current mode The OAM modes of each order are sequentially distributed from low to high order into concentric ring domains arranged from the inside out, so that each OAM mode is configured with array elements only within its corresponding continuous radial action range. Through the above radial partitioning method, radial partitioning of different OAM modes can be realized on the array surface, and independent radial design degrees of freedom can be provided for the pitch response adjustment of each OAM mode.

[0039] For the current mode set Using the deviation between the main lobe pitch angle of each OAM mode's single-mode radiation pattern and the target pitch angle as the evaluation index, a radial partition radius optimization objective function is constructed: in, Indicates the first The first OAM mode in its corresponding radial action region When an array element is configured internally, the pitch angle of the main lobe of its single-mode radiation pattern.

[0040] The radial partition radius optimization satisfies the following constraints: in, The maximum usable radius of the array. The minimum radial width of the concentric ring domain is used to ensure that each concentric ring domain has physical space in the radial direction to arrange the corresponding OAM mode array elements, and to avoid the overlap of the radial action regions of adjacent OAM modes.

[0041] In the above optimization process, OAM modes are introduced sequentially from low to high modal order, and the radial partition radius corresponding to the current mode set is optimized and its feasibility is determined. If the current mode set can satisfy the array aperture constraint and the minimum radial width constraint, the current mode set is retained and higher-order OAM modes are introduced; if a feasible partitioning result satisfying the constraints cannot be obtained after introducing higher-order OAM modes, the mode introduction is stopped. The last mode set that satisfies the constraints is determined as the target pitch angle. The effective OAM mode set below and the corresponding partition radius vector The optimized result is determined to be the target pitch angle. Therefore, the main lobe of each OAM mode participating in the superposition can be aligned as closely as possible with the target pitch angle within its corresponding radial action range, thereby reducing the pointing deviation of the synthesized main lobe caused by the inconsistent divergence angles of different modes during multi-mode superposition.

[0042] Step 4: OAM mode amplitude weight optimization In step 3, the effective OAM mode set is determined. and partition radius vector Subsequently, amplitude weights were introduced for each OAM mode. Let the weight vector be... in, For the effective mode set The number of modes contained therein.

[0043] In the weight vector Under the influence of the multimode synthesis pattern, the pitch angle of the main lobe is denoted as . Using the minimum deviation between the main lobe pitch angle and the target pitch angle in the multi-mode synthesized radiation pattern as the primary objective, a main lobe alignment target function is constructed: Preferably, to improve the stability and engineering feasibility of the multimode synthesis pattern, weight optimization also includes modal cooperation terms and weight regularization terms. The OAM modes of each order are defined at the target pitch angle. The normalized contribution vector at is Among them, the The normalized effective contribution of the OAM mode is The variance of the normalized effective contribution vector is used as the modal cooperation term: By minimizing This can suppress the instability of the radiation pattern caused by excessive differences in the contributions of different OAM modes at the target pitch angle. Simultaneously, to avoid excessive concentration of amplitude weights on a few modes, a weight regularization term is introduced: Therefore, the objective function for optimizing the comprehensive weights can be written as follows: in, and These are the tradeoff coefficients. They are used to adjust the proportions of the modal synergy term and the weight regularization term in the overall weight optimization objective function, respectively.

[0044] The weight optimization satisfies the following constraints: Among them, the nonnegativity constraint is used to ensure the physical realizability of the amplitude weights of each OAM mode, and the normalization constraint is used to eliminate the influence of the overall amplitude scale on the optimization results, so that the weight optimization mainly reflects the relative amplitude distribution relationship between each OAM mode.

[0045] By optimizing the partition radius in step 3 and the amplitude weight in step 4, the main lobe contributions of each OAM mode can be made more consistent near the target pitch angle, and the multi-mode synthesized main lobe can be stably concentrated in the target pitch direction, thereby improving the pointing accuracy and main lobe gain in the pitch direction.

[0046] Step 5: Unified phase bias loading In steps 3 and 4, the effective OAM mode set corresponding to the target pitch angle is determined. After determining the partition radius and amplitude weight, the partition radius and amplitude weight remain unchanged, and a uniform phase offset controlled by the target azimuth angle is applied to each OAM mode.

[0047] Let the target azimuth be For order of The OAM mode, its original azimuth phase term is To ensure the multimode synthesized beam is aligned with the target azimuth angle... The direction forms the main lobe, and the azimuth phase term is... Replace with The azimuth phase term after applying a uniform phase offset is obtained. Accordingly, the multimode synthesis array factor after applying a uniform phase bias can be expressed as: When the spatial azimuth angle satisfies At that time, the azimuth phase terms of each OAM mode satisfy... Therefore, each order of OAM mode at the target azimuth angle The direction satisfies the coherent superposition condition, thus forming the synthetic main lobe in that direction.

[0048] For those located at the The radial action range corresponding to the OAM mode of the first order. The first Each array element's phase excitation can be expressed as: in, For the first The array azimuth angle of each array element. Therefore, combined with the amplitude weights obtained in step 4... The target azimuth angle can be obtained. Corresponding array element complex excitation: By using the aforementioned unified phase offset loading method, the target azimuth angle can be obtained without changing the target's pitch angle response. The corresponding array element phase excitation distribution enables independent control of the azimuth direction.

[0049] Step 6: Two-dimensional angular domain scanning For different pitch angles Repeat steps 3 and 4 to make the effective OAM mode set. The partition radius and amplitude weights are adaptively updated according to the target elevation angle, thus obtaining the array element amplitude excitation configuration corresponding to each target elevation angle. This is done for different target azimuth angles. While keeping the effective OAM mode set, partition radius, and amplitude weights corresponding to the current target pitch angle unchanged, step 5 is executed, by changing the unified phase offset. This generates the array element phase excitation configuration corresponding to the target azimuth angle. Therefore, for any combination of target angles... Each of these can yield a corresponding set of array element amplitude and phase excitations: in, Target pitch angle The first result obtained after optimization in step 4 OAM mode amplitude weights. This is achieved by sequentially changing the target pitch angle. and target azimuth This allows for the formation of multiple array element amplitude and phase excitation configurations covering the two-dimensional angular domain, enabling the scanning of directional vortex electromagnetic beams within the two-dimensional angular domain of elevation and azimuth.

[0050] This invention is applicable to wireless communication systems that utilize OAM modes for information carrying or spatial multiplexing. By jointly designing the radial partitioning, amplitude weighting, and phase excitation of multi-order OAM modes, this invention can achieve scanning of the synthesized main lobe in the two-dimensional angular domains of elevation and azimuth while maintaining the modal characteristics of vortex electromagnetic beams. This provides an array implementation method for mode multiplexing transmission, beam alignment, and user direction tracking of vortex electromagnetic beams.

[0051] Example 1: This example illustrates the present invention when the target pitch angle is... The target azimuth is The two-dimensional vortex beam generation process at that time. (Refer to...) Figure 1 Generate a directional vortex electromagnetic beam at the target's two-dimensional angle by following these steps.

[0052] Step 1: In this embodiment, a multi-ring circular array is used as the array surface structure, and the maximum usable radius of the array surface is... mm. The radial partitioning method of the multi-ring circular array is as follows: Figure 2 As shown, one or more physically concentric rings can be divided into a radial partition, and each radial partition is configured with an OAM mode. Let the operating frequency be... GHz, corresponding to the operating wavelength is mm. Establish a polar coordinate system with the geometric center of the array as the origin, denoted as _mm_. The radial distance of each array element is The azimuth of the formation is To introduce a larger number of OAM modes within a finite aperture, a set of candidate OAM modes arranged sequentially from the lowest-order modes is pre-selected. This serves as the initial modal pool for subsequent step-by-step introduction and partition radius optimization.

[0053] Step 2: In this embodiment, the target pitch angle is... Since the pitch response of the OAM mode is related to the mode order and the radial action range, the effective set of OAM modes participating in the superposition is determined through the partition radius optimization in step 3. and partition radius vector Different orders of OAM modes are configured within corresponding radial partitions; based on this, the amplitude weights of each order of OAM mode are determined through amplitude weight optimization in step 4. This is to improve the pointing accuracy and main lobe gain of the synthesized main lobe in the target pitch direction. (Target azimuth angle) By introducing a unified phase bias in step 5, the OAM modes of each order satisfy the in-phase superposition condition in the target azimuth direction, thereby making the synthesized main lobe point in the azimuth direction. This leads to a goal-oriented perspective. A two-dimensional control mechanism that is independent of pitch and azimuth.

[0054] Step 3: Pitch angle at the target From the candidate OAM mode set OAM modes are introduced sequentially from low to high modal order, with the minimum radial partition width set to [value missing]. mm. For the currently introduced A mode set consisting of OAM modes The effective aperture of the array is divided radially into The system consists of three consecutive radial partitions, each corresponding to a single OAM mode, with the main lobe pitch angle of each OAM mode's single-mode pattern being as close as possible to the desired value. The objective function for optimizing the partition radius is: The partition radius optimization satisfies the following optimization conditions: After optimization using a step-by-step introduction and feasibility assessment method, the target pitch angle is obtained. The effective set of OAM modes that actually participate in the superposition is as follows: Combination The optimized partition radius vector is: Therefore, the effective aperture of the array is divided into 10 consecutive radial sections, the first... Radial partitions , , used to configure the The OAM mode was used, and the above results were used as the target pitch angle. The modal partitioning and radius optimization results are used for subsequent amplitude weight optimization.

[0055] Step 4: Determine the target pitch angle in step 3 The effective OAM mode set below and partition radius vector Then, amplitude weights are introduced for each OAM mode. Let the weight vector be... .

[0056] The main lobe elevation angle of the multimode synthesis pattern should be as close as possible to... To achieve the objective, and combining modal cooperation terms and weight regularization terms, we construct the magnitude weight optimization objective function: in, Indicated in the weight vector The pitch angle corresponding to the main lobe of the multimode synthesis pattern under the action; For each OAM mode at the target pitch angle The normalized effective contribution vector at the location; and These are the tradeoff coefficients, used to adjust the proportions of the modal cooperation term and the weight regularization term in the optimization objective function, respectively.

[0057] The magnitude weights satisfy the following constraints: After optimization based on the above objective function and constraints, the target pitch angle is obtained. The magnitude weight vector is as follows: Based on the modal partitioning results obtained in step 3, the first... The amplitude of the array elements within each radial partition is set to the corresponding amplitude weight. Thus, the array amplitude excitation distribution of this embodiment is obtained, such as Figure 3 As shown. Figure 3 In the diagram, different gray levels represent different normalized amplitudes, and the amplitudes of the array elements exhibit regional variation along the radial direction, indicating that each radial region has been configured with amplitude excitation according to the optimized modal weights.

[0058] Step 5: Determine the target pitch angle in steps 3 and 4. The corresponding effective OAM mode set Partition radius vector and magnitude weight vector Then, targeting the azimuth angle Apply a uniform phase bias. For the first... The array elements within each radial partition correspond to OAM mode orders of: Let the first... The azimuth angle of each array element is If the array element is located at the th Within each radial partition, the phase excitation is set as follows: Therefore, the complex excitation corresponding to this array element can be expressed as: in, The first one obtained in step 4 OAM modal normalized amplitude weights, For the first The radial distance of each array element For the first Radial partitions.

[0059] Using the aforementioned unified phase offset loading method, the OAM modes of each order are at the target azimuth angle. The direction satisfies the in-phase superposition condition, causing the synthesized main lobe to point in the azimuth direction. The phase is applied to each array element according to the phase excitation formula, and the phase value is mapped to... Within the range, the phase excitation distribution of the array elements in this embodiment is obtained, such as... Figure 4 As shown. Figure 4 In the diagram, different gray levels represent different array element phase sizes, and the array phase exhibits a spiral variation characteristic along the azimuth direction, indicating that each radial partition has completed phase excitation configuration according to the corresponding OAM mode order and unified phase offset.

[0060] Step 6: Apply the array amplitude excitation distribution obtained in Step 4 and the array phase excitation distribution obtained in Step 5 to the multi-ring circular array to obtain the target angle. The following array element complex excitation configuration is used. To verify the beam pointing effect of the complex excitation configuration, a full-wave electromagnetic simulation was performed in FEKO using an equivalent current source array, resulting in the far-field three-dimensional radiation pattern and the far-field two-dimensional radiation pattern of this embodiment, as shown below. Figure 5 and Figure 6 As shown. Simulation results show that the synthesized main lobe points near the target direction, while the actual main lobe direction is... The pitch angle direction error is Azimuth direction error The main lobe gain is 16.99 dBi. This indicates that at a target pitch angle of... The target azimuth is In this case, this embodiment can achieve effective pointing of the directional vortex electromagnetic beam in the two-dimensional angular domain.

[0061] Example 2: This example illustrates the change of the target angle to... The reusability of the method of the present invention is demonstrated. The array structure and basic optimization process of this embodiment are the same as those of Embodiment 1. The optimization results and excitation configurations are described below from the perspective of the objective of this embodiment.

[0062] Step 1: This embodiment uses the same multi-ring circular array as Embodiment 1 as the array surface structure, and the operating frequency is... GHz, corresponding to the operating wavelength is mm. The candidate OAM mode set is still [number missing]. This serves as the initial mode pool for the step-by-step introduction of OAM modes and the optimization of partition radius in this embodiment.

[0063] Step 2: This embodiment still uses the same pitch-azimuth independent control mechanism as Embodiment 1. For the target pitch angle... The effective OAM mode set, radial partitioning, and amplitude excitation are determined through subsequent partition radius optimization and amplitude weight optimization; for the target azimuth angle By applying a uniform phase bias, the OAM modes of each order satisfy the in-phase superposition condition in this azimuth direction, thereby making the synthesized main lobe point to the target azimuth angle.

[0064] Step 3: Pitch angle at the target The partition radius optimization is performed using the same step-by-step introduction and feasibility determination method as in Example 1. In this example, the objective function for partition radius optimization is written as: Under the conditions of satisfying the array aperture constraint and the minimum radial partition width constraint, the effective OAM mode set actually participating in the stacking is obtained after optimization as follows: The corresponding partition radius vector is Therefore, the effective aperture of the array is divided into 8 consecutive radial sections, the first... One radial partition is , And used to configure the first OAM mode.

[0065] Step 4: The set of valid OAM modes determined in Step 3 and partition radius vector Based on this, the amplitude weight optimization method is used to solve the problem, similar to that in Example 1. In this example, the amplitude weight optimization objective function is written as: After optimization, the target pitch is obtained. The magnitude weight vector is Based on the modal partitioning results obtained in step 3, the first... The amplitude of the array elements within each radial partition is set to the corresponding amplitude weight. The array amplitude excitation distribution of this embodiment is obtained, such as... Figure 7 As shown. Figure 7 In this model, different gray levels represent different normalized amplitudes, and the amplitudes of the array elements exhibit regional variations along the radial direction. Compared to Example 1, Figure 7 The amplitude distribution changes with the target pitch angle, indicating that the present invention can adaptively update the modal partitions and amplitude weights according to different target pitch angles, so that each OAM mode forms a corresponding amplitude excitation configuration in the target pitch direction.

[0066] Step 5: Target azimuth angle Based on the modal partitioning and amplitude weights determined in steps 3 and 4, a uniform phase bias is applied to the array elements within each radial partition. If the... The element is located in the first Radial partitions If the element is inside, then the OAM mode order corresponding to that element is: Its phase excitation is set to Combined with the amplitude weights obtained in step 4 The complex excitation of this array element can be expressed as Using the aforementioned unified phase offset loading method, the OAM modes of each order are at the target azimuth angle. The direction satisfies the in-phase superposition condition, causing the synthesized main lobe to point in the azimuth direction. The phase is applied to each array element according to the phase excitation formula, and the phase value is mapped to... Within the range, the phase excitation distribution of the array elements in this embodiment is obtained, such as... Figure 8 As shown. Figure 8 In the diagram, different gray levels represent different phase magnitudes of array elements, and the phase of the array surface exhibits a spiral variation characteristic along the azimuth direction.

[0067] Step 6: To verify the beam pointing effect of the directional vortex electromagnetic beam generated in this embodiment, a full-wave electromagnetic simulation was performed in FEKO using an equivalent current source array to obtain the far-field three-dimensional radiation pattern and the far-field two-dimensional radiation pattern, as shown below. Figure 9 and Figure 10 As shown. Simulation results show that the actual direction of the synthesized main lobe in this embodiment is approximately... The corresponding main lobe gain is approximately 17.47 dBi. (Regarding the target angle...) In comparison, the pitch angle direction error is The azimuth direction error is This result demonstrates that, when the target angle changes, the present invention can achieve effective scanning of a directional vortex electromagnetic beam in a two-dimensional angular domain by updating the partition radius and amplitude weights and adjusting the uniform phase offset.

[0068] Furthermore, based on Embodiments 1 and 2, for a set of preset target pitch angles (For example …), respectively re-execute partition radius optimization and amplitude weight optimization to make the effective OAM mode set Partition radius vector and magnitude weight vector The synthesized main lobe is adaptively updated according to the target pitch angle, thus pointing to the corresponding target pitch direction, achieving pitch angle scanning. The far-field patterns under different target pitch angles are shown below. Figure 11 As shown; for a set of preset target azimuth angles (For example …), based on the amplitude excitation configuration corresponding to the current target pitch angle, only the uniform phase offset is changed. The phase excitation of each array element is updated to ensure that the OAM modes of each order satisfy the in-phase superposition condition in the target azimuth direction, thereby causing the synthesized main lobe to rotate in the azimuth direction and achieving azimuth scanning. The far-field patterns under different target azimuth angles are shown in the figure. Figure 12 As shown. By Figure 11 and Figure 12 It can be seen that the present invention can achieve scanning of directional vortex electromagnetic beams in a two-dimensional angular domain by modal partitioning and amplitude weighting updates in the pitch direction and unified phase offset adjustment in the azimuth direction.

Claims

1. A two-dimensional scanning design method for a directional vortex electromagnetic beam, characterized in that, Includes the following steps: Step 1: Determine the multi-ring circular array as the array surface structure, and pre-select a set of candidate OAM modes arranged continuously starting from the lower-order modes. This serves as the initial mode pool for subsequent step-by-step introduction and partition radius optimization. Step 2: Establish a two-dimensional scanning mechanism in which the pitch and azimuth directions are independent of each other. The pitch response of the OAM mode is determined by its mode order and radial action range, while the azimuth response is determined by the OAM spiral phase and unified phase offset. Step 3: For a given target pitch angle, select from the candidate OAM mode set OAM modes are introduced step by step from low to high according to modal order. The effective aperture of the plane is radially partitioned, and the effective set of OAM modes participating in the superposition and the corresponding partition radius are determined by optimizing the partition radius. Step 4: Based on the effective OAM mode set and partition radius determined in Step 3, optimize the amplitude weights of each OAM mode to obtain the array element amplitude excitation configuration corresponding to the target pitch angle; Step 5: For a given target azimuth angle, add a uniform phase offset to the original spiral phase of each OAM mode so that each OAM mode satisfies the in-phase superposition condition in the target azimuth angle direction, and generate the array element phase excitation configuration corresponding to the target azimuth angle. Step 6: Repeat steps 3 and 4 for different target elevation angles, and step 5 for different target azimuth angles to obtain the array element amplitude and phase excitation configuration covering the two-dimensional angular domain, thereby realizing the two-dimensional scanning of the directional vortex electromagnetic beam.

2. The two-dimensional scanning design method for a directional vortex electromagnetic beam according to claim 1, characterized in that, The multi-ring circular array in step 1 consists of multiple physically concentric rings with the geometric center of the same array surface as the center. Multiple radiation elements capable of independently loading amplitude and phase are arranged on each physically concentric ring. The radiation elements on the same physically concentric ring are evenly distributed along the azimuth direction. When performing radial partitioning, one or more adjacent physically concentric rings are assigned to the same radial partition, and an OAM mode is configured in each radial partition.

3. The two-dimensional scanning design method for a directional vortex electromagnetic beam according to claim 2, characterized in that, In step 2, let the first... The first OAM mode is configured in the radial action region. Within this order, the single-mode array factor of the OAM mode is expressed as: in, For spatial pitch angle, It is the spatial azimuth angle. To characterize the first OAM mode in radial action region The pitch response formed within the single mode.

4. The two-dimensional scanning design method for a directional vortex electromagnetic beam according to claim 3, characterized in that, For the case where multiple OAM modes participate in the superposition, the multimode synthesis array factor is expressed as: in, For an effective OAM mode set, For the first Amplitude weights of the first-order OAM mode; by adjusting the radial action range. and magnitude weight The pitch direction of the synthesized main lobe is controlled by a uniform phase offset, and the azimuth direction of the synthesized main lobe is controlled by a uniform phase offset.

5. The two-dimensional scanning design method for a directional vortex electromagnetic beam according to claim 1, characterized in that, In step 3, regarding the currently introduced The current mode set consisting of OAM modes The effective aperture of the multi-ring circular array is divided radially into... There are three consecutive radial partitions, each consisting of one or more adjacent physically concentric rings, and each partition corresponds to an OAM mode. Let the partition radius vector be: No. The radial partitions are: And with the objective of minimizing the deviation between the main lobe pitch angle of each OAM mode's single-mode radiation pattern and the target pitch angle, a partition radius optimization objective function is constructed: in, For the target pitch angle, For the first OAM mode in radial partition The pitch angle of the main lobe of the single-mode radiation pattern when the array element is configured internally.

6. The two-dimensional scanning design method for a directional vortex electromagnetic beam according to claim 5, characterized in that, The optimization of the partition radius satisfies the following constraints: in, The maximum usable radius of the array. The minimum radial partition width is defined. If the current mode set satisfies the constraints, higher-order OAM modes are introduced. If no feasible partitioning result is obtained after introducing higher-order OAM modes, mode introduction is stopped, and the last mode set that satisfies the constraints is determined as the valid OAM mode set. .

7. The two-dimensional scanning design method for a directional vortex electromagnetic beam according to claim 1, characterized in that, In step 4, let the effective OAM mode set be... The magnitude weight vector is With the pitch angle of the main lobe of the multi-mode synthesized radiation pattern approaching the target pitch angle as the main objective, and combining modal coordination terms and weight regularization terms, an amplitude weight optimization objective function is constructed: in, Alignment with the main lobe. For modal cooperation terms, For weight regularization terms, and The weighting factor is: The main lobe alignment term is: in, Weight vector The pitch angle corresponding to the main lobe of the multimode synthesis pattern under the action. For the target pitch angle; the first The normalized effective contribution of the OAM mode at the target pitch angle is: The modal cooperation term is: in, This is a vector composed of the normalized effective contributions of each order of OAM mode; the weight regularization term is: The magnitude weight optimization satisfies the following constraints: 。 8. The two-dimensional scanning design method for a directional vortex electromagnetic beam according to claim 1, characterized in that, In step 5, the target azimuth angle is set as... For those located at the th Within the radial partition, the first Each array element corresponds to an OAM mode order of . The azimuth of the formation is Then the phase excitation of the array element is: The complex excitation of this array element is: This allows each OAM mode to be positioned at the target azimuth angle. The direction satisfies the in-phase superposition condition and makes the multimode synthesized main lobe point to the target azimuth angle.

9. The two-dimensional scanning design method for a directional vortex electromagnetic beam according to claim 1, characterized in that, In step 6, the modal radial partitioning parameters and multimode superposition amplitude excitation determined in steps 3 and 4 are kept unchanged, and only the unified phase offset parameters are used. As an azimuth scan control variable, among which For the corresponding target azimuth angle, for the first Within the radial annular region, the first Phase excitation applied to array elements of the OAM mode ,in The azimuth angle of the array element is changed by altering... Each OAM mode relative to the original spiral phase Synchronous introduction The initial phase offset causes the main lobe of the multimode superposition pattern to rotate as a whole in the azimuth direction. The specified target azimuth angle enables the scanning design of the vortex electromagnetic beam in the azimuth direction.

10. The application of a two-dimensional scanning design method for a directional vortex electromagnetic beam according to any one of claims 1-9, characterized in that, The method is applied to two-dimensional scanning and high-precision pointing control of vortex electromagnetic beams in electromagnetic wave systems for millimeter-wave communication and radar detection. In millimeter-wave communication systems, it is used for OAM mode directional transmission, beam alignment, and user direction tracking; in radar detection systems, it is used for target search, angular domain scanning, and target tracking. In space multiplexing transmission and reconfigurable array antenna systems, it is used for pointing control and two-dimensional scanning of multimode vortex beams.

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