Circumferential pirsche beam design method based on spatial scaling factor

Abstract

This invention proposes a circular Pircy beam design method based on a spatial scaling factor. The steps are as follows: initializing parameters; performing a substitution on the Pircy function; calculating the amplitude and phase of each array element based on the spatial scaling factor; and obtaining the design results of the circular Pircy beam. This invention achieves in-phase superposition at a greater distance along the central axis of the circular Pircy beam propagation direction by transforming the values ​​of two variables in the substituted Pircy function, resulting in a smoother phase distribution on the initial plane and enhanced obstacle avoidance capabilities. Simultaneously, the spatial scaling factor allows for scaling of the array element spatial coordinates, enabling adjustment of the focal length and improving flexible control over the energy transmission range. Furthermore, the substitution on the Pircy function ensures the accuracy of the aperture field calculation results for each array element, thereby improving the accuracy of the field distribution on the initial plane.

Description

Technical Field

[0001] This invention belongs to the field of near-field beam design technology and relates to a circular Pircy beam design method based on spatial scaling factor, which can be applied to the integration of intelligent sensing and energy supply. Background Technology

[0002] A near-field beam is an electromagnetic field with specific energy spatial distribution characteristics formed within the Fresnel zone of a radiation source. Commonly used near-field beams with focusing capabilities include Bessel beams, circular Airy beams, and circular Pilsier beams. The circular Pilsier beam, based on the Pilsier function, is a three-dimensional, diffraction-free beam formed by the coherent interference of a series of plane wave components with specific angular spectra. It can propagate around obstacles and exhibits a sharp main lobe and side lobe structure, possessing self-focusing characteristics. The core parameter of the circular Pilsier beam, the focal length, is defined as the maximum distance between two points along the central axis along the propagation direction where the power density drops from its peak to half; that is, the focal start and end positions. The focal length of the circular Pilsier beam can serve multiple targets located at different distances on the same axis, enabling multi-target energy transmission and other functions, making it suitable for integrated intelligent sensing and energy supply applications requiring precise wireless energy transmission.

[0003] The main idea behind circular Pircy beam design is as follows: First, initialize the array size. Second, determine the correspondence between the independent variables in the Pircy function and the spatial coordinates to calculate the initial plane, i.e., the amplitude and phase of the plane where the array antenna or metasurface is located. Then, use the angular spectrum method, which is a numerical calculation method to solve for the field amplitude and phase propagating to any point in free space from the field distribution containing amplitude and phase distributions on the initial plane, to calculate the field distribution of the Pircy beam propagating from the initial plane to any point in free space, thus obtaining the circular Pircy beam. Finally, design and excite the array antenna or metasurface at the required wavelength to generate the desired circular Pircy beam.

[0004] The key to generating circular Pircy beams lies in accurately calculating the amplitude and phase of the initial plane based on the Pircy function. Traditional circular Pircy beam design methods, which rely on the correspondence between the independent variable and spatial coordinates in the Pircy function, produce a large-scale oscillating amplitude distribution in the initial plane, leading to low efficiency and a large phase gradient in the initial plane, resulting in the beam focus starting position being close to the initial plane. To eliminate the oscillations in the amplitude distribution on the initial plane, patent application CN118277712A discloses a method for achieving high-efficiency Pircy beams using asymptotic expressions. This invention first calculates the Pircy function and its asymptotic expression for subsequent discretization calculations to obtain the compensated amplitude and phase of the array elements; then, it calculates the required compensated amplitude and phase for each array element to design the state of the metasurface elements or the amplitude and phase excitation of the array antenna; and finally, based on the designed metasurface or array antenna, generates a self-focusing Pircy beam. This invention achieves high-efficiency self-focusing Pilsier beam generation by fitting an asymptotic expression of the amplitude required for each antenna element or metasurface unit to generate a self-focusing Pilsier beam, and then shifting and truncating the asymptotic expression. This method, through asymptotic fitting, takes the upper envelope of the amplitude distribution, eliminating oscillations in the amplitude distribution on the initial plane, thereby reducing the amplitude modulation range and improving the generation efficiency of the Pilsier beam. However, because the phase distribution gradient on the initial plane is still large, the Pilsier beam focuses at a close distance on the initial plane, resulting in a short focal point and an inability to achieve long-range illumination, as well as weak obstacle avoidance capabilities. Furthermore, the Pilsier function itself is an infinite integral expression; in actual numerical calculations, the upper and lower limits of the integral must be truncated. This truncation introduces numerical errors, affecting the accuracy of calculating the amplitude and phase distributions on the initial plane using the Pilsier function. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a circular Pircy beam design method based on spatial scaling factor, which aims to ensure design efficiency while enhancing the ability to avoid obstacles, improving the flexibility of energy transmission range control, and increasing the accuracy of amplitude and phase distribution on the initial plane.

[0006] To achieve the above objectives, the technical solution adopted by the present invention includes the following steps:

[0007] (1) Initialize parameters:

[0008] Initialize with the origin of the spatial rectangular coordinate system Centered and located Planar periodic arrays on the surface include periodically arranged Each array unit is located at the origin. Pointing to the Line number The vector of the center of the column array cell is the spatial coordinate. The space scaling factor is ,in , They are respectively , Coordinates of direction;

[0009] (2) Substitute the Pircy function:

[0010] Pircy function Feature parameters in By performing substitution, the characteristic parameters are obtained as follows: Pircy function ,in, The base of the natural logarithm. Represents the imaginary unit;

[0011] (3) Calculate the amplitude and phase of the array elements based on the spatial scaling factor:

[0012] The Pirci function after substitution middle The value changes from 0 to At the same time The value is determined by Transform it to 0, that is, let , And through the transformed Pilsier function Calculate the aperture field of each array element Afterwards, through Calculate the amplitude of each array element and phase ,in, This indicates a modulo operation;

[0013] (4) Obtain the design results of the circular Pircy beam:

[0014] The amplitude passing through each array element is calculated using the angular spectral method. and phase Excites the aperture field generated on the initial plane of the periodic array Field distribution propagating to the normal direction located at the center of the unit , obtained by The circular Pircy beam is composed of field distributions. .

[0015] Compared with the prior art, the present invention has the following advantages:

[0016] 1. This invention transforms the values ​​of two variables in the Pircy function after substitution, resulting in a continuous and smooth single-ring structure for the amplitude distribution on the initial plane. This enables in-phase superposition at a greater distance along the central axis of the circular Pircy beam propagation direction, and the phase distribution on the initial plane is smoother, enhancing the ability to avoid obstacles. Simultaneously, by scaling the spatial coordinates of the array units using a spatial scaling factor, the radial width and phase distribution gradient of the single-ring structure can be adjusted, thereby adjusting the focal length and improving the flexible control of the energy transmission range.

[0017] 2. This invention, by substituting the Pilsier function, changes the integration path and bypasses the complex poles, transforming the infinite integral of complex variables, which cannot be directly calculated by the computer, into an equivalent real integral. This avoids the numerical errors introduced by truncation in the prior art, ensuring the accuracy of the aperture field of each array unit calculated by the Pilsier function after the substitution, thereby improving the accuracy of the amplitude and phase distribution on the initial plane. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating the implementation of the present invention.

[0019] Figure 2 This is a schematic diagram of the initial planar amplitude distribution in Embodiment 1 of the present invention.

[0020] Figure 3 This is a comparison diagram of the initial planar phase distribution of Embodiment 1 of the present invention and the prior art.

[0021] Figure 4 This is a comparison diagram of the field distribution of the xoz section of the circular Pircy beam in Embodiment 1 of the present invention and the prior art.

[0022] Figure 5 This is a schematic diagram of the xoz cross-sectional field distribution of the circular Pircy beam under different spatial scaling factors in Embodiment 1 of the present invention.

[0023] Figure 6 This is a comparison diagram of the field distribution of the xoz section of the circular Pircy beam in Embodiment 2 of the present invention and the prior art. Detailed Implementation

[0024] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0025] Example 1: The periodic array in this example is a planar array antenna;

[0026] Reference Figure 1 The present invention includes the following steps:

[0027] Step 1) Initialize parameters:

[0028] Initialize with the origin of the spatial rectangular coordinate system Centered and located Planar periodic arrays on the surface include periodically arranged Each array unit is located at the origin. Pointing to the Line number The vector of the center of the column array cell is the spatial coordinate. The space scaling factor is ,in , They are respectively , Coordinates of direction;

[0029] In this embodiment , The space scaling factor is .

[0030] The aforementioned planar periodic array employs a planar array antenna, which is provided with an excitation signal through an internal feeding network.

[0031] The aforementioned spatial scaling factor Its focal length compared to the circular Pircy beam The relationship and range of values ​​are as follows:

[0032] ;

[0033] ;

[0034] ;

[0035] in, Indicates the distance between adjacent units. This indicates the wavelength of the circular Pircy beam to be designed.

[0036] In this embodiment, the distance between adjacent units is The wavelength of the circular Pircy beam to be designed .

[0037] This invention introduces a spatial scaling factor. Spatial coordinates of array elements By performing a scaling transformation and increasing the spatial scaling factor, the gradient of the phase distribution determined by the Pilsey function in physical space is reduced. This widens the radial width of the main lobe of the beam while extending its focal length L, and vice versa. Therefore, by adjusting this parameter, flexible and continuous control over the range of the energy transmission focal region can be achieved, improving the system's adaptability to distance requirements in different application scenarios.

[0038] Step 2) Substitute the Pircy function:

[0039] Pircy function Feature parameters in By performing substitution, the characteristic parameters are obtained as follows: Pircy function ,in, The base of the natural logarithm. Represents the imaginary unit; where:

[0040] ;

[0041] ;

[0042] ;

[0043] in, express The characteristic parameters in Represents the complex exponential function The phase function.

[0044] By substituting the Pircy function, the integration path is changed, thus bypassing the complex poles and transforming the infinite integral of complex variables, which cannot be directly calculated by computers, into an equivalent real integral.

[0045] This invention mathematically alters the integration path by substituting the Pircy function, thereby bypassing the complex poles present in the original integral. This core improvement transforms the complex infinite integral, which was originally impossible for a computer to calculate directly, into a completely equivalent real integral that can be calculated efficiently and with high precision. This avoids the inherent numerical errors introduced by directly truncating the integration range in existing technologies, ensuring that the aperture field results for each array unit calculated by the substituted Pircy function have high precision, and thus fundamentally improving the accuracy of the generated initial planar amplitude and phase distribution.

[0046] Step 3) Calculate the amplitude and phase of the array elements based on the spatial scaling factor:

[0047] The Pirci function after substitution middle The value changes from 0 to At the same time The value is determined by Transform it to 0, that is, let , And through the transformed Pilsier function Calculate the aperture field of each array element Afterwards, through Calculate the amplitude of each array element and phase ;in:

[0048] ;

[0049] ;

[0050] ;

[0051] ;

[0052] ;

[0053] ;

[0054] in, This indicates the modulo operation. This indicates the operation of taking the complex argument.

[0055] By transforming the values ​​of the two variables in the Pircy function after substitution, the amplitude distribution on the generated initial plane presents a continuous and smooth single ring structure, which can achieve in-phase superposition at a greater distance along the central axis of the circular Pircy beam propagation direction, and the phase distribution on the initial plane is smoother, enhancing the ability to avoid obstacles.

[0056] Step 4) Obtain the design results of the circular Pircy beam:

[0057] The amplitude passing through each array element is calculated using the angular spectral method. and phase Excites the aperture field generated on the initial plane of the periodic array Field distribution propagating to the normal direction located at the center of the unit , obtained by The circular Pircy beam is composed of field distributions. .

[0058] ;

[0059] .

[0060] Circular Pircy Beam The calculation formula is:

[0061] ;

[0062] ;

[0063] ;

[0064] ;

[0065] ;

[0066] in, Represents the Fast Fourier Transform. This represents the inverse fast Fourier transform. This represents the field distribution matrix generated on the initial plane of the periodic array. Represents the spatial propagation operator matrix. This indicates a multiplication operation. express The propagation characteristics of the corresponding multiple angular spectral components, This represents the speed of light in a vacuum. Represents field distribution exist Directional coordinates Indicates the frequency of the circular Pilsner beam. This indicates the distance between adjacent array cells.

[0067] Example 2: In this example, the periodic array is a planar metasurface, and the field amplitude generated by illuminating each array unit through a horn feed is... and field phase amplitude of the array element and phase Compensation will be provided, and the actual amount of compensation will be determined accordingly. and phase It provides incentives.

[0068] , Spatial scaling factor The wavelength of the circular Pircy beam to be designed .

[0069] in and field phase The calculation formulas are as follows:

[0070] ;

[0071] ;

[0072] in Represent any positive real number, This indicates the height of the excitation source from the initial plane.

[0073] Actual range after compensation and phase The calculation formula is:

[0074] ;

[0075] .

[0076] The technical effects of this invention will be further explained below with reference to simulation experiments:

[0077] 1. Experimental conditions and contents:

[0078] Experiment 1 simulates the initial planar amplitude distribution of Embodiment 1 of the present invention, and the results are as follows: Figure 2 As shown;

[0079] Experiment 2 compares the initial planar phase distribution of Embodiment 1 of the present invention with that of the prior art through simulation, and the results are as follows: Figure 3 As shown;

[0080] Experiment 3 compares the field distribution of the xoz section of the circular Pircy beam in Embodiment 1 of this invention with that of the prior art. The results are as follows: Figure 4 As shown;

[0081] Experiment 4 simulates the xoz cross-sectional field distribution of the circular Pircy beam under different spatial scaling factors in Embodiment 1 of the present invention. The results are as follows: Figure 5 As shown;

[0082] Experiment 5 compares the field distribution of the xoz section of the circular Pircy beam in Example 2 of this invention with that of the prior art. The results are as follows: Figure 6 As shown;

[0083] 2. Analysis of experimental results:

[0084] Reference Figure 2 ,exist , The coordinate ranges of the directions are respectively , Interval length The minimum color saturation value is 0, and the maximum value is... The amplitude distribution in the figure is a continuous and smooth single high-intensity ring structure with no oscillation, which reduces the amplitude modulation range and ensures the generation efficiency of the Pilsier beam.

[0085] Reference Figure 3 ,exist , The coordinate ranges of the directions are respectively , , The minimum color swatch is 0, and the maximum color swatch is 0. . Reference Figure 3 (a) represents the initial planar phase distribution of Example 1, referring to Figure 3(b) represents the initial planar phase distribution of the prior art. By comparison, it is found that the phase distribution generated by the present invention on the initial plane changes more slowly than that of the prior art, so that the energy carried in the annular region can be superimposed in phase at a greater distance from the central axis of the circular Pircy beam propagation direction, and the focal starting position is further away.

[0086] Reference Figure 4 ,exist , The coordinate ranges of the directions are respectively , . Figure 4 (a) indicates the spatial scaling factor of the present invention. The generated circular Pircy beam xoz section field distribution has a minimum color scale of 0 and a maximum color scale of 0. . Figure 4 (b) represents the xoz cross-sectional field distribution of the circular Pircy beam generated by the prior art, with a minimum color scale of 0 and a maximum color scale of . A comparison revealed that the starting position of the circular Pircy beam focus generated by existing technologies is... Left and right, focal length is The focal starting position of the beam generated by this invention is approximately [left and right]. Left and right, focal length is Left and right, the focal point is farther away from the beamforming array, and the focal length is longer.

[0087] Reference Figure 5 ,exist , The coordinate ranges of the directions are respectively , . Figure 5 (a) indicates the spatial scaling factor of the present invention. The generated circular Pircy beam xoz section field distribution has a minimum color scale of 0 and a maximum color scale of 0. ; Figure 5 (b) indicates the spatial scaling factor of the present invention. The generated circular Pircy beam xoz section field distribution has a minimum color scale of 0 and a maximum color scale of 0. ; Figure 5 (c) indicates the spatial scaling factor of the present invention. The generated circular Pircy beam xoz section field distribution has a minimum color scale of 0 and a maximum color scale of 0. The comparison revealed that the focal lengths were respectively , , Satisfying the focal length The phase distribution gradient was adjusted by scaling the spatial coordinates of the array elements using a spatial scaling factor, thereby changing the focal length.

[0088] Reference Figure 6 ,exist , The coordinate ranges of the directions are respectively , . Figure 6 (a) indicates the spatial scaling factor of the present invention. The generated circular Pircy beam xoz section field distribution has a minimum color scale of 0 and a maximum color scale of 0. . Figure 6 (b) represents the xoz cross-sectional field distribution of the circular Pircy beam generated by the prior art, with a minimum color scale of 0 and a maximum color scale of . A comparison revealed that the starting position of the circular Pircy beam focus generated by existing technologies is... The focal length is The focal point of the beam generated by this invention starts at... The focal length is The focal point is farther from the initial plane, and the focal length is longer.

Claims

1. A circular Pircy beam design method based on spatial scaling factor, characterized in that, Includes the following steps; (1) Initialize parameters: Initialize with the origin of the spatial rectangular coordinate system Centered and located Planar periodic arrays on the surface include periodically arranged Each array unit is located at the origin. Pointing to the Line number The vector of the center of the column array cell is the spatial coordinate. The space scaling factor is ,in , They are respectively , Coordinates of direction; (2) Substitute the Pircy function: Pircy function Feature parameters in By performing substitution, the characteristic parameters are obtained as follows: Pircy function ,in, The base of the natural logarithm. Represents the imaginary unit; (3) Calculate the amplitude and phase of each array element based on the spatial scaling factor: The Pirci function after substitution middle The value changes from 0 to At the same time The value is determined by Transform it to 0, that is, let , And through the transformed Pilsier function Calculate the aperture field of each array element Afterwards, through Calculate the amplitude of each array element and phase ,in, This indicates a modulo operation; (4) Obtain the design results of the circular Pircy beam: The amplitude passing through each array element is calculated using the angular spectral method. and phase Excites the aperture field generated on the initial plane of the periodic array Field distribution propagating to the normal direction located at the center of the unit , obtained by The circular Pircy beam is composed of field distributions. .

2. The method according to claim 1, characterized in that, The planar periodic array described in step (1) uses a planar array antenna or a planar metasurface.

3. The method according to claim 1, characterized in that, The spatial scaling factor mentioned in step (1) Its focal length compared to the circular Pircy beam The relationship and range of values ​​are as follows: ； ； ； in, Indicates the distance between adjacent array cells. This indicates the wavelength of the circular Pircy beam to be designed.

4. The method according to claim 1, characterized in that, The Pilsier function described in step (2) And the Pilsier function after substitution Their expressions are as follows: ； ； ； in, express The characteristic parameters in Represents the complex exponential function The phase function.

5. The method according to claim 4, characterized in that, The aperture field described in step (3) The calculation formula is: ； ； ； 。 6. The method according to claim 4, characterized in that, The amplitude of each array element described in step (3) and phase The calculation formulas are as follows: ； ； in, This indicates the modulo operation. This indicates the operation of taking the complex argument.

7. The method according to claim 4, characterized in that, The excitation in step (4) generates an aperture field on the initial plane of the periodic array. The specific method is as follows: When the periodic array is a planar array antenna, the amplitude passing through each array element... and phase Incentivize them; When the periodic array is a planar metasurface, the field amplitude generated by illuminating each array element through the feed source and field phase amplitude of the array element and phase Compensation will be provided, and the actual amount of compensation will be determined accordingly. and phase Incentivize them.

8. The method according to claim 7, characterized in that, The field amplitude generated by each array unit and field phase The calculation formulas are as follows: ； ； in Represent any positive real number, This indicates the height of the feed source from the initial plane of the periodic array.

9. The method according to claim 7, characterized in that, The amplitude for each array unit and phase Compensation will be provided, and the compensation formulas are as follows: ； 。 10. The method according to claim 4, characterized in that, The circular Pircy beam described in step (4) The calculation formula is: ； ； ； ； ； in, Represents the Fast Fourier Transform. This represents the inverse fast Fourier transform. This represents the field distribution matrix generated on the initial plane of the periodic array. Represents the spatial propagation operator matrix. This indicates a multiplication operation. express The propagation characteristics of the corresponding multiple angular spectral components, This represents the speed of light in a vacuum. Represents field distribution exist Directional coordinates Indicates the frequency of the circular Pilsner beam. This indicates the distance between adjacent array cells.

Images