Single-layer transmission array design method for generating quasi-diffraction-free beams based on Huygens metasurface

Abstract

The invention discloses a single-layer transmission array design method for generating quasi-diffraction-free beams based on a Huygens metasurface, and the method comprises the steps: 1), designing an electric dipole and a magnetic dipole of each transmission unit on a dielectric substrate based on a Huygens metasurface theory; wherein the electric dipoles on the two sides of the dielectric substrate are of a symmetrical structure; the two groups of electric dipoles on the same side of the dielectric substrate are of asymmetric structures; 2) adjusting the size of the magnetic dipole in each transmission unit on the dielectric substrate to realize phase regulation and control in a 360-degree range; 3) deriving a plane transmission array phase distribution formula required for generating a Bessel beam based on a non-diffraction beam forming theory and a geometrical optics theory; and 4) designing unit structure arrangement on the single-layer transmission array based on the transmission performance of the designed metasurface unit in combination with a phase distribution formula. The structure is simple, the two sides are symmetrical, electromagnetism can be accurately regulated and controlled, phase regulation and control within the range of 360 degrees are achieved, and meanwhile it is ensured that the transmission amplitude is kept above-1.6 dB.

Description

Technical Field

[0001] The present invention relates to the field of planar transmission array antennas, and in particular to a design method for a single-layer transmission array based on a Huygens metasurface for generating quasi-diffracting beams. Background Art

[0002] With increasing demands for universal, portable, and sustainable power supply for electronic products, microwave wireless energy transmission for medium and long distances indoors has garnered widespread attention in recent years as a novel and practical energy supply technology. Microwave wireless energy transmission, due to its long transmission distance and strong environmental adaptability, has become an important means of achieving wireless energy transmission. However, its research and application still face numerous challenges, particularly in improving the transmission efficiency of wireless energy transmission, which remains a core issue that needs to be addressed.

[0003] To improve the efficiency of microwave wireless energy transmission systems, metasurface-based antenna designs are often used, particularly planar transmission array antennas and planar reflector array antennas spatially fed by horn antennas. These antennas offer advantages such as low profile, high radiation efficiency, and simple feeding, making them ideal for high-efficiency wireless energy transmission transmitters. Planar transmission array antennas, which avoid feed source obstruction, have attracted increasing attention in recent years. To improve efficiency, these structures typically achieve beamforming by adjusting the amplitude or phase of the radiated electromagnetic field to concentrate electromagnetic energy. Commonly used beamforming techniques include near-field focusing, high-gain beamforming, and quasi-diffraction-free beamforming. Quasi-diffraction-free beamforming offers advantages over other beamforming techniques primarily in reducing diffraction losses during electromagnetic wave propagation and enabling precise control of beam direction to concentrate energy along the transmission path. However, traditional transmission metasurface designs typically require multiple layers of dielectric plates to achieve 360° transmission phase control, which increases the difficulty of metasurface fabrication and hinders increasing transmission amplitude, limiting overall system performance.

[0004] Faced with the requirements of high transmission efficiency of wireless energy transmission systems, the traditional multi-layer transmissive metasurface design method is limited by its multi-layer structure, and has problems such as complex design and the transmission amplitude is usually limited to around -3dB. Summary of the Invention

[0005] The present invention aims to provide a method for designing a single-layer transmission array for generating a quasi-diffraction-free beam based on a Huygens metasurface, comprising the following steps:

[0006] 1) Based on Huygens metasurface theory, the electric dipoles and magnetic dipoles of each transmission unit on the dielectric substrate are designed. The electric dipoles on both sides of the dielectric substrate are symmetrical, while the two sets of electric dipoles on the same side of the dielectric substrate are asymmetrical.

[0007] 2) Adjusting the size of the magnetic dipoles in each transmission unit on the dielectric substrate to achieve 360° phase control;

[0008] 3) Based on the theory of non-diffraction beamforming and geometric optics, derive the phase distribution formula for the planar transmission array required to generate Bessel beams;

[0009] 4) Based on the transmission performance of the designed metasurface unit and the phase distribution formula, the unit structure arrangement on the single-layer transmission array is designed.

[0010] Furthermore, the electric dipole structure designed in step 1) is used to simultaneously excite the resonance phenomenon of the electric dipole and the magnetic dipole.

[0011] Furthermore, the two groups of electric dipoles on the same side of the dielectric substrate have different sizes and are staggered in position.

[0012] Furthermore, the dielectric substrate is a single-layer dielectric substrate.

[0013] Furthermore, the electric dipoles are metal patches, and the patches are arranged along the y direction.

[0014] Furthermore, the magnetic dipole has an I-shaped structure, and the double-open resonant square rings are both placed along the polarization direction of the electric field.

[0015] Furthermore, the quasi-diffraction-free beam generated by the single-layer transmission array is formed by the superposition of several plane waves of equal amplitude; the propagation directions of these plane waves have the same angle with the transmission axis and have symmetrical azimuth angles around the transmission axis;

[0016] At this time, the transmission array compensates the equiphase surface of the electromagnetic wave from the spherical surface to the conical surface, and the maximum undiffraction distance Z of the generated quasi-diffraction beam is max As shown below:

[0017]

[0018] Where D is the aperture of the transmission array; α is the cone half angle.

[0019] Furthermore, the phase distribution formula of the planar transmission array is as follows:

[0020]

[0021] Where k is the free space wave number, azimuth F is the distance between the feed source and the transmission array; φ R (x i ,y j ) is the plane transmission array phase; α is the cone half angle of the cone surface; (x i ,y j ) is the position of unit (i,j).

[0022] Furthermore, the adjustable dimensions include the horizontal rod length lcx, the vertical rod length lcy, the vertical rod width lcw, and the opening width dx of the double-opening square ring.

[0023] Furthermore, the adjustment range of the magnetic dipole size is determined by the sensitivity of the physical size of the magnetic dipole and the electromagnetic resonance characteristics to parameter changes.

[0024] The technical effects of the present invention are undoubted, and the beneficial effects of the present invention are:

[0025] 1. The present invention is based on Huygens metasurface theory. By designing electric resonant structures of varying sizes on the same side of a dielectric substrate and designing the same structure on both sides of the dielectric substrate to perform electric and magnetic resonance control, the optimized design of a single-layer transmission metasurface unit is achieved. The unit has a simple structure and is bilaterally symmetrical, which allows for precise control of electromagnetics. This method achieves phase control over a 360° range while ensuring that the transmission amplitude remains above -1.6dB. Therefore, this method is not only applicable to diffraction-free beam generation, but also to other phase-based wavefront control. The single-layer transmission array can be used in fields such as wireless energy transmission, radar systems, and wireless communications, and has excellent versatility.

[0026] 2. Existing single-layer Huygens metasurfaces usually rely on complex structures to excite magnetic resonance, such as connecting the metal structures on both sides of the dielectric substrate through metal through-holes to form a magnetic resonance ring, or by designing the upper and lower metal structures to be complementary or antisymmetric to induce reverse currents to excite magnetic resonance. However, these methods are relatively complex in processing and structural design. The present invention proposes a simplified design method: by designing electric dipole structures of different sizes on the same side of the dielectric substrate to excite electric and magnetic resonance, and the structures on both sides of the dielectric substrate are the same, by adjusting the horizontal rod length lcx, vertical rod length lcy, vertical rod width lcw of the I-shaped structure, and the opening width dx of the double-open square ring, the electromagnetic resonance can be flexibly and relatively independently controlled. This design not only ensures the range of phase control, but also improves the transmission efficiency, and has a simple structure and is easy to implement.

[0027] 3. Based on the theory of non-diffraction beamforming and geometric optics, this paper proposes a method for phase distribution in transmission arrays. This method establishes a geometric mapping relationship between the optical paths on the feed and target beam sides, calculates the optical path difference between each array element and the wavefronts on both sides, then superimposes them. It then incorporates the free-space wave number for phase compensation design, thereby obtaining the array phase distribution. This wavefront manipulation-based strategy is flexibly applicable to a variety of target wavefront forms, including plane waves and near-field focused beams, providing an effective phase distribution design solution for the design of high-performance transmission arrays.

[0028] 4. Based on the design method of single-layer transmissive metasurface units and the phase distribution method of the transmissive metasurface array, this paper proposes a design method for a single-layer transmissive array that can arbitrarily control the target beam wavefront. This method is not only applicable to wireless energy transmission, but also meets the requirements of high-performance electromagnetic wave control in radar systems, wireless communications, and other fields. Due to its single-layer structure, it has a simple design and flexible use, making it suitable for integrated electromagnetic system applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 (a) 3D view, (b) front view of the transmission unit based on Huygens principle

[0030] Figure 2 is the equivalent impedance of the transmission unit

[0031] Figure 3 Surface current distribution of the transmission unit under the condition of vertical incidence of y-polarized wave (a) frequency f = 5.2 GHz, (b) frequency f = 5.8 GHz, (c) frequency f = 6.1 GHz

[0032] Figure 4 The imaginary part of the equivalent impedance when dx = 4mm, 6mm, 8mm, 10mm, and 12mm (a) Equivalent electrical admittance, (b) Equivalent magnetic impedance

[0033] Figure 5 The imaginary part of the equivalent impedance when lcx = 4mm, 6mm, 8mm, 10mm, and 12mm (a) Equivalent electrical admittance, (b) Equivalent magnetic impedance

[0034] Figure 6 The imaginary part of the equivalent impedance when lcy = 4mm, 6mm, 8mm, 10mm, and 12mm (a) Equivalent electrical admittance, (b) Equivalent magnetic impedance

[0035] Figure 7 The imaginary part of the equivalent impedance when lcw = 1 mm, 2 mm, 3 mm, 4 mm, and 5 mm (a) Equivalent electrical admittance, (b) Equivalent magnetic impedance

[0036] Figure 8 Schematic diagram of generating a quasi-diffraction-free beam for a transmission array (a) 2D, (b) 3D

[0037] Figure 9 12 phase modulation unit structures covering 360° phase

[0038] Figure 10 Calculate the phase distribution of the transmission array

[0039] Figure 11 Front view of a single-layer transmission array

[0040] Figure 12Diagram of the transmission array electric field distribution test system

[0041] Figure 13 (a) Simulation results and (b) test results of the radial electric field distribution of the transmission array

[0042] Figure 14 The received power on the front and rear receiving apertures of the horn antenna loaded with the transmission array. DETAILED DESCRIPTION

[0043] The present invention will be further described below with reference to the following examples, but it should not be understood that the scope of the present invention is limited to the following examples. Without departing from the above technical ideas of the present invention, various substitutions and modifications can be made according to common technical knowledge and customary means in the art, and all should be included in the scope of protection of the present invention.

[0044] Example 1:

[0045] See also Figures 1 to 14 A method for designing a single-layer transmission array for generating a quasi-diffraction-free beam based on a Huygens metasurface comprises the following steps:

[0046] 1) Based on Huygens metasurface theory, the electric dipoles and magnetic dipoles of each transmission unit on the dielectric substrate are designed. The electric dipoles on both sides of the dielectric substrate are symmetrical, while the two sets of electric dipoles on the same side of the dielectric substrate are asymmetrical.

[0047] 2) Adjusting the size of the magnetic dipole and electric dipole in each transmission unit on the dielectric substrate to achieve 360° phase control;

[0048] 3) Based on the theory of non-diffraction beamforming and geometric optics, derive the phase distribution formula for the planar transmission array required to generate Bessel beams;

[0049] 4) Based on the transmission performance of the designed metasurface unit and the phase distribution formula, the unit structure arrangement on the single-layer transmission array is designed. The specific steps are: According to the calculated phase distribution ( Figure 10 The calculated phase distribution of the transmission array) combined with the transmission performance of the unit ( Figure 9 The structure distribution is designed to cover the 12 phase modulation unit structures ( Figure 11 (a front view of a single-layer transmission array).

[0050] The electric dipole structure designed in step 1) is used to simultaneously excite the resonance phenomenon of the electric dipole and the magnetic dipole.

[0051] The two sets of electric dipoles on the same side of the dielectric substrate have different sizes and are staggered in position.

[0052] The dielectric substrate is a single-layer dielectric substrate.

[0053] The electric dipoles are metal patches, and the patch directions are arranged along the y direction.

[0054] The magnetic dipole has an I-shaped structure, and the double-open resonant square rings are placed along the polarization direction of the electric field.

[0055] The quasi-diffraction-free beam generated by the single-layer transmission array is formed by the superposition of several plane waves of equal amplitude; the propagation directions of these plane waves are at the same angle to the transmission axis and have symmetrical azimuths around the transmission axis;

[0056] At this time, the transmission array compensates the equiphase surface of the electromagnetic wave from the spherical surface to the conical surface, and the maximum undiffraction distance Z of the generated quasi-diffraction beam is max As shown below:

[0057]

[0058] Where D is the aperture of the transmission array; α is the cone half angle of the cone surface.

[0059] The phase distribution formula of the planar transmission array is as follows:

[0060]

[0061] Where k is the free space wave number, azimuth F is the distance between the feed source and the transmission array; φ R (x i ,y j ) is the plane transmission array phase; α is the cone half angle of the cone surface; (x i ,y j ) is the position of unit (i,j).

[0062] The adjustable dimensions include the horizontal rod length lcx, the vertical rod length lcy, the vertical rod width lcw, and the opening width dx of the double-opening square ring.

[0063] The adjustment range of the magnetic dipole size is determined by the sensitivity of the physical size of the magnetic dipole and the response of the electromagnetic resonance characteristics to parameter changes.

[0064] The adjustment range of these parameters is affected by the physical size limitation and the sensitivity of the electromagnetic resonance characteristics to parameter changes (see Figures 4 and 5 After optimization design, 12 parameter combinations are finally determined as shown in Table 1, and the corresponding unit structures are shown in Figure 9 Specifically, the adjustment range of the horizontal bar length lcx is 4mm to 12mm, the adjustment range of the vertical bar length lcy is 4mm to 12mm, the adjustment range of the vertical bar width lcw is 1mm to 5mm, and the adjustment range of the opening width dx of the double-opening square ring is 4mm to 12mm.

[0065] Example 2:

[0066] A method for designing a single-layer transmission array for generating a quasi-diffraction-free beam based on a Huygens metasurface comprises the following steps:

[0067] 1) Based on Huygens metasurface theory, the electric dipoles and magnetic dipoles of each transmission unit on the dielectric substrate are designed. The electric dipoles on both sides of the dielectric substrate are symmetrical, while the two sets of electric dipoles on the same side of the dielectric substrate are asymmetrical.

[0068] 2) Adjusting the size of the magnetic dipoles in each transmission unit on the dielectric substrate to achieve 360° phase control;

[0069] 3) Based on the theory of non-diffraction beamforming and geometric optics, derive the phase distribution formula for the planar transmission array required to generate Bessel beams;

[0070] 4) Based on the transmission performance of the designed metasurface unit and the phase distribution formula, the unit structure arrangement on the single-layer transmission array is designed. The specific steps are: According to the calculated phase distribution ( Figure 10 The calculated phase distribution of the transmission array) combined with the transmission performance of the unit ( Figure 9 The structure distribution is designed to cover the 12 phase modulation unit structures ( Figure 11 (a front view of a single-layer transmission array).

[0071] Example 3:

[0072] A method for designing a single-layer transmission array based on a Huygens metasurface to generate a quasi-diffracting beam has the same technical content as Example 2. Furthermore, the electric dipole structure designed in step 1) is used to simultaneously excite the resonance phenomenon of the electric dipole and the magnetic dipole.

[0073] Example 4:

[0074] A method for designing a single-layer transmission array for generating a quasi-diffracting beam based on a Huygens metasurface, the technical content of which is the same as any one of Examples 2-3, further comprising two sets of electric dipoles on the same side of the dielectric substrate having different sizes and staggered positions.

[0075] Example 5:

[0076] A method for designing a single-layer transmission array for generating a quasi-diffraction-free beam based on a Huygens metasurface, the technical content of which is the same as any one of Examples 2-4, further, the dielectric substrate is a single-layer dielectric substrate.

[0077] Example 6:

[0078] A method for designing a single-layer transmission array based on a Huygens metasurface to generate a quasi-diffraction-free beam, the technical content of which is the same as any one of Examples 2-5, further, the electric dipoles are metal patches, and the patch direction is arranged along the y direction.

[0079] Example 7:

[0080] A method for designing a single-layer transmission array for generating a quasi-diffracting beam based on a Huygens metasurface, the technical content of which is the same as any one of Examples 2-6, furthermore, the magnetic dipole has an "I"-shaped structure, and the double-open resonant square rings are placed along the electric field polarization direction.

[0081] Example 8:

[0082] A method for designing a single-layer transmission array based on a Huygens metasurface for generating a quasi-non-diffracting beam, the technical content of which is the same as any one of Examples 2-7, wherein the quasi-non-diffracting beam generated by the single-layer transmission array is formed by the superposition of a plurality of plane waves of equal amplitude; the propagation directions of these plane waves are at the same angle to the transmission axis and have symmetrical azimuth angles around the transmission axis;

[0083] At this time, the transmission array compensates the equiphase surface of the electromagnetic wave from the spherical surface to the conical surface, and the maximum undiffraction distance Z of the generated quasi-diffraction beam is max As shown below:

[0084]

[0085] Where D is the aperture of the transmission array; α is the cone half angle of the cone surface.

[0086] Example 9:

[0087] A method for designing a single-layer transmission array based on a Huygens metasurface to generate a quasi-diffracting beam, the technical content of which is the same as any one of Examples 2-8. Furthermore, the phase distribution formula of the planar transmission array is as follows:

[0088]

[0089] Where k is the free space wave number, azimuth FF is the distance between the feed source and the transmission array.

[0090] Example 10:

[0091] A method for designing a single-layer transmission array for generating quasi-diffracting beams based on a Huygens metasurface, the technical content of which is the same as any one of Examples 2-9. Furthermore, the adjustable dimensions include the length lcx of the I-shaped magnetic dipole crossbar, the length lcy of the vertical bar, the width lcw of the vertical bar, and the opening width dx of the double-open square ring (electric dipole).

[0092] Example 11:

[0093] A method for designing a single-layer transmission array based on a Huygens metasurface to generate a quasi-diffracting beam, the technical content of which is the same as any one of Examples 2-10. Furthermore, the adjustment range of the magnetic dipole size is determined by the sensitivity of the magnetic dipole physical size and electromagnetic resonance characteristic response to parameter changes.

[0094] Example 12:

[0095] A method for designing a single-layer transmission array based on a Huygens metasurface to generate a quasi-diffraction-free beam, the technical content of which is the same as any one of Examples 2-11. Furthermore, the adjustment range of these parameters is affected by the physical size limitation and the sensitivity of the electromagnetic resonance characteristic response to parameter changes (see Figures 4 and 5 After optimization design, 12 parameter combinations are finally determined as shown in Table 1, and the corresponding unit structures are shown in Figure 9 Specifically, the adjustment range of the horizontal bar length lcx is 4mm to 12mm, the adjustment range of the vertical bar length lcy is 4mm to 12mm, the adjustment range of the vertical bar width lcw is 1mm to 5mm, and the adjustment range of the opening width dx of the double-opening square ring is 4mm to 12mm.

[0096] Example 13:

[0097] A design method for a single-layer transmission array based on a Huygens metasurface to generate quasi-diffraction-free beams is described as follows:

[0098] Based on Huygens metasurface theory, by designing electric dipole structures of different sizes on the same side of a dielectric substrate and designing the same structure on both sides of the dielectric substrate, electric and magnetic resonances are simultaneously stimulated to control the amplitude and phase of the transmitted electromagnetic wave, thereby realizing the design of a single-layer transmission metasurface unit. This method overcomes the problem that traditional frequency selective surfaces usually require at least three layers of dielectric substrates to achieve 360° phase modulation. First, electric dipole structures of different sizes are designed on the same side of the dielectric substrate, and the same structure is designed on both sides of the dielectric substrate to simultaneously stimulate the resonance of electric and magnetic dipoles. Second, by adjusting the horizontal rod length lcx, vertical rod length lcy, vertical rod width lcw of the I-shaped structure in each transmission unit, and the opening width dx of the double-open square ring, 360° phase control is achieved. At the same time, the transmission amplitude of the designed unit is improved from -3dB to -1.6dB compared with the traditional transmission unit, that is, the microwave energy passing through the transmission unit is increased from 50% to 69.2%, which significantly improves the energy transmission efficiency; then, based on the theory of non-diffraction beamforming and geometric optics theory, the phase distribution formula of the planar transmission array required to generate Bessel beams is derived. Finally, combining the above-mentioned metasurface unit design and phase distribution formula, a single-layer transmission array is designed to achieve the generation of quasi-diffraction-free beams within a certain distance, meeting the requirements of high efficiency in wireless energy transmission systems, and forming a single-layer transmission array design method that meets the phase control needs in beamforming. This method can be directly used for electromagnetic wave control of quasi-diffraction-free beams, providing a design method and technical means for conducting experimental tests of quasi-diffraction-free beam wireless energy transmission.

[0099] The present invention typically uses a traditional frequency-selective surface structure to generate quasi-diffracting beams. This structure requires at least three layers of dielectric substrate to achieve 360° phase modulation, making it difficult to meet the requirements of wireless energy transmission systems for simple equipment installation and high transmission efficiency. This leads to increased system installation complexity, reduced transmission efficiency, and inevitably increased system costs, which in turn affects the practical application performance of wireless energy transmission systems. Therefore, optimizing the number of layers of the transmissive metasurface and increasing the transmission amplitude are crucial to the design of the transmissive array. This can lay the foundation for the overall optimization design of the transmission efficiency improvement system of subsequent wireless energy transmission systems, which is of great significance.

[0100] The present invention proposes a single-layer transmission array method for generating quasi-diffraction-free beams based on a Huygens metasurface. Using Huygens metasurface theory, the method excites electric and magnetic resonances by designing electric dipole structures of different sizes on the same side of a dielectric substrate and identical structures on both sides of the dielectric substrate to control the amplitude and phase of the electromagnetic wave, thereby realizing a single-layer transmission metasurface with 360° phase modulation capability. On this basis, by deriving a phase distribution formula for generating quasi-diffraction-free beams, the design of a single-layer transmission array was ultimately completed, forming a design method for a single-layer transmission array that meets the phase control requirements of beamforming, achieving the generation of a quasi-diffraction-free beam within a transmission distance of 0.86 meters. Within the entire quasi-diffraction-free transmission area, the rate of attenuation of received power with distance is significantly reduced after loading the metasurface. At around 900 mm, the received power difference is 257% of the received power without the metasurface. This method can achieve electromagnetic wave control of quasi-diffracting beams, and has the advantages of single-layer structure, simple design, and high transmission efficiency. It solves the problem that the complex structure and high transmission amplitude of traditional multi-layer structures are difficult to meet the requirements of high transmission efficiency and stable beams in wireless energy transmission systems. In response to the above problems, the present invention proposes a single-layer transmission array design method for generating quasi-diffracting beams based on Huygens metasurfaces. Based on the Huygens metasurface theory, this method excites electric and magnetic resonances by designing electric dipole structures of different sizes on the same side of the dielectric substrate and designing the same structure on both sides of the dielectric substrate to control the amplitude and phase of the transmitted electromagnetic wave, thereby realizing the design of a single-layer transmission metasurface unit. This method overcomes the problem of too many dielectric substrate layers when traditional frequency selective surfaces achieve 360° phase modulation. First, electric dipole structures of varying sizes were designed on the same side of a dielectric substrate, while identical structures were designed on both sides of the substrate to simultaneously stimulate the resonance of both electric and magnetic dipoles. Second, by adjusting the horizontal rod length lcx, vertical rod length lcy, vertical rod width lcw, and the opening width dx of the double-open square rings in each transmission unit, phase control over a 360° range was achieved while ensuring that the transmission amplitude remained above -1.6 dB. Subsequently, based on the theory of non-diffracting beamforming and geometric optics, the phase distribution formula for a planar transmission array required for Bessel beam generation was derived. Finally, combining the aforementioned metasurface unit design and phase distribution formula, a single-layer transmission array was designed that achieved quasi-diffracting beam generation within a certain distance, meeting the high efficiency requirements of wireless energy transmission systems. This method, a single-layer transmission array design approach that meets the phase control requirements of beamforming, was developed. This method can be directly applied to electromagnetic wave control of quasi-diffracting beams, providing a design method and technical means for conducting experimental tests of wireless energy transmission based on quasi-diffracting beams.

[0101] This method can be used to design a single-layer transmission array with quasi-diffraction-free beamforming. The implementation method is as follows:

[0102] 1. Design of single-layer transmission metasurface unit structure based on Huygens metasurface theory.

[0103] Based on Huygens metasurface theory, this method employs electric dipole structures of varying sizes on the same side of a dielectric substrate, and identical structures on both sides of the substrate. This stimulates electric and magnetic resonances to manipulate the amplitude and phase of the transmitted electromagnetic wave, thereby achieving a single-layer transmissive metasurface unit. This approach overcomes the problem that conventional frequency-selective surfaces typically require at least three layers of dielectric substrate to achieve 360° phase modulation.

[0104] 1) In order to design the initial unit structure of a single-layer metasurface that can simultaneously excite electric and magnetic resonances, the design of a resonant excitation mechanism is prioritized. To this end, the present invention adopts two magnetic resonance excitation mechanisms: first, a symmetrical structure is designed on both sides of the dielectric substrate. This design excites magnetic resonances at two different frequencies through two groups of electric dipoles of different sizes; second, electric dipoles of staggered sizes and positions are designed on both sides of the dielectric substrate, and additional magnetic resonance points are excited through the staggered coupling of different structures between layers, thereby obtaining a more flexible controllable magnetic resonance capability near the operating frequency. In terms of electric resonance excitation design, the designed "I"-shaped structure and double-open resonant square rings are placed along the direction of electric field polarization. The final designed transmission unit based on the Huygens metasurface is as follows Figure 1 As shown, it mainly includes a single-layer dielectric substrate and metal patches, and the patches are arranged along the y direction.

[0105] 2) To optimize transmission characteristics and meet operating frequency requirements, the unit size and related parameters need to be adjusted during design. For high-frequency applications, the overall unit size should be reduced, and the I-shaped structure width lcx and the double-ring opening width dx should be reduced. For low-frequency applications, the overall unit size should be increased, and the I-shaped structure width lcx and the double-ring opening width dx should be increased. The remaining parameters (metal line width and dielectric substrate thickness) should be kept within a reasonable range, taking into account factors such as machining accuracy, physical deformation, and the impact on transmission coefficient linearity.

[0106] 2. Analysis of electric and magnetic resonance and control parameter design of single-layer transmission metasurface units based on Huygens metasurface theory.

[0107] 1) In order to analyze the electric and magnetic resonances excited by the designed metasurface unit, the transmission coefficient T and reflection coefficient R of the metasurface are extracted through simulation to calculate its equivalent impedance. Based on the Huygens metasurface theory, for the Huygens metasurface that simultaneously excites electric and magnetic resonances, the transmission coefficient T and reflection coefficient R can be used to extract the equivalent electrical admittance Y es and equivalent magnetic impedance Z msThe relationship between the two is shown in formula (1) and (2). According to formula (1) and (2), the equivalent impedance of the transmission unit is calculated and Figure 2 The imaginary part of the equivalent impedance is displayed, and the electric and magnetic resonance points are displayed. It can be seen that the designed structure has three magnetic resonance points and one electric resonance point, which are denoted as f M1 ,f M2 ,f M3 ,f E1 .

[0108]

[0109] Where η is the wave impedance in free space. By adjusting the equivalent admittance Y es and equivalent magnetic impedance Z ms , the transmission coefficient T and reflection coefficient R can be adjusted, and their relationship is shown in Equations (3) and (4).

[0110]

[0111] 2) In the equivalent admittance Y es and equivalent magnetic impedance Z ms At the resonance point of the metal patch, analyzing the surface current distribution on the metal patch can reveal the formation mechanism of electromagnetic resonance and its control method. Taking three resonance points near the resonance point, when the y-polarized wave is vertically incident, the surface current distribution of the transmission unit is as follows Figure 3 As shown. At low frequency f M1 The magnetic flux loop at the position is mainly formed by the reverse current on the I-shaped patch and the square ring respectively located on the upper and lower layers. At this time, the magnetic flux loop size is the largest; at the intermediate frequency f M1 The magnetic flux loop at the location is mainly formed by the reverse current on the double-open square ring located between the upper and lower layers. At this time, the size of the magnetic flux loop is slightly smaller; and the high frequency f M3 The magnetic flux loop at f is mainly formed by the reverse current of the I-shaped patches located in the upper and lower layers, and the size of the magnetic flux loop is the smallest at this time. E1 At the corresponding frequency, the currents in the same direction induced on the I-shaped patch and the double-open square ring on the same layer can be equivalent to electric dipoles, which is basically consistent with the design idea of ​​implementation method (1).

[0112] 3) Based on the above electromagnetic resonance analysis, the horizontal rod length lcx, vertical rod length lcy, vertical rod width lcw, and opening width dx of the double-opening square ring of the I-shaped structure are selected as the control parameters. By controlling these four parameters, the frequency of electromagnetic resonance can be effectively and relatively independently controlled. The equivalent impedance imaginary part when these four parameters are swept is as follows: Figures 4 to 7 shown.

[0113] 3. Derivation of the phase distribution formula and array arrangement of transmission array based on non-diffraction beamforming theory and geometric optics theory.

[0114] According to the theory of non-diffraction beamforming, a quasi-non-diffraction beam can be formed by the superposition of several plane waves of equal amplitude, and the propagation directions of these plane waves have the same angle with the transmission axis (denoted as the cone half-angle α), and have symmetrical azimuth angles (0 to 2π) around the transmission axis. Moreover, at this time, the transmission array is located in the near field area of ​​the feed horn antenna and can be regarded as a spherical wave source. In order to achieve the generation of a quasi-non-diffraction beam, the transmission array needs to compensate the equiphase surface of the electromagnetic wave from the spherical surface to the conical surface. Therefore, the two-dimensional principle diagram of the transmission array generating a quasi-non-diffraction beam is shown as follows: Figure 8 (a) shows that the maximum non-diffraction distance Z max It is determined by the designed cone half-angle α and the aperture size D of the transmission array, and the relationship is shown in formula (5).

[0115]

[0116] Figure 8 (b) 3D schematic diagram of the principle of generating quasi-non-diffraction beams for a transmission array. Taking the unit (i, j) on the transmission array as an example, the geometric relationship of the optical path required for non-diffraction beam forming is demonstrated. The coordinate origin is established with the center of the transmission array as the coordinate system. Figure 8 (b) The rectangular coordinates shown in Figure 2, the position coordinates of the feed phase center are S(0,0,-F), and the position coordinates of the unit (i,j) are P(x i ,y j ,0), the azimuth of unit (i,j) on the xoy plane is Therefore, according to the position P(x i ,y j ,0)The compensation phase is calculated as shown in formula (6).

[0117]

[0118] Where k is the free space wave number, azimuth Example 14:

[0119] A design method for a single-layer transmission array based on a Huygens metasurface to generate quasi-diffracting beams was demonstrated. The following is the content:

[0120] Taking the design of a transmission array for 5.8GHz microwave wireless energy transmission as an example, the array has a quasi-diffraction-free beamforming function, and the specific implementation of the patent of this invention is demonstrated through simulation verification. First, a transmission unit based on the Huygens metasurface is designed, such as Figure 1As shown. Among them, the transmission unit period P = 18mm, the dielectric substrate thickness h = 3mm, the metal line width w0 = 1mm, these parameters are fixed parameters and are the same on each transmission unit. Table 1 shows the selection of control parameters for the designed 12 transmission units, aiming to achieve 360° phase coverage and a transmission amplitude greater than -1.6dB. These parameters include: the horizontal rod length lcx of the I-shaped structure, the vertical rod length lcy, the vertical rod width lcw, and the opening width dx of the double-opening square ring. Table 1 also shows the transmission phase and transmission amplitude under these control parameters. These 12 unit structures are as follows Figure 9 shown.

[0121] Table 1 Control parameters and transmission coefficients of 12 units covering 360°

[0122]

[0123] Select the standard gain horn antenna with a gain of 15dBi as the feed source, according to Figure 8 The feed and transmission array are placed schematically. The distance F between the feed and the transmission array is selected to be 320 mm. The side length of the transmission array is set to D = 306 mm (17 units with a period of 18 mm). The cone half angle of the quasi-diffraction-free beam is α = 10°. According to formula (5), the maximum undiffraction distance Z max is about 868mm; according to formula (6), the phase distribution diagram is as follows Figure 10 As shown. According to the calculated phase distribution and the transmission phase of the corresponding unit in Table 1, the distribution of the metasurface on the transmission array is designed as follows Figure 11 As shown. Based on the transmission array designed above, the radial electric field distribution obtained by simulation is set as Figure 13 (a) As shown; Based on the transmission array designed above, refer to Figure 12 A transmission array test system was built, which tested distances from the metasurface ranging from 350 mm to 1000 mm.

[0124] The radial electric field distribution within the range, the test results are as follows Figure 13 (b) The test shows that the diffraction-free distance can reach the maximum diffraction-free distance Z calculated theoretically. max =868mm, and it is in good agreement with the simulation results.

[0125] It can be found that the single-layer transmission array design method proposed in this paper for generating quasi-diffraction-free beams in wireless energy transmission systems forms high-quality quasi-diffraction-free beams. Figure 12 As shown, the maximum non-diffraction distance Z in the theoretical design max = A bright spot channel with little width change appears in the center of the electric field distribution diagram within 868mm. Figure 13The received power on a 138mm×250mm horn antenna was compared when the horn antenna was loaded with a transmissive array and when it was not. As can be seen from the figure, as the distance between the receiving antenna and the metasurface increases, the received power shows a gradual attenuation trend, regardless of whether the transmissive metasurface is loaded. It is worth noting that although loading the metasurface will cause the received power closer to the metasurface to decrease, the rate of power attenuation is significantly slowed. Experimental data shows that within the entire quasi-diffraction-free transmission region, the received power advantage after loading the metasurface continues to increase with distance: power overtaking is achieved at 400mm, and the maximum power gain is reached near 900mm, at which point the received power difference reaches 59.81mW, equivalent to 257% of the received power when the metasurface is not loaded.

Claims

1. A method for designing a single-layer transmission array for generating quasi-diffraction-free beams based on a Huygens metasurface, characterized in that: The following steps are involved: 1) Based on Huygens metasurface theory, the electric dipoles and magnetic dipoles of each transmission unit on the dielectric substrate are designed. The electric dipoles on both sides of the dielectric substrate are symmetrical, while the two sets of electric dipoles on the same side of the dielectric substrate are asymmetrical. 2) Adjusting the size of the magnetic dipoles in each transmission unit on the dielectric substrate to achieve 360° phase control; 3) Based on the theory of non-diffraction beamforming and geometric optics, derive the phase distribution formula for the planar transmission array required to generate Bessel beams; 4) Based on the transmission performance of the designed metasurface unit and the phase distribution formula, the unit structure arrangement on the single-layer transmission array is designed.

2. The method for designing a single-layer transmission array for generating quasi-diffracting beams based on a Huygens metasurface according to claim 1, characterized in that: The electric dipole structure designed in step 1) is used to simultaneously excite the resonance phenomenon of the electric dipole and the magnetic dipole.

3. The method for designing a single-layer transmission array for generating quasi-diffracting beams based on a Huygens metasurface according to claim 1, characterized in that: The two sets of electric dipoles on the same side of the dielectric substrate have different sizes and are staggered in position.

4. The method for designing a single-layer transmission array for generating quasi-diffracting beams based on a Huygens metasurface according to claim 1, wherein: The dielectric substrate is a single-layer dielectric substrate.

5. The method for designing a single-layer transmission array for generating quasi-diffracting beams based on a Huygens metasurface according to claim 1, characterized in that: The electric dipoles are metal patches, and the patch directions are arranged along the y direction.

6. The method for designing a single-layer transmission array for generating quasi-diffracting beams based on a Huygens metasurface according to claim 1, characterized in that: The magnetic dipole has an "I"-shaped structure, and the double-open resonant square rings are placed along the polarization direction of the electric field.

7. The method for designing a single-layer transmission array for generating quasi-diffracting beams based on a Huygens metasurface according to claim 1, characterized in that: The quasi-diffraction-free beam generated by the single-layer transmission array is formed by the superposition of several plane waves of equal amplitude; the propagation directions of these plane waves are at the same angle to the transmission axis and have symmetrical azimuths around the transmission axis; At this time, the transmission array compensates the equiphase surface of the electromagnetic wave from the spherical surface to the conical surface, and the maximum undiffraction distance Z of the generated quasi-diffraction beam is max As shown below: Where D is the aperture of the transmission array; α is the cone half angle of the cone surface.

8. The method for designing a single-layer transmission array for generating quasi-diffracting beams based on a Huygens metasurface according to claim 1, characterized in that: The phase distribution formula of the planar transmission array is as follows: Where k is the free space wave number, azimuth F is the distance between the feed source and the transmission array; φ R (x i ,y j ) is the plane transmission array phase; α is the cone half angle of the cone surface; (x i ,y j ) is the position of unit (i,j).

9. The method for designing a single-layer transmission array for generating quasi-diffracting beams based on a Huygens metasurface according to claim 1, wherein: The adjustable dimensions include the horizontal rod length lcx, the vertical rod length lcy, the vertical rod width lcw, and the opening width dx of the double-opening square ring.

10. The method for designing a single-layer transmission array for generating quasi-diffracting beams based on a Huygens metasurface according to claim 1, wherein: The adjustment range of the magnetic dipole size is determined by the sensitivity of the physical size of the magnetic dipole and the response of the electromagnetic resonance characteristics to parameter changes.

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