Ultra-wideband full-polarization large-angle beam scanning theory based on electromagnetic metasurface

Abstract

The invention relates to the technical field of electromagnetics, in particular to an ultra-wideband full-polarization large-angle beam scanning theory based on an electromagnetic metasurface, which comprises the following steps of: S1, regulating and controlling a beam far-field phase based on an array global reference phase; s2, adjusting and controlling far-field orthogonal polarization vector field superposition based on array factors to realize full-polarization beam control; and S3, theoretical calculation verification of full-polarization beam regulation and full-wave simulation verification of the full-polarization beam. According to the invention, a novel full-polarization wave beam regulation and control theory based on array factor regulation and control orthogonal polarization vector field superposition is provided, and theoretical calculation and full-wave simulation are carried out on the provided full-polarization wave beam regulation and control theory; according to the theory, the effectiveness and universality of realizing ultra-wideband and large-angle full-polarization beam regulation and control by only using one-bit phase resolution are verified.

Description

Technical Field

[0001] The present invention relates to the technical field of electromagnetics, and particularly to the theory of ultra-wideband full-polarization large-angle beam scanning based on electromagnetic metasurfaces. Background Technique

[0002] The polarization of electromagnetic waves (EM) is described by the trajectory of the electric field vector direction over time. In practical applications, the operating polarization mode of the receiving antenna must match that of the incident electromagnetic wave to maximize the reception of the information carried by the signal. For example, circularly polarized antennas are used in satellite communication, while base station antennas operate in a linearly polarized mode. In the field of radar, the polarization of electromagnetic waves can be used for target recognition, target detection, and super-resolution imaging. In terms of anti-jamming, advanced polarization control techniques can be applied to radome design, electronic interference suppression and protection, and electromagnetic compatibility. Given the above extensive application scenarios, the realization of electromagnetic wave polarization control has attracted extensive attention from researchers. Metasurfaces are sub-wavelength-scale, quasi-periodic planar artificial electromagnetic structures. By carefully designing their geometry, material properties, and arrangement, they can flexibly manipulate the amplitude, phase, polarization, and propagation direction of electromagnetic waves, thereby achieving efficient control of electromagnetic waves. Therefore, metasurfaces have become an effective tool for realizing electromagnetic wave polarization control due to their advantages in manipulating electromagnetic waves. In recent years, researchers at home and abroad have proposed many dynamic polarization control metasurface schemes to achieve flexible control of electromagnetic wave polarization, including mechanical control, liquid metal, and paper-cut metasurface technologies. Electronically reconfigurable polarization conversion metasurfaces (PCMs) can achieve real-time control of electromagnetic wave polarization by integrating adjustable lumped elements such as PIN diodes and varactor diodes in the unit structure and combining with a field-programmable gate array (FPGA) system. Compared with the above polarization control schemes, it has significant advantages, including fast response speed, high integration, and flexible design. Therefore, PCM has become an effective way to flexibly control electromagnetic wave polarization. Currently, relying on electronically reconfigurable metasurface technology, multi-band and multi-functional polarization conversion can be achieved. For example, when the PIN diodes in the metasurface are in the conducting state, in the case of linearly polarized wave incidence, it can be converted into a cross-polarized wave in the frequency bands of 7.30–8.90 GHz and 19.40–24.92 GHz, and into a circularly polarized wave in the frequency band of 9.79–17.42 GHz. When the diodes are in the cutoff state, cross-polarization conversion can be achieved in the frequency band of 8.9–13.22 GHz, and the conversion from linear polarization to circular polarization can be achieved in the frequency bands of 7.60–8.30 GHz and 14.71–16.83 GHz. In addition, multiple polarization conversions can also be achieved within the same frequency band. For example, in a reflective four-polarization reconfigurable conversion metasurface, by adjusting the bias voltage of the diodes, efficient switching between horizontal linear polarization (HP), vertical linear polarization (VP), left-handed circular polarization (LHCP), and right-handed circular polarization (RHCP) can be achieved.In a broadband multifunctional reconfigurable polarization conversion metasurface, by controlling the "on" and "off" states of PIN diodes, linear polarization to cross-polarization conversion with a relative bandwidth of 88.4% (5.69 GHz - 15.34 GHz) and linear polarization to circular polarization conversion with a relative bandwidth of 83.75% (6.05 GHz - 14.76 GHz) can be achieved.

[0003] Although PMC has the ability to achieve fast conversion between different electromagnetic wave polarizations, it can only perform dynamic polarization control on plane waves incident at a fixed angle and cannot meet the polarization matching reception requirements for electromagnetic wave signals from different incident angles, thus greatly limiting their signal reception range in communication systems. To address the above challenges, reconfigurable metasurface antenna technology has achieved efficient modulation of electromagnetic wave signals with different directions and polarizations. The prior art has proposed a one-bit beam scanning reflectarray antenna with four polarization switching functions. By changing the operating state of the PIN diodes, dynamic conversion between HP, VP, LHCP, and RHCP can be achieved within the beam scanning range of 0° to 40°. Drawing on the polarization conversion principle, the prior art has proposed a novel broadband and efficient beam scanning transmit array that converts the x-polarized electromagnetic wave emitted by a horn feed into a y-polarized electromagnetic wave and achieves beam scanning within the range of 0° to 50°. Subsequently, the prior art has also proposed a bidirectional beam scanning aperture with a switchable transmission-reflection mode, which can simultaneously achieve dynamic regulation of the co-polarized reflected beam and the cross-polarized transmitted beam within the scanning angle range of 0° to 45°. It can be clearly seen from the previous related work that although the current reconfigurable metasurface antennas have made breakthrough progress in controlling the polarization of the scanning beam, the polarization conversion function is regulated at the unit level. This approach has led to several common problems, including difficulty in expanding the working bandwidth, limited polarization control types, and poor polarization stability. Due to the current lack of an effective control theory for full-polarization beams, these problems have not been solved. Summary of the Invention

[0004] To solve the above problems, the present invention provides a theory of ultra-wideband full-polarization large-angle beam scanning based on electromagnetic metasurfaces. By proposing a novel full-polarization beam control theory based on the superposition of orthogonal polarization vector fields regulated by the array factor and performing theoretical calculations and full-wave simulations on the proposed full-polarization beam control theory, the effectiveness and generality of realizing ultra-wideband full-polarization large-angle beam scanning with only one-bit phase resolution are verified.

[0005] To achieve the above object, the technical solution of the present invention is as follows: The theory of ultra-wideband full-polarization large-angle beam scanning based on electromagnetic metasurfaces includes the following steps: S1, regulating the far-field phase of the beam based on the global reference phase of the array, including the following steps: S11. According to the array synthesis theory, the expression of the radiation pattern of a reflectarray antenna is the product of the element factor and the array factor. Traditional multi-polarization beam control based on element level requires multi-bit phase resolution. A method of one-bit array phase encoding based on the global reference phase of the array is proposed to achieve beam far-field 0° - 360° phase control; S12. Calculate the phase compensation amount of each element in the array for generating a fixed radiation beam according to the beam scanning phase compensation formula; S13. By changing the global reference phase, perform phase encoding arrangement for each element in the array according to the one-bit phase quantization rule to achieve one-bit array phase encoding for beam far-field 0° - 360° phase control; S2. Based on array factor control, realize the full-polarization beam control technology by superposing orthogonal polarization vector fields; S3. Theoretical calculation verification of ultra-wideband full-polarization large-angle beam scanning and full-wave simulation verification of full-polarization beams.

[0006] Furthermore, in S11, by depicting a reflectarray composed of M×N elements placed on the xoy plane, the phase center of the feed horn is located at (F, 0, 0). According to the array theory, the far-field radiation pattern expression of the reflectarray antenna is:

[0007] where, q e is the element pattern power factor, q f is the feed horn pattern power factor, θ f ( m , n ) is the spherical angle in the feed coordinate system, and are the position vectors of the feed horn and the ( m , n )-th element in the reflectarray respectively, k is the wave number in free space, is the radiation beam direction, | R m,n | is the reflection amplitude of the ( m , n )-th element, φ m,n is the compensation phase provided by the ( m , n )-th element.

[0008] Furthermore, in S11, according to the product theorem of the radiation pattern, the array far-field pattern E (θ , φ ) is the element factor EF ( θ ) and the array factor AF ( θ , φ ) is the product:

[0009] Calculate the phase compensation amount of each element in the array to achieve a radiation beam in a specified direction; In S12, the calculation formula for the phase compensation amount of each element in the array is as follows:

[0010] Among them, Ψ 0 represents the global reference phase of the array.

[0011] Furthermore, in S13, the one-bit phase quantization rule is described by the following expression:

[0012] Among them, the compensation phase of each element in the array is quantized into the "0" state or the "π" state. Different values of the global reference phase will affect the phase coding arrangement of each element in the array. By theoretically calculating the far-field phase corresponding to the global reference phase from 0° to 360° in the array, there is a good linear mapping relationship between the global reference phase difference in the array and the far-field phase difference in different main lobe directions. Therefore, the array phase coding with one-bit resolution can be used to achieve the regulation of the far-field phase of the beam from 0° to 360°.

[0013] Furthermore, in S2, using the array factor regulation to achieve full-polarization beam control includes the following steps: S21, decompose the electromagnetic wave using the electromagnetic field vector synthesis principle, and set the scanning angle of the beam ( ) and the polarization mode ( ; S22, based on the electromagnetic field vector synthesis principle, decompose the electromagnetic wave of any polarization into two orthogonal linearly polarized waves, and realize the effective regulation of the full-polarization radiation beam by independently coding the global reference phases of the x-polarized component and the y-polarized component in the array; S23, based on the one-bit phase quantization rule, the compensation phases of the x-polarized component and the y-polarized component in the array are quantized into two states: "0" and "π"; Assume that the polarization direction of the feed horn makes an angle of 45° with the positive x-axis direction, and the incident field will be decomposed into x-polarized and y-polarized electric field components with equal amplitude and the same phase; S24. By performing one-bit array phase encoding on the x-polarized and y-polarized component fields, two beams with the same scanning direction are generated. The far-field phase difference between the two beams is controlled by the global reference phase difference between two orthogonal linear polarizations in the array. S25. Based on the theory of controlling the far-field phase of the radiation beam by the global reference phase of the array, by setting the global reference phase difference between two orthogonal linear polarizations in the array, the far-field phase difference between the two beams is accurately controlled. In the far-field region, the components of the x-polarized and y-polarized are vectorially superimposed, thereby realizing the efficient regulation of the full-polarization beam.

[0014] Furthermore, in S22, the phase distributions of the x-polarized and y-polarized electric fields in the array are expressed as follows:

[0015] Among them, and are the global reference phases of the x-polarized electric field and the y-polarized electric field respectively, and their relationship is:

[0016] Among them, δ is an uncertain value, which depends on the polarization mode of the reflectarray antenna.

[0017] Furthermore, in S23, the expression of the one-bit phase quantization rule is: .

[0018] Furthermore, in S3, the theoretical calculation verification of the full-polarization beam regulation and the full-wave simulation verification of the full-polarization beam include the following steps: S31. By using the particle swarm optimization algorithm to optimize the global reference phase to achieve the optimal control of the scanning angle, polarization and gain of the radiation beam. Finally, the theoretical calculation verification of the ultra-wideband full-polarization large-angle beam scanning based on the array factor regulation of the orthogonal polarization vector field superposition is completed. S32. The full-wave simulation verification of the full-polarization beam control theory is carried out through unit design and analysis; the relationship between different global reference phase differences and the far-field phase differences of the beams is obtained through theoretical calculation, and the effectiveness of the relationship under the conditions of ultra-wideband and large-angle beam scanning is verified through full-wave simulation.

[0019] Furthermore, in S31, the PSO optimization process of the scanning angle, axial ratio and radiation gain of the generated beam includes the following steps: S311. Define the solution space, overall size and fitness function; S312. Initialize the position and velocity of each particle; S313. Update the position and velocity of each particle by generating a global reference phase. , generate the phase compensation for x - polarization and y - polarization, calculate the scanning angle, axial ratio and radiation gain of the generated beam, and evaluate the fitness function, thereby updating the best position found by each particle so far and the best position found by all particles in the entire population. S314. Determine whether convergence has occurred. If so, obtain the finally optimized , if not, repeat the steps of S313 until the particle swarm converges.

[0020] Furthermore, in S32, full - wave simulation verification of the full - polarization beam control theory is carried out through element design and analysis, including designing a reconfigurable reflective element with one - bit phase resolution that can independently control x - polarization and y - polarization, and performing full - polarization array antenna simulation to verify the effectiveness and generality of the full - polarization beam control theory.

[0021] The above - mentioned scheme has the following beneficial effects: 1. For the present scheme, aiming at the disadvantages in the prior art that only the polarization mode of plane waves can be adjusted, the phase delay of the feed source from the array surface is not considered, and it is difficult to be applied to the polarization control of antennas. This paper proposes to combine a dual - polarization one - bit reconfigurable metasurface with a single antenna. By adjusting the amplitude, phase and polarization and other characteristics of the radiation beam of the feed source, it overcomes the limitation that the polarization control metasurface cannot be applied to receiving antennas. It can not only achieve multiple functions in one system, such as multi - polarization conversion and beam scanning, but also improve the integration and working efficiency of the antenna system, and is expected to provide a solution for the efficient reception of full - polarization electromagnetic wave signals.

[0022] 2. For the present scheme, aiming at the disadvantages in the prior art that the polarization control working bandwidth is narrow and the polarization stability of the large - angle beam scanning range is poor, a method for regulating the far - field phase of the beam from 0° to 360° based on the global reference phase in the array is proposed. It is verified that within the ultra - wideband range of 10 octaves, the global reference phase difference in the array shows a good linear mapping relationship with the far - field phase difference of the beam. At the same time, this relationship is not affected by the beam scanning angle and the array phase coding resolution. Therefore, by performing one - bit coding on the array phase, the regulation of the far - field phase of the beam in the range of 0° to 360° can be achieved. Based on the above principle, first, the phase compensation for generating two orthogonally polarized beams with the same pointing direction is determined through theoretical calculation. Then, the global reference phase difference of the x - polarization and y - polarization components in the array is set according to the polarization mode of the expected beam. Finally, one - bit phase regulation is performed on the phase compensation of the two orthogonally polarized components in the array to control the far - field phase difference between the two orthogonally polarized beams, thereby realizing the ultra - wideband full - polarization large - angle beam scanning. This method has important value for the design and application of full - polarization array antennas.

[0023] 3. In view of the problem of limited polarization mode regulation in the prior art, this solution proposes a full-polarization beam regulation theory based on the superposition of array factor regulation vector fields, innovatively proposes a mechanism for ultra-wideband regulation of the beam far-field radiation phase from 0° to 360° by using the global reference phase of the array surface, and establishes a mapping relationship between beam and polarization regulation and phase coding. Combining with the electronically reconfigurable technology, only one-bit coded array phase is used to flexibly regulate any polarization mode of the far-field beam, providing theoretical support for simplifying the architecture of the metasurface antenna for receiving full-polarization signals.

[0024] 4. This solution first proposes a method for regulating the far-field phase of the beam by modulating the global reference phase in the array. Subsequently, it is verified that within the ultra-wideband range of 10 octaves, there is a good linear mapping relationship between the global reference phase difference in the array and the far-field phase difference of the beam. At the same time, this relationship is not affected by the beam scanning angle and the array phase coding resolution. Therefore, one-bit array phase coding can be used to achieve the regulation of the far-field phase of the beam in the range of 0° to 360°. Based on the above principle, we propose a theory for ultra-wideband full-polarization large-angle beam scanning based on the superposition of array factor regulation vector fields. First, the array phase coding for generating two orthogonally polarized beams with the same radiation direction is calculated and determined through the phase compensation formula. Then, the global reference phase difference between the x-polarized and y-polarized components in the array is set according to the polarization mode of the expected beam. Finally, one-bit phase regulation is performed on the phase compensation of the two orthogonally polarized components in the array to control the far-field phase difference between the two orthogonally polarized beams, thereby realizing ultra-wideband full-polarization large-angle beam scanning. This method has important value for the design and application of full-polarization array antennas.

[0025] Additional aspects and advantages of the present invention will be given in part in the following description, become apparent in part from the following description, or be learned through the practice of the present invention. Description of the Drawings

[0026] Figure 1 Schematic diagram of the method steps of the embodiment of the ultra-wideband full-polarization large-angle beam scanning theory based on the electromagnetic metasurface of the present invention; Figure 2 Schematic diagram of the reflective array antenna architecture with spatial feeding in S11 of the embodiment of the ultra-wideband full-polarization large-angle beam scanning theory based on the electromagnetic metasurface of the present invention; Figure 3 In S13 of the embodiment of the ultra-wideband full-polarization large-angle beam scanning theory based on the electromagnetic metasurface of the present invention Ψ 0 =0° and Ψ 0 Schematic diagram of the far-field theoretical calculation results under the condition of =90°; Figure 4 For the S13 in the theoretical embodiment of the ultra-wideband all-polarization large-angle beam scanning based on electromagnetic metasurface of the present invention, at Ψ 0 = 40° and Ψ 0 = 130°, it is a schematic diagram of the far-field theoretical calculation results; Figure 5 For the global reference phase difference in the array in the theoretical embodiment of the ultra-wideband all-polarization large-angle beam scanning based on electromagnetic metasurface of the present invention δ and the far-field phase difference △ φ between them; it is a schematic diagram of the relationship; Figure 6 For the theoretical embodiment of the ultra-wideband all-polarization large-angle beam scanning based on electromagnetic metasurface of the present invention, it is a schematic diagram of the relationship between the global reference phase difference and the beam far-field phase difference in the array within a 10-octave bandwidth; Figure 7 For the theoretical embodiment of the ultra-wideband all-polarization large-angle beam scanning based on electromagnetic metasurface of the present invention, it is a schematic diagram of the phase configuration of the x-polarization, y-polarization and overall phase distribution in the array required to achieve an all-polarization beam; Figure 8 For the theoretical embodiment of the ultra-wideband all-polarization large-angle beam scanning based on electromagnetic metasurface of the present invention, it is a schematic diagram of the Poincaré sphere and the calculated polarization efficiency; Figure 9 For the theoretical embodiment of the ultra-wideband all-polarization large-angle beam scanning based on electromagnetic metasurface of the present invention, it is a schematic diagram of the relationship between the far-field phase difference between the x-polarization and y-polarization components of the all-polarization beam and the corresponding global reference phase difference in the array; Figure 10 For the theoretical embodiment of the ultra-wideband all-polarization large-angle beam scanning based on electromagnetic metasurface of the present invention, when using a one-bit phase array coding, it is a schematic diagram of the control results of the orthogonal polarization far-field phase difference before and after optimizing the global reference phase ;

[0027] Figure 11 For the theoretical embodiment of the ultra-wideband all-polarization large-angle beam scanning based on electromagnetic metasurface of the present invention, it is a schematic diagram of the unit structure; Figure 12 For the theoretical embodiment of the ultra-wideband all-polarization large-angle beam scanning based on electromagnetic metasurface of the present invention, it is a schematic diagram of the simulation results of the unit reflection coefficient when the y-polarization and x-polarization are vertically incident under different PIN diode states; Figure 13 For the theoretical embodiment of the ultra-wideband all-polarization large-angle beam scanning based on electromagnetic metasurface of the present invention, it is a schematic diagram of the reconfigurable reflectarray antenna of the all-polarization beam; Figure 14Schematic diagram of the full-wave simulation results of beam scanning in the right-hand circular polarization (RHCP) mode for the embodiment of the ultra-wideband full-polarization large-angle beam scanning theory based on electromagnetic metasurfaces of the present invention; Figure 15 Schematic diagram of the full-wave simulation results of beam scanning in the left-hand circular polarization (LHCP) mode for the embodiment of the ultra-wideband full-polarization large-angle beam scanning theory based on electromagnetic metasurfaces of the present invention Figure 16 Schematic diagram of the full-wave simulation results of beam scanning in the horizontal polarization (HP) and vertical polarization (VP) modes for the embodiment of the ultra-wideband full-polarization large-angle beam scanning theory based on electromagnetic metasurfaces of the present invention; Figure 17 Schematic diagram of the simulation gain curves of the HP, LHCP, RHCP, and VP beams radiated along the normal direction at 6 GHz for the embodiment of the ultra-wideband full-polarization large-angle beam scanning theory based on electromagnetic metasurfaces of the present invention. Detailed implementation manners

[0028] The technical solutions of the present invention will be described clearly and completely below with reference to the accompanying drawings. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0029] In the description of the present invention, it should be noted that the orientation or positional relationship indicated by the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. is based on the orientation or positional relationship shown in the accompanying drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, specific orientation structure and operation, so it cannot be understood as a limitation of the present invention. In addition, the terms "first", "second", "third" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0030] In the description of the present invention, it should be noted that unless otherwise clearly specified and limited, the terms "installed", "connected", "connected" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected, or indirectly connected through an intermediate medium, and it can be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific situations.

[0031] The following is a further detailed description through specific implementation manners: Embodiment: As shown in the attaFigures 1 - 17 As shown: The theory of ultra-wideband full-polarization large-angle beam scanning based on electromagnetic metasurfaces includes the following steps: S1. Adjust the far-field phase of the beam based on the global reference phase of the array, including the following steps: S11. As Figure 2 Depict the reflecting array antenna and express the far-field radiation direction expression of the reflecting array antenna according to the array theory. By depicting a reflecting array composed of M×N elements placed on the xoy plane, the phase center of the feed horn is located at (F,0,0). According to the array theory, the far-field radiation pattern expression of the reflecting array antenna is: (1) Where q e is the element pattern power factor, q f is the feed horn pattern power factor. θ f ( m , n ) are the spherical angles in the feed coordinate system, and are the position vectors of the feed horn and the ( m , n )-th element in the reflecting array respectively. k is the wave number in free space, is the radiation beam direction, | R m,n | is the reflection amplitude of the ( m , n )-th element, φ m,n is the compensation phase provided by the ( m , n )-th element.

[0032] S12. Calculate the far-field pattern of the array according to the radiation pattern and calculate the phase compensation amount of each element in the array according to the phase compensation formula. According to the product theorem of the radiation pattern, the far-field pattern of the array E ( θ , φ ) is the product of the element factor EF ( θ ) and the array factor AF ( θ , φ ): (2) Since the element factor EF ( θ ) and the array factor AF ( θ ,φ ) jointly affect the far-field radiation pattern and polarization mode. The research on traditional polarization-reconfigurable metasurface antennas is based on the principle of realizing polarization conversion by adjusting the element factor EF ( θ ). Different types of polarization beam conversions are achieved by phase modulating the two orthogonal polarization components of the incident wave at the element level. For example, to convert a horizontally polarized (HP) beam to a vertically polarized (VP) beam, the metasurface element is required to have one-bit orthogonal linear polarization phase control ability. To achieve polarization beam conversion from linear polarization (LP) to circular polarization (CP), the element must provide two-bit phase resolution for the two orthogonal linear polarization components, as shown in Table I. However, polarization control based on the element factor EF ( θ ) faces three major problems, including: 1) the design of multi-bit phase resolution elements is complex; 2) the types of polarization regulation are limited; 3) the working bandwidth of polarization regulation is narrow and the angular stability of polarization is poor.

[0033] Table I: Polarization states corresponding to different phase delays of orthogonal polarization vectors

[0034] Based on the above problems, a theory of ultra-wideband full-polarization large-angle beam scanning is proposed based on regulating the superposition of orthogonal polarization vector fields by array factor. First, the implementation method of controlling the far-field phase of the beam based on the global reference phase in the array will be elaborated in detail.

[0035] For a space-fed reflectarray antenna, to realize a radiation beam along the direction, according to the array phase compensation formula, the phase compensation amount of each element in the array is calculated to realize the radiation beam along the specified direction. The calculation formula for the phase compensation amount of each element in the array is as follows: (3) where, Ψ 0 represents the global reference phase of the array.

[0036] S13, through the one-bit phase quantization rule for the coding arrangement of each phase in the array, realizes one-bit dual-polarization reconfigurable elements to independently control the phases of the two orthogonal linear polarizations in the array to achieve full-polarization beam control. The one-bit phase quantization rule is described by the following expression: (4) where, the compensation phase of each element in the array is quantized to the "0" state or the "π" state. Although the Ψ 0They will not change the direction of the radiation beam, but they will affect the phase-coded arrangement of each element in the array. To explore Ψ 0 the influence on the far-field characteristics of the beam, according to Equation (1), the relationship curves between the amplitude and phase of the main beam and Ψ 0 can be obtained. Assume that the operating frequency of the reflectarray antenna is f 0 , the aperture size consists of 16×16 elements, and the period of each element is λ 0 λ / 2. The horn feed is vertically placed at the normal position of the array center. Its radiation power factor q f = 3.5, and the focal diameter ratio F f / D D = 1. Through theoretical calculations based on Equations (3) and (4), the normalized far-field amplitude and far-field phase at the beam pointing of ([[]]END]] Ψ 0 θ = 0° and Ψ 0 φ = 90°) are obtained respectively in two cases, as θ θ = 10°, φ φ = 0°), as Figure 3 shown. The results show that although the far-field amplitudes of the two beams are the same, different codings will affect the sidelobes of the beam. It is found by observation that in the direction of the radiation beam, an 86° phase shift occurs in the far-field radiation phase, which is basically consistent with the given global reference phase difference of the array.

[0037] As Figure 4 shown, under the conditions of Ψ 0 θ = 40° and Ψ 0 φ = 130°, the normalized far-field amplitudes of the two beams with the radiation direction of ([[]]END]] θ θ = 30°, φ φ = 0°) are equal, and the far-field phase difference is 90°. These phenomena indicate that there may be a specific relationship between the far-field phase difference of the radiation beam and the global reference phase difference in the array.

[0038] Considering that different values of the global reference phase will affect the phase-coded arrangement of each element in the array, by theoretically calculating the far-field phases corresponding to the global reference phases from 0° to 360° in the array, it is found that there is a good linear mapping relationship between the global reference phase difference in the array and the far-field phase differences of different main lobe directions, as Figure 5 shown in (a). Figure 5 (b) shows the global reference phase difference in the array and the pointing ([[]]END]] θ=0°, φ The relationship curve between the global reference phase difference in the array and the far-field phase difference of the main lobe at = 0°). The results show that this linear mapping relationship between the global reference phase difference in the array and the far-field phase difference of the main lobe pointing direction is not affected by the phase encoding resolution. Therefore, in order to simplify the design of the metasurface unit and reduce the system structure complexity, one-bit array phase encoding can be used to achieve the control of the beam far-field phase from 0° to 360°.

[0039] Based on the above analysis, further use one-bit dual-polarization reconfigurable units to independently control the phases of two orthogonal polarizations in the array to achieve full-polarization beam control. This method greatly simplifies the complex structure design of the unit caused by polarization control based on unit factor regulation and provides theoretical support for achieving full-polarization beam control. Figure 6 Shows when the main lobe points to ( θ = 30°, φ = 0°) and ( θ = 45°, φ = 30°), the relationship between the global reference phase difference in the array and the far-field phase difference of the radiation beam direction. It can be seen that within a 10-octave bandwidth, when the beam points to different directions, the far-field phase difference of the main beam maintains a good linear mapping relationship with the global reference phase difference in the array. This indicates that using one-bit phase resolution in the array can achieve precise control of the 0°~360° far-field phase difference for radiation beams at different scanning angles within an ultra-wide operating frequency band range.

[0040] S2. Based on the regulation of the array factor to achieve full-polarization beam control by superimposing the far-field orthogonal polarization vector fields includes the following steps: S21. Using the principle of electromagnetic field vector synthesis to decompose electromagnetic waves, set the scanning angle of the beam ( ) and the polarization mode ( .

[0041] S22. Using the principle of electromagnetic field vector synthesis, any polarized electromagnetic wave can be decomposed into two orthogonal linearly polarized waves. By independently encoding the global reference phases of the x-polarized component and the y-polarized component in the array, effective regulation of the full-polarization radiation beam is achieved. The phase distributions of the x-polarized and y-polarized electric fields in the array are expressed as follows: (5) Where, and are the global reference phases of the x-polarized electric field and the y-polarized electric field respectively, and their relationship is: (6) Where, δ is an uncertain value, which depends on the polarization mode of the reflectarray antenna.

[0042] S23. Based on the one-bit phase quantization rule, the compensation phases of the x-polarized component and the y-polarized component in the array are quantized into two states, "0" and "π". The expression of the one-bit phase quantization rule is: (7) Assume that the polarization direction of the feed horn makes an angle of 45° with the positive x-axis direction. Then the incident field can be decomposed into x-polarized and y-polarized electric field components with equal amplitudes and the same phases. To achieve the full-polarization beam with the main lobe pointing to ( θ =0°, φ =0°), the array phase encoding required is as Figure 7 shown. Correspondingly, Table II shows the Figure 7 conditions satisfied by the global reference phases of the x-polarization and y-polarization in the array described by the full-polarization mode in

[0043] Table II: Global reference phase difference and array phase encoding in the full-polarization mode

[0044] To more intuitively explain the formation principle of the above full-polarization state, Figure 8 (a)shows the representation form of the full-polarization state on the Poincaré sphere. When representing the polarization of an electromagnetic wave on the Poincaré sphere, the azimuth angle ψ is defined as the angle between the major axis of the polarization ellipse and the positive H-axis direction. The polarization ellipse is formed by the superposition of two linearly polarized field components. The ellipticity angle χ is defined as , where a and b are the major semi-axis and minor semi-axis of the polarization ellipse, respectively. The Poincaré sphere can represent any polarization state of an electromagnetic wave. Each point on the sphere corresponds to a unique polarization state, characterized by the coordinate latitude 2 χ and longitude 2 ψ , where χ represents the ellipticity angle and ψ represents the azimuth angle.

[0045] In addition, the Poincaré sphere provides an effective method for calculating the polarization efficiency ( η ). As shown in Figure 8 (b), the desired polarization state of the electromagnetic wave is represented by the point w on the sphere, and the polarization of the reflectarray antenna is represented by the point c . The angle between these two points, denoted as ∠ wc , and the expression of the polarization efficiency is as shown in (8).

[0046] (8) Considering the applicability of using the global reference phase in the array to adjust the far-field phase of the beam in the ultra-wideband scenario, we calculated the phase difference between the x-polarized and y-polarized far-field components of the fully polarized beam, as well as the corresponding global reference phase difference in the array, within a 10-octave frequency range. As Figure 9 shown, it is obvious that there is good consistency between them. Therefore, it can be concluded that the theory of fully polarized beam control based on the superposition of orthogonal polarization vector fields by array factor regulation is also applicable to ultra-wideband operation.

[0047] S24, by performing one-bit array phase encoding on the x-polarized and y-polarized component fields, two beams with the same scanning direction are generated, and the far-field phase difference between the two beams is controlled through the global reference phase difference between two orthogonal linear polarizations in the array.

[0048] S25, based on the theory of controlling the far-field phase of the radiation beam by the global reference phase of the array, by setting the global reference phase difference between two orthogonal linear polarizations in the array, the far-field phase difference between the two beams is accurately controlled, and the component fields of x-polarization and y-polarization are vectorially superimposed in the far-field region, thereby realizing the efficient regulation of the fully polarized beam.

[0049] S3, the theoretical calculation verification of the fully polarized beam regulation and the full-wave simulation verification of the fully polarized beam include the following steps: S31, taking the polarization regulation of the reflected beam as an example, assuming that the number of array elements is 32×32 and the power factor of the feed horn q f =1.675. The polarization direction of the feed is at a 45° angle with the positive x-axis direction. By using the particle swarm optimization algorithm to optimize the global reference phase to achieve the optimal control of the scanning angle, polarization, and gain of the radiation beam. The PSO optimization process of the scanning angle, axial ratio, and radiation gain of the generated beam includes the following steps:

[0050] S311, define the solution space, overall size, and fitness function.

[0051] S312, initialize the position and velocity of each particle.

[0052] S313, update the position and velocity of each particle, generate the global reference phase , generate the phase compensation of x-polarization and y-polarization, calculate the scanning angle, axial ratio, and radiation gain of the generated beam and evaluate the fitness function, and update the best position found by each particle so far and the best position found by all particles in the entire population.

[0053] S314, judge whether it converges. If so, obtain the finally optimized , if not, repeat the steps of S313 until the particle swarm converges.

[0054] Figure 12 shows the results of adjusting the phase difference of the cross-polarized far field before and after optimizing the global reference phase θ = 0°, φ = 0°) when generating a full-polarization beam with a radiation direction of using one-bit array phase coding. It can be found that by optimizing the global reference phase , the global reference phase difference of the cross-polarization in the array satisfies a proportional function relationship with the far-field phase difference of the corresponding beam. Therefore, using one-bit array phase coding can achieve precise control of the full-polarization beam.

[0055] The theoretical calculation verification of the full-polarization beam control principle based on adjusting the superposition of cross-polarized vector fields by the array factor is shown in Table III.

[0056] Table III: Theoretical calculation results of six polarization beam controls in different scanning directions

[0057] Table III shows the theoretical calculation results of the normalized far-field amplitude and far-field phase of two cross-polarized beams, as well as the three-dimensional radiation patterns and polarization efficiencies of six target polarization beams at different beam scanning angles. The theoretical calculation results show that the method of adjusting the superposition of two cross-polarized vector fields by the array factor can achieve precise control of the full-polarization beam, with high accuracy in both beam pointing and polarization efficiency.

[0058] S32. The full-wave simulation verification of the full-polarization beam control theory through element design and analysis includes: designing a reconfigurable reflection element with one-bit phase resolution that can independently control the x-polarization and y-polarization, as Figure 11 shown. Two cross-polarized dipoles are mounted on an F4B substrate with a thickness of 1 mm (dielectric constant , loss tangent ). The geometric parameters of the dual-polarization reconfigurable reflection element are given in Table IV.

[0059] Table IV: Parameters of the reconfigurable element

[0060] The simulation results of this element are as Figure 12 shown. From Figure 12As can be seen from (a) and (b), when the unit is vertically incident by a y-polarized wave, the reflection amplitudes of the four states of "01", "00", "11", and "10" are all greater than -1 dB. Among them, in the frequency range from 3.49 GHz to 8.94 GHz, the two states of "01" and "00" and the two states of "11" and "10" have a stable co-polarization reflection phase difference within 180° ± 37°. Similarly, in Figure 12 As can be observed in (c) and (d), when the unit operates in the x-polarization state, the reflection amplitudes of the four states of "10", "00", "11", and "01" are all greater than -1 dB, and the co-polarization reflection phase differences of the two states of "10" and "00" and the two states of "11" and "01" fluctuate within the range of 180° ± 37° in the frequency range from 3 GHz to 9 GHz.

[0061] The relationship between different global reference phase differences and far-field phase differences is obtained through theoretical calculations, and a full-wave simulation of the fully polarized array antenna is carried out to verify the effectiveness of the full-polarization beam control based on the superposition of orthogonal polarization vector fields by array factor regulation in ultra-wideband and large-angle beam scanning. Figure 13 Shown is a reconfigurable reflectarray antenna composed of 22×22 units (PIN diodes). The polarization direction of the dual-ridge horn antenna is placed at an angle of 45° with the positive x-axis direction as the feeding antenna, and its phase center is located in the normal direction of the metasurface.

[0062] The full-wave simulation software CST Microwave Studio® is used to perform full-wave simulation on the beam scanning of the reconfigurable reflectarray antenna under different polarization modes in the ultra-wideband. From Figure 14 It can be seen that the far-field radiation pattern of the right-hand circular polarization (RHCP) beam operating at a frequency of 3.5 GHz from 0° to 60° in the φ = 90° plane is in good agreement with the expected direction, and the axial ratio in the radiation direction is completely less than -3 dB. From Figure 15 It can be seen that the beam scanning result of the left-hand circular polarization (LHCP) beam operating at a frequency of 6 GHz from 0° to 60° in the φ = 0° plane is in line with the theoretical calculation, and the axial ratios are all lower than -3 dB. As Figure 16 shown, the horizontally polarized (HP) beam operating at a frequency of 8 GHz and the vertically polarized (VP) beam operating at a frequency of 8.5 GHz are respectively in the φ = 45° and φThe far - field radiation patterns of the scanning beam from 0° to 60° in the 135° plane are all in agreement with the theoretical situation. In addition, the simulated gains and aperture efficiencies of the above - mentioned different polarization beams at the corresponding frequencies are listed in Table V. These simulation results jointly verify the effectiveness of the full - polarization beam control theory proposed in this paper, which is based on the superposition of orthogonal polarization vector fields regulated by column factors, for ultra - wideband and large - angle beam scanning.

[0063] The simulated gain curves of the radiation beam of the reflectarray antenna along the normal direction are as Figure 17 shown. At a frequency of 6 GHz, the gains of horizontal polarization (HP), left - hand circular polarization (LHCP), right - hand circular polarization (RHCP), and vertical polarization (VP) are 20.67 dBi, 20.04 dBic, 20.17 dBic, and 19.97 dBi respectively. Their 3 - dB gain bandwidths are 39.7%, 36.4%, 46.2%, and 43.6% respectively.

[0064] Table V: Simulation results of beam scanning, polarization type, gain, and aperture efficiency

[0065] In the present invention, we propose a full - polarization beam control theory based on the superposition of orthogonal polarization vector fields regulated by array factors. First, by performing one - bit phase coding on two orthogonal linearly polarized component fields in the array, two beams with the same radiation direction are generated. The global reference phase difference between the two orthogonal linear polarizations in the array is used to precisely regulate the far - field phase difference between the two orthogonal polarization beams, so as to achieve full - polarization beam control in the main lobe direction. Through theoretical calculation and full - wave simulation verification: this technology can achieve full - polarization beam scanning in the ultra - wideband and large - angle domain with only one - bit phase resolution. It is no longer limited to complex unit structures that can independently control the multi - bit orthogonal linear polarization phase, greatly simplifies the unit structure design, reduces the complexity and production cost of the array antenna system, and provides important theoretical support for the research of full - polarization array antennas.

[0066] Obviously, the above - mentioned embodiments are only examples given for clear illustration and are not limitations on the implementation manners. For those of ordinary skill in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation manners here. And the obvious changes or modifications derived therefrom are still within the protection scope of the present invention.

Claims

1. Ultra-wideband fully polarized large-angle beam scanning theory based on electromagnetic metasurface, characterized by: The following steps are involved: S1, controlling the far-field phase of the beam based on the array global reference phase, including the following steps: S11, according to the array synthesis theory, the expression of the reflectarray antenna radiation pattern is derived as the product of the unit factor and the array factor. The traditional unit-level multi-polarization beam steering requires multi-bit phase resolution. A method based on one-bit array phase coding of the global reference phase of the array to achieve 0°~360° phase steering in the far field of the beam is proposed; S12, calculating the phase compensation amount of each unit in the array for generating a fixed radiation beam according to a beam scanning phase compensation formula; S13, by changing the global reference phase, phase encoding and arranging each unit in the array according to a one-bit phase quantization rule, so as to achieve one-bit array phase coding to control the far-field 0°~360° phase of the beam; S2, based on array factor control, far-field orthogonal polarization vector field superposition is used to achieve full polarization beam steering technology; S3, theoretical calculation verification of ultra-wideband fully polarized large-angle beam scanning and full-wave simulation verification of fully polarized beam.

2. According to the ultra-wideband fully polarized large-angle beam scanning theory based on electromagnetic metasurface according to claim 1, it is characterized in that: In S11, a reflectarray consisting of M×N units placed on the xoy plane is depicted, and the phase center of the feed horn is located at (F, 0, 0). According to array theory, the far-field radiation pattern of the reflectarray antenna is expressed as: in, q e is the unit pattern power factor, q f is the feed horn pattern power factor, θ f ( m , n ) is the spherical angle in the feed coordinate system, and They are the feed horn and the first one in the reflection array. m , n ) unit position vector, k is the wave number in free space, is the radiation beam direction, | R m,n | is the first ( m , n ) units’ reflection amplitude, φ m,n It is the first m , n ) units provide compensation phase.

3. The ultra-wideband fully polarized large-angle beam scanning theory based on electromagnetic metasurface according to claim 2 is characterized in that: In S11, according to the product theorem of radiation patterns, the array far-field pattern E ( θ , φ ) is the unit factor EF ( θ ) and the array factor AF ( θ , φ ) is the product of: Calculate the phase compensation of each unit in the array to achieve the radiation beam along the specified direction; In S12, the calculation formula for the phase compensation amount of each unit in the array is as follows: in, Ψ 0 indicates the global reference phase of the array.

4. The ultra-wideband fully polarized large-angle beam scanning theory based on electromagnetic metasurface according to claim 3 is characterized in that: In S13, the one-bit phase quantization rule is described by the following expression: Among them, the compensation phase of each unit in the array is quantized to the "0" state or the "π" state. Different values ​​of the global reference phase will affect the phase coding arrangement of each unit in the array. By theoretically calculating the far-field phase corresponding to the global reference phase from 0° to 360° in the array, there is a good linear mapping relationship between the global reference phase difference in the array and the far-field phase difference in different main lobe directions. Therefore, the array phase coding with one-bit resolution can realize the control of the far-field phase of the 0° to 360° beam.

5. The ultra-wideband fully polarized large-angle beam scanning theory based on electromagnetic metasurface according to claim 4 is characterized in that: In S2, the full polarization beam control is realized by superposition of far-field orthogonal polarization vector fields based on array factor control, which includes the following steps: S21, using the principle of electromagnetic field vector synthesis to decompose electromagnetic waves and set the scanning angle of the beam ( ) and polarization mode ( ; S22, based on the principle of electromagnetic field vector synthesis, any polarized electromagnetic wave is decomposed into two orthogonal linearly polarized waves. By independently encoding the global reference phase of the x-polarization component and the y-polarization component in the array, effective control of the fully polarized radiation beam is achieved; S23, based on a one-bit phase quantization rule, the compensation phases of the x-polarization component and the y-polarization component in the array are quantized into two states of "0" and "π"; Assuming that the polarization direction of the feed horn is at an angle of 45° to the positive direction of the x-axis, the incident field will be decomposed into x-polarized and y-polarized electric field components with equal amplitude and the same phase; S24, generating two beams with the same scanning direction by performing one-bit array phase encoding on the x-polarization and y-polarization component fields, and controlling the far-field phase difference between the two beams by a global reference phase difference between two orthogonal linear polarizations in the array; S25, based on the theory of far-field phase control of radiated beam by global reference phase of array, accurately controls the far-field phase difference between the two beams by setting the global reference phase difference between the two orthogonal linear polarizations in the array, and realizes efficient control of the fully polarized beam by vector superposition of the x-polarization and y-polarization components in the far-field region.

6. The ultra-wideband fully polarized large-angle beam scanning theory based on electromagnetic metasurface according to claim 5 is characterized in that: In S22, the phase distribution of the x-polarized and y-polarized electric fields in the array is expressed as follows: in, and are the global reference phases of the x-polarized electric field and the y-polarized electric field, respectively, and their relationship is: in, δ is an uncertain value that depends on the polarization pattern of the reflectarray antenna.

7. The ultra-wideband fully polarized large-angle beam scanning theory based on electromagnetic metasurface according to claim 6 is characterized in that: In S23, the one-bit phase quantization rule expression is: 。 8. The ultra-wideband fully polarized large-angle beam scanning theory based on electromagnetic metasurface according to claim 7 is characterized in that: In S3, the theoretical calculation verification of the full polarization beam steering and the full-wave simulation verification of the full polarization beam include the following steps: S31, by using the particle swarm optimization algorithm to optimize the global reference phase, to achieve the optimal control of the scanning angle, polarization and gain of the radiation beam, and finally complete the theoretical calculation verification of ultra-wideband full-polarization large-angle beam scanning based on array factor control of orthogonal polarization vector field superposition; S32, through unit design and analysis, the full-wave simulation is carried out to verify the full-polarization beam control theory; the relationship between different global reference phase differences and the far-field phase difference of the beam is obtained through theoretical calculation, and the effectiveness of the relationship under ultra-wideband and large-angle beam scanning conditions is verified through full-wave simulation.

9. The ultra-wideband fully polarized large-angle beam scanning theory based on electromagnetic metasurface according to claim 8 is characterized in that: In S31, the PSO optimization process of the scanning angle, axial ratio and radiation gain of the generated beam includes the following steps: S311, define the solution space, the overall size and the fitness function; S312, initializing the position and velocity of each particle; S313, update the position and velocity of each particle by generating a global reference phase , generate phase compensation for x-polarization and y-polarization, calculate the scanning angle, axial ratio and radiation gain of the generated beam and evaluate the fitness function to update the best position found so far by each particle and the best position found by all particles in the entire group; S314, determine whether it converges, if so, obtain the final optimized If not, repeat step S313 until the particle swarm converges.

10. The ultra-wideband fully polarized large-angle beam scanning theory based on electromagnetic metasurface according to claim 9 is characterized in that: In S32, a full-wave simulation is performed to verify the full-polarization beam control theory through unit design and analysis, including designing a reconfigurable reflection unit with one-bit phase resolution that can independently control the x-polarization and y-polarization, and performing array full-wave simulation to verify the effectiveness and versatility of the ultra-wideband full-polarization large-angle beam scanning theory.

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