Far-field multi-beam achromatic method based on Fourier harmonic regulation and control

Abstract

The invention belongs to the technical field of microwave and millimeter wave communication, and particularly relates to a far-field multi-beam dispersion elimination method based on Fourier harmonic regulation and control, which eliminates dispersion of beams under multiple frequencies based on a Fourier harmonic component regulation and control method. A de-dispersion structure combining a chiral phase, a propagation phase and a geometric phase is provided, and dispersion is regulated and controlled at will through the synergistic effect of the three phases. And finally, providing an optimal combination method for searching the distribution of the dedispersion metasurface units, and realizing the dedispersion of two diffraction beams transmitted in the same direction and in the back direction. The method provided by the invention fills the blank of far-field diffraction dispersion regulation and control by the metasurface.

Description

Technical Field

[0001] The present invention belongs to the field of microwave and millimeter wave communication technology, and in particular relates to a far-field multi-beam dispersion elimination method based on Fourier harmonic control. Background Art

[0002] In satellite communications, in addition to using multiple beams to cover the ground, communication capacity can also be further improved through multi-band multiplexing. In radar detection, the object to be detected usually has stealth characteristics in a single frequency band, and it is necessary to detect it through multiple beams in multiple frequency bands. However, due to the dispersion characteristics of the metasurface unit, its phase, amplitude, and impedance information will change with frequency. As a result, the diffraction angle of the beam gradually decreases with increasing frequency, resulting in performance deterioration in the actual application of multi-band multi-beam. Current dispersion-eliminating devices are all based on phase compensation, but they can only achieve single-beam dispersion-eliminating, and the beam diffraction angle in the microwave band is relatively small. There has been no research on multi-beam dispersion-eliminating, which has certain limitations on the practical application of far-field multi-beam excitation based on metasurface platforms.

[0003] Existing design methods can only achieve single-beam dispersion elimination, and there is no dispersion elimination method for multi-beam transmission, which limits the scenarios in practical applications. Summary of the Invention

[0004] The purpose of the present invention is to propose a far-field multi-beam de-dispersion method based on Fourier harmonic control, which can excite multi-order diffraction beams based on a metasurface platform and maintain stable propagation angles at multiple frequencies in the microwave band (taking the C, X and Ku bands as examples).

[0005] In order to solve the above technical problems, the specific technical solutions of the present invention are as follows:

[0006] In some embodiments of the present application, a far-field multi-beam dispersion elimination method based on Fourier harmonic control is provided, comprising the following steps:

[0007] 1) Fixing the diffraction period of the metasurface and using the overall size of the metasurface as the diffraction period to improve the diffraction angle resolution;

[0008] 2) Iteratively control the diffraction harmonics through Fourier coefficients, select specific diffraction orders, and generate achromatic phase distribution at multiple frequency points;

[0009] 3) Based on the energy conservation constraint, the metasurface amplitude is kept uniformly distributed, and multi-beam superposition is achieved through phase control;

[0010] 4) In the microwave band, verify that the deviation between the beam propagation direction and the desired direction is less than 3°.

[0011] In some embodiments of the present application, the specific method of iteratively controlling the Fourier coefficients in step 2 is:

[0012] Calculate all diffraction orders and their corresponding propagation angles based on the metasurface size and operating frequency to determine the diffraction order that needs to be excited;

[0013] Taking the size of the entire metasurface as a period, the corresponding diffraction order can be deduced according to the desired achromatic angle as follows:

[0014]

[0015] The excitation phase distribution of the m-order diffraction beam is defined as:

[0016]

[0017] Where L is the diffraction period, φm(f) is the initial phase of the beam at different frequencies;

[0018] The total phase distribution on the metasurface is the result of all beam effects and is expressed as:

[0019]

[0020] Where Gm(f) is the weighting factor for adjusting the beam amplitude, Γ m (x,f) is the modulation amplitude correction term, which provides a degree of freedom to uniform the amplitude on the element surface. The product term G m (f)Γ m (x,f) is the amplitude of the beam, verified by the single beam case with m set to 1. Let the amplitude on the metasurface be uniformly distributed, and assume that all the incident energy enters the scattered field. The energy distribution on the metasurface is:

[0021]

[0022] Assuming that the energy on the metasurface is uniformly distributed, that is, I(x,f) = 1, the modulation amplitude correction term Γ is derived m (x,f) and weighting factor G m (f) relationship;

[0023] Weighting factor G m (f) through the Fourier coefficient F m (f) Iterative control is performed in the following manner:

[0024]

[0025] where R m (f) is the desired beam amplitude, and t represents the number of iterations;

[0026] In the iteration, through R m(f) Determine the desired diffraction field and obtain the appropriate weight factor G through iteration. m (f) According to the energy conservation principle, the modulation amplitude correction term Γ is obtained m The expression of (x, f) is substituted into formula (2) to obtain the phase distribution of the metasurface.

[0027] In some embodiments of the present application, the metasurface includes:

[0028] The double-layer split resonant ring with quadrilateral periodic arrangement has two dielectric layers, and its period is d x =d y =10mm, the thickness of the dielectric layer is h1=h2=2mm;

[0029] The upper and lower rings introduce chiral phases through relative rotation, with a rotation angle range of 0° to 360°. The phase responses of left-handed and right-handed waves are symmetrically distributed.

[0030] The propagation phase is introduced by adjusting the opening angle (α, β) and the ring radius (r1, r2);

[0031] The geometric phase is introduced by the synchronous rotation of the dual rings to compensate for the phase shift caused by frequency change.

[0032] In some embodiments of the present application, the chiral phase is realized as follows: when a left-handed circularly polarized wave is incident, the relative rotation angle ξ = 120°; when a right-handed circularly polarized wave is incident, the relative rotation angle ξ = 240°, and the phase responses of the two satisfy a symmetrical relationship.

[0033] In some embodiments of the present application, the method for optimizing a metasurface includes the following steps:

[0034] 1) Construct a cell library and screen candidate cells with a copolarization amplitude exceeding 0.9;

[0035] 2) Using the initial phase difference as the optimization variable, the minimum variance matching formula is used

[0036]

[0037] Perform global optimization on the candidate units and select the unit combination with the minimum variance;

[0038] 3) Verify the dispersion-free performance of the optimized metasurface in multiple frequency bands and ensure that the beam direction deviation is less than 3°.

[0039] In some embodiments of the present application, the construction of the cell library in step 1 must satisfy the following requirements: the phase response of the cell at different frequencies is discretely distributed, and the slope of the phase difference varying with frequency matches the achromatic dispersion target.

[0040] Compared with the prior art, the present invention has the following advantages:

[0041] The present invention fixes the diffraction period, iteratively controls the diffraction harmonics through Fourier coefficients, selects a specific excitation diffraction order according to the desired propagation angle, and ultimately achieves dispersion-free beam propagation direction at multiple frequency points. The discrete phase distribution design solves the failure problem of traditional continuous phase in multiple frequency bands. The chiral phase, propagation phase and geometric phase are combined to achieve arbitrary control of the dispersion characteristics. Only the phase is controlled, and the amplitude remains uniform. Combined with the unit library optimization method, the design difficulty is significantly reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Various other advantages and benefits will become apparent to those skilled in the art upon reading the detailed description of the preferred embodiment below. The accompanying drawings are for illustration purposes only and are not to be considered as limiting the present invention. The same reference symbols are used throughout the drawings to represent the same components. In the drawings:

[0043] Figure 1 A schematic diagram of multi-frequency multi-beam dispersion elimination provided by an embodiment of the present invention;

[0044] Figure 2 Schematic diagram of an achromatic metasurface unit provided in an embodiment of the present invention;

[0045] Figure 3 The co-polarization reflection coefficient (a) R of the achromatic unit provided in the embodiment of the present invention at different relative rotation angles RR The amplitude response of (b) R LL The amplitude response, (c) R RR The phase response, (d)R LL Phase response diagram of ;

[0046] Figure 4 -30° and 15° achromatic diffraction angles and phase distributions provided by an embodiment of the present invention (a) The relationship between diffraction angle and frequency (b) Schematic diagram of phase distribution at three frequencies;

[0047] Figure 5 Co-polarized far-field simulation results of the -30° and 15° achromatic metasurfaces provided in an embodiment of the present invention: (a) Far-field pattern at 7 GHz; (b) Far-field pattern at 10 GHz; (c) Schematic diagram of far-field pattern at 13 GHz.

[0048] Figure 6 -40° and -10° achromatic diffraction angles and phase distributions provided by an embodiment of the present invention (a) The relationship between diffraction angle and frequency (b) Schematic diagram of phase distribution at three frequencies;

[0049] Figure 7Diffraction angles of -40° and -10° achromatic metasurfaces at three frequencies provided by an embodiment of the present invention: (a) far-field pattern at 7 GHz; (b) far-field pattern at 10 GHz; (c) far-field pattern at 13 GHz. DETAILED DESCRIPTION

[0050] The following embodiments of the present invention are described in further detail with reference to the accompanying drawings and examples. The following examples are used to illustrate the present invention but are not intended to limit the scope of the present invention.

[0051] In order to better understand the purpose, structure and function of the present invention, the present invention is further described in detail below with reference to the accompanying drawings.

[0052] The existing single-beam achromatic method essentially changes the period length according to the frequency change. The present invention fixes the diffraction period, iteratively controls the diffraction harmonics through Fourier coefficients, selects a specific excitation diffraction order according to the desired propagation angle, and finally achieves the achromatic aberration of the beam propagation direction at multiple frequency points, as shown in the attached figure. Figure 1 As shown in the figure, the propagation angles of the two beams do not change at three different frequencies. First, all diffraction orders and their corresponding propagation angles are calculated based on the size of the metasurface and the operating frequency to determine the diffraction order that needs to be excited. Since the larger the diffraction period, the more diffraction orders it contains, and the higher the diffraction angle resolution, the size of the entire metasurface is considered as a period. The corresponding diffraction order can be deduced based on the desired achromatic angle, which can be expressed as:

[0053]

[0054] Where [m] is a rounding symbol. The present invention achieves multi-beam achromatism by controlling the metasurface to excite specific diffraction orders at different frequencies. The excitation phase distribution of the m-order diffraction beam is defined as:

[0055]

[0056] Where L is the diffraction period and φm(f) is the initial phase of the beam at different frequencies. The total phase distribution on the metasurface is the result of all beams and can be expressed as:

[0057]

[0058] Here, Gm(f) is a weighting factor that adjusts the beam amplitude. Γm(x,f) is the modulation amplitude correction term, which provides a degree of freedom to uniformize the amplitude on the metasurface. The product term Gm(f)Γm(x,f) is the amplitude of the beam, which can be verified by the single beam case with m equal to 1. Assuming that the amplitude on the metasurface is uniformly distributed and that all the incident energy enters the scattered field, the energy distribution on the metasurface is:

[0059]

[0060] Assuming that the energy on the metasurface is uniformly distributed, that is, I(x,f) = 1, the relationship between the modulation amplitude correction term Γm(x,f) and the weighting factor Gm(f) is derived. The weighting factor Gm(f) is iteratively controlled by the Fourier coefficient Fm(f) as follows:

[0061]

[0062] Where Rm(f) is the desired beam amplitude, and t represents the number of iterations. During the iteration, the desired diffraction field is determined by Rm(f). After several iterations, the appropriate weight factor Gm(f) is obtained. Based on the energy conservation principle, the expression for the modulation amplitude correction term Γm(x, f) is obtained. Substituting this into formula (2) yields the phase distribution of the metasurface, with a uniform amplitude distribution.

[0063] The design method proposed in this invention does not limit the type of metasurface unit, nor does it limit the operating frequency band. The present invention designs a metasurface structure that realizes multi-beam de-dispersion. The schematic diagram of the unit structure is shown in the attached figure. Figure 2 As shown. The achromatic unit proposed in the present invention introduces chiral phase by the relative rotation of two rings, introduces propagation phase by adjusting parameters, and introduces geometric phase by the simultaneous rotation of two rings. The propagation phase and chiral phase are combined to regulate the dispersion characteristics of the metasurface. The geometric phase regulates the initial phase of each position of the metasurface to meet the achromatic phase distribution. The unit is a quadrilateral periodic structure, and the unit period is dx=dy=10mm. There are two dielectric layers, and their thickness is h1=h2=2mm. The bottom is a metal floor, and the first and second layers are two open resonant rings, and the width of the ring is w1=w2=0.4mm. The openings of the upper and lower rings are different, denoted as α and β respectively, and the radii are denoted as r1 and r2. At the same time, the two rings have a relative rotation angle, and the angle is. The chiral phase of the unit is shown in the attached figure. Figure 3 The results in Figure 2 show that the phase responses of left-handed and right-handed waves differ at the same relative rotation angle, but the effects of left-handed waves at ξ = 120° and right-handed waves at ξ = 240° are the same. By adjusting the structural parameters of the two split-ring resonators, a library of achromatic units was constructed.

[0064] Due to the different theories of multi-beam and single-beam dispersion elimination, the latter typically uses a continuous phase because the phase delay varies slowly with frequency. However, the phase distribution of multi-beam dispersion elimination varies very rapidly with frequency, making it unsuitable to design with a continuous phase. Instead, a discrete phase distribution is used. Therefore, the phase variation between different frequencies is no longer suitable to be described by phase delay. The initial phase difference of this distribution can also be used as an optimization variable to select the best from all units in the unit library to optimize the multi-beam dispersion elimination effect. The steps for selecting the appropriate unit in the unit library are as follows:

[0065] 1. Select cells with a copolarization amplitude exceeding 0.9 to form a new library.

[0066] 2. Pick a cell from the library and record the phase response. Calculate the phase difference between the frequencies, P1(f) and P1(Δf), respectively.

[0067] 3. Taking P1(f) as the first unit on the metasurface, select other suitable unit cells by minimum variance, which can be expressed as:

[0068]

[0069] Where n represents the number of the new library.

[0070] 4. Replace the unit at position x1 and repeat steps 2-3. The best unit combination is determined by the minimum value of the sum of δ(x), which is:

[0071]

[0072] Two backpropagating beam scenarios were used for verification, with desired propagation angles of -30° and +15°, respectively. The frequencies chosen were 7 GHz, 10 GHz, and 13 GHz, corresponding to the C, X, and Ku bands commonly used in radar and satellite communications. The metasurface measured 400 mm × 400 mm and had only one period in the diffraction direction.

[0073] Attachment Figure 4 The relationship between the two beam dispersion angles, the achromatic angle and the dispersion-free angle as a function of frequency, as well as the metasurface phase distribution at three frequencies are demonstrated. Generally, the dispersion characteristics of a beam are positively correlated with its propagation angle. The 15° diffraction at 7GHz will shift to 8° at 13GHz due to dispersion, while the -30° diffraction will shift to -15.6°. The method proposed in the present invention can constrain the propagation angle of the beam to the desired direction. It should be noted that the method proposed in the present invention only needs to regulate the phase response, while the amplitude remains uniformly distributed, which greatly reduces the design difficulty.

[0074] Attachment Figure 5 The far-field patterns at 7 GHz, 10 GHz, and 13 GHz are shown. The beam diffraction angles at these three frequencies are -32.9°, +12.2°; -31.5°, +12.8°; and -32°, +13.2°, respectively. The deviation between the actual beam propagation direction and the desired direction is within 3°, achieving excellent dispersion reduction compared to dispersive transmission (-15.6° and 8°).

[0075] Attachment Figure 6The dispersion and de-dispersion angles of two beams with the same desired transmission angle of -40° and -10° are shown. The -10° diffraction at 7GHz will shift to -5.4° at 13GHz due to dispersion, while the -40° diffraction will shift to -20.2°. The larger the diffraction angle, the more serious the dispersion effect, so it is very necessary to perform de-dispersion processing.

[0076] Attachment Figure 7 The two-beam directivity patterns at 7 GHz, 10 GHz, and 13 GHz are demonstrated. The diffraction angles at these three frequencies are: -39.6°, -11.7°; -42.1°, -8.8°; and -39.6°, -10°. The beam propagation direction is constrained to the desired direction, with the deviation between the actual transmission direction and the desired direction within 2°, achieving excellent dispersion reduction.

[0077] In the description of this application, it should be understood that the terms "center", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on this application.

[0078] The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referred to. Thus, a feature specified as "first" or "second" may explicitly or implicitly include one or more of such features. Throughout this application, unless otherwise specified, "plurality" means two or more.

[0079] In the description of this application, it should be noted that, unless otherwise expressly specified or limited, the terms "mounted," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections; mechanical connections or electrical connections; direct connections or indirect connections through an intermediate medium; and internal connections between two components. Those skilled in the art will understand the specific meanings of the above terms in this application based on the specific circumstances.

[0080] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0081] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A far-field multi-beam dispersion elimination method based on Fourier harmonic control, characterized in that: The following steps are involved: 1) Fixing the diffraction period of the metasurface and using the overall size of the metasurface as the diffraction period to improve the diffraction angle resolution; 2) Iteratively control the diffraction harmonics through Fourier coefficients, select specific diffraction orders, and generate achromatic phase distribution at multiple frequency points; 3) Based on the energy conservation constraint, the metasurface amplitude is kept uniformly distributed, and multi-beam superposition is achieved through phase control; 4) In the microwave band, verify that the deviation between the beam propagation direction and the desired direction is less than 3°.

2. The far-field multi-beam de-dispersion method based on Fourier harmonic control according to claim 1, characterized in that: The specific method of iterative control of the Fourier coefficients in step 2 is: Calculate all diffraction orders and their corresponding propagation angles based on the metasurface size and operating frequency to determine the diffraction order that needs to be excited; Taking the size of the entire metasurface as a period, the corresponding diffraction order can be deduced according to the desired achromatic angle as follows: The excitation phase distribution of the m-order diffraction beam is defined as: Where L is the diffraction period, φm(f) is the initial phase of the beam at different frequencies; The total phase distribution on the metasurface is the result of all beam effects and is expressed as: Where Gm(f) is the weighting factor for adjusting the beam amplitude, Γ m (x,f) is the modulation amplitude correction term, which provides a degree of freedom to uniform the amplitude on the element surface. The product term G m (f)Γ m (x,f) is the amplitude of the beam, verified by the single beam case with m set to 1. Let the amplitude on the metasurface be uniformly distributed, and assume that all the incident energy enters the scattered field. The energy distribution on the metasurface is: Assuming that the energy on the metasurface is uniformly distributed, that is, I(x,f) = 1, the modulation amplitude correction term Γ is derived m (x,f) and weighting factor G m (f) relationship; Weighting factor G m (f) through the Fourier coefficient F m (f) Iterative control is performed in the following manner: where R m (f) is the desired beam amplitude, and t represents the number of iterations; In the iteration, through R m (f) Determine the desired diffraction field and obtain the appropriate weight factor G through iteration. m (f) According to the energy conservation principle, the modulation amplitude correction term Γ is obtained m The expression of (x, f) is substituted into formula (2) to obtain the phase distribution of the metasurface.

3. The far-field multi-beam de-dispersion method based on Fourier harmonic control according to claim 1, characterized in that: The metasurface comprises: The double-layer split resonant ring with quadrilateral periodic arrangement has two dielectric layers, and its period is d x =d y =10mm, the thickness of the dielectric layer is h1=h2=2mm; The upper and lower rings introduce chiral phases through relative rotation, with a rotation angle range of 0° to 360°. The phase responses of left-handed and right-handed waves are symmetrically distributed. The propagation phase is introduced by adjusting the opening angle (α, β) and the ring radius (r1, r2); The geometric phase is introduced by the synchronous rotation of the dual rings to compensate for the phase shift caused by frequency change.

4. The far-field multi-beam de-dispersion method based on Fourier harmonic control according to claim 3, characterized in that: The chiral phase is realized in the following way: when a left-handed circularly polarized wave is incident, the relative rotation angle ξ =120°; when the right-hand circularly polarized wave is incident, the relative rotation angle ξ=240°, and the phase responses of the two satisfy the symmetrical relationship.

5. The far-field multi-beam de-dispersion method based on Fourier harmonic control according to claim 3, characterized in that: The method for optimizing the metasurface comprises the following steps: 1) Construct a cell library and screen candidate cells with a copolarization amplitude exceeding 0.9; 2) Using the initial phase difference as the optimization variable, the minimum variance matching formula is used Perform global optimization on the candidate units and select the unit combination with the minimum variance; 3) Verify the dispersion-free performance of the optimized metasurface in multiple frequency bands and ensure that the beam direction deviation is less than 3°.

6. The far-field multi-beam de-dispersion method based on Fourier harmonic control according to claim 5, characterized in that: The construction of the cell library in step 1 must meet the following requirements: the phase response of the cell at different frequencies is discretely distributed, and the slope of the phase difference changing with frequency matches the achromatic dispersion target.

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