Any-cylinder conformal meta-surface conformal antenna and design method thereof

Abstract

The application provides an arbitrary cylindrical conformal metasurface conformal antenna and a design method thereof. The method comprises the following steps: step 1, calculating a conformal compensation phase at an arbitrary point on a given conformal surface; step 2, on the given conformal surface, a starting point is specified, metasurface units are distributed on the given conformal surface at a set interval arc length from the starting point, a metasurface unit at the starting point is taken as a starting unit, and spatial position coordinates of each metasurface unit on the given conformal surface are calculated according to a horizontal coordinate of the starting unit; step 3, conformal compensation phases of positions of each metasurface unit are calculated according to the spatial position coordinates of each metasurface unit and the calculation mode of step 1, then structure parameters of each metasurface unit are obtained according to the conformal compensation phase of each metasurface unit, and the metasurface units are printed by using a 3D printing technology according to the structure parameters to construct a conformal cylindrical lens antenna; and step 4, a Vivaldi antenna is used as an antenna feed source of the conformal cylindrical lens antenna.

Description

Technical Field

[0001] This invention relates to the field of communication technology, specifically to the field of electromagnetic metasurfaces and lens antennas, and particularly to a conformal antenna with an arbitrary cylindrical conformal metasurface and its design method. Background Technology

[0002] Conformal antennas are widely used because their shape can conform to the shape of the carrier platform. However, theoretical and design challenges still exist in the shape and structural design of conformal antennas. Metasurfaces are novel artificial electromagnetic materials that can flexibly control electromagnetic waves, and their combination with antennas can effectively improve antenna performance. With the continuous deepening of research on the electromagnetic wave modulation mechanism of metasurfaces and the continuous development of practical application needs, the conformal design of metasurfaces has become one of the inevitable trends for the further development of metasurface research.

[0003] Existing research on conformal metasurfaces mainly includes: conformal cloak research, such as XJNi, ZJWong, M.Mrejen, et al., An ultrathin invisibility skin cloak for visible light.[J].Science,2015,349(6254):1310-1314; RCS reduction or scattering enhancement of conformal structures, such as H.Xu, TangShiWei, Sun Chen, Liu HaiWen, High-efficiency broadband polarization-independent superscatterer using conformal metasurfaces.[J].Photonics Research,2018,v.6(08):40-46; and conformal reflective array antennas based on conformal metasurfaces, such as Zhang A Fang, Yang R, Li D, et al. Metasurface-based tapered waveguide slot array antennas for wide angularscanning in a narrow frequency band[J].IEEE Transactions on Antennas and Propagation, 2018, 66(8): 4052-4059; and conformal lens research, such as HPLi, GMWang, GWHu. et al., 3D-printed curved metasurface with multifunctional wavefronts.[J].Advanced Optical Materials, 2020: 2000-129, etc.

[0004] Unlike planar metasurface design, the shape of conformal devices is determined by factors other than their electromagnetic properties. By designing the surface structure of metasurfaces, they can flexibly adapt to the shape of the carrier, greatly expanding their application scenarios. In the literature H.Xu, Tang ShiWei, Sun Chen, Liu HaiWen, High-efficiency broadband polarization-independent superscatterer using conformal metasurfaces.[J]. Photonics Research, 2018, v.6(08):40-46, Xu et al. designed a cylindrical conformal scattering-enhanced metasurface that can achieve dual-beam scattering in the Ku band. In the literature HPLi, GMWang, GWHu. et al., 3D-printed curved metasurface with multifunctional wavefronts.[J]. Advanced Optical Materials, 2020:2000129, Li et al. designed a cylindrical conformal metasurface lens based on grating metasurface units.

[0005] However, current research on conformal metasurfaces mainly focuses on cylindrical carriers. In practical applications, the carrier shape is often not a simple cylinder, thus necessitating research on conformal metasurfaces with arbitrary cylindrical surfaces. Especially in some applications, such as aircraft antennas, placing them outside the aircraft would affect aerodynamics. Therefore, to avoid compromising aerodynamics, aircraft antennas can be placed inside the fuselage. If the conformal metasurface can conform to the fuselage structure, the antenna and the conformal metasurface form a conformal lens antenna, maintaining both good antenna radiation performance and the aircraft's aerodynamic shape. To maintain good aerodynamic performance, the two-dimensional contours of aircraft components are generally designed using quadratic curves or combinations of quadratic curves with good convexity preservation. Quadratic curves include circles, ellipses, parabolas, and hyperbolas. However, current research on conformal phase-modulated metasurface shapes mainly focuses on cylindrical surfaces. Therefore, it is necessary to study design methods for conformal metasurfaces with elliptical, parabolic, and hyperbolic contours. Summary of the Invention

[0006] To address the problem that existing conformal metasurface conformal antenna research mainly focuses on cylindrical surfaces and cannot be applied to other scenarios requiring non-cylindrical conformal antennas, such as aircraft antennas, this invention provides an arbitrary cylindrical conformal metasurface conformal antenna and its design method.

[0007] On one hand, the present invention provides a design method for a conformal antenna with an arbitrary cylindrical conformal metasurface, comprising:

[0008] Step 1: Calculate the conformal compensation phase at any point on the given conformal surface;

[0009] Step 2: On the given conformal surface, designate a point as the starting point, and distribute the superstructure units at equal intervals on the given conformal surface starting from the starting point according to the set interval arc length. Take the superstructure unit located at the starting point as the starting unit, and calculate the spatial position coordinates of each superstructure unit on the given conformal surface according to the abscissa of the starting unit.

[0010] Step 3: Based on the spatial coordinates of each meta-unit, calculate the conformal compensation phase of each meta-unit according to the calculation method in Step 1. Then, obtain the structural parameters of each meta-unit based on its conformal compensation phase. Use 3D printing technology to print the meta-units according to the structural parameters to construct the conformal cylindrical lens antenna.

[0011] Step 4: Use a Vivaldi antenna as the antenna feed for the conformal cylindrical lens antenna.

[0012] Furthermore, step 1 specifically includes:

[0013] Let surface C be a surface generated by the curve z = f(x) as the directrix; let surface C be a given conformal surface, S be a point source with coordinates (x0, 0, F); where z = f(x) is a curve on the xoz surface and is differentiable;

[0014] For any point P on surface C, let its coordinates be (x, y, z), and calculate the compensation phase Φ at point P according to formula (6). P :

[0015]

[0016] Where k is the free space wavenumber, k = 2π / λ.

[0017] Furthermore, the curve z = f(x) is a quadratic curve.

[0018] Furthermore, the quadratic curve can be any one of an elliptic curve, a hyperbola, and a parabola, or a combination of two of them.

[0019] Furthermore, step 2 specifically includes:

[0020] Given the x-coordinate of the initial element, the problem of calculating the spatial position coordinates of each superstructure element on a given conformal surface is transformed into the following mathematical problem: Let the length of the line L0 be np. Points are taken and marked at equal intervals with a step size of p on the interval [p / 2, np+p / 2], thus obtaining the point set S = {s0, s1, s2, s3, ..., s...} on the line L0. n}, and has |s j+1 -s j |2=p;Now, keeping the length of the straight line L0 unchanged, it is bent. During the bending process, the point set S lies on the curve L… c Their relative positions remain unchanged, and they are arranged along the trajectory corresponding to the given function f(x) to form curve L. c Solve for curve L c Above, when the x-coordinate of the starting point s0 is p / 2, the coordinates of each point in the point set S; where each point in the point set S corresponds to each superstructure unit, the starting point s0 corresponds to the starting unit, p corresponds to the interval arc length, and curve L c The expression for z is z = f(x).

[0021] Further, in step 2, the spatial position coordinates of each hyperstructure element on the given conformal surface are calculated using arc differential and numerical integration, specifically including:

[0022] Surface C is defined as curve L c The surface generated for the directrix is ​​used as a given conformal surface, and surface C is used as the given conformal surface.

[0023] Solve for the arc differential of surface C using formula (7):

[0024]

[0025] Set curve L c If it is integrable, then its line integral can be obtained according to formula (8):

[0026]

[0027] Combining formulas (7) and (8), we obtain the curve L shown in formula (9). c Upper limit function for integration:

[0028]

[0029] The abscissa of each point in the point set S can be obtained according to formula (9). The solution process is expressed by formula (10), thus obtaining the coordinates of each point in the point set S on the curve L. c The coordinates on the x-axis are denoted as the x-axis set.

[0030]

[0031] in, Representing point s j In curve L c The corresponding x-coordinate;

[0032] Using the calculated set of x-coordinates The coordinate set of each point in the point set S is obtained by calculating z = f(x).

[0033] On the other hand, the present invention provides an arbitrary cylindrical conformal metasurface conformal antenna, which is obtained by any of the design methods described above.

[0034] The beneficial effects of this invention are:

[0035] This invention is based on the optical path tracing method to calculate the distance from the radiation source to a point on the conformal surface, thereby obtaining the compensated phase without the need for cumbersome geometric derivation and applicable to any cylindrical surface. The spatial coordinates of the unit on the surface can be solved using arc differential and numerical integration methods. A conformal cylindrical lens is constructed using a double-layer 3D printed unit. A Vivaldi antenna is used as the antenna feed for the lens antenna. In summary, according to the method provided by this invention, any conformal metasurface antenna on a cylindrical surface can be designed simply by using the equation of the cylindrical directrix. Attached Figure Description

[0036] Figure 1 A flowchart illustrating the design method of an arbitrary cylindrical conformal metasurface conformal antenna provided in an embodiment of the present invention;

[0037] Figure 2 A schematic diagram illustrating the principle of calculating conformal compensation phase provided in an embodiment of the present invention;

[0038] Figure 3 This is a schematic diagram of the distribution of superstructure units on a conformal cross-section provided in an embodiment of the present invention;

[0039] Figure 4 The following schematic diagrams of the surface directrix and surface subdivision provided for embodiments of the present invention are as follows: (a) and (b) represent the elliptical cylindrical surface directrix and surface subdivision schematic diagrams; (c) and (d) represent the hyperbolic cylindrical surface directrix and surface subdivision schematic diagrams; (e) and (f) represent the parabolic cylindrical surface directrix and surface subdivision schematic diagrams.

[0040] Figure 5 The following is a schematic diagram of the directrix and point source position of the combined quadratic curve provided for the embodiments of the present invention: (a) shows that the combined quadratic curve is a directrix composed of two quadratic curves, namely parabola and ellipse; (b) is a schematic diagram of the point source position when the directrix is ​​a combined quadratic curve.

[0041] Figure 6The phase distribution and structural parameter distribution of the combined quadratic cylindrical conformal metasurface lens antenna provided in the embodiments of the present invention are as follows: (a) shows the phase distribution diagram; (b) shows the parameter α distribution diagram; (c) shows the parameter β distribution diagram.

[0042] Figure 7 The electric field Re(E) of the combined quadratic cylindrical conformal metasurface lens antenna provided in the embodiments of the present invention x ) and Re(E y Distribution: (a) and (b) represent Re(E) on the xoz plane, respectively. x ) and Re(E y (c) and (d) represent the Re(E) distribution on the yoz surface, respectively. x ) and Re(E y )distributed;

[0043] Figure 8 The three-dimensional far-field radiation pattern of the combined secondary cylindrical conformal metasurface lens antenna provided in the embodiments of the present invention is as follows: (a) is the far-field radiation pattern and conformal metasurface structure at 10 GHz, and (b) to (g) are the three-dimensional far-field radiation patterns in the broadband range.

[0044] Figure 9 The conformal metasurface, testing environment, and testing results provided for embodiments of the present invention are as follows: (a) 3D printed dielectric layer, with the outer dielectric layer on the left and the inner dielectric layer on the right; (b) Flexible PCB of half-wave plate layer corresponding to the focusing lens; (c) Assembled conformal lens; (d) Far-field testing platform; (e) Normalized two-dimensional far-field pattern of the 10GHz conformal lens on the xoz plane; (f) Normalized two-dimensional far-field pattern of the 10GHz conformal lens on the yoz plane. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be clearly described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0046] It is understood that a cylindrical surface is defined as follows: a surface formed by moving a fixed straight line parallel to a certain curve is a cylindrical surface; wherein, the fixed straight line is called the generatrix of the surface, and the fixed curve is called the directrix of the surface. For example, a cylindrical surface whose directrix is ​​a circle is called a cylindrical surface; a cylindrical surface whose directrix is ​​a quadratic curve is called a quadratic cylindrical surface. Furthermore, it should be noted that the surface mentioned in this invention refers to a cylindrical surface.

[0047] Example 1

[0048] The conformal surface in this embodiment is a surface C formed under the following conditions: The surface C is generated with the curve z = f(x) as the directrix. z = f(x) is a curve on the xoz plane and is differentiable (to ensure that the generated surface is smooth, the function z = f(x) must be differentiable). Based on this type of conformal surface, combined with Figure 1 As shown, the design method of the arbitrary cylindrical conformal metasurface conformal antenna provided in this embodiment includes the following steps:

[0049] S101: Calculate the conformal compensation phase at any point on the given conformal surface;

[0050] Specifically, for a planar structure, the reference plane and the metasurface are parallel to each other, and it is only necessary to calculate the optical path that the electromagnetic wave travels in space from the feed source to the metasurface. However, for a curved surface structure, since the metasurface is no longer planar and there is a distance between the metasurface and the reference plane, during the process of calculating the phase, not only the distance that the electromagnetic wave travels in space to reach the metasurface needs to be considered, but also the distance between the metasurface and the reference plane caused by the curvature of the metasurface itself needs to be considered. In this embodiment, the optical path tracing method is used to calculate the compensation phase. Specifically: Select a plane as the reference plane, and calculate the optical path that the electromagnetic wave radiated from the feed source travels to reach the reference plane to compensate for the phase difference.

[0051] As Figure 2 shown, z = f(x) is a curve on the xoz plane, the surface C is a surface generated with the curve z = f(x) as the directrix, the plane M is a reference plane parallel to the xoy plane, the expression of the reference plane M is z = L (L < f(x)), S is a point source, and its coordinates are (x0, 0, F). Select any point P on the surface C, the coordinates of point P are (x, y, z), draw a straight line perpendicular to the reference plane M through point P, and the intersection point of the straight line and the reference plane M is P'. Let the compensation phase at point P be Φ P , in order to make the phase of the electromagnetic wave radiated from the point source S reach the reference plane M as a constant Θ0 after passing through the surface C, the following equation can be deduced:

[0052] k|SP| - Φ P + k|PP'| = Θ0 (1)

[0053] where k is the wave number, |SP| represents the distance from the point source S to point P, |PP'| represents the distance from point P to point P', and by transposing the above formula (1), we can get:

[0054] Φ P = k(|SP| + |PP'|) - Θ0 (2)

[0055] The calculation formulas for |SP| and |PP′| in equations (1) and (2) are shown in equations (3) and (4):

[0056]

[0057] |PP′|=zL (4)

[0058] Combining equations (2), (3), and (4), we get:

[0059]

[0060] In equation (5), F, L, and Θ0 are all constants, so equation (5) can be further simplified to equation (6):

[0061]

[0062] As can be seen from equation (6), once the position of the point source S is determined, the compensation phase at point P is only related to the spatial coordinates of point P. Therefore, the problem of solving the compensation phase is transformed into the problem of solving the spatial coordinates of point P. Solving the spatial coordinates of point P requires combining the specific superstructure and directrix function, which will be detailed in the next step and will not be repeated here.

[0063] Therefore, the calculation method for the compensation phase given in this embodiment is based on the optical path tracing method, which calculates the distance from the radiation source to the point on the conformal surface, thereby obtaining the compensation phase. This method does not require complicated geometric derivation and is applicable to any cylindrical surface.

[0064] For example, considering the aircraft's profile, a surface structure formed by a quadratic curve with good convexity preservation can be used as the conformal metasurface. This can be any quadratic curve among elliptic curves, hyperbolas, and parabolas. Since the directrix is ​​symmetrical about the z-axis, to ensure that the point source S is directly opposite the "center" of the metasurface, it only needs to be located on the z-axis, i.e., the coordinates of the point source S are (0,0,F). Therefore, the phase compensation calculation formula (6) should be:

[0065]

[0066] S102: On a given conformal surface, a point is designated as the starting point, and the superstructure units are distributed at equal intervals on the given conformal surface starting from the starting point according to a set interval arc length. The superstructure unit located at the starting point is used as the starting unit, and the spatial position coordinates of each superstructure unit on the given conformal surface are calculated based on the abscissa of the starting unit.

[0067] Specifically, there are two key issues in the modeling of conformal metasurfaces: First, it is necessary to determine the conformal surface structure. The selection of the surface structure should generally be based on the requirements and should be a surface with practical application scenarios. Second, it is necessary to solve the spatial position coordinates of the metaunits on the surface. Formula (6) has given the calculation formula for the compensation phase. The key to the compensation phase calculation is to solve the spatial position coordinates of each metaunit on the surface.

[0068] When calculating phase distribution, the superstructure elements are typically discretized according to the element period p, and the coordinates of each element's center point are used as the coordinates of that element. On a plane, the interval between adjacent elements is the period p, so the coordinates can be represented by integer multiples of the element period p based on the element number. However, on a curved surface, since the superstructure elements are built along the surface, the planar method is no longer applicable. Considering that the element interval is the arc between adjacent elements, in this embodiment, the conformal strategy is to distribute the elements with equal arc length intervals of period p, that is, the arc length between each pair of adjacent elements is always p. Figure 3 As shown.

[0069] However, for any surface, since the curvature is not equal at every point on its directrix, it is impossible to solve for the position coordinates of each point using the geometric relationship of the curve. Therefore, the inventors considered using a method combining arc differential and numerical analysis to solve for the spatial position coordinates of the elements. Specifically, this embodiment transforms the problem of "given the abscissa of the starting element, calculating the spatial position coordinates of each superstructure element on a given conformal surface based on the abscissa of the starting element" into the following mathematical problem:

[0070] Let the length of line L0 be np. On the interval [p / 2, np+p / 2], take points at equal intervals with a step size of p and mark them, thus obtaining a point set S = {s0, s1, s2, s3, ..., s} on line L0. n}, and has |s j+1 -s j |2=p;Now, keeping the length of the straight line L0 unchanged, it is bent. During the bending process, the point set S lies on the curve L… c The relative positions of the points remain unchanged (i.e., the points are still divided into equal intervals of length p), and they are arranged along the trajectory corresponding to the given function f(x) to form curve L. c Solve for curve L c Above, when the x-coordinate of the starting point s0 is p / 2, the coordinates of each point in the point set S; where each point in the point set S corresponds to each superstructure unit, the starting point s0 corresponds to the starting unit, p corresponds to the interval arc length, and curve L c The expression for z is z = f(x).

[0071] By transforming the problem, this embodiment further utilizes arc differential and numerical integration to calculate the spatial position coordinates of each hyperstructure element on a given conformal surface. The specific process is as follows:

[0072] Solve for the arc differential of surface C using formula (7):

[0073]

[0074] Set curve L c If it is integrable, then its line integral can be obtained according to formula (8):

[0075]

[0076] Because curve L c The x-coordinate of the starting unit on is Combining formulas (7) and (8), we obtain the curve L shown in formula (9). c Upper limit function for integration:

[0077]

[0078] Because curve L c Each marker point on the curve L is distributed at equal intervals with a step size of length p, thus shaping the curve L of length np. c Divided into n segments, we can obtain equation (10):

[0079]

[0080] in, Indicates the marker point s j In curve L c The corresponding x-coordinate.

[0081] Since the definite integral of g(q) cannot be directly solved analytically, numerical integration is used for approximation. Furthermore, the coordinates of all marked points in the point set S on the curve L can be obtained. c set of x-coordinates on Then, based on the function z = f(x), use the calculated set of x-coordinates. We can obtain the coordinates of each point in the point set S on the curve L. c The set of coordinates corresponding to X

[0082] In this embodiment, a curved surface structure formed by a quadratic curve with good convexity preservation is used as a conformal metasurface, taking into account the aircraft's outline shape.

[0083] Specifically, to further illustrate the process of solving for the spatial coordinates of each superstructure unit in this embodiment, the coordinate solution process is given using an elliptic curve function in a quadratic curve as an example. For curve L...c Using elliptic curve functions hour:

[0084] Referring to formula (7), we can obtain formula (11):

[0085]

[0086] Referring to formula (8), we can obtain formula (12):

[0087]

[0088] Referring to formula (9), its upper limit function for integration can be further obtained as follows:

[0089]

[0090] Then, according to and Finally, we can obtain the position of all markers in the marker set S along the function. The set of coordinate values ​​on the new trajectory after bending.

[0091] As an example, the above solution algorithm can be implemented through programming to calculate the curve L. c When the function is an elliptic curve function (e.g., as shown in Equation (14)), a hyperbola function (e.g., as shown in Equation (15)), or a parabola function (e.g., as shown in Equation (16)), the curve L c The coordinates of points on the curve L. Assume there are 24 points in total. c It was divided into 23 segments, p = 5.8.

[0092]

[0093]

[0094] z = f3(x) = 0.02x 2 (16)

[0095] Then the position of each point on the function f(x) is as follows: Figure 4 (a), Figure 4 (c), Figure 4 As shown in (e), the black "o" represents points on the straight line L0 with a spacing of p, and the red "*" represents the curve L formed by bending the straight line L0 along the function f(x). c The position of the point above, the arc length between two adjacent red "*" points is p. The superstructure element is arranged according to L. c The coordinates of the points are arranged so that the center of the superunit falls at the position of the asterisk (*). Therefore, the x-coordinate of the superunit is in the set. In the middle, the corresponding z-coordinate is

[0096] Next, using curves f1(x), f2(x), and f3(x) as directrixes, elliptical cylinders, hyperbolic cylinders, and parabolic cylinders are generated, respectively. The cylinders are discretized along the directrix and the y-axis at intervals of the superstructure element period p, dividing the cylinders into n×n (n=24) grids, each corresponding to one superstructure element, as shown below. Figure 4 (b), Figure 4 (d) and Figure 4 As shown in (f), the position coordinates of the j-th superunit in the i-th row can be denoted as:

[0097]

[0098] y ij = (i-0.5)p (17b)

[0099]

[0100] Where i and j are the indices of the superunit in the x and y directions (i, j = 1, 2, ..., n), and All have been determined using numerical analysis methods and belong to sets respectively. and

[0101] S103: Based on the spatial coordinates of each meta-unit, the conformal compensation phase of each meta-unit is calculated according to the calculation method in step S101. Then, the structural parameters of each meta-unit are obtained based on the conformal compensation phase. The meta-units are then printed using 3D printing technology according to the structural parameters to construct a conformal cylindrical lens antenna. This step can be referred to in the following embodiments for details, and will not be repeated here.

[0102] S104: A Vivaldi antenna is used as the antenna feed for the conformal cylindrical lens antenna.

[0103] Example 2

[0104] Unlike the conformal surface in Embodiment 1 above, the conformal surface C in this embodiment is formed under the following conditions: surface C is generated with the curve z = f(x) as the directrix, and z = f(x) contains two types of curves. Based on this type of conformal surface, the design method of the arbitrary cylindrical conformal metasurface conformal antenna provided in this embodiment includes the following steps:

[0105] S201: Calculate the conformal compensation phase at any point on a given conformal surface;

[0106] Specifically, in conjunction with the aircraft's outline shape, this embodiment still uses a curved surface structure formed by a quadratic curve with good convexity preservation as the conformal metasurface; it should be noted that the guideline is composed of two quadratic surfaces.

[0107] For example, the directrix is ​​composed of a parabola and an elliptic curve. The equation and graph of the directrix are given as follows: Figure 5 As shown in (a), its function expression is a piecewise function: when x < 0, the curve is a parabola, and its function expression is f(x) = g(x) = 0.03x. 2 When x > 0, the curve is an elliptic curve, and its function expression is:

[0108] It is important to note that when the directrix is ​​a combination of different types of quadratic curves, it is not symmetric about the z-axis due to changes in the curve structure. Assume that points are taken at equal intervals along this directrix with an arc length p as the step size, n = 24. To ensure that the point source S is directly aligned with the "center" of the metasurface, the abscissa of S is x0 = (x1 + x...). 24 Therefore, in this embodiment, the point source S is located at ) / 2. At this point, the projection of point source S onto the x-axis falls on o′, as shown. Figure 5 (b) shows point S and the blue dashed line. Point o' in the figure is the projection of the directrix onto the x-axis, the line X1X. 24 The midpoints of x1 and x 24 Define the lower and upper limits of the domain interval for the directrix function. Therefore, the phase compensation calculation formula (6) should be:

[0109]

[0110] As can be seen from the compensation phase calculation formula (18), when the point source position is determined, the compensated phase is only related to the position of the point. Using the above formula (18), the phase distribution of the conformal metasurface in converting spherical waves into plane waves can be obtained, which also lays the foundation for the design of other functional devices.

[0111] S202: On a given conformal surface, a point is designated as the starting point, and the superstructure units are distributed at equal intervals on the given conformal surface starting from the starting point according to a set interval arc length. The superstructure unit located at the starting point is used as the starting unit, and the spatial position coordinates of each superstructure unit on the given conformal surface are calculated based on the abscissa of the starting unit.

[0112] Still using the example directrix in step S201 as a basis, taking points at equal intervals along the directrix with arc length p as the step size, n=24 as an example, since g(0)=h(0)=0 and g′(0)=h′(0)=0, the function f(x) in the domain x∈[x1,x2] is valid. 24The curve is continuous and differentiable within the interval, and can be used as a guideline for constructing cylindrical conformal hypersurfaces. The projection of this curve onto the x-axis is a straight line, denoted as X1X2.

[0113] Using the method for solving the position coordinates of the superstructure in Embodiment 1 above, the set of coordinates of the superstructure on the x-axis is obtained as X = {x1, x2, x3, x4, ..., x...} 24}, and thus we can obtain the set of coordinates on the z-axis Z = {z1, z2, z3, z4, ..., z}. 24},like Figure 5 As shown in (b), the red "*" in the figure indicates the location of the center of the hyperstructure unit.

[0114] S203: Based on the spatial coordinates of each meta-unit, calculate the conformal compensation phase of each meta-unit according to the calculation method in step S201. Then, obtain the structural parameters of each meta-unit based on its conformal compensation phase. Use 3D printing technology to print the meta-units according to the structural parameters to construct a conformal cylindrical lens antenna.

[0115] In this embodiment, as an example, the printed metacellular unit consists of three layers of flexible PCB coated with metallic copper and two layers of 3D printing medium. Specifically, the ε of the PCB substrate... r =2.65, tanδ = 0.003, thickness is 0.127mm, the 3D printing medium is ABS-M30, and the relative permittivity is ε. r =2.7, tanδ=0.005, thickness is 2mm. In this three-layer flexible PCB coated with copper, the first and third layers are mutually orthogonal polarization gates, and the second layer is a half-wave plate with an "I"-shaped ring structure. By adjusting the arc length of the "I"-shaped ring structure, good phase modulation can be achieved over a wide bandwidth. By changing the arc length angle α and the rotation angle β of the "I"-shaped ring structure (α varies from 33° to 88°, β takes values ​​of +45° or -45°), t can be adjusted. yx The phase change range covers 360°.

[0116] In this embodiment, the designed conformal metasurface is composed of 24×24 metaunits, with a focal length F = 100mm and an operating frequency of 10GHz. When the directrix of the metasurface is as follows... Figure 5 When the combined quadratic function is shown, the phase distribution of the transformation from spherical wave to plane wave can be calculated according to formula (18). The phase distribution and the corresponding unit structure parameters α and β are as follows: Figure 6 As shown.

[0117] S204: A Vivaldi antenna is used as the antenna feed for the conformal cylindrical lens antenna.

[0118] In this embodiment, a broadband Vivaldi antenna is used as the feed antenna to illuminate the metasurface. The incident wave is polarized in the x direction. The projection of the antenna center onto the xoy plane coincides with the center of the projection of the curved surface onto the xoy plane. In order to meet the condition of focal length F = 100 mm and to consider the influence of the phase center of the Vivaldi antenna, the distance from the bottom of the feed antenna to the xoy plane is finally set to 77 mm.

[0119] The metasurface was simulated as a whole in CST Microwave Studio software, and its electric field Re(E) was obtained. x ) and Re(E y Distribution as follows Figure 7 As shown. In the incident field, since the Vivaldi antenna radiates x-polarized spherical waves, E y The component is very small, and after passing through a conformal lens, E x The amount is very small, while E y The wave exhibits planar wave characteristics on both the xoz and yoz planes. This indicates that the combined quadric conformal lens achieves good conversion of spherical waves to plane waves, while also realizing cross-polarization conversion.

[0120] Meanwhile, the three-dimensional far-field distribution of this conformal metasurface lens antenna is given as follows: Figure 8 As shown, the y-polarized emitted wave from the conformal metasurface at 10 GHz is a very good pencil beam with a radiation direction along the negative z-axis. Furthermore, it maintains good radiation characteristics over a wide bandwidth, with a radiation gain exceeding 18.3 dB in the 8.5–13 GHz frequency band, which is more than 11.2 dB higher than the gain of a single-feed antenna. This indicates that the device can achieve good beam focusing performance over a relatively wide bandwidth.

[0121] To further verify the performance of this conformal metasurface lens antenna, the inventors further fabricated and assembled the combined secondary cylindrical conformal metasurface and tested it in a microwave anechoic chamber. The curved dielectric layer of the metasurface was fabricated using 3D printing technology. The material used for 3D printing was ABS-M30 with a relative permittivity of 2.7. The grating layer and half-wave plate layer were only 0.127 mm thick with ε... r =2.65 flexible PCB board, the half-wave plate layer corresponding to the focusing lens is as follows Figure 9 As shown in (b), the 3D-printed dielectric layer and flexible PCB board are assembled using dielectric screws in the order of vertical grating, inner dielectric layer, half-wave plate layer, outer dielectric layer, and horizontal grating. The Vivaldi antenna is then assembled with the conformal metasurface using dielectric pillars to form a lens antenna, as shown in [example diagram]. Figure 9As shown in (c), the distance between the bottom of the Vivaldi antenna and the tangential surface of the conformal metastructure is maintained at 7.7 cm. Measurements are performed on the assembled conformal lens in a microwave anechoic chamber. The sample under test is placed on a test turntable that can rotate 360°. The receiver is a double-ridged horn operating at 1–18 GHz. The test platform is as follows: Figure 9 As shown in (d), the measured x-polarized and y-polarized two-dimensional far-field radiation patterns are as follows. Figure 9 As shown in (e) and (f), the simulation and experimental results agree well. The simulated and tested main beam curves largely coincide. After loading the metasurface, the antenna gain increased by 12.2 dB. In the main radiation direction, the x-polarization is 23.2 dB lower than the y-polarization (simulation 22.6 dB), the sidelobe level on the xoz plane is -15.2 dB lower (simulation -17.4 dB), and the sidelobe level on the yoz plane is -18.1 dB lower (simulation -21.7 dB). The good performance of this device indicates that the spherical wave radiated from the Vivaldi antenna is well converted into a plane wave, further verifying the rationality and correctness of the combined quadratic cylindrical conformal metasurface design, and providing a foundation for the subsequent design of conformal metasurfaces with other functions.

[0122] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for designing an arbitrary cylindrical conformal meta-surface conformal antenna, characterized in that, Comprise: Step 1: calculating the conformal compensation phase at any point on a given conformal surface; specifically including: setting the surface C as a surface generated with the curve as the guide line; taking the surface C as the given conformal surface, S as the point source, and the coordinates as (x0, 0, F); wherein, is the curve on the xoz plane and is derivable; For any point on surface C Set its coordinates as Calculated according to formula (6) Compensation phase at point : (6) Wherein, k is the free space wave number, k=2π / λ; Step 2: on the given conformal surface, a point is specified as a starting point, and the superstructure units are distributed at equal intervals on the given conformal surface according to the set interval arc length from the starting point, the superstructure unit located at the starting point is taken as a starting unit, and the spatial position coordinates of each superstructure unit on the given conformal surface are calculated according to the horizontal coordinates of the starting unit; specifically including: the problem of converting the horizontal coordinates of the given starting unit to calculate the spatial position coordinates of each superstructure unit on the given conformal surface into the following mathematical problem: let the length of the straight line L0 be np, and the straight line L0 is divided into n segments by taking points at equal intervals on the interval [p / 2, np+p / 2] with a length p as a step, so that the point set S is obtained on the straight line L0 , and |s j+1 -s j |2= p; the length of the straight line L0 is kept unchanged, and the straight line L0 is curved, the relative positions of the point set S on the curve L c remain unchanged during the bending process, and the point set S is arranged along the trajectory corresponding to the given function f(x) to form the curve L c ; the coordinates of each point in the point set S on the curve L c are solved when the horizontal coordinate of the starting point s0 is p / 2; wherein each point in the point set S corresponds to each superstructure unit, the starting point s0 corresponds to the starting unit, p corresponds to the interval arc length, and the expression of the curve L c is ; The spatial position coordinates of each super unit on the given conformal curved surface are calculated by using arc differential and numerical integration, specifically comprising: The curved surface C is a curved surface generated with the curve L c as a guide line, and the curved surface C is taken as a given conformal curved surface. Solve the arc differential of the curved surface C according to formula (7): (7) Set curve L c If the integral is convergent, then its curve integral is obtained according to formula (8): (8) Combining equation (7) and equation (8) gives the curve L shown in equation (9) c The upper limit function of the integral: (9) According to formula (9), the abscissa of each point in the point set S can be obtained, and the solving process is represented by formula (10), so as to obtain the coordinates of each point in the point set S on the curve L c , recorded as the abscissa set : (10) wherein representing a point s j corresponding to the ordinate on the curve L c corresponding to the abscissa on the curve L The calculated set of abscissas , according to The calculated set of coordinates of the points of the set S ; Step 3: According to the spatial position coordinates of each super unit, the conformal compensation phase of the position of each super unit is calculated according to the calculation method of step 1, and then the structure parameters of each super unit are obtained according to the conformal compensation phase of each super unit, and the super unit is printed by using 3D printing technology according to the structure parameters to construct the conformal cylindrical lens antenna; Step 4: A Vivaldi antenna is used as the antenna feed source of the conformal cylindrical lens antenna.

2. The method of designing an arbitrary cylindrical conformal metamaterial surface conformal antenna according to claim 1, wherein, curve is a conic.

3. The method of designing an arbitrary cylindrical conformal metamaterial surface conformal antenna according to claim 2, wherein, The conic curve adopts any one of an elliptic curve, a hyperbolic curve and a parabolic curve, or a combination of two of them.

4. An arbitrary cylindrical conformal meta-surface conformal antenna, characterized in that, The design method of any one of claims 1 to 3 is used.

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