Deployable flexible luneberg lens antenna based on Kigami structure

Abstract

The invention discloses an expandable flexible luneberg lens antenna based on a Kigami structure, and belongs to the technical field of antennas. The antenna comprises a feed source and a spherical luneberg lens structure, the feed source is arranged on one side of the spherical luneberg lens structure and right faces the geometric center of the spherical luneberg lens structure, shaping and focusing of radiation beams are achieved, and directivity and gain performance are remarkably improved. The spherical Luneberg lens structure is composed of a plurality of lens units, and each lens unit is formed by a nested truncated octahedron structure and a three-dimensional periodic hole array and has variable structure parameters so as to regulate and control an effective dielectric constant. By adjusting the parameter value of the structure, the dielectric constant can be continuously adjusted within the range of 1.1-1.95, and the radial dielectric constant distribution requirement of the spherical Lunburg lens is met. Simulation and actual measurement results show that the structure has good gain performance and stable directional diagram characteristics within the frequency band of 12-26.5 GHz, and is suitable for a miniaturized and deployable high-frequency antenna system.

Description

Technical Field

[0001] This invention belongs to the field of antenna technology, specifically relating to a deployable flexible Luneburg lens antenna based on a Kirigami structure. Background Technology

[0002] With the rapid development of modern communication, radar imaging, and satellite remote sensing technologies, antenna systems are facing higher demands for high gain, wide bandwidth, beam control capabilities, and system integration. Luneburg lens antennas, due to their ideal spherical-to-plane wave transformation capability, can achieve multi-directional beam scanning and wide beam coverage, and possess significant advantages such as high gain, low sidelobes, and wide bandwidth. They have been widely used in millimeter-wave and terahertz communication, target detection, and imaging.

[0003] Traditional Luneburg lens antennas are mostly constructed from rigid dielectric materials. Their spherical structures are often bulky and heavy, and difficult to fold or deploy portablely, making them unsuitable for space-constrained scenarios or those requiring high reconfigurability and flexible integration. Furthermore, an ideal Luneburg lens needs to achieve a continuously varying dielectric constant distribution within the sphere, a requirement that existing materials often cannot meet. A layered approximation method is typically used, dividing the lens into several concentric spherical shells with different dielectric constants, and controlling the equivalent dielectric constant through different materials or structural parameters.

[0004] Kirigami structures originate from traditional paper-cutting geometry, achieving a two-dimensional to three-dimensional transformation by introducing slits and unit reconstruction methods into the material. Compared to origami structures, Kirigami offers greater freedom and deformation capabilities, making it suitable for constructing compressible, deployable, and programmable three-dimensional media structures. Introducing Kirigami structures into antenna lens design promises to achieve lightweight, flexible, and deployable structures without sacrificing radiation performance, thereby improving the integration and adaptability of antenna systems.

[0005] However, research on the fusion of Kirigami structures and dielectric lenses is still in its early stages. A mature solution for achieving effective electromagnetic parameter control and wavefront modulation while maintaining three-dimensional deformation capability remains elusive. Therefore, there is an urgent need to propose a flexible lens antenna structure that is deployable, suitable for the Ku / K band, and possesses excellent electromagnetic performance to meet the technical requirements of high-frequency communication systems for high gain, miniaturization, and reconfigurability.

[0006] To address the aforementioned issues, there is an urgent need to propose a Luneburg lens antenna structure that combines high performance, lightweight design, and flexible deployability to meet the practical needs of complex application environments such as next-generation high-speed communications, UAV platforms, and portable radar. Summary of the Invention

[0007] The purpose of this invention is to overcome the problems of the prior art and provide a deployable flexible Luneburg lens antenna based on the Kirigami structure.

[0008] The technical problem addressed by this invention is solved as follows:

[0009] A deployable flexible Luneburg lens antenna based on a Kirigami structure includes a feed source and a spherical Luneburg lens structure; the feed source is disposed on one side of the spherical Luneburg lens structure, facing the geometric center of the spherical Luneburg lens structure;

[0010] The spherical Luneburg lens structure is an eight-layer spherical structure. In each layer, the distance between each lens unit and the center of the sphere is the same, and the adjacent layers are closely fitted together. The spherical Luneburg lens structure is composed of two types of lens units, and the dielectric constant distribution ranges of the two types of lens units are different. The first layer is a single lens unit located at the center of the sphere.

[0011] Based on the formula for calculating the dielectric constant distribution of lens units in a spherical Luneburg lens structure, the dielectric constant values ​​of each lens unit in the eight-layer spherical structure are calculated. The lens units whose dielectric constant distribution range can cover the dielectric constant value are arranged at the position to finally form a complete spherical Luneburg lens structure.

[0012] Furthermore, the first type of lens unit is a nested truncated octahedral-hexagonal aperture array; the main body of the first type of lens unit is a truncated octahedral frame, with a coaxial truncated octahedral cavity nested inside; on the eight regular hexagonal faces of the truncated octahedral frame, regular hexagonal columnar holes are symmetrically excavated along the surface normal direction, and the regular hexagonal columnar holes corresponding to two parallel hexagonal faces are in a through state; all hexagonal columnar holes have the same size, and the cavity height of the truncated octahedral cavity is twice the hexagonal side length of the hexagonal columnar holes;

[0013] The second type of lens unit is a nested truncated octahedron-hybrid aperture array; based on the first type of lens unit, the second type of lens unit further symmetrically removes cubic columnar holes along the surface normal direction on the 6 square faces of the truncated octahedron frame; the side length of the square of the cubic columnar hole is the same as the side length of the hexagon of the regular hexagonal columnar hole; the cubic columnar holes corresponding to the two parallel square faces are in a through state.

[0014] Furthermore, for both types of lens units, the cavity height of the coaxial truncated octahedral cavities nested inside can be varied, thereby achieving adjustment of the dielectric constant of the lens unit; for the second type of lens unit, the cavity height varies from 0.9mm to 1.15mm; for the first type of lens unit, the cavity height varies from 0.25mm to 1mm.

[0015] Furthermore, the dielectric material used in the lens unit has a dielectric constant of 2.94 and a loss tangent of 0.06.

[0016] Furthermore, the lens unit is made of M-FL90 (black / transparent elastic resin).

[0017] Furthermore, the feed source is a Ku-band horn antenna or a K-band horn antenna.

[0018] Furthermore, the dielectric constant distribution ε of the lens unit r The formula for calculating (r) is:

[0019]

[0020] Where R is the radius of the spherical Luneburg lens structure, and r is the distance to the center of the spherical Luneburg lens structure.

[0021] Furthermore, the diameter of the spherical Luneburg lens structure is 45mm.

[0022] Furthermore, the feed source is made of aluminum alloy.

[0023] Furthermore, the focal length of the deployable flexible Luneburg lens antenna is 2mm.

[0024] Furthermore, the spherical Luneburg lens structure was fabricated using 3D printing.

[0025] The beneficial effects of this invention are:

[0026] The lens antenna described in this invention is the first to introduce nested truncated octahedron (TO) lattice units as the basis for the dielectric metastructure in a Luneburg lens. The truncated octahedron is a configuration that can completely fill space, and the unit walls are composed of regular hexagonal and square faces, facilitating the creation of through-hole arrays (Type B: hexagonal aperture array; Type A: hybrid hexagonal + cubic aperture array) along the hexagonal / quadrilateral normal directions. This lens structure has the following advantages:

[0027] (1) Easier to print: The wall angle and channel direction of the truncated octahedral unit are consistent with the stacking direction of 3D printing. There is no large area of ​​suspended structure inside, and no additional support is needed during printing. The channels are interconnected, which can avoid resin residue, ensure a high molding success rate and more stable dimensions.

[0028] (2) More stable structure: The truncated octahedral lattice is a three-dimensional uniformly connected structure with uniform stress distribution. It is not easy to deform or crack and has better mechanical strength than the traditional layered assembly structure. At the same time, the structure still maintains flexibility and can be folded and stored to about 30% of its original volume, making it easy to carry and deploy.

[0029] (3) Adjustable electromagnetic performance: By adjusting the internal cavity height sa and the size of the hole, the equivalent dielectric constant of the unit can be continuously varied in the range of 1.1 to 1.95, thereby meeting the requirements of Luneburg lens for dielectric constant at different positions; it is not sensitive to the change of incident angle in the Ku / K band, and the beam remains stable in a wide angle range; the material is a flexible resin that can be 3D printed (dielectric constant of about 2.94, loss tangent of about 0.06), and different dielectric constants are achieved by geometric design rather than splicing multiple materials, which makes the process simpler and the performance more consistent. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the overall structure of the deployable flexible Luneburg lens antenna described in this invention;

[0031] Figure 2 This is a schematic diagram of the cross-sectional structure of the deployable flexible Luneburg lens antenna described in this invention;

[0032] Figure 3 This is a schematic diagram of the lens unit structure in the deployable flexible Luneburg lens antenna of the present invention, wherein (a) is the second type of lens unit and (b) is the first type of lens unit;

[0033] Figure 4 This is a schematic diagram of the simulation curves showing the change of dielectric constant of the two lens elements in the deployable flexible Luneburg lens antenna described in this embodiment as a function of structural parameter sa.

[0034] Figure 5 This is a schematic diagram of the simulation curve of the equivalent dielectric constant of the lens unit in the deployable flexible Luneburg lens antenna described in this embodiment as a function of operating frequency and incident wave angle θ, where (a) is the second type of lens unit with sa = 0.9 mm; (b) is the first type of lens unit with sa = 0.7 mm.

[0035] Figure 6 This is a schematic diagram of the dielectric constant distribution of each slice in the upper hemisphere region of the spherical Luneburg lens structure in the deployable flexible Luneburg lens antenna described in this embodiment. (a) z = 0 is the slice where the center of the sphere is located, (b) z = 1 is the slice where the layer above the center of the sphere is located, (c) z = 2 is the slice where the two layers above the center of the sphere are located, (d) z = 3 is the slice where the three layers above the center of the sphere are located, (e) z = 4 is the slice where the four layers above the center of the sphere are located, (f) z = 5 is the slice where the five layers above the center of the sphere are located, (g) z = 6 is the slice where the six layers above the center of the sphere are located, and (h) z = 7 is the slice where the seven layers above the center of the sphere are located.

[0036] Figure 7 The following are the gain and S11 simulation curves of the Ku / K band horn antenna in this embodiment, where (a) is the Ku band horn antenna and (b) is the K band horn antenna.

[0037] Figure 8 The normalized radiation pattern for the simulation test of the deployable flexible Luneburg lens antenna described in this embodiment is shown in (a) for 12 GHz, xoz plane; (b) for 12 GHz, yoz plane; (c) for 22 GHz, xoz plane; (d) for 22 GHz, yoz plane; (e) for 26.5 GHz, xoz plane; and (f) for 26.5 GHz, yoz plane.

[0038] Figure 9 The gain curves are from the simulation test of the deployable flexible Luneburg lens antenna described in this embodiment, where (a) is the Ku band and (b) is the K band. Detailed Implementation

[0039] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0040] This embodiment provides a deployable flexible Luneburg lens antenna based on a Kirigami structure, and its overall structural schematic diagram is shown below. Figure 1 As shown, the system includes a Ku / K band horn antenna 1 and a spherical Luneburg lens structure 2. The Ku / K band horn antenna serves as a feed source, positioned on one side of the spherical Luneburg lens structure, with the feed source directly facing the geometric center of the spherical Luneburg lens structure. The feed source generates spherical wave signals, and the all-dielectric circular lens structure focuses and converts the spherical wave signals into plane waves through its focusing function. This achieves beam shaping and focusing of the horn antenna's radiation beam, thereby effectively improving the system's radiation directivity and gain performance.

[0041] The dielectric constant of an ideal Luneburg lens is a function of the distance to the center of the sphere, and currently, no dielectric material possesses this property. Therefore, a spherical all-dielectric Luneburg lens is typically discretized into multiple uniform concentric spherical shells, each with its own dielectric constant. These shells can then be further subdivided into smaller unit cells, each corresponding to a lens unit. The desired effective dielectric constant for each layer can be achieved by varying the fill ratio of the inclusion material within the unit cell.

[0042] The dielectric constant distribution ε of the lens unit r The formula for calculating (r) is:

[0043]

[0044] Where R is the radius of the Luneburg lens, and r is the distance to the center of the Luneburg lens.

[0045] The specific implementation method is as follows: Figure 2As shown, R is set to 22.5 mm, and r is the distance from any point inside the discrete sphere to the center of the sphere. The dielectric constant distribution at any point inside the sphere is calculated. The spherical Luneburg lens structure is modeled using a fast modeling method based on the HFSS-MATLAB-API tool library.

[0046] In this embodiment, the spherical Luneburg lens structure is an eight-layer spherical structure, with each lens unit in each layer having the same distance from the center of the sphere; the spherical Luneburg lens structure is composed of two types of lens units arranged in close fit between adjacent layers; the first layer is a single lens unit located at the center of the sphere.

[0047] Common lens unit structures in existing technologies include rod-shaped, aperture-shaped, cubic, and cubic unit cell forms. The lens unit in the spherical Luneburg lens structure described in this embodiment adopts a composite metaunit based on a truncated octahedral unit cell, whose design balances high-order symmetry and tunable anisotropy. It is divided into two types, and their geometric configurations and electromagnetic properties are compared below. In this embodiment, the lens unit is divided into two types of structures, such as... Figure 3 As shown.

[0048] The first type of lens unit is designated as Type B, and its structural diagram is shown below. Figure 3 As shown in (b), a nested truncated octahedron-hexagonal aperture array is presented. The first type of lens unit consists of a truncated octahedron frame of height la, within which a small, coaxially centered truncated octahedron cavity of height la1 is nested. Hexagonal columnar holes are symmetrically excavated along the surface normal on the eight regular hexagonal faces of the truncated octahedron frame. All hexagonal holes have the same size, matching the size of the regular hexagons in the nested truncated octahedron cavity, and extend axially through the entire lens unit, starting from the center of the bottom surface. The first type of lens unit structure achieves geometric fusion of the nested cavity and aperture array through Boolean operations, forming a three-dimensional periodic hollowed-out metasurface. The original symmetry of the truncated octahedron is preserved, and the uniform distribution of the hexagonal aperture array does not disrupt the in-plane 60° rotational symmetry. Key parameters: The overall height of the first lens unit is la = 3mm; the dimensional relationship between the inner cavity height la1 of the small truncated octahedral cavity and the parameter sa is la1 = 2sa, and the aperture ratio can be controlled by adjusting the parameter sa.

[0049] The second type of lens unit is designated as Type A, and its structural diagram is shown below. Figure 3As shown in (a), this is a nested truncated octahedron-hybrid aperture array. The second lens unit, based on the first lens unit, further incorporates symmetrically carved cubic prism-shaped holes along the surface normal direction on the six square faces of the truncated octahedron frame. The side length of the cubic prism-shaped holes is consistent with the quadrilateral dimensions of the nested truncated octahedron cavities; that is, the side length of the square of the cubic prism-shaped cavity is the same as the side length of the hexagon of the regular hexagonal prism-shaped hole. The cubic prism-shaped holes originate from the unit vertex, penetrate the entire lens unit along three axes, and are formed through orthogonal rotation replication. The final structure contains two types of holes: regular hexagonal holes distributed on the hexagonal faces, maintaining in-plane isotropy; and cubic holes distributed on the square faces.

[0050] In this embodiment, for the two types of lens units, the cavity height of the coaxial small truncated octahedral cavities nested inside them is variable; for the second type of lens unit, the variation range of sa is 0.9mm-1.15mm; for the first type of lens unit, the variation range of sa is 0.25mm-1mm.

[0051] Figure 4 This is a schematic diagram of the simulation curves showing the variation of the dielectric constant of the two lens elements in the deployable flexible Luneburg lens antenna described in this embodiment with the structural parameter sa. The simulation model uses periodic boundary conditions to set two pairs of master-slave boundaries and introduces two Floquet mode ports to obtain the equivalent dielectric constant of the element under vertical incidence conditions. The dielectric material used has a dielectric constant of 2.94 and a loss tangent of 0.06. By analyzing the electromagnetic response of the element structure under different sa values, the range of its equivalent dielectric constant variation is obtained. In the two different types of element structures, adjusting the parameter sa can achieve continuous adjustment of the equivalent dielectric constant of the lens element in the range of approximately 1.1 to 1.95, which can meet the design requirements of the radial dielectric constant distribution in the spherical Luneburg lens.

[0052] Figure 5 This is a schematic diagram of the simulation curves showing the variation of the equivalent dielectric constant of the lens element in the deployable flexible Luneburg lens antenna described in this embodiment with the operating frequency and the incident wave angle θ. (a) represents the second type of lens element, sa = 0.9 mm; (b) represents the first type of lens element, sa = 0.7 mm. The figure shows the trend of dielectric constant variation under four incident angles (θ = 0°, 15°, 30°, and 45°) in the Ku / K band (12 GHz – 26.5 GHz). The results show that the equivalent dielectric constant of the element maintains a small fluctuation with frequency under different incident angles and exhibits good stability.

[0053] Based on the formula for calculating the dielectric constant distribution of lens units in a spherical Luneburg lens structure, the dielectric constant values ​​of each lens unit in the eight-layer spherical structure are calculated. The lens units whose dielectric constant distribution range can cover the dielectric constant value are arranged at the position to finally form a complete spherical Luneburg lens structure. Figure 6 This diagram illustrates the dielectric constant distribution of each slice in the upper hemisphere region of the spherical Luneburg lens structure in the deployable flexible Luneburg lens antenna described in this embodiment. (a) z = 0 represents the slice containing the center of the sphere; (b) z = 1 represents the slice containing the layer above the center; (c) z = 2 represents the slice containing two layers above the center; (d) z = 3 represents the slice containing three layers above the center; (e) z = 4 represents the slice containing four layers above the center; (f) z = 5 represents the slice containing five layers above the center; (g) z = 6 represents the slice containing six layers above the center; and (h) z = 7 represents the slice containing seven layers above the center. Due to the inherent symmetry of the Luneburg lens structure, the dielectric constant distribution in its lower hemisphere is mirror-symmetrical to that in the upper hemisphere. Therefore, during construction, only the functional units need to be arranged according to the upper hemisphere distribution shown in the diagram, and then the entire spherical lens can be constructed by mirror replication.

[0054] Figure 7 The following are simulation curves of the gain and S11 of the Ku / K band horn antenna in this embodiment, where (a) is the Ku band horn antenna and (b) is the K band horn antenna. The gain of the Ku band horn antenna is 8.05dBi-10.2dBi, and the gain of the K band horn antenna is 9.6dBi-12.8dBi; the S11 is basically below 20dB. The radiation pattern of the feed should have good axisymmetry performance, the side lobes and back lobes should be as small as possible, the main lobe should have a low illumination level at the edge of the array, and the radiation level outside the illumination angle should be low; secondly, within the illumination angle range, the feed should have a clear phase center and its phase fluctuation should be small; as a feed, its reflection coefficient bandwidth should be greater than the working bandwidth of the lens unit, and the beamwidth should remain stable within the working frequency band.

[0055] Figure 8The normalized radiation pattern of the deployable flexible Luneburg lens antenna described in this embodiment is shown in the simulation test. (a) represents the 12 GHz xoz plane; (b) the 12 GHz yoz plane; (c) the 22 GHz xoz plane; (d) the 22 GHz yoz plane; (e) the 26.5 GHz xoz plane; and (f) the 26.5 GHz yoz plane. As can be seen from the figure, the antenna structure described in this embodiment exhibits good radiation performance within the operating frequency band, with a clear main lobe direction, significant sidelobe suppression, and good directivity. Furthermore, the simulation results are highly consistent with the measured results in terms of main lobe direction, beamwidth, and overall beam shape, verifying the feasibility and effectiveness of the antenna structure design described in this embodiment. This demonstrates the stable electromagnetic characteristics of the structure at high frequencies, as well as its good manufacturability and practicality.

[0056] Figure 9 This is a gain curve from the simulation test of the deployable flexible Luneburg lens antenna described in this embodiment, where (a) is the Ku band (12GHz–18GHz) and (b) is the K band (18GHz–26.5GHz). Figure 9 As can be seen, in the Ku-band (12GHz–18GHz) and K-band (18GHz–26.5GHz) ranges, the antenna structure described in this embodiment, after loading the spherical Luneburg lens, shows a significant increase in gain compared to using only the horn antenna. The gain ranges obtained from testing and simulation are 12.81–17.36 dBi and 13.3–17.57 dBi, respectively, indicating that the lens structure has a good focusing effect on the beam and effectively improves the radiation efficiency and directivity performance of the system.

[0057] This embodiment establishes an automated toolchain of HFSS–MATLAB–API, providing a parametric modeling and mapping process:

[0058] a) Generate TO element parameters (period p, wall thickness t, cavity height sa, aperture / hole type and array pitch) using MATLAB, and then use scripts to call HFSS to build a periodic element model;

[0059] b) Automatically apply two pairs of master-slave boundaries and dual Floquet ports to complete frequency and incident angle scanning of 12–26.5 GHz and extract S-parameters in batches;

[0060] c) MATLAB performs equivalent parameter inversion on the results to obtain the equivalent dielectric constant distribution;

[0061] d) The target Luneburg radial distribution εr(r) = 2 - (r / R) 2 Discretize to an eight-layer spherical shell and voxel lattice, automatically match Type A / Type B and sa, and generate Luneburg lens model;

[0062] e) Export STL files with one click, link the slicing software to set the printing direction and layer thickness to ensure channel penetration and surface quality; after printing, perform cleaning, curing and dimensional compensation.

[0063] Based on this process, lenses can be 3D printed in one step without internal support, resulting in simple assembly, high repeatability, and significantly improved efficiency and consistency from design to manufacturing. Specifically:

[0064] (1) Excellent electromagnetic properties

[0065] By optimizing the geometric parameters of the nested cavity and aperture array, this invention achieves continuously adjustable equivalent dielectric constant, avoids multi-material splicing, and ensures dielectric continuity within the lens. Simulation and experimental results show that in the 12–26.5 GHz frequency band, the antenna gain ranges from 12.81 to 17.57 dBi. Compared with a simple horn feed, the gain is significantly improved while the radiation pattern remains stable, meeting the requirements for multi-beam scanning and wide-angle coverage.

[0066] (2) Manufacturing-friendly and engineering-adaptable

[0067] The overall structure is made of black flexible elastic resin, which supports standard 3D printing process. It has low material cost, short processing cycle, high product consistency, and can be mass-produced quickly, significantly reducing the difficulty of engineering implementation.

[0068] (3) Comprehensive application value

[0069] This invention combines flexibility, deployability, and high-performance electromagnetic properties, overcoming the limitations of traditional rigid Luneburg lenses, which are large in size, heavy in weight, and non-foldable. It is suitable for various application scenarios such as miniaturized high-frequency communication, radar imaging, and unmanned systems, and has high potential for promotion and application.

[0070] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A deployable flexible Luneburg lens antenna based on a Kirigami structure, characterized in that, It includes a feed source and a spherical Luneburg lens structure; the feed source is located on one side of the spherical Luneburg lens structure, directly opposite the geometric center of the spherical Luneburg lens structure; The spherical Luneburg lens structure is an eight-layer spherical structure. In each layer, the distance between each lens unit and the center of the sphere is the same, and the adjacent layers are closely fitted together. The spherical Luneburg lens structure is composed of two types of lens units, and the dielectric constant distribution ranges of the two types of lens units are different. The first layer is a single lens unit located at the center of the sphere. Based on the formula for calculating the dielectric constant distribution of lens units in a spherical Luneburg lens structure, the dielectric constant values ​​of each lens unit in the eight-layer spherical structure are calculated. The lens units whose dielectric constant distribution range can cover the dielectric constant value are arranged at the position to finally form a complete spherical Luneburg lens structure.

2. The deployable flexible Luneburg lens antenna based on the Kirigami structure according to claim 1, characterized in that, The first type of lens unit is a nested truncated octahedral-hexagonal aperture array; the main body of the first type of lens unit is a truncated octahedral frame, with a coaxial truncated octahedral cavity nested inside; on the 8 regular hexagonal faces of the truncated octahedral frame, regular hexagonal columnar holes are symmetrically excavated along the surface normal direction, and the regular hexagonal columnar holes corresponding to two parallel hexagonal faces are in a through state; all hexagonal columnar holes are of the same size; The second type of lens unit is a nested truncated octahedron-hybrid aperture array; based on the first type of lens unit, the second type of lens unit further symmetrically removes cubic columnar holes along the surface normal direction on the 6 square faces of the truncated octahedron frame; the side length of the square of the cubic columnar hole is the same as the side length of the hexagon of the regular hexagonal columnar hole; the cubic columnar holes corresponding to the two parallel square faces are in a through state.

3. The deployable flexible Luneburg lens antenna based on the Kirigami structure according to claim 1, characterized in that, For the two types of lens units, the height of the coaxial truncated octahedral cavities nested inside can be varied, thereby adjusting the dielectric constant of the lens unit; for the second type of lens unit, the height of the built-in cavity varies from 0.9mm to 1.15mm; for the first type of lens unit, the height of the built-in cavity varies from 0.25mm to 1mm.

4. The deployable flexible Luneburg lens antenna based on the Kirigami structure according to claim 1, characterized in that, The lens unit is made of black or transparent elastic resin, and the dielectric material used has a dielectric constant of 2.94 and a loss tangent of 0.

06.

5. The deployable flexible Luneburg lens antenna based on the Kirigami structure according to claim 1, characterized in that, The feed source is a Ku-band horn antenna or a K-band horn antenna.

6. The deployable flexible Luneburg lens antenna based on the Kirigami structure according to claim 1, characterized in that, The dielectric constant distribution ε of the lens unit r The formula for calculating (r) is: Where R is the radius of the spherical Luneburg lens structure, and r is the distance to the center of the spherical Luneburg lens structure.

7. The deployable flexible Luneburg lens antenna based on the Kirigami structure according to claim 1, characterized in that, The diameter of the spherical Luneburg lens structure is 45mm.

8. The deployable flexible Luneburg lens antenna based on the Kirigami structure according to claim 1, characterized in that, The feed source is made of aluminum alloy.

9. The deployable flexible Luneburg lens antenna based on the Kirigami structure according to claim 1, characterized in that, The focal length of the deployable flexible Luneburg lens antenna is 2mm.

10. The deployable flexible Luneburg lens antenna based on the Kirigami structure according to claim 1, characterized in that, The spherical Luneburg lens structure was fabricated using 3D printing.

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