A multilayer nested metal mesh metamaterial unit, a preparation method thereof and an antenna array

Abstract

The application relates to the technical field of metamaterials and lens antennas, and discloses a multilayer nested metal mesh metamaterial unit, a preparation method thereof and an antenna array.The metamaterial unit comprises an outer spherical framework and an inner spherical framework; the outer spherical framework and the inner spherical framework are respectively surrounded by three mutually orthogonal metal wire rings to form a spherical hollow network structure; the outer spherical framework and the inner spherical framework are concentrically nested, the spherical centers coincide and are spatially parallel, the inner spherical framework is rotated by a preset angle relative to the outer spherical framework in the spatial orientation, and the two are not in physical contact, the layers are filled with air, and a double-layer nested hollow configuration without medium support is formed.The application introduces a double-resonance mode through interlayer electromagnetic coupling between the double-layer frameworks, widens the flat regulation range of the equivalent dielectric constant in the working frequency band while reducing the weight by about 93% of the same solid metal spherical shell of the same outer shape size, and maintains excellent electromagnetic isotropy.

Description

Technical Field

[0001] This invention relates to the field of metamaterials and lens antenna technology, and more specifically, to a multilayer nested metal mesh metamaterial unit, its fabrication method, and an antenna array thereof. Background Technology

[0002] With the continuous evolution of satellite communication, radar detection, and 5G mobile communication systems, high-gain, wide-bandwidth, and low-profile lens antennas have become an important technological path to meet the requirements of high directivity and high-capacity transmission. In lens antenna design, the introduction of metamaterial elements makes it possible to manipulate the equivalent dielectric constant through artificial structures, thereby achieving flexible control over the electromagnetic wavefront. Typical metamaterial lens antennas use periodically arranged metal-dielectric composite elements or all-dielectric elements to construct a gradient refractive index distribution. Common configurations include printed metal resonator stacked structures, dielectric perforated arrays, and three-dimensional metal mesh structures. However, as application platforms extend to airborne, spaceborne, and portable terminals, the demand for lightweight antenna systems is becoming increasingly prominent. Traditional metamaterial elements often employ high-density metal structures or high-dielectric-constant dielectric materials to achieve the target equivalent electromagnetic parameters, resulting in a significant increase in element weight, which has become a key bottleneck restricting the application of lens antennas on load-sensitive platforms.

[0003] Regarding the lightweighting of metamaterial units, existing technologies mainly focus on three directions: dielectric material replacement, internal hole densification, and metal structure hollowing. In terms of dielectric material replacement, patent CN114976665B proposes a lightweight Luneburg lens antenna based on a multilayer dielectric substrate stack. It utilizes alternating layers of low-density foam dielectric layers and printed metal patterns to construct a gradient dielectric constant distribution, achieving overall weight reduction through the low-density characteristics of the foam dielectric. This approach replaces solid dielectric spheres with a stacked structure, reducing antenna weight to some extent. However, the multilayer stacked structure relies on precise interlayer alignment and bonding processes; accumulated manufacturing tolerances can easily lead to deviations in equivalent electromagnetic parameters from design values. Simultaneously, impedance discontinuities exist at the interface between the metal pattern layer and the foam dielectric layer, introducing additional reflection losses and affecting the aperture efficiency of the lens antenna. More importantly, this approach is essentially still a continuous dielectric stack configuration; the inherent volume and mass of the dielectric substrate are difficult to effectively eliminate, failing to achieve orders-of-magnitude weight reduction.

[0004] Regarding internal pore formation for density reduction, patent CN115882234A discloses a lightweight gradient dielectric lens and its fabrication method. This method involves three-dimensional perforation or chemical foaming of the dielectric matrix to introduce ordered or random air pores within the medium. The weighted average effect of the equivalent dielectric constants of air and the dielectric matrix is ​​used to reduce the equivalent density and equivalent dielectric constant of the unit cell. The advantage of this approach lies in the flexible adjustment of the local equivalent dielectric constant through the duty cycle of the pores, while simultaneously achieving weight reduction by replacing solid dielectric material with air pores. However, the internal pore formation process demands extremely stringent process control over the uniformity of pore distribution and size consistency. Taking the foaming process as an example, the foaming nucleation and growth processes are influenced by multiple factors such as temperature and pressure fields, resulting in a significant randomness in the final pore distribution. This random pore distribution disrupts the electromagnetic field symmetry within the metamaterial unit, leading to uncontrollable deviations in the equivalent dielectric constant under different polarization directions and incident angles, i.e., introducing electromagnetic anisotropy. For gradient refractive index lens antennas that rely on precise phase control, this anisotropy will directly lead to wavefront phase error and pattern distortion, severely degrading the antenna's radiation performance.

[0005] Regarding perforated and hollowed-out metal structures, patent US11489255B2 discloses a three-dimensional metal wire mesh unit for metamaterial lenses. This unit consists of a spherical or near-spherical skeleton network structure made of metal wires, forming an equivalent electromagnetic resonant response through the spatial distribution of the metal wires. This scheme replaces continuous metal shells or solid metal blocks with skeleton networks, effectively reducing the metal fill rate of the unit by utilizing the air gaps between the wire meshes, thus achieving a significant reduction in weight. Simultaneously, the three-dimensional wire mesh structure has high geometric symmetry in space; the projection distribution of the metal wires is basically consistent when incident from different angles, which is beneficial for maintaining electromagnetic isotropy. However, this scheme uses a single-layer skeleton structure, which can only excite one main resonant mode. Its equivalent dielectric constant dispersion characteristic with frequency is relatively steep, and the range and flatness of the equivalent dielectric constant within the operating frequency band are limited by the single resonant mode. When a wider frequency band needs to be covered, a single-layer skeleton cannot meet the requirement of equivalent parameter consistency across the entire frequency band. Furthermore, single-layer skeletons are prone to mode degeneracy or local field concentration under oblique incidence conditions, leading to deviations of the equivalent electromagnetic parameters from the design values ​​and affecting the wide-angle scanning performance of the lens antenna. In contrast, this invention employs a nested double-layer skeleton configuration, introducing dual resonant modes through interlayer electromagnetic coupling, resulting in a flatter frequency response for the equivalent dielectric constant within the operating frequency band. Simultaneously, the double-layer spherical symmetric network topology further enhances electromagnetic isotropy under multi-angle and multi-polarization conditions.

[0006] Based on the aforementioned single-layer metal mesh metamaterial unit structure, patent CN110380230A proposes a spherical multilayer nested metamaterial unit. This unit achieves multi-resonant mode collaboration by depositing metal ring resonant structures of different radii layer by layer on a spherical dielectric substrate and utilizing interlayer coupling between the multilayer metal rings. This scheme broadens the control dimension of equivalent electromagnetic parameters by introducing a multilayer structure, showing certain advantages in bandwidth expansion. However, this scheme uses a dielectric substrate as the supporting carrier for each layer of metal rings. The continuous solid portion of the dielectric substrate occupies a large proportion of the unit volume, resulting in a still relatively high equivalent density and self-weight. Simultaneously, the dielectric constant and loss tangent of the dielectric substrate itself participate in the synthesis of the equivalent electromagnetic parameters of the entire unit, introducing additional dielectric losses. This makes the scheme insufficient in achieving both lightweight and low-loss balance. From the perspective of structural weight reduction, this scheme fails to simultaneously remove redundant material from the dielectric substrate when introducing the multilayer coupling mechanism. Its weight reduction effect is essentially still limited by the inherent volume and mass of the dielectric carrier, failing to achieve sufficient lightweighting at the structural level.

[0007] In summary, existing technologies have not yet formed an effective solution that balances the three core indicators of lightweight metamaterial units: maintaining the equivalent dielectric constant and electromagnetic isotropy. Dielectric material replacement and internal perforation methods are prone to disrupting electromagnetic symmetry or introducing additional losses during weight reduction; single-layer metal skeleton solutions are limited by the single resonant mode and insufficient consistency of equivalent parameters within the frequency band; multi-layer dielectric support solutions are constrained by the redundant mass of the dielectric matrix, limiting the upper limit of weight reduction. Therefore, a new structured weight reduction scheme is urgently needed that, while introducing multi-layer resonant coupling to expand electromagnetic control capabilities, achieves orders-of-magnitude weight reduction with a dielectric-free hollow skeleton structure, and relies on a highly geometrically symmetrical spherical network topology to maintain the consistency of the equivalent dielectric constant and electromagnetic isotropy. Summary of the Invention

[0008] In view of this, the present invention proposes a multi-layer nested metal mesh metamaterial unit, its preparation method and antenna array, to solve the problems existing in the prior art.

[0009] To achieve the above objectives, the present invention proposes the following technical solution: A multi-layer nested metal mesh metamaterial unit includes an inner spherical skeleton and an outer spherical skeleton. The centers of the inner and outer spherical skeletons coincide and are spatially parallel. The inner spherical skeleton rotates at a predetermined angle relative to the outer spherical skeleton in spatial orientation. Each skeleton is formed by three mutually orthogonal metal wire rings enclosing a spherical hollow network structure. The three rings are arranged along the X-axis, Y-axis, and Z-axis respectively and converge at the center of the sphere. The inner and outer spherical skeletons are structurally independent and have no physical contact. The interlayer is filled with air, forming a double-layer nested hollow structure without dielectric support. The inner and outer spherical skeletons generate a dual-resonance mode through electromagnetic coupling in the free space between the layers.

[0010] Furthermore, the outer spherical skeleton has a spherical radius of 6.5 mm and an inner diameter of 6.4 mm, the inner spherical skeleton has a spherical radius of 6.0 mm and an inner diameter of 5.9 mm, the ring thickness of both skeletons is 0.1 mm, and the interlayer spacing is 0.4 mm.

[0011] Furthermore, the outer spherical skeleton has a spherical radius of 5.5 mm to 7.5 mm, the inner spherical skeleton has a spherical radius of 5.0 mm to 6.5 mm, and the inner spherical skeleton has a smaller spherical radius than the outer spherical skeleton. The interlayer spacing is not less than 0.3 mm, and the ring thickness of the two skeletons is within 0.08 mm to 0.3 mm.

[0012] Furthermore, the metal wire ring is made of an aluminum-silicon-magnesium alloy, a titanium alloy, or a nickel-based alloy.

[0013] This invention proposes a method for preparing the aforementioned multi-layer nested metal mesh metamaterial unit. It adopts a metal selective laser melting 3D printing process for integrated molding. The overall structure of the outer and inner spherical skeletons is constructed in a digital model. The spherical hollow skeleton is directly formed by utilizing the temporary support of unmelted metal powder. Through process optimization, low-angle unsupported printing is achieved, and the manufacturing accuracy reaches ±0.02 mm. After printing, residual powder inside is removed by powder cleaning or vibration physical methods to obtain a complete double-layer nested hollow metal mesh skeleton unit.

[0014] Furthermore, the selective laser melting 3D printing process uses aluminum alloy powder, titanium alloy powder, or nickel-based alloy powder as raw materials.

[0015] Furthermore, the preparation method employs a combination of metal 3D printing and surface metallization processes. First, a polymer skeleton template is fabricated using high-precision photopolymerization 3D printing. Then, a conductive seed layer is deposited on the polymer surface using chemical plating. Subsequently, the metal layer is thickened to the designed thickness using electroforming. Finally, the internal polymer template is removed using high temperature or solvent to obtain a hollow metal mesh skeleton structure.

[0016] The present invention further proposes an antenna array comprising, as described above, a multi-layer nested metal mesh metamaterial unit. The multiple metamaterial units are arranged periodically in a two-dimensional plane or in a three-dimensional spatial curved surface to form a unit array of a gradient refractive index metamaterial lens. By independently adjusting the ratio of the inner and outer spherical radii of each metamaterial unit, the required spatial distribution of the equivalent dielectric constant is achieved on the lens aperture surface.

[0017] Furthermore, there is no physical connection between the metamaterial units in the unit array, and they are each independently installed on a low dielectric constant foam support frame.

[0018] Furthermore, the cell period of the cell array is 15 mm, and the cell spacing is selected from half a wavelength to one wavelength according to the working wavelength.

[0019] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) Double-layer nested, medium-free support structure with significant and controllable weight reduction. This invention proposes a medium-free metamaterial structure with concentric nested inner and outer spherical skeletons and air filling between the layers, eliminating the redundant mass of the continuous medium matrix in traditional multi-layer medium support schemes from the structural root. Each skeleton consists of a spherical hollow network composed of three mutually orthogonal metal wire rings with an extremely low metal filling rate, forming a second dimension of weight reduction inside the skeleton. When the outer spherical radius is 6.5 mm, the inner spherical radius is 6.0 mm, and the ring thickness is 0.1 mm, the unit weight within a 15 mm periodic unit is reduced by approximately 93% compared to a solid metal spherical shell of the same size, a weight reduction far exceeding the weight reduction levels of existing medium replacement or internal perforation schemes. By adjusting geometric parameters such as the inner and outer spherical radii and ring thickness, the weight reduction ratio can be flexibly controlled within a wide range to adapt to the weight constraints of different load platforms.

[0020] (2) The dual resonant modes work together, significantly improving the frequency flatness of the equivalent dielectric constant. This invention utilizes the resonant modes excited by the outer and inner skeletons respectively, and generates mode splitting and bandwidth broadening effects through electromagnetic coupling in the free space between the two layers, so that the equivalent dielectric constant of the metamaterial unit obtains a relatively flat frequency response range between the two resonant frequencies. Compared with the steep dispersion curve of a single-layer skeleton that relies on only a single resonant mode, the double-layer nested configuration effectively alleviates the problem of the equivalent dielectric constant deviating from the design value of the center frequency at the edge frequencies in broadband applications. Under normal incident conditions, the double-layer structure of this invention increases by 5.41%, which is about 0.62 percentage points narrower than the single-layer nested structure (6.03%), approaching the spherical shell (5.04%); when rotated 45° around the X-axis, Under a 90° oblique incidence condition, the double-layer structure increases the efficiency by only 4.70%, which is better than the 5.03% of the spherical shell, providing a more stable basis for the unit electromagnetic parameters of the lens antenna for broadband phase modulation.

[0021] (3) Excellent electromagnetic isotropy is maintained in multi-angle and multi-polarization, and the equivalent dielectric constant is highly consistent under various test conditions. Each layer of the skeleton in this invention consists of three mutually orthogonal circular rings forming a spherical symmetric network. The centers of the inner and outer layers coincide and are spatially parallel, and the metamaterial unit as a whole retains the spherical symmetric geometric features. After comprehensive testing of the equivalent dielectric constant in the TE and TM dual polarization directions and multiple incident angles, the difference in the equivalent dielectric constant of the double-layer nested unit in this invention in the two orthogonal polarization directions is less than 0.2%. The equivalent dielectric constant curves under each polarization and angle are highly coincident and have good parallelism. The isotropy index is comparable to that of a solid metal spherical shell. From the configuration root, the electromagnetic isotropy of the metamaterial unit under multi-angle and multi-polarization conditions is guaranteed, effectively solving the electromagnetic anisotropy problem introduced by the randomness or asymmetry of the hole distribution in the existing perforation or foaming scheme.

[0022] (4) Integrated, media-free support structure with simple and reliable manufacturing process. The double-layer nested metal mesh metamaterial skeleton of this invention is an integrated structure with no media support between the inner and outer skeleton layers. It eliminates the need for complex processes such as multi-layer media bonding, interlayer alignment, or foaming temperature control, and can be formed in one step through metal 3D printing. The manufacturing process is free from random factors, has good geometric consistency, avoids the introduction of interlayer alignment errors and media loss, and is suitable for various manufacturing needs from prototype verification to mass production.

[0023] (5) Flexible and adjustable geometric parameters to suit various application needs. By adjusting key geometric parameters such as the radius of the outer sphere, the radius of the inner sphere, and the thickness of the ring, this invention can independently control the position and coupling strength of the two resonant frequencies of the metamaterial unit, flexibly balancing the weight reduction ratio and the frequency flatness of the equivalent dielectric constant. The greater the difference between the inner and outer radii, the weaker the interlayer coupling, the more significant the separation of the dual resonant modes, and the more obvious the bandwidth broadening effect; the smaller the ring thickness, the higher the weight reduction ratio; when higher structural strength is required, the ring thickness can be appropriately increased, making it suitable for platforms that need to bear large mechanical loads.

[0024] (6) Strong array scalability, adaptable to various lens configurations. Multiple of the above-mentioned double-layer nested metal mesh metamaterial units can be arranged in a two-dimensional planar periodic arrangement or a three-dimensional spatial curved surface arrangement to form a unit array of gradient refractive index metamaterial lenses. By independently adjusting the ratio of the inner and outer spherical radii of each metamaterial unit, the required spatial distribution of the equivalent dielectric constant on the lens aperture surface can be achieved, which can be used to construct high-gain, low-sidelobe lens antennas, and has good application scalability and cross-platform adaptability. Attached Figure Description

[0025] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. In the drawings: Figure 1 is a schematic diagram of the structure of the double-layer nested metal mesh metamaterial unit of the present invention. Among them, Figure 1(a) is a three-dimensional schematic diagram of the overall structure of the metamaterial unit of the present invention from a 45° oblique top view; Figure 1(b) is a front view in the X-axis direction; Figure 1(c) is a front view in the Y-axis direction; and Figure 1(d) is a top view in the Z-axis direction.

[0026] Figure 2 is a schematic diagram of the comparative structure used in this invention. In particular, Figure 2(a) is a schematic diagram of the structure of a single-layer nested metal mesh metamaterial unit; Figure 2(b) is a schematic diagram of the cross-sectional structure of a solid metal spherical shell.

[0027] Figure 3 shows the equivalent dielectric constant curves of the double-layer nested metal mesh metamaterial unit of the present invention under multiple angle conditions in the 0.5–3.5 GHz frequency band. In the figure, the X-axis represents frequency (GHz), and the Y-axis represents the equivalent dielectric constant. Figure 3(a) shows the equivalent dielectric constant when the unit as a whole is not rotated. A family of equivalent dielectric constant frequency response curves at four incident angles of 0°, 30°, 45°, and 90°; Figure 3(b) shows the frequency response curves of the unit of the present invention after rotating the entire unit around the X-axis by 45°. A family of equivalent dielectric constant frequency response curves at four incident angles of 0°, 30°, 45°, and 90°; Figure 3(c) shows the frequency response curves of the unit of the present invention after rotating the entire unit around the Z-axis by 45°. Frequency response curves of equivalent dielectric constant at four incident angles of 0°, 30°, 45°, and 90°.

[0028] Figure 4 shows the equivalent dielectric constant curves of a single-layer nested metal mesh metamaterial unit under multiple angle conditions within the 0.5–3.5 GHz frequency band. In the figure, the X-axis represents frequency (GHz), and the Y-axis represents the equivalent dielectric constant. Figure 4(a) shows the equivalent dielectric constant when the single-layer unit is not rotated. A family of equivalent dielectric constant frequency response curves at four incident angles of 0°, 30°, 45°, and 90°; Figure 4(b) shows the frequency response curves of the single-layer unit after rotating it 45° around the X-axis. A family of equivalent dielectric constant frequency response curves at four incident angles of 0°, 30°, 45°, and 90°; Figure 4(c) shows the frequency response curves of the single-layer unit after rotating it 45° around the Z-axis. =A family of frequency response curves of equivalent dielectric constant at four incident angles: 0°, 30°, 45°, and 90°.

[0029] Figure 5 The graph shows the equivalent dielectric constant of a solid metal spherical shell unit with the same outer diameter in the 0.5–3.5 GHz frequency band. The X-axis represents the frequency (GHz) and the Y-axis represents the equivalent dielectric constant.

[0030] Figure 6 Solid metal spherical shells, single-layer nested metal mesh metamaterial units, and double-layer nested metal mesh metamaterial units rotated 45° around the X-axis, The graph shows the comparison of equivalent dielectric constants under a 90° incident angle. The X-axis represents the frequency (GHz), and the Y-axis represents the equivalent dielectric constant. Detailed Implementation

[0031] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the disclosure to those skilled in the art. It should be noted that, unless otherwise specified, the embodiments and features described herein can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0032] This embodiment proposes a multi-layered nested metal mesh metamaterial unit, which consists of two spherical skeletons with overlapping centers and parallel spatial dimensions. Each skeleton layer is formed by three mutually orthogonal metal wire rings enclosing a spherical hollow network structure. The outer skeleton has a spherical radius of 6.5 mm (inner diameter 6.4 mm), and the inner skeleton has a spherical radius of 6.0 mm (inner diameter 5.9 mm). The thickness of the rings in both skeletons is 0.1 mm. The inner spherical skeleton rotates at a predetermined angle relative to the outer spherical skeleton in spatial orientation, causing the inner and outer rings to be arranged in an alternating pattern in space. The two skeletons are structurally independent and have no physical contact, with air filling between the layers. The interlayer spacing is 0.4 mm, forming a double-layered nested hollow structure without dielectric support. In each spherical skeleton layer, the three orthogonal rings are arranged along the X-axis, Y-axis, and Z-axis directions, respectively, and converge at the center of the sphere, forming a highly symmetrical spherical hollow network electromagnetic response structure in space. Within a 15 mm periodic cell, this structure generates a dual resonant mode through electromagnetic coupling between the inner and outer skeleton layers. This significantly reduces cell weight, expands the flat tuning range of the equivalent dielectric constant within the operating frequency band, and maintains excellent electromagnetic isotropy.

[0033] The manufacturing methods for the double-layer nested metal mesh metamaterial unit of the present invention include, but are not limited to, the following: I. Integrated molding using Selective Laser Melting (SLM) 3D printing technology. SLM technology is one of the most widely used metal additive manufacturing technologies. Following the discrete-stacking principle, it uses a high-energy laser beam to melt metal powder layer by layer, directly obtaining solid parts with complex internal structures. This process uses aluminum alloy powder, titanium alloy powder, or nickel-based alloy powder as raw materials to construct an integrated structure of an outer and inner spherical skeleton in a digital model. The SLM powder bed process naturally possesses self-supporting characteristics: unmelted metal powder naturally surrounds and supports the part being formed, allowing internal cavities and complex hollow structures to be directly formed without additional support structures. For the spherical hollow skeleton in this invention, with a ring thickness of only 0.1 mm and a cantilever span of less than 1 mm, the temporary support of the powder bed is sufficient to ensure the structural integrity of the suspended ring during the printing process.

[0034] Traditionally, it is believed that no supporting structure is needed when the angle between the suspended structure and the forming surface is greater than 45° for the forming of overhanging structures. Currently, laser selective melting forming of low-angle unsupported structures has become an important research direction in additive manufacturing. Studies have shown that unsupported printing of overhanging structures with angles below 30° can be achieved through process optimization. The spherical skeleton of this invention consists of three orthogonal rings arranged along the spherical arc, with a reasonable distribution of overhang angles, naturally satisfying the geometric conditions for unsupported forming. Even if there are near-horizontal overhanging areas, their span is much smaller than the horizontal overhang limit achievable by current unsupported printing technology. After printing, residual powder is removed internally by powder cleaning or vibration, resulting in a complete double-layer nested hollow metal mesh skeleton unit. This process is applicable to aluminum-silicon-magnesium alloys, titanium alloys, nickel-based alloys, and other metal materials, with a manufacturing accuracy of ±0.02 mm, meeting the forming requirements of a ring thickness of 0.1 mm, without the need for complex post-processing procedures such as multi-layer media bonding or interlayer alignment.

[0035] II. A combined process of metal 3D printing and surface metallization is employed. First, a polymer skeleton template is fabricated using high-precision photopolymerization 3D printing. Then, a conductive seed layer is deposited on the polymer surface using chemical plating. Subsequently, the metal layer is thickened to the designed thickness using electroforming. Finally, the internal polymer template is removed using high temperature or solvent treatment to obtain a hollow metal mesh skeleton structure. This approach balances the precision of complex geometric forming with the density of the metal layer, making it suitable for prototype verification and small-batch customized manufacturing needs.

[0036] As shown in Figure 1(a), the metamaterial unit of this invention is composed of an outer spherical skeleton and an inner spherical skeleton nested concentrically. The outer spherical radius is 6.5 mm, and the inner spherical radius is 6.0 mm. The thickness of both rings is 0.1 mm. The centers of the two skeletons coincide and are parallel in space. The inner spherical skeleton rotates at a predetermined angle relative to the outer spherical skeleton in spatial orientation, causing the inner and outer rings to be arranged in an alternating pattern in space. Each skeleton is formed by three mutually orthogonal metal wire rings enclosing a spherical hollow network structure. The three rings are arranged along the X-axis, Y-axis, and Z-axis directions, respectively, and converge at the center of the sphere. The two skeletons are structurally independent and have no physical contact with each other. The space between the layers is filled with air, forming a double-layered nested hollow structure without any supporting medium.

[0037] As can be seen from the three orthogonal perspectives in Figures 1(b), 1(c), and 1(d), the three rings of each skeleton layer are spatially highly symmetrically distributed. The three orthogonal rings are arranged along the X, Y, and Z axes, respectively, and converge at the center of the sphere to form a self-stabilizing spherical spatial frame structure. The three views collectively demonstrate that the double-layer nested layout based on three mutually orthogonal rings ensures the complete preservation of the structural symmetry of the metamaterial unit in all directions, intuitively showcasing the design features of the medium-free, double-layer nested hollow structure.

[0038] As shown in Figure 2(a), the single-layer nested metal mesh metamaterial unit is composed of a single-layer spherical skeleton with a radius of 6.5 mm (inner diameter of 6.4 mm) and a ring thickness of 0.1 mm. This skeleton is formed by three mutually orthogonal metal wire rings enclosing a spherical hollow network structure. The three rings are arranged along the X, Y, and Z axes respectively, converging at the center of the sphere to form a spherical hollow network consistent with the geometric features of each layer of the skeleton in the double-layer structure of this invention. This single-layer structure serves as a comparative object with the double-layer nested structure of this invention, used to verify the improvement effect of the double-layer nested configuration on the frequency flatness of the equivalent dielectric constant and electromagnetic isotropy after introducing interlayer electromagnetic coupling and dual resonant modes.

[0039] As shown in Figure 2(b), the solid metal spherical shell has an outer diameter of 6.5 mm, an inner diameter of 6.4 mm, and a wall thickness of 0.1 mm. It is constructed using the same metal material with the same outer diameter and wall thickness as the double-layer nested metal mesh metamaterial unit of this invention. This solid spherical shell possesses complete rotational symmetry, and its equivalent dielectric constant versus frequency curve serves as an ideal benchmark for quantitatively evaluating the degree to which the double-layer nested metal mesh metamaterial unit of this invention approximates and surpasses the electromagnetic properties of the solid spherical shell under the premise of extreme lightweight design (weighing only about 6.7% of the spherical shell).

[0040] The outer spherical radius of the double-nested unit is R1=6.5 mm, the inner spherical radius is R2=6.0 mm, and the thickness of both rings is t=0.1 mm. The inner skeleton rotates at a preset angle relative to the outer skeleton in spatial orientation.

[0041] This invention addresses the technical challenges in lightweight metamaterial unit design, such as the limited flatness of the equivalent dielectric constant within the frequency band due to the single resonant mode of single-layer metal mesh metamaterial units, and the weight reduction limit of multilayer dielectric support schemes due to the redundant matrix mass. It proposes a double-layer nested metal mesh metamaterial unit. This unit consists of two spherical skeletons with overlapping centers and parallel spatial dimensions. Each skeleton layer is formed by three mutually orthogonal metal wire rings enclosing a spherical hollow network structure. The inner spherical skeleton rotates at a predetermined angle relative to the outer spherical skeleton in spatial orientation. A dual resonant mode is introduced through interlayer electromagnetic coupling between the two skeletons. This reduces the weight by approximately 93% compared to a solid metal spherical shell of the same size, while widening the flatness control range of the equivalent dielectric constant within the operating frequency band and maintaining excellent electromagnetic isotropy.

[0042] The double-layer nested metal mesh metamaterial unit proposed in this invention is a dedicated metamaterial configuration designed to meet the dual requirements of high performance and extreme lightweight for lens antennas in load-sensitive platforms such as airborne and spaceborne systems. Its core configuration is a dielectric-free double-layer spherical hollow skeleton: the outer skeleton has a spherical radius of 6.5 mm (inner diameter 6.4 mm), and the inner skeleton has a spherical radius of 6.0 mm (inner diameter 5.9 mm). The thickness of the rings in both skeletons is 0.1 mm, and the centers of the spheres completely coincide. Furthermore, the equatorial and meridian planes of the two skeletons remain spatially parallel, forming a strictly concentric nested layout. The inner skeleton rotates at a predetermined angle relative to the outer skeleton in spatial orientation. Each spherical skeleton consists of three mutually orthogonal metal wire rings, arranged along the X, Y, and Z axes respectively, converging at the center of the sphere to form a highly symmetrical spherical hollow network structure in space. The two skeletons are structurally independent and have no physical contact, achieving electromagnetic coupling only through the free space between them, with an interlayer spacing of 0.4 mm. This double-nested configuration without dielectric support completely replaces the continuous dielectric matrix in traditional multilayer schemes with the air gap between the two skeletons, eliminating redundant mass of the dielectric matrix at the structural source and achieving a significant weight reduction in the first dimension. Simultaneously, each skeleton layer itself consists of a perforated network of fine rings with extremely low metal infill, creating a second dimension of weight reduction within the skeleton itself. When compared with the same metal material, within a 15 mm periodic unit, the total volume of this unit is only about 6.7% of the volume of a solid spherical shell with the same outer diameter, resulting in a weight reduction of approximately 93%.

[0043] At the level of electromagnetic performance regulation, this invention achieves independent adjustment and coordinated control of dual resonant modes by precisely designing the spherical radii of the inner and outer skeletons. Each of the outer and inner skeletons excites a resonant mode, and the two resonant modes generate mode splitting and bandwidth broadening effects through electromagnetic coupling in the free space between the layers. This results in a relatively flat frequency response range for the unit's equivalent dielectric constant between the two resonant frequencies. Compared to the steep dispersion curve of a single-layer skeleton that relies solely on a single resonant mode, the double-layer nested configuration effectively expands the flat control range of the equivalent dielectric constant within the frequency band by utilizing the combined effect of the dual resonant modes, alleviating the problem of equivalent parameter deviation at edge frequencies in broadband applications. Simultaneously, since each skeleton layer consists of a spherically symmetrical network composed of three mutually orthogonal rings, with the centers of the two layers coinciding and spatially parallel, the unit as a whole retains spherically symmetrical geometric characteristics. Under different polarization directions and incident angles, the projection distribution of the metal network perceived by the electromagnetic wave exhibits high consistency, thus ensuring the isotropic electromagnetic response of the unit from a structural perspective. Through comprehensive testing of the equivalent dielectric constant of the dual polarization directions of TE (transverse electric wave) and TM (transverse magnetic wave) and multiple incident angles, the equivalent dielectric constant curves of the unit of this invention under various test conditions are highly coincident and have good parallelism. The difference between the two orthogonal polarization directions is less than 0.2%, which shows excellent multi-angle multi-polarization electromagnetic isotropy. Its isotropy index is comparable to that of a solid metal spherical shell and is significantly better than that of a single-layer skeleton structure.

[0044] By adjusting geometric parameters such as the outer sphere radius, inner sphere radius, and ring thickness, the position and coupling strength of the two resonant frequencies can be independently controlled, thereby flexibly balancing the weight reduction ratio and equivalent dielectric constant frequency flatness of the unit: the greater the difference between the inner and outer radii, the weaker the interlayer coupling, the more significant the separation of the dual resonant modes, and the more obvious the bandwidth broadening effect; the smaller the ring thickness, the lower the metal filling rate, and the higher the weight reduction ratio. Under the typical parameters given in this invention (outer radius 6.5 mm, inner radius 6.0 mm, ring thickness 0.1 mm, 15 mm periodic unit), the unit weight is reduced by approximately 93% compared to a solid metal spherical shell of the same dimensions, while the equivalent dielectric constant approaches that of a solid spherical shell across the entire frequency band: under normal incidence conditions, the equivalent dielectric constant gradually increases from approximately 1.659 at 0.5 GHz to approximately 1.749 at 3.5 GHz, an increase of approximately 5.41%, which is approximately 0.62 percentage points narrower than that of a single-layer nested structure (6.03%), and very close to that of a spherical shell (5.04%); when rotated 45° around the X-axis, Under a 90° oblique incidence condition, the increase in frequency of the double-layer structure is only 4.70%, which is better than the 5.03% of the spherical shell and the 5.91% of the single layer, indicating that the double-layer structure also exhibits excellent frequency flatness under the special oblique incidence angle.

[0045] This invention also realizes a lens antenna array scheme based on this double-layer nested skeleton. Multiple of the aforementioned double-layer nested metal mesh metamaterial units can be arranged periodically in a two-dimensional plane or on a three-dimensional curved surface to form a unit array of a gradient refractive index lens. By independently adjusting the ratio of the inner and outer spherical radii of each unit, the required spatial distribution of the equivalent dielectric constant on the lens aperture surface can be achieved, enabling the construction of high-gain, low-sidelobe lens antennas. In terms of unit manufacturing, this double-layer nested metal mesh skeleton is an integrated, dielectric-free structure that can be formed in one step using selective laser melting metal 3D printing technology. It eliminates the need for multi-layer dielectric bonding or foaming temperature control processes, avoiding the introduction of interlayer alignment errors and dielectric losses. This provides a new technical approach for the large-scale production and multi-platform application of lightweight, high-performance lens antennas.

[0046] Figure 3 shows the equivalent dielectric constant curves of the double-layer nested metal mesh metamaterial unit of the present invention under multiple angle conditions in the 0.5–3.5 GHz frequency band. In the figure, the X-axis represents frequency (GHz), and the Y-axis represents the equivalent dielectric constant. As shown in Figure 3(a), under the condition of no overall rotation, the equivalent dielectric constant curves at the four incident angles highly overlap and exhibit good parallelism. Taking 0.5 GHz as an example, the average equivalent dielectric constant at the four angles is 1.659, with the maximum deviation between each angle being less than 0.003; taking 3.5 GHz as an example, the average equivalent dielectric constant at the four angles is 1.749, with the maximum deviation between each angle being less than 0.005. The full-band amplification at the four incident angles is as follows: =0° is 5.41%, =30° is 5.39%, =45° is 5.58%, =90° is 5.41%, with a range of only 0.19 percentage points. The difference in equivalent dielectric constant between different angles is extremely small, indicating that the double-layer structure of the present invention has excellent multi-angle electromagnetic consistency under normal incident conditions.

[0047] As shown in Figure 3(b), after rotating the entire system by 45° around the X-axis, the family of equivalent dielectric constant curves at the four incident angles also highly overlap, exhibiting consistent trends and closely clustered values. With normal incidence (… Taking 0° as an example, the equivalent dielectric constant at 0.5 GHz is 1.638, and at 3.5 GHz it is 1.715, with a full-band increase of 4.70%. The increase is 4.68% when incident at 30°. The increase was 4.73% at 45°. The increase is 4.70% at 90°, and the range of increase across the four angles is only 0.05 percentage points. The range of the endpoint values ​​at 3.5 GHz for each angle is less than 0.004, indicating that even under the harsh conditions of model rotation, the double-layer structure of this invention maintains good multi-angle electromagnetic isotropy.

[0048] As shown in Figure 3(c), after rotating the entire system by 45° around the Z-axis, the family of equivalent dielectric constant curves at the four incident angles also exhibit a high degree of overlap. With normal incidence (… Taking 0° as an example, the equivalent dielectric constant at 0.5 GHz is 1.628, and at 3.5 GHz it is 1.705, with a full-band increase of 4.69%. The increase range of the four incident angles is about 1.0 percentage point, the dispersion between the curves of each angle is very small, and the parallelism is good, which further verifies the consistency of electromagnetic response of the double-layer nested spherical symmetrical skeleton structure of the present invention under multi-angle conditions.

[0049] Based on the test results in Figures 3(a), 3(b), and 3(c), the equivalent dielectric constant curves of the double-layer nested metal mesh metamaterial unit of this invention highly overlap at each incident angle under three model states: no overall rotation, rotation around the X-axis by 45°, and rotation around the Z-axis by 45°. The range of the endpoint values ​​between each angle is less than 0.01, and the range of the increase is less than 1.1 percentage points. This indicates that the unit maintains excellent electromagnetic isotropy under different model orientations and different incident angles, ensuring a high degree of consistency in the electromagnetic response of the unit under multi-angle and multi-polarization conditions from the configuration source.

[0050] The single-layer metal mesh metamaterial unit has a spherical radius of 6.5 mm and a ring thickness of t=0.1 mm. The skeleton structure consists of three mutually orthogonal metal wire rings forming a spherical hollow network structure. The three rings are arranged along the X-axis, Y-axis and Z-axis respectively and intersect at the center of the sphere. The unit period is 15 mm.

[0051] As shown in Figure 4(a), under the condition of no overall rotation, there is a significant separation between the equivalent dielectric constant curves at the four incident angles: the maximum deviation of the average value at each angle at 0.5 GHz is approximately 0.006 (relative deviation of approximately 0.4%), and the maximum deviation of the average value at each angle at 3.5 GHz is approximately 0.015 (relative deviation of approximately 0.9%). The curves at each angle show large deviations at multiple frequency points, indicating poor parallelism. The multi-angle consistency of the single-layer structure across the entire frequency band is significantly inferior to that of the double-layer structure of this invention.

[0052] As shown in Figure 4(b), after rotating the entire system by 45° around the X-axis, the family of equivalent dielectric constant curves at the four incident angles diverges further, and the dispersion between the curves at each angle increases significantly. =0° and The curve under a 90° incident condition shows a deviation of 0.011 at 3.5 GHz (relative deviation of approximately 0.7%), indicating poor parallelism at various angles. This contrasts sharply with the performance of the double-layer structure under the same conditions (where the curves highly overlap).

[0053] As shown in Figure 4(c), after rotating the whole around the Z-axis by 45°, the family of equivalent dielectric constant curves at the four incident angles also shows a significant divergence compared to the double-layer structure. The range of the curves at the endpoint (3.5 GHz) is 0.0108 (relative fluctuation of about 0.65%).

[0054] Combining the test results in Figures 4(a), 4(b), and 4(c), the equivalent dielectric constant curves of the single-layer nested metal mesh metamaterial unit under three model states—no overall rotation, rotation around the X-axis by 45°, and rotation around the Z-axis by 45°—show varying degrees of divergence at different incident angles, indicating poor consistency across multiple angles. Taking normal incidence (… Taking 0° as an example, the equivalent dielectric constant of the single-layer structure under the condition of no overall rotation increases from approximately 1.608 at 0.5 GHz to approximately 1.705 at 3.5 GHz, an increase of approximately 6.03%, which is about 0.62 percentage points higher than that of the double-layer structure of the present invention (5.41%). Under the condition of rotating 45° around the X-axis, the increase in normal incidence of the single-layer structure is 5.27%, which is about 0.57 percentage points higher than that of the double-layer structure (4.70%). Under the condition of rotating 45° around the Z-axis, the increase in normal incidence of the single-layer structure is 4.97%, which is about 0.28 percentage points higher than that of the double-layer structure (4.69%). This figure serves as comparative data to demonstrate the significant improvement effect of the double-layer nested configuration of the present invention in suppressing angular sensitivity and improving multi-angle electromagnetic consistency.

[0055] Figure 5 The figure shows the equivalent dielectric constant curves of a solid metal spherical shell unit with the same outer diameter in the 0.5–3.5 GHz frequency band. The X-axis represents frequency (GHz), and the Y-axis represents the equivalent dielectric constant. The solid metal spherical shell has an outer diameter of 6.5 mm and a wall thickness of 0.1 mm. The figure shows the frequency response curves of the equivalent dielectric constant under two orthogonal polarization directions: TE (transverse electric wave) and TM (transverse magnetic wave). Due to the perfect rotational symmetry of the solid metal spherical shell, the electromagnetic responses under the two orthogonal polarization directions are theoretically consistent. As can be seen from the figure, within the 0.5–3.5 GHz frequency band, the equivalent dielectric constant curves under the two polarization directions of TE and TM highly overlap, the trends of the two curves are completely consistent, the values ​​are closely clustered, and the difference between the two polarization directions is less than 0.2%, exhibiting excellent isotropy. The equivalent dielectric constant of the solid metal spherical shell unit gradually increases from approximately 1.653 at 0.5 GHz to approximately 1.736 at 3.5 GHz, representing an increase of approximately 5.04% across the entire frequency band, demonstrating excellent overall electromagnetic performance. This solid metal spherical shell serves as a performance comparison object, used to compare the electromagnetic performance of the double-layer nested metal mesh metamaterial unit of this invention.

[0056] Figure 6Solid metal spherical shells, single-layer nested metal mesh metamaterial units, and double-layer nested metal mesh metamaterial units rotated 45° around the X-axis, The graph shows the equivalent dielectric constant comparison curves under a 90° incident condition. The X-axis represents frequency (GHz), and the Y-axis represents the equivalent dielectric constant. All three structures have an outer diameter of 6.5 mm, a wall thickness / ring thickness of 0.1 mm, and a unit cell period of 15 mm. Data for the double-layer structure is taken from the double-layer nested metal mesh metamaterial unit of this invention under a 45° rotation around the X-axis. Simulation results under a 90° incident angle. In this paper, "increase" refers to the relative percentage change in the equivalent dielectric constant from 0.5 GHz to 3.5 GHz. The smaller the value, the better the frequency flatness, which is the core indicator for measuring the electromagnetic performance stability of metamaterial units in the broadband operating frequency band.

[0057] Depend on Figure 6 It can be seen that when rotating 45° around the X-axis, Under a 90° oblique incidence condition, the equivalent dielectric constant increase of the double-layer nested metal mesh metamaterial unit is 4.70%, lower than the 5.03% of the solid metal spherical shell and the 5.91% of the single-layer nested metal mesh metamaterial unit. Compared with the single-layer structure, the frequency increase of the double-layer structure is narrowed by about 1.21 percentage points; compared with the solid metal spherical shell, the frequency increase of the double-layer structure is narrowed by about 0.33 percentage points, indicating that the present invention still has better frequency flatness and stable oblique incidence electromagnetic response under extreme lightweight conditions.

[0058] Under this specific incident angle, the amplification of the double-layer nested structure is almost identical to that of the solid metal spherical shell, with their curves highly overlapping, achieving frequency flatness comparable to the spherical shell. Simultaneously, the amplification of the double-layer structure is approximately 0.7 percentage points narrower than that of the single-layer structure, demonstrating significantly better frequency flatness. While the single-layer structure is closer to the spherical shell in its endpoint value, it exhibits the largest amplification and the worst frequency stability.

[0059] Furthermore, under other incident angles with a 45° rotation around the X-axis, the double-layer structure also exhibits superior frequency flatness compared to the spherical shell: At 0°, the double-layer increase is 4.70% (5.03% for the spherical shell). =30° is 4.68% (5.03% for spherical shell). At 45°, the gain is 4.73% (compared to 5.03% for the spherical shell). The increase in frequency of the double-layer structure at all the above angles is lower than that of the spherical shell, and the average increase at the four angles is 4.70%, which is about 0.33 percentage points narrower than the 5.03% of the spherical shell. In summary, the double-layer nested configuration of this invention can achieve frequency flatness that is almost identical to that of a solid metal spherical shell under oblique incidence conditions, and is even better than the spherical shell at some angles. Moreover, it is better than the single-layer nested structure at most incident angles, verifying the core feature of this invention that combines multi-angle electromagnetic performance advantages under the premise of extreme lightweighting.

[0060] To verify the technical effect of the present invention, the following preferred embodiments are provided: Example 1: A double-layer nested metal mesh metamaterial unit was manufactured using aluminum alloy via selective laser melting 3D printing. The outer skeleton has a spherical radius R1 = 6.5 mm, and the inner skeleton has a spherical radius R2 = 6.0 mm. The thickness of both skeleton rings is t = 0.1 mm, and the material is aluminum-silicon-magnesium alloy. Each skeleton layer consists of a spherical hollow network composed of three mutually orthogonal metal wire rings. The inner skeleton is rotated at a predetermined angle relative to the outer skeleton in spatial orientation. The centers of the two skeletons coincide and are spatially parallel, with an interlayer spacing of 0.4 mm filled with air. Within a 15 mm periodic unit, calculations show that the volume of this unit is only about 6.7% of that of a solid metal spherical shell of the same outer diameter, resulting in a weight reduction of approximately 93%.

[0061] The equivalent dielectric constant of the aforementioned double-layer nested metallic mesh metamaterial unit was extracted in multiple polarizations and angles within the 0.5–3.5 GHz frequency band. Test conditions covered combinations of TE (transverse electric wave) and TM (transverse magnetic wave) dual polarization directions and multiple incident angles. Results show that: Under normal incidence conditions, the equivalent dielectric constant of the double-layer nested metal mesh metamaterial unit of this invention gradually increases from approximately 1.659 at 0.5 GHz to approximately 1.749 at 3.5 GHz, an increase of approximately 5.41%. In contrast, the equivalent dielectric constant of a single-layer nested metal mesh metamaterial unit with the same outer diameter increases from approximately 1.608 at 0.5 GHz to approximately 1.705 at 3.5 GHz under the same conditions, an increase of approximately 6.03%. The increase in dielectric constant of the double-layer structure of this invention is approximately 0.62 percentage points narrower than that of the single-layer structure, resulting in a significant improvement in frequency flatness. The equivalent dielectric constant curves for each polarization and angle show high overlap and good parallelism, with the difference between the two orthogonal polarization directions TE and TM being less than 0.2%, comparable to the isotropic properties of a solid metal spherical shell.

[0062] Under oblique incidence conditions with a 45° rotation around the X-axis, the double-layer structure also exhibits excellent frequency flatness. =90°, the equivalent permittivity of the double-layer structure rises gently from about 1.576 at 0.5 GHz to about 1.650 at 3.5 GHz, with an increase of only 4.70%, which is better than 5.03% of the solid metal spherical shell, and significantly better than 5.91% of the single-layer nested structure. At =30° and =45° incidence conditions, the increase rates of the double-layer structure are 4.68% and 4.73% respectively, both lower than 5.03% of the spherical shell.

[0063] Further compared with the solid metal spherical shell with the same outer diameter (outer diameter 6.5 mm, wall thickness 0.1 mm), the 3.5 GHz end value (1.749) of the unit of the present invention under normal incidence conditions is about 0.74% higher than that of the spherical shell (1.736), which surpasses the electromagnetic performance of the spherical shell, while the weight is only about 6.7% of that of the spherical shell, achieving a weight reduction of about 93% on the premise of maintaining high electromagnetic isotropy.

[0064] Example 2: On the basis of the double-layer nested skeleton structure in the above Example 1, flexible regulation of different weight reduction ratios and electromagnetic properties is realized by adjusting the spherical radius ratio of the inner and outer layers and the thickness of the ring body. The outer spherical radius R1 can be selected in the range of 5.5–7.5 mm, the inner spherical radius R2 is selected in the range of 5.0–6.5 mm (it is required to ensure that R2<R1 and the interlayer spacing is not less than 0.3 mm), and the thickness of the two ring bodies is independently adjusted in the range of 0.08–0.3 mm. When the radius difference between the inner and outer layers increases, the interlayer coupling weakens, the separation of the dual resonance modes is more significant, and the bandwidth broadening effect is enhanced; when the thickness of the ring body decreases, the weight reduction ratio further increases. Through parameter combination optimization, it can adapt to the differentiated requirements of different application scenarios for weight, bandwidth and permittivity accuracy.

[0065] Example 3: A plurality of the above double-layer nested metal mesh metamaterial units are periodically arranged in a two-dimensional plane to form a gradient refractive index metamaterial lens array with a rectangular or circular aperture. The unit period is 15 mm. By independently adjusting the spherical radius ratio of the inner and outer layers of each unit, the required spatial distribution of equivalent permittivity is realized on the aperture surface of the lens, for example, decreasing gradiently from the center to the edge, which is used to construct a lens antenna with high gain and low sidelobe. The unit spacing is selected according to the operating wavelength, usually from half a wavelength to one wavelength. There is no physical connection between the units in this array, and each unit can be independently installed on a low-permittivity foam support frame.

[0066] 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 it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A multi-layered nested metal mesh metamaterial unit, characterized in that, It includes an inner spherical skeleton and an outer spherical skeleton. The centers of the inner and outer spherical skeletons coincide and are parallel in space. The inner spherical skeleton rotates at a predetermined angle relative to the outer spherical skeleton in spatial orientation. Each skeleton is formed by three mutually orthogonal metal wire rings to form a spherical hollow network structure. The three rings are arranged along the X-axis, Y-axis and Z-axis respectively and intersect at the center of the sphere. The inner and outer spherical skeletons are structurally independent and have no physical contact. The spaces between the layers are filled with air, forming a double-layer nested hollow structure without dielectric support. The inner and outer spherical skeletons generate a double resonant mode through electromagnetic coupling in the free space between the layers.

2. The multi-layer nested metal mesh metamaterial unit according to claim 1, characterized in that, The outer spherical skeleton has a spherical radius of 6.5 mm and an inner diameter of 6.4 mm, the inner spherical skeleton has a spherical radius of 6.0 mm and an inner diameter of 5.9 mm, the ring thickness of both skeletons is 0.1 mm, and the interlayer spacing is 0.4 mm.

3. The multi-layer nested metal mesh metamaterial unit according to claim 1 or 2, characterized in that, The outer spherical skeleton has a spherical radius of 5.5 mm to 7.5 mm, the inner spherical skeleton has a spherical radius of 5.0 mm to 6.5 mm, and the inner spherical skeleton has a smaller spherical radius than the outer spherical skeleton. The interlayer spacing is not less than 0.3 mm, and the ring thickness of the two skeletons is within 0.08 mm to 0.3 mm.

4. The multi-layer nested metal mesh metamaterial unit according to claim 1, characterized in that, The metal wire ring is made of aluminum-silicon-magnesium alloy, titanium alloy, or nickel-based alloy.

5. A method for preparing a multi-layered nested metal mesh metamaterial unit, characterized in that, The metal selective laser melting 3D printing process is used for integrated molding. The overall structure of the outer and inner spherical skeletons is constructed in the digital model. The spherical hollow skeleton is directly formed by the temporary support of unmelted metal powder. Through process optimization, low-angle supportless printing is achieved, and the manufacturing accuracy reaches ±0.02 mm. After printing, the residual powder inside is removed by cleaning or vibration physical method to obtain a complete double-layer nested hollow metal mesh skeleton unit.

6. The preparation method according to claim 5, characterized in that, The selective laser melting 3D printing process for metals uses aluminum alloy powder, titanium alloy powder, or nickel-based alloy powder as raw materials.

7. The preparation method according to claim 5, characterized in that, The preparation method employs a combination of metal 3D printing and surface metallization. First, a polymer skeleton template is fabricated using high-precision photopolymerization 3D printing. Then, a conductive seed layer is deposited on the polymer surface using chemical plating. Subsequently, the metal layer is thickened to the designed thickness using electroforming. Finally, the internal polymer template is removed using high temperature or solvent to obtain a hollow metal mesh skeleton structure.

8. An antenna array, characterized in that, The lens comprises multiple multilayer nested metal mesh metamaterial units as described in any one of claims 1 to 4. The multiple metamaterial units are arranged in a two-dimensional planar periodic arrangement or a three-dimensional spatial curved surface arrangement to form a unit array of gradient refractive index metamaterial lenses. By independently adjusting the ratio of the inner and outer spherical radii of each metamaterial unit, the required spatial distribution of the equivalent dielectric constant is achieved on the lens aperture surface.

9. The antenna array according to claim 8, characterized in that, The metamaterial units in the unit array are not physically connected to each other and are independently installed on a low dielectric constant foam support frame.

10. The antenna array according to claim 8, characterized in that, The cell period of the cell array is 15 mm, and the cell spacing is selected from half a wavelength to one wavelength according to the working wavelength.

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