A rectangular Luneburg lens antenna, its design method and application

Abstract

This invention belongs to the field of lens antenna technology, and discloses a rectangular Luneburg lens antenna, its design method, and its application. The lens is cut to create a flat surface while retaining the rest of the lens structure. A dielectric material is added along the outer surface of the original lens to form an air-dielectric composite structure, which is then supplemented into a rectangular plane to form the rectangular Luneburg lens antenna. This invention achieves the flattening of the Luneburg lens, solving the problems of difficulty in fitting the dielectric constant distribution and achieving excessively high dielectric constant values ​​in deformed Luneburg lens antennas. The air-dielectric composite structure enables the antenna to achieve a specific dielectric constant distribution, and it is lightweight and easy to manufacture. The antenna achieves a gain of 19.2 dBi in the 24-28 GHz range, enabling one-dimensional beam coverage of 100° horizontally or 100° vertically, and possesses the capability to achieve two-dimensional beam coverage. The antenna has a simple structure, is manufactured using 3D printing technology, and the process is simple, economical, and practical.

Description

Technical Field

[0001] This invention belongs to the field of lens antenna technology, and particularly relates to a rectangular Luneburg lens antenna, its design method, and its application. Background Technology

[0002] Currently, lens antennas, as a type of aperture antenna, possess the ability to control the propagation of electromagnetic waves in a propagation field. The Luneburg lens antenna is a typical example. Originally proposed by the American mathematician Luneburg, the Luneburg lens is a non-uniform spherical medium lens whose refractive index is a univariate function that continuously varies with the radial distance from the center of the sphere. The Luneburg lens can transform a spherical wavefront incident from any direction into a planar wavefront, producing a focusing and shaping effect on the beam in space, and is widely used in multi-beam and high-gain scenarios. Due to the perfect symmetry of the spherical Luneburg lens, placing the feed source at different positions on the lens surface can produce a highly consistent beam; however, its non-conformal spherical structure limits its further applications to some extent.

[0003] Currently, the academic community has conducted extensive research on how to modify the spherical structure and achieve the flattening of Luneburg lenses. With the emergence of transformation optics theory (coordinate mapping, conformal transformation, and quasi-conformal transformation), Luneburg lenses can be transformed into structures with lower profiles and easier conformal adaptation. This not only improves the matching problem between the lens and the feed source but also retains the original electromagnetic wave modification performance of Luneburg lenses. However, in order to design deformable lenses with lower curvature, transformation optics disrupts the original circular dielectric constant distribution and low dielectric constant value of the spherical lens, resulting in deformable lenses with irregular dielectric constant distributions that are difficult to fit and extremely high dielectric constant values. In the literature "Research on Key Technologies of Ultra-Wide Angle Scanning Multibeam Lens Antennas," the GA genetic algorithm in MATLAB was used to fit the transformed irregular dielectric constant distribution, and the design and simulation were carried out based on the curves in the fitting results. In the literature "Design and Fabrication of Non-Resonant Metamaterial Luneburg Lenses," a quasi-conformal transformation was used to compress a spherical lens. When the compression ratio was 1 / 2, the highest dielectric constant value reached 20.05. After processing the extremely high dielectric constant value, BaTiO3 powder was added to PLA material to create a novel dielectric material with a relative dielectric constant of 5.3. The literature "Multi-Material3D Printed Compressed Luneburg Lens for mm-Wave Beam Steering" designed various novel materials using FDM technology to fabricate Luneburg lens antennas in order to achieve high dielectric constant distributions of 7.5, 6.5, 5.5, 4.5, and 3.

[0004] In summary, when using transformation optics to change the shape of a Luneburg lens antenna, two major problems need to be addressed: the irregular dielectric constant distribution resulting from the deformation and the extremely high dielectric constant value. This increases the design difficulty and workload. Therefore, how to design a deformable Luneburg lens antenna while addressing these issues is currently a key research challenge.

[0005] Based on the above analysis, the problems and defects of the existing technology are as follows: when changing the shape of the Luneburg lens antenna, it is easy to encounter irregular dielectric constant distributions and extremely high dielectric constant values ​​that are difficult to fit. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention provides a rectangular Luneburg lens antenna, its design method, and its application.

[0007] This invention is implemented as follows: A design method for a rectangular Luneburg lens antenna includes:

[0008] Step 1: Make a single cut on the spherical Luneburg lens. The cutting direction is perpendicular to the horizontal plane. After cutting, the lens produces a flat surface, achieving one deformation. In order to reduce the impact of deformation on the structure and performance of the Luneburg lens, the rest of the lens is retained here.

[0009] Step 2: Five rectangular planes are added along the spherical outer surface of the cut lens to achieve secondary deformation. The newly added rectangular planes and the planes generated in Step 1 form a rectangular Luneburg lens. At the same time, extremely high dielectric constant values ​​and irregular dielectric constant distributions are avoided. In order to maximize the gain generated by the lens antenna, a cost function is introduced to calculate the gradient dielectric constant and radius corresponding to the layered lens. Then, a concentric multilayer air-dielectric composite structure is used to design the rectangular Luneburg lens antenna.

[0010] Furthermore, in the step of cutting a pair of spherical Luneburg lenses, D is the height of the cut rounded corner, and R is the radius of the spherical lens. Let D = 36mm and R = 60mm.

[0011] Furthermore, in step two, five rectangular planes are added along the spherical outer surface of the cut lens to form a rectangular body. The dielectric constant added in the rectangular body is the same as that of the outermost layer of the original spherical lens, which is 1.182.

[0012] Furthermore, in step two, the air-dielectric composite structure is constructed by inserting a spherical air-dielectric medium (ε) into the spherical high-dielectric-constant medium. r =1, tanδ=0) change the dielectric constant within the interval, forming an air-dielectric composite structure, where ε r δ is the relative permittivity, and tanδ is the tangent loss.

[0013] Furthermore, based on the principle of using the gradient dielectric constant as an equivalent continuous dielectric constant, the ideal dielectric constant of the normalized spherical Luneburg lens is described. With the reconstructed gradient dielectric constant The cost function J for the differences between them is:

[0014]

[0015] Due to the symmetry of a sphere, dV = 4πr here. 2 dr, V lens Let V be the volume of the lens.

[0016] Suppose the lens is layered N times, resulting in N+1 spherical shells and N+1 dielectric constants. The dielectric constant of each spherical shell is a fixed value, i.e., a gradient. Let ε be the dielectric constant within the i-th spherical shell. i That is, r i-1 ≤r≤r i At that time, ε rec (r)=ε i Then equation (1) can be further simplified to:

[0017]

[0018] To minimize the cost function, we minimize its maximum value within each spherical interval. When the exponent q = ∞, we have: M i It is the maximum value of the error within each interval, which remains constant throughout the entire interval of the i-th spherical shell, and is located inside the i-th spherical shell at r. i-1 or outer r i It is obtained that when the dielectric constant ε i When the same difference is produced at both boundaries, M i When the minimum value is reached, we have:

[0019]

[0020]

[0021] The radius and relative permittivity of the spherical concentric layered Luneburg lens can be obtained from (3) and (4).

[0022] Furthermore, in the air-dielectric composite structure, an N-order gradient dielectric constant is achieved by i layers of air and i layers of dielectric, with each air layer having a duty cycle p. i for:

[0023]

[0024] Among them, l i R is the radius corresponding to the i-th layer of medium. i=ir0 is the radius corresponding to the i-th air-medium composite structure, R i-1 = (i-1)r0 is the radius corresponding to the (i-1)th air-medium composite structure, and r0 represents the thickness of each air-medium composite structure, which is 3mm.

[0025] Then the thickness d of each medium layer i for:

[0026] d i =R i -l i (6)

[0027] The A-BG formula is:

[0028]

[0029] Where, ε h ε is the dielectric constant of the substrate material. i ε is the dielectric constant of the inserted material (if the inserted material is air, then the dielectric constant is equal to 1). eff Let be the overall equivalent dielectric constant, and p be the volume fraction of the inserted material relative to the total material, i.e., the duty cycle in equation (5). Based on the gradient relative dielectric constant, ε in equation (7) is... eff By assigning values ​​and combining them with equations (5) and (6), the thickness of the medium in each layer of the composite structure can be obtained.

[0030] Furthermore, the high dielectric constant medium is 3D printed nylon (relative dielectric constant 2.6, tangent loss 0.005).

[0031] Another aspect of the present invention is to provide a rectangular Luneburg lens antenna, which includes a deformed Luneburg lens antenna composed of an air-dielectric nested structure and a feed antenna.

[0032] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows:

[0033] First, addressing the technical problems existing in the prior art and the difficulty in solving them, and closely combining the technical solution to be protected by this invention with the results and data from the research and development process, this paper provides a detailed and in-depth analysis of how the technical solution of this invention solves the technical problems, and the inventive technical effects brought about after solving the problems. The specific description is as follows:

[0034] 1. This invention achieves the flattening of Luneburg lenses, solving the problems of difficulty in fitting the dielectric constant distribution of deformed Luneburg lens antennas and the difficulty in achieving excessively high values.

[0035] 2. The air-dielectric composite structure enables the antenna to achieve a specific dielectric constant distribution, and it is lightweight and easy to manufacture.

[0036] 3. The antenna's S11 is less than -10dB within the 24-28GHz range, fully covering part of the millimeter-wave frequency bands in my country's current fifth-generation mobile communication.

[0037] 4. The antenna achieves a gain of 19.2 dBi within the 24-28 GHz range and can achieve one-dimensional beam coverage of 100° in the horizontal or vertical plane, and also has the capability to achieve two-dimensional beam coverage.

[0038] 5. The antenna has a simple structure and is manufactured using 3D printing technology. The process is simple, economical, and practical.

[0039] Second, considering the technical solution as a whole or from a product perspective, the technical effects and advantages of the technical solution to be protected by this invention are specifically described as follows:

[0040] This invention designs a rectangular Luneburg lens antenna to achieve a flattened Luneburg lens antenna design. After analyzing the electric and magnetic field distributions of a spherical Luneburg lens antenna composed of multiple spherical shells, the gain of the antenna is optimized using a cost function method. Then, a plane is obtained by cutting the lens, which serves as the incident surface for electromagnetic waves. Simultaneously, to reduce the impact of cutting on the lens, no further cutting is done, and a rectangular plane is used to supplement the remaining part of the lens, resulting in a rectangular Luneburg lens antenna. A concentric air-dielectric composite structure is then proposed to achieve the gradient dielectric constant distribution of the rectangular Luneburg lens antenna. Analysis results show that when this rectangular Luneburg lens antenna is excited using five feed sources, one-dimensional beam coverage of 100° horizontally or 100° vertically can be achieved. The antenna operates in the 24-28 GHz range, covering the entire n258 frequency band and parts of the n257 and n261 frequency bands. These frequency bands offer advantages such as extremely high transmission rates, low air interface delays, and large communication capacity, and have broad application prospects.

[0041] Third, as supplementary evidence of the inventive step of the claims of this invention, it is also reflected in the following important aspects:

[0042] The technical solution of this invention solves a long-standing but unresolved technical problem: to achieve beamforming and wide-range scanning, an increasing number of Luneburg lenses use array antennas as feed sources. Due to limitations imposed by power divider networks and phase-shifting structures, current array antennas are mostly linear configurations. Correspondingly, the surface into which the incident wave enters the Luneburg lens should also be as flat as possible to better match the feed source. Furthermore, a flat structure facilitates the miniaturization, integration, and compactness of Luneburg lens antennas. However, existing flattened designs have resulted in Luneburg lenses with extremely high dielectric constant values ​​and irregular dielectric constant distributions that are difficult to fit, hindering simulation and actual fabrication. Therefore, designing a flattened Luneburg lens antenna with an easily achievable dielectric constant distribution is a problem of significant research value. Attached Figure Description

[0043] Figure 1 This is a flowchart of the design method for a rectangular Luneburg lens antenna provided in an embodiment of the present invention;

[0044] Figure 2 This is an illustration of the effect of cutting a Luneburg lens according to an embodiment of the present invention;

[0045] Figure 3 This is an effect diagram of the rectangular Luneburg lens provided in an embodiment of the present invention;

[0046] Figure 4 This is a schematic diagram of the air-medium composite structure provided in an embodiment of the present invention;

[0047] Figure 5 This is a schematic diagram of the rectangular Luneburg lens antenna based on an air-dielectric composite structure provided in an embodiment of the present invention;

[0048] Figure 6 This is a horizontal radiation pattern provided in an embodiment of the present invention;

[0049] Figure 7 This is a vertical plane radiation pattern provided in an embodiment of the present invention;

[0050] Figure 8 This is a normalized electric field diagram provided in an embodiment of the present invention. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0052] I. Explanatory and Illustrative Embodiments. To enable those skilled in the art to fully understand how the present invention is specifically implemented, this section provides an explanatory and illustrative description of the embodiments described in the claims.

[0053] like Figure 1 As shown, the design method for a rectangular Luneburg lens antenna provided in this embodiment of the invention includes:

[0054] S101, the spherical lens is cut to create a flat surface while retaining the rest of the lens structure;

[0055] S102 adds five rectangular planes along the outer surface of the original lens to form a rectangular Luneburg lens antenna, and uses an air-dielectric composite structure to realize it.

[0056] The design method for a rectangular Luneburg lens antenna provided in this embodiment of the invention specifically includes:

[0057] Step 1: Make a single cut on the spherical Luneburg lens. The cutting direction is perpendicular to the horizontal plane. After cutting, the lens produces a flat surface, achieving one deformation. In order to reduce the impact of deformation on the structure and performance of the Luneburg lens, the rest of the lens is retained here.

[0058] Step 2: Five rectangular planes are added along the spherical outer surface of the cut lens to achieve secondary deformation. The newly added rectangular planes and the planes generated in Step 1 form a rectangular Luneburg lens. At the same time, extremely high dielectric constant values ​​and irregular dielectric constant distributions are avoided. In order to maximize the gain generated by the lens antenna, a cost function is introduced to calculate the gradient dielectric constant and radius corresponding to the layered lens. Then, a concentric multilayer air-dielectric composite structure is used to design the rectangular Luneburg lens antenna.

[0059] The present invention relates to a rectangular Luneburg lens antenna designed based on geometric optics theory, comprising a deformed Luneburg lens antenna composed of an "air-dielectric" nested structure and a feed antenna.

[0060] For concentric lens antennas, Benjamin Fuchs investigated how to achieve the highest gain. Building upon the idea of ​​using the gradient dielectric constant as an equivalent continuous dielectric constant, he proposed an ideal dielectric constant to describe the normalized spherical Luneburg lens. With the reconstructed gradient dielectric constant The cost function J for the differences between them is:

[0061]

[0062] Due to the symmetry of a sphere, dV = 4πr here. 2 dr;

[0063] Suppose the lens is layered N times, resulting in N+1 spherical shells and N+1 dielectric constants. The dielectric constant of each spherical shell is a fixed value, i.e., a gradient. Let ε be the dielectric constant within the i-th spherical shell. i That is, ri-1 ≤r≤r i At that time, ε rec (r)=ε i Then equation (1) can be further simplified to:

[0064]

[0065] To minimize the cost function, we minimize its maximum value within each spherical interval. When the exponent q = ∞, we have: M i It represents the maximum value of the error within each interval, which remains constant throughout the entire interval of the i-th layer of the spherical shell, and is located inside the spherical shell layer r. i-1 or outer r i It is obtained that when the dielectric constant ε i When the same difference is produced at both boundaries, M i When the minimum value is reached, we have:

[0066]

[0067]

[0068] The radius and relative permittivity of the spherical concentric layered Luneburg lens can be obtained from (3) and (4).

[0069] Table 1 shows the normalized radius and dielectric constant of the optimized layered spherical Luneburg lens antenna calculated according to equations (3) and (4). This lens is divided into i layers and has an Nth-order gradient dielectric constant.

[0070] Table 1. Gain-optimized spherical Luneburg lens antenna

[0071]

[0072]

[0073] In the design of a rectangular Luneburg lens antenna with a flat surface, the lens is first cut, such as... Figure 2 As shown. D is the height of the cut fillet, and R is the radius of the spherical lens. Let D = 36mm, R = 60mm. After cutting, the lens has a flat surface. To minimize the impact of the cutting on the lens and avoid correcting the electric and magnetic fields generated by the lens, the rest of the lens structure is retained, and a rectangular plane is added along the outer surface of the original lens to form a shape as shown. Figure 3 The rectangular Luneburg lens antenna shown is provided. The dielectric constant of the supplementary medium is the same as that of the outermost layer of the original spherical lens, which is 1.182.

[0074] The air-dielectric composite structure is an improvement on the traditional spherical shell structure, achieved by inserting a spherical shell-shaped air medium (ε) into a spherical shell-shaped high dielectric constant medium.r By varying the dielectric constant within a certain range (e.g., tanδ = 1, tanδ = 0), a composite structure of two media can be formed. This structure also achieves precise calculation of the dielectric constant for each range using equivalent medium theory, and utilizes gradient dielectric constants to achieve an equivalent dielectric constant distribution for the spherical Luneburg lens. Furthermore, inserting air significantly reduces the lens's weight, alleviating the burden during practical use.

[0075] For ease of fabrication, the high dielectric constant medium used in this section is nylon (ε-N), a common material for 3D printing. r =2.6, tanδ=0.005), the cross-sectional schematic diagram of the air-medium composite structure is as follows. Figure 4 This structure can also be viewed as a superposition of multiple dielectric spherical shells and multiple air spherical shells.

[0076] Before using the gradient dielectric constant of the air-dielectric composite, the normalized radii in Table 1 must be approximated to simplify subsequent calculations. When the radius R = 60 mm, the maximum radii corresponding to the 1st to 5th order gradient dielectric constants are set to 27 mm, 36 mm, 45 mm, 51 mm, and 60 mm, respectively. The lens is then divided into 20 layers: layers 1-9 correspond to gradient 1, layers 10-12 to gradient 2, layers 13-15 to gradient 3, layers 16-17 to gradient 4, and layers 18-20 to gradient 5. The dimensions of the five gradient intervals of the optimized lens are shown in Table 2.

[0077] The dielectric constant will now be studied and calculated. Figure 5 The duty cycle p of each air layer in the air-medium composite structure i for:

[0078]

[0079] Among them, l i R is the radius corresponding to the i-th layer of medium. i =ir0 is the radius corresponding to the i-th air-medium composite structure, R i-1 = (i-1)r0 is the radius corresponding to the (i-1)th air-medium composite structure, and r0 represents the thickness of each air-medium composite structure, which is 3mm.

[0080] Then the thickness d of each medium layer i for:

[0081] d i =R i -l i (6)

[0082] The A-BG formula is:

[0083]

[0084] Where, ε h ε is the dielectric constant of the substrate material. i ε is the dielectric constant of the inserted material (if the inserted material is air, then the dielectric constant is equal to 1). eff Let be the overall equivalent dielectric constant, and p be the volume fraction of the inserted material relative to the total material, i.e., the duty cycle in equation (5). Based on the gradient relative dielectric constant, ε in equation (7) is... eff By assigning values ​​and combining them with equations (5) and (6), the thickness of the medium in each layer of the composite structure can be obtained. The final calculation results are shown in Table 2.

[0085] Table 2 Air-medium composite structure parameters

[0086]

[0087] II. Application Examples. To demonstrate the inventiveness and technical value of the technical solution of this invention, this section provides application examples of the technical solution of the claims on specific products or related technologies.

[0088] The rectangular Luneburg lens antenna provided in this embodiment of the invention can be used in satellite communication systems or ship navigation systems.

[0089] III. Evidence of the Relevant Effects of the Embodiments. The embodiments of the present invention have achieved some positive effects during research and development or use, and indeed possess significant advantages compared to existing technologies. The following description, in conjunction with data, charts, and other materials from the experimental process, illustrates these advantages.

[0090] Figure 6 , Figure 7 The horizontal (xoy) and vertical (yoz) radiation patterns of the antenna operating at 28 GHz are shown respectively. When the five feed antennas are evenly arranged in the xoy plane, the antenna achieves a 100° beam coverage range in this plane, as shown below. Figure 6 As shown. Figure 7 The diagram shows the radiation pattern of the antenna when five feed antennas are evenly arranged in the yoz plane. This arrangement also achieves a 100° beam coverage range in the plane, and the beam shape is similar to... Figure 6 It exhibits a high degree of consistency. Simulation results demonstrate that this centrally symmetric rectangular Luneburg lens antenna provides the same beamforming effect for feeds on different planes. When using an m×n array antenna as the feed, the rectangular Luneburg lens antenna can achieve two-dimensional beam scanning.

[0091] Figure 8 The normalized electric field diagram of the lens antenna is shown. The diagram reveals that the phase of the electromagnetic wave radiated from the feed can be reconstructed by the cut Luneburg lens. This reconstruction not only increases the gain but also transforms the original spherical wave into a plane wave.

[0092] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A design method for a rectangular Luneburg lens antenna, characterized in that, The design method for the rectangular Luneburg lens antenna includes: Step 1: Make a single cut on the spherical Luneburg lens, with the cutting direction perpendicular to the horizontal plane; after cutting, the lens produces a flat surface, achieving one deformation. Step 2: Add 5 rectangular planes along the spherical outer surface of the cut lens to achieve secondary deformation. The newly added rectangular planes and the planes generated in Step 1 form a rectangular Luneburg lens. Introduce a cost function to calculate the gradient dielectric constant and radius corresponding to the layered lens, and then use a concentric multilayer air-dielectric composite structure to design a rectangular Luneburg lens antenna. The second step, which constructs an air-dielectric composite structure, involves inserting a spherical air medium into a spherical high-dielectric-constant medium to change the dielectric constant within a certain range, thus forming an air-dielectric composite structure.

2. The design method of the rectangular Luneburg lens antenna as described in claim 1, characterized in that, The step described above involves making a single cut to a pair of spherical Luneburg lenses, where D is the height of the cut fillet and R is the radius of the spherical lens. Let D = 36 mm and R = 60 mm.

3. The design method of the rectangular Luneburg lens antenna as described in claim 1, characterized in that, Step 2: Add 5 rectangular planes along the spherical outer surface of the cut lens to form a rectangular body. The dielectric constant of the medium added in the rectangular body is the same as that of the outermost layer of the original spherical lens, which is 1.

182.

4. The design method of the rectangular Luneburg lens antenna as described in claim 1, characterized in that, Based on the principle of using the gradient dielectric constant as an equivalent continuous dielectric constant, the ideal dielectric constant of a normalized spherical Luneburg lens is described. With the reconstructed gradient dielectric constant Cost function of differences between for: ， Based on the symmetry of a sphere, here , Let V be the volume of the lens; Suppose the lens is layered N times, resulting in N+1 spherical shells and N+1 order dielectric constants. The dielectric constant of each spherical shell is a fixed value, i.e., a gradient. The dielectric constant within the i-th spherical shell is defined as... ,Right now hour, Then the cost function This can be further simplified to: ； To minimize the cost function, we minimize its maximum value within each spherical interval, when the exponential... Sometimes, ; It represents the maximum value of the error within each interval, remains constant throughout the entire interval of the i-th spherical shell, and is located inside the i-th spherical shell. or outside The dielectric constant is obtained from the location. When the same difference is produced at both boundaries By obtaining the minimum value, the radius and relative permittivity of the spherical concentric layered Luneburg lens can be determined: ， ， Furthermore, in the air-dielectric composite structure, an N-order gradient dielectric constant is achieved by i layers of air and i layers of dielectric, with each air layer having a duty cycle of... for: ， in, Let be the radius corresponding to the i-th layer of medium. Let be the radius corresponding to the i-th air-medium composite structure. The radius corresponding to the (i-1)th air-dielectric composite structure is This represents the thickness of each air-medium composite layer, which is 3 mm. Then the thickness of each medium layer for: ， The A-BG formula is: ， in, The dielectric constant of the substrate material is . The dielectric constant of the inserted material is The overall equivalent dielectric constant is denoted as . The duty cycle is the volume fraction of the inserted material relative to the total material volume; based on the gradient dielectric constant... By assigning values, the thickness of the medium in each layer of the composite structure can be obtained through calculation.

5. The design method of the rectangular Luneburg lens antenna as described in claim 1, characterized in that, The high dielectric constant medium is 3D-printed nylon. , .

6. A rectangular Luneburg lens antenna using the design method of any one of claims 1 to 5, characterized in that, The rectangular Luneburg lens antenna includes a deformed Luneburg lens antenna composed of an air-dielectric nested structure and a feed antenna.

7. A satellite communication system, characterized in that, The satellite communication system uses the rectangular Luneburg lens antenna as described in claim 6.

8. A ship navigation system, characterized in that, The ship navigation system uses the rectangular Luneburg lens antenna as described in claim 6.

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