CN109586037B - a lens antenna - Google Patents

Abstract

The invention proposes a lens antenna, which aims to ensure the directivity of the lens antenna while realizing the illusion effect of optical devices, including a point light source, a sphere structure with a radius of r, a hemisphere structure with a radius of R, a sphere structure and a hemisphere structure. The structures are all left-handed materials. The spherical surface of the hemispherical structure is provided with a concave structure. The curved surface of the concave structure has the same curvature radius as the spherical surface of the spherical structure. The curved surfaces are closely attached, and the refractive index of the spherical structure gradually increases along the positive direction of the axis X passing through the spherical center O' of the spherical structure and the virtual spherical center O of the hemispherical structure in the same spherical form as the spherical surface of the hemispherical structure. The refractive index of the structure gradually increases along the direction from the spherical surface and the concave structure of the hemispherical structure to the virtual sphere center O. The point light source is inside the spherical structure, and its luminous point is located at the virtual vertex A of the hemispherical structure.

Description

a lens antenna

technical field

The invention belongs to the field of wireless communication, and particularly relates to a lens antenna.

Background technique

A lens antenna is an antenna that can pass electromagnetic waves and convert spherical waves of point sources or cylindrical waves of line sources into plane waves to obtain pencil-shaped, sector-shaped or other shaped beams. In the microwave communication system, the index to characterize the lens antenna is mainly directivity. In order to improve the weak directivity of traditional lens antennas, researchers have proposed a metamaterial-based lens antenna, such as Aghanejad I et al. In the paper "lens antenna based on transformation optics", a high-gain lens antenna based on transformation optics is disclosed, including a feed source and a hemispherical structure. A lens antenna that uses plane waves to enhance the directivity, this structure can only achieve directivity enhancement, and does not have the illusion effect of optical devices.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a lens antenna in view of the above-mentioned deficiencies of the prior art, which aims to realize the illusion effect of the optical device while ensuring the directivity of the lens antenna.

In order to achieve the above purpose, the technical solution adopted in the present invention includes a point light source 1, a spherical structure 2 with a radius of r, and a hemispherical structure 3 with a radius of R, where r<R, the spherical structure 2 and the hemispherical structure 3 are both made of left-handed materials. , the spherical surface of the hemispherical structure 3 is provided with a concave structure, the curved surface of the concave structure is the same as the radius of curvature of the spherical surface of the spherical structure 2, and the spherical structure 2 is nested in the concave structure of the hemispherical structure 3, and with The curved surface of the concave structure is closely attached; the refractive index n of the spherical structure 2 is along the positive direction of the axis X passing through the spherical center O' of the spherical structure 2 and the virtual spherical center O of the hemispherical structure 3, so as to be consistent with the spherical bending direction of the hemispherical structure 3 The same spherical form gradually increases, the refractive index n1 of the hemispherical structure ₃ gradually increases along the direction from the spherical and concave structures of the hemispherical structure 3 to the virtual sphere center O, and the virtual vertex A of the hemispherical structure 3 to the concave The distance between the curved surface of the structure and the intersection B of the axis x is d, d=0.4r～0.6r; the point light source 1 is arranged inside the spherical structure 2, and the central axis of the spherical wave emitted by the point light source 1 coincides with the axis X , the light-emitting point of the point light source 1 is located at the position of the virtual vertex A of the hemispherical structure 3 .

In the above-mentioned lens antenna, the bottom surface of the hemispherical structure 3 is obtained by truncating a circular frustum with a width l along the negative direction of the axis X of the hemisphere, and the diameter of the bottom surface is less than 2R.

In the above-mentioned lens antenna, the apex of the curved surface of the concave structure is located on the axis X.

In the above lens antenna, the refractive index n of the spherical structure is calculated by the following formula:

Among them, a represents the X-axis coordinate of the luminous point of the point light source, b represents the Y-axis coordinate of the luminous point of the point light source, A ₁ =1-ax-by, B ₁ =bx-ay, x represents the X-axis coordinate in the spherical structure, y represents the Y-axis coordinate within the sphere structure.

In the above lens antenna, the refractive index n ₁ of the hemispherical structure is calculated by the following formula:

a表示点光源的X轴坐标，b表示点光源的Y轴坐标，x表示球体结构内的X轴坐标，y表示球体结构内的Y轴坐标。Among them, n ₀ represents the refractive index at the virtual center of the hemisphere structure, R represents the radius of the hemisphere structure, r ₁ represents the distance from the point inside the hemisphere to the virtual center O,

a represents the X-axis coordinate of the point light source, b represents the Y-axis coordinate of the point light source, x represents the X-axis coordinate in the sphere structure, and y represents the Y-axis coordinate in the sphere structure.

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

First, because the present invention adopts a hemispherical structure with a defective structure, the structure utilizes the feature that the curvature radius of the curved wave front of the curved surface of the spherical wave reaching the curved surface of the defective structure is exactly the same as the curvature radius of the curved surface of the defective structure of the hemispherical structure. , the spherical wave can be converted into a plane wave; at the same time, it is precisely because the spherical structure is filled with a refractive index that gradually increases along the positive direction of the axis X in the same spherical form as the spherical surface of the hemispherical structure, which can make the point light source A phantom image point located at the center of the spherical structure is generated, so that the actual feed filled with refractive index and the phantom feed in the air medium generate the same spherical wave, but the position of the feed is different, and the illusion effect of the optical device is realized.

Description of drawings

Fig. 1 is the overall structure schematic diagram of the present invention;

Fig. 2 is the distribution schematic diagram of the refractive index of spherical structure of the present invention and hemispherical structure;

Fig. 3 is the electric field simulation result diagram of three embodiments of the present invention;

FIG. 4 is an orientation diagram of three embodiments of the present invention.

Detailed ways

Below in conjunction with accompanying drawing and specific embodiment, the present invention is described in further detail:

Embodiment 1, in this embodiment, the distance d=0.5r from the virtual vertex A of the hemispherical structure 3 to the intersection B of the curved surface of the concave structure and the axis X.

Referring to FIG. 1, a lens antenna includes a point light source 1, a spherical structure 2 with a radius of r, and a hemispherical structure 3 with a radius of R, r<R, the spherical structure 2 and the hemispherical structure 3 are both made of left-handed materials, so The spherical surface of the hemispherical structure 3 is provided with a concave structure, and the curved surface of the concave structure is the same as the radius of curvature of the spherical surface of the spherical structure 2. The curved surfaces of the spherical structure 2 are closely attached to each other; the refractive index n of the spherical structure 2 is along the positive direction of the axis X passing through the spherical center O' of the spherical structure 2 and the virtual spherical center O of the hemispherical structure 3, in the same direction as the bending direction of the spherical surface of the hemispherical structure 3. The spherical form gradually increases, and the refractive index n1 of the hemispherical structure ₃ gradually increases along the direction from the spherical surface and the concave structure of the hemispherical structure 3 to the virtual sphere center O, and the virtual vertex A of the hemispherical structure 3 to the concave structure. The distance between the intersection point B of the curved surface and the axis x is d, d=0.4r～0.6r; the point light source 1 is arranged inside the spherical structure 2, and the central axis of the spherical wave emitted by the point light source 1 coincides with the axis X, the The light-emitting point of the point light source 1 is located at the position of the virtual vertex A of the hemispherical structure 3 .

The point light source 1 is fed by a horn antenna, so that the light-emitting point of the horn antenna coincides with the light-emitting point of the point light source 1. The point light source 1 is located inside the sphere structure 2 and is on the axis X passing through the center O' of the sphere structure 2. The refractive index n filled in structure 2 is calculated by the following process:

Let the point in virtual space be w, take the point in physical space as z=x+iy, x represents the X-axis coordinate in the sphere structure, y represents the Y-axis coordinate in the sphere structure; the virtual vertex A of the hemisphere structure is located in the sphere structure Inside, A=a+ib, a represents the X-axis coordinate of the point light source, a=0.5cm, b represents the Y-axis coordinate of the point light source, b=0. Then the mapping relationship from physical space to virtual space is:

where A* is the complex conjugate of A, and both the left and right ends of formula (1) are derived from z to obtain

where dw represents the differential of w, dz represents the differential of z, A ₁ =1-ax-by and B ₁ =bx-ay.

So the refractive index n inside the sphere structure is:

表示

的模值。in

express

the modulo value.

The refractive index n of the spherical structure 2 increases gradually along the positive direction of the axis X passing through the spherical center O' of the spherical structure 2 and the virtual spherical center O of the hemispherical structure 3 in the same spherical form as the spherical surface of the hemispherical structure 3, as shown in the figure As shown in 2, the refractive index is related to the color of the figure. The darker the color, the lower the refractive index, the lighter the color, the higher the refractive index. The right gradually increases.

In formula (3), the spherical structure 2 can be made larger or smaller by making the following modifications to each variable. When N<1, the volume becomes larger, and when N>1, the volume becomes smaller.

The point B where the spherical surface of the spherical structure 2 intersects with the positive direction of the axis X is embedded in the interior of the hemispherical structure 3, forming a concave structure. The point B where the spherical surface of structure 2 intersects the positive direction of axis X perfectly coincides with the vertex of the curved surface of the concave structure, and in order to obtain better directionality, the bottom surface of the hemispherical structure 3 is truncated by the hemispherical structure along the negative direction of the axis X. The width is The diameter of the bottom surface of l is less than 2R, R=1.5cm, l=0.135R=0.2025cm, and the refractive index n ₁ of the hemispherical structure 3 is calculated by the following formula:

Among them, n ₀ represents the refractive index at the virtual center of the hemisphere structure, n ₀ =1.33, R represents the radius of the hemisphere structure, r ₁ represents the distance from the point inside the hemisphere to the virtual center O,

The refractive index n1 of the hemispherical structure ₃ gradually increases along the direction from the spherical surface and the concave structure of the hemispherical structure 3 to the virtual sphere center O. As shown in Figure 2, the refractive index is related to the color of the figure, and the darker the color, the more refraction The smaller the ratio and the lighter the color, the greater the refractive index. The color in the figure goes from dark to light from the spherical surface and the concave structure surface of the hemispherical structure 3 to the virtual sphere center O, indicating that the refractive index changes from small to large.

The left-handed material refers to a material whose dielectric constant and magnetic permeability are both negative values, and the refractive index calculated by the dielectric constant and the magnetic permeability is used in the present invention.

In the present invention, the refractive index inside the spherical structure and the inside of the hemispherical structure can be realized by two methods. In the first method, the refractive index can be obtained by using formula (3) and formula (5); By discretizing the graded refractive index of formula (3) and formula (5), since the refractive index of the spherical structure is the same on the spherical surface with the same bending direction as the spherical surface of the hemispherical structure 3, it can be obtained by such a spherical surface The graded index of refraction is discretized in the form of increasing m; the curved surface formed by the points with the same refractive index in the hemispherical structure is a spherical surface, which is discretized in the form of increasing m by the concentric sphere with the virtual sphere center O. If the number of discrete layers is high, the two methods will give similar results, but in general, the results obtained by discretizing the index are slightly worse than those obtained by the graded index, because the discrete index does not fully All graded refractive index values are included, so the present invention adopts the graded refractive index for simulation implementation.

Embodiment 2, the structure of this embodiment is the same as that of Embodiment 1, only the distance from the virtual vertex A of the hemispherical structure 3 to the intersection B of the curved surface of the concave structure and the axis X is adjusted: d=0.4r.

Embodiment 3, the structure of this embodiment is the same as that of Embodiment 1, only the distance from the virtual vertex A of the hemispherical structure 3 to the intersection B of the curved surface of the concave structure and the axis X is adjusted: d=0.6r.

The technical effects of the present invention will be described in detail below in conjunction with simulation experiments.

1. Simulation conditions and content:

The following simulation experiments are carried out based on the three embodiments of the present invention, which are all completed by using COMSOL Multiphysics 5.2 multiphysics simulation software.

Simulation 1, the electric fields of the three embodiments are simulated, and the results are shown in FIG. 3 .

In simulation 2, the direction diagrams of the three embodiments are simulated, and the results are shown in FIG. 4 .

2. Analysis of simulation results:

Referring to Figure 3, the spherical wave emitted by the point light source is still spherical in space only when it passes through the spherical structure. The wave image is emitted from the feed located at the center of the spherical structure, but is generated by the feed located at the virtual vertex A of the hemispherical structure, which realizes the illusion effect of the optical device; and the spherical wave turns through the spherical structure first and then through the hemispherical structure. For plane waves, this is due to the fact that the wavefront from a point light source travels the same optical path to the bottom surface of the hemispherical structure, so the spherical wave turns into a plane wave. The plane wave in Fig. 3(a) is slightly better than that in Fig. 3(b) and Fig. 3(c), because the distance d from the virtual vertex A of the hemispherical structure 3 to the intersection B of the curved surface of the concave structure and the axis X deviates from 0.5 When r, the spherical wave emitted by the point light source 1 passes through the refractive index inside the spherical structure 2 and reaches the curved surface of the concave structure. The curvature radius of the curved surface is different from the curvature radius of the curved surface of the concave structure.

Referring to Fig. 4, the far-field mode exhibits good directivity between angles of -30° to +30°, and the main beam of Fig. 4(a) is located in the range of -7° to +7°, which can reach more than 20dB, and The beam is narrower; while the main beam in Fig. 4(b) is in the range of -12°～+12, the beam is wider than that in Fig. 4(a), and the result is slightly worse; the main beam in Fig. 4(c) is located at -15°～+15 Within the range, the beam is wider than that of Fig. 4(a), and the side lobes are larger. The result of this graph is not as good as that of Fig. 4(a) and Fig. 4(b), but the directivity can also be achieved.

The above simulation results show that the present invention can realize the illusion effect of the antenna while realizing the transformation of the spherical wave to the plane wave to enhance the directivity of the lens antenna.

Claims (3)

1. A lens antenna, characterized in that it comprises a point light source (1), a spherical structure (2) with a radius of r and a hemispherical structure (3) with a radius of R, r<R, the spherical structure (2) and The hemispherical structure (3) is made of left-handed material, and the spherical surface of the hemispherical structure (3) is provided with a concave structure, and the curved surface of the concave structure has the same curvature radius as the spherical surface of the spherical structure (2). 2) Nested in the concave structure of the hemispherical structure (3) and closely attached to the curved surface of the concave structure; the refractive index n of the spherical structure (2) passes through the spherical center O' of the spherical structure (2) and the hemisphere The positive direction of the axis X of the virtual sphere center O of the body structure (3) starts from the intersection of the negative direction of the axis X and the spherical structure (2), and takes the intersection of the positive direction of the axis X and the spherical structure (2) as the end point. increases, the refractive index n formula is:

where a represents the X-axis coordinate of the luminous point of the point light source (1), b represents the Y-axis coordinate of the luminous point of the point light source (1), A ₁ =1-ax-by, B ₁ =bx-ay, x represents the spherical structure ( 2) X-axis coordinate, y represents the Y-axis coordinate in the spherical structure (2); the refractive index n ₁ of the hemispherical structure (3) passes through the spherical structure (2) sphere center O' and the hemispherical structure ( 3) The positive direction of the axis X of the virtual sphere center O starts from the intersection of the hemispherical structure (3) and the spherical structure (2), and gradually increases with the intersection of the positive direction of the axis X and the hemispherical structure (3) as the end point. large, its refractive index n ₁ formula is:

where n ₀ represents the refractive index at the virtual center O of the hemispherical structure (3), R represents the radius of the hemispherical structure (3), and r ₁ represents the distance from a point inside the hemispherical structure (3) to the virtual center O,

a represents the X-axis coordinate of the light-emitting point of the point light source (1), b represents the Y-axis coordinate of the light-emitting point of the point light source (1), x represents the X-axis coordinate in the spherical structure (2), and y represents the Y-axis coordinate; the distance from the virtual vertex A of the hemispherical structure (3) to the intersection B of the curved surface of the concave structure and the axis X is d, d=0.4r～0.6r; the point light source (1) is arranged on the sphere Inside the structure (2), and the central axis of the spherical wave emitted by the point light source (1) coincides with the axis X, the luminous point of the point light source (1) is located at the virtual vertex A of the hemispherical structure (3). 2. A lens antenna according to claim 1, characterized in that the bottom surface of the hemispherical structure (3) is obtained by truncating a circular frustum with a width of l along the negative direction of the axis X by the hemispherical body, and the hemispherical body The diameter of the bottom surface of the structure (3) is less than 2R. 3 . The lens antenna according to claim 1 , wherein the apex of the curved surface of the concave structure is located on the axis X. 4 .

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