WO2021012715A1 - 一种基于三维阻抗匹配透镜的超宽带高增益透镜天线及其设计方法 - Google Patents

一种基于三维阻抗匹配透镜的超宽带高增益透镜天线及其设计方法 Download PDF

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WO2021012715A1
WO2021012715A1 PCT/CN2020/083888 CN2020083888W WO2021012715A1 WO 2021012715 A1 WO2021012715 A1 WO 2021012715A1 CN 2020083888 W CN2020083888 W CN 2020083888W WO 2021012715 A1 WO2021012715 A1 WO 2021012715A1
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lens
impedance matching
refractive index
equivalent refractive
dimensional impedance
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PCT/CN2020/083888
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English (en)
French (fr)
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蒋卫祥
田翰闱
李欣
崔铁军
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东南大学
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q1/00—Details of, or arrangements associated with, antennas
    • H01Q1/36—Structural form of radiating elements, e.g. cone, spiral, umbrella; Particular materials used therewith
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q1/00—Details of, or arrangements associated with, antennas
    • H01Q1/50—Structural association of antennas with earthing switches, lead-in devices or lightning protectors
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q13/00—Waveguide horns or mouths; Slot antennas; Leaky-waveguide antennas; Equivalent structures causing radiation along the transmission path of a guided wave
    • H01Q13/02—Waveguide horns
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q13/00—Waveguide horns or mouths; Slot antennas; Leaky-waveguide antennas; Equivalent structures causing radiation along the transmission path of a guided wave
    • H01Q13/02—Waveguide horns
    • H01Q13/0283—Apparatus or processes specially provided for manufacturing horns
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q15/00—Devices for reflection, refraction, diffraction or polarisation of waves radiated from an antenna, e.g. quasi-optical devices
    • H01Q15/02—Refracting or diffracting devices, e.g. lens, prism
    • H01Q15/10—Refracting or diffracting devices, e.g. lens, prism comprising three-dimensional array of impedance discontinuities, e.g. holes in conductive surfaces or conductive discs forming artificial dielectric
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q19/00—Combinations of primary active antenna elements and units with secondary devices, e.g. with quasi-optical devices, for giving the antenna a desired directional characteristic
    • H01Q19/06—Combinations of primary active antenna elements and units with secondary devices, e.g. with quasi-optical devices, for giving the antenna a desired directional characteristic using refracting or diffracting devices, e.g. lens
    • H01Q19/062—Combinations of primary active antenna elements and units with secondary devices, e.g. with quasi-optical devices, for giving the antenna a desired directional characteristic using refracting or diffracting devices, e.g. lens for focusing
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q19/00—Combinations of primary active antenna elements and units with secondary devices, e.g. with quasi-optical devices, for giving the antenna a desired directional characteristic
    • H01Q19/06—Combinations of primary active antenna elements and units with secondary devices, e.g. with quasi-optical devices, for giving the antenna a desired directional characteristic using refracting or diffracting devices, e.g. lens
    • H01Q19/08—Combinations of primary active antenna elements and units with secondary devices, e.g. with quasi-optical devices, for giving the antenna a desired directional characteristic using refracting or diffracting devices, e.g. lens for modifying the radiation pattern of a radiating horn in which it is located

Definitions

  • the invention relates to an ultra-wideband high-gain three-dimensional impedance matching lens antenna and a design method thereof, and belongs to the field of new artificial electromagnetic devices.
  • the horn antenna is a kind of surface antenna, which is characterized in that the terminal of the feeder waveguide section is gradually opened at a certain angle, most of which are circular or rectangular openings, and the overall shape is horn-like. It is the most common and widely used type of microwave device .
  • the horn antenna is widely used because of its simple structure, wide operating frequency, large power capacity, low return loss, and low insertion loss. However, in order to obtain better directivity or higher gain, it must have a larger size, which also limits its practical application in many occasions.
  • the dielectric material can be made into a certain shape based on geometric optics theory, and placed on the mouth surface of the horn antenna to form a lens antenna to converge electromagnetic signals to form a narrower beam and improve The directionality of the horn antenna.
  • most of the existing lenses use uniform dielectric materials and exhibit a predetermined shape through mechanical processing. Their large volume, high processing accuracy, and high cost are all shortcomings that limit their wide application.
  • the object of the invention is to realize an ultra-wideband high-gain lens antenna with simple structure, low cost, wide working frequency, good directivity, and low return loss.
  • An ultra-wideband high-gain lens antenna based on a three-dimensional impedance matching lens including a three-dimensional impedance matching lens, a double-ridged horn antenna and a waveguide extension.
  • the double-ridged horn antenna opening is connected to the waveguide extension, and the three-dimensional impedance matching lens is embedded in the waveguide In the extension section, the length of the waveguide extension section is equal to the thickness of the three-dimensional impedance matching lens to completely cover the sides of the three-dimensional impedance matching lens.
  • the three-dimensional impedance matching lens has a certain thickness and the shape is consistent with the shape of the horn antenna mouth surface.
  • the three-dimensional impedance matching lens includes several equivalent refractive index units.
  • the equivalent refractive index units include two types. One type includes a pair of perforated dielectric substrates and a medium covered with a square metal patch on both sides. The substrate, the pair of perforated dielectric substrates are symmetrically attached to both sides of the double-sided metal-covered dielectric substrate; the other type includes three perforated dielectric substrates, of which two perforated dielectric substrates have a fixed and equal hole size, so The two dielectric substrates with fixed and equal-sized holes are symmetrically and closely attached to both sides of the remaining perforated dielectric substrate.
  • the equivalent refractive index subsections of the three-dimensional impedance matching lens are in the three orthogonal directions of x, y, and z in a gradually decreasing distribution from the center to both sides.
  • the equivalent refraction at both ends of the lens The rate is 1, which perfectly matches the free space.
  • the double-ridged horn antenna is a broadband horn antenna, which is used as a feed source to radiate broadband-like spherical waves, and the working bandwidth of the lens antenna depends on the working bandwidth of the double-ridged horn antenna.
  • the present invention also provides a design method of an ultra-wideband high-gain lens antenna based on a three-dimensional impedance matching lens, which includes the following steps:
  • the double-ridged horn antenna is a double-ridged pyramid horn antenna with a square mouth surface.
  • the extension of the horn mouth surface is the waveguide extension.
  • the horn aperture surface is set to ensure that the waveguide extension completely covers the three-dimensional impedance Match the side of the lens and set the length of the waveguide extension;
  • the three-dimensional impedance matching lens Considering the square mouth of the double-ridged pyramid horn antenna, set the three-dimensional impedance matching lens to a rectangular parallelepiped shape, and set the length, width and thickness of the three-dimensional impedance matching lens according to the design formula of the three-dimensional impedance matching lens; the three-dimensional impedance matching lens includes several, etc.
  • the equivalent refractive index unit is composed of two types: one type includes a pair of perforated dielectric substrates, a dielectric substrate covered with a square metal patch on both sides, and the pair of perforated dielectric substrates are symmetrically attached On both sides of a dielectric substrate covered with metal on both sides; one type includes three perforated dielectric substrates, of which two perforated dielectric substrates have fixed and equal hole sizes, and the two fixed and equal-sized holes are symmetrically tight Paste on both sides of the remaining perforated dielectric substrate.
  • (21) Use Matlab software to calculate and extract the discrete equivalent refractive index distribution of the three-dimensional matching lens. It is specified that the discrete interval in the x and y directions is about 0.1 wavelengths, and the discrete interval in the z direction is about 0.06 wavelengths, and the corresponding lens is obtained.
  • the size of the equivalent refractive index unit is set to be about 0.1 wavelengths in the x and y directions.
  • the two equivalent refractive index units one type is adjusted by changing the side length of the two layers of square metal patches in the equivalent refractive index unit; Adjust the size of the equivalent refractive index by changing the hole size in the middle layer of the equivalent refractive index unit; when designing the two types of equivalent refractive index units, the dielectric substrate used is a Teflon sheet with a dielectric constant of 2.2 and a loss tangent of 0.0001.
  • the metal patch is made of pure copper;
  • the equivalent refractive index units of different sizes are correspondingly arranged according to the equivalent refractive index three-dimensional matrix to form the three-dimensional impedance matching lens with a rectangular parallelepiped shape.
  • n 1 is the free-space refractive index
  • t is the thickness of the lens
  • f is the vertical distance between the point source and the edge of the lens
  • the equivalent refractive index of the three-dimensional impedance matching lens in the three orthogonal directions of x, y, z is gradually decreasing from the center to the two sides.
  • the orthogonal directions all change linearly, so the above formula changes to:
  • the equivalent refractive index on both sides of the lens should be 1, and the equivalent refractive index of the lens changes linearly with a decreasing center, so:
  • n m (0) is the maximum value of the equivalent refractive index of the lens
  • n m (z) 2n(x,y)-1 (9);
  • the present invention has the following advantages:
  • the three-dimensional impedance matching lens of the present invention is quickly designed according to the existing formula, adapts to different application scenarios, and only needs to adjust the parameters in the formula for different application scenarios.
  • the three-dimensional impedance matching lens of the present invention is formed by stacking microwave dielectric plates, which can be processed by PCB technology, with low design difficulty, low precision requirements and low cost.
  • the equivalent refractive index unit used in the present invention has a flat refractive index curve and can work in a very wide frequency band.
  • the working bandwidth of the lens antenna depends only on the bandwidth of the double-ridged horn antenna as the feed source And the double-ridged horn antenna can be replaced by other types of broadband horn antennas.
  • the mechanism of the present invention is that the coherent electromagnetic wave emitted from the high-frequency signal source radiates spherical waves through the double-ridged horn antenna, and passes through the three-dimensional impedance matching lens fixed in the extension of the waveguide on the horn antenna mouth surface.
  • the non-uniform plane wave transformed into the isophase plane orthogonal to the propagation direction radiates to the free space, so the far field has good directivity and high gain.
  • the equivalent refractive index of the three-dimensional impedance matching lens of the present invention is in the three orthogonal directions of x, y, and z in a gradually decreasing distribution from the center to both sides, especially in the z direction of electromagnetic wave propagation ,
  • the equivalent refractive index at both ends of the lens is 1, which is fully matched with free space, and there is no electromagnetic wave reflection, so there is no need to add a matching layer or use other techniques to reduce the antenna return loss.
  • Figure 1 is a schematic diagram of an ultra-wideband high-gain lens antenna structure based on a three-dimensional impedance matching lens
  • Figure 2 is a schematic diagram of the structure of a double-ridged pyramid horn antenna with a waveguide extension
  • Figure 3 is a schematic diagram of the coaxial-double-ridge waveguide conversion structure
  • Figure 4 is the simulation result of the -10dB return loss of the double-ridged pyramid horn antenna with waveguide extension
  • Fig. 5 is an equivalent refractive index distribution diagram of a three-dimensional impedance matching lens shaped as a cuboid
  • Fig. 6 is a schematic diagram of the equivalent refractive index unit structure with double-sided covering square metal patches
  • Fig. 7 is a schematic diagram of the equivalent refractive index unit structure including a three-layer perforated dielectric substrate;
  • Fig. 8 is a schematic diagram of the structure of layers 1-3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29-31 of a three-dimensional impedance matching lens;
  • FIG. 9 is a schematic diagram of the fourth and 28th layers of the three-dimensional impedance matching lens.
  • FIG. 10 is a schematic diagram of the sixth and 26th layers of the three-dimensional impedance matching lens
  • 11 is a schematic diagram of the eighth and 24th layers of the three-dimensional impedance matching lens
  • Figure 12 is a schematic diagram of the 10th and 22nd layers of a three-dimensional impedance matching lens
  • Figure 13 is a schematic diagram of the 12th and 20th layers of a three-dimensional impedance matching lens
  • 14 is a schematic diagram of the 14th and 18th layers of the three-dimensional impedance matching lens
  • 15 is a schematic diagram of the 16th layer structure of a three-dimensional impedance matching lens
  • Figure 16 is a simulation result of -10dB return loss of an ultra-wideband high-gain lens antenna based on a three-dimensional impedance matching lens
  • Figure 17 is a comparison diagram of the gain results of an ultra-wideband high-gain lens antenna based on a three-dimensional impedance matching lens and a double-ridged pyramid horn antenna without a three-dimensional impedance matching lens.
  • An ultra-wideband high-gain lens antenna based on a three-dimensional impedance matching lens includes a cuboid-shaped three-dimensional impedance matching lens 1, a square-shaped double-ridged pyramid horn antenna feed 2 and a waveguide extension 3
  • the opening of the double-ridged horn antenna is connected to the waveguide extension, and the three-dimensional impedance matching lens is embedded in the waveguide extension.
  • the length of the waveguide extension is equal to the thickness of the three-dimensional impedance matching lens to completely cover the side of the three-dimensional impedance matching lens.
  • the double-ridged pyramid horn antenna with waveguide extension is shown in Figure 2.
  • the coherent electromagnetic wave emitted from the high-frequency signal source is coaxially fed into the double-ridged pyramid horn antenna, and converted into a spherical wave through the coaxial-double-ridged waveguide conversion structure 11.
  • the side view of the coaxial-dual-ridge waveguide conversion structure is shown in Fig. 3.
  • Two ridges 4 are connected symmetrically around the z-axis on the inner wall of the waveguide section at the rear end of the double-ridged horn antenna to form a double-ridged waveguide structure.
  • the end of the waveguide is inserted into the coaxial structure 5 along the y-axis.
  • One end of the coaxial is higher than the double-ridge waveguide.
  • the probe 6 at the other end is connected with the ridge on the lower side of the double-ridge waveguide to ensure the coaxial and double-ridge waveguide.
  • the spherical-like electromagnetic wave obtained by the coaxial-double-ridge waveguide conversion structure is transformed into a non-uniform plane wave with an isophase plane orthogonal to the propagation direction through a three-dimensional impedance matching lens fixed in the extension of the waveguide of the horn antenna mouth surface, and is free Space radiation.
  • the lens antenna is easy to design, simple in structure, and low in cost. It has been verified by simulation to have a wide operating frequency, high gain, and low return loss.
  • the design principle of the three-dimensional impedance matching lens antenna is as follows, assuming that the thickness of the lens is t and the distance between the point source and the edge of the lens is f. Based on the geometric optics theory, the electromagnetic wave radiated from a point source passes through a three-dimensional impedance matching lens, and the phase of the emitted wave is corrected to become a non-uniform plane wave with the isophase plane orthogonal to the propagation direction. According to Fermat's theorem, in order to ensure that the emitted waves are plane waves of equal phase, it is necessary to ensure that any electromagnetic wave radiated from a point source passes through the free space and the total optical path of the lens is equal. Therefore, assuming that the center of the lens is the origin of the coordinate axis, and the direction of the line connecting the point source to the center of the lens is the z direction, for any point (x, y, z) on the lens, there are:
  • n 1 is the free-space refractive index, generally taken as 1, Is the refractive index of the lens at (x, y, z), ⁇ x, ⁇ y are the position changes along the x-axis and y-axis, respectively.
  • the equivalent refractive index of the three-dimensional impedance matching lens in the three orthogonal directions of x, y, z is gradually decreasing from the center to the two sides.
  • the equation (1) changes to:
  • n m (z) is the maximum refractive index of the lens in the direction perpendicular to the z-axis, and n m (z) is only a function of the variable z.
  • the equivalent refractive index on both sides of the lens should be 1, and the equivalent refractive index of the lens changes linearly with a decreasing center, so:
  • n m (0) is the maximum value of the equivalent refractive index of the lens.
  • n m (z) 2n(x,y)-1 (9);
  • Double-ridged horn antenna and waveguide extension In order to simplify the design of the three-dimensional impedance matching lens, the double-ridged horn antenna uses a square-faced double-ridged pyramid horn antenna. As shown in Figure 2, the extension of the horn face is a waveguide extension.
  • the waveguide extension is a square frame, and the shape and size of the waveguide aperture are the same as that of the double-ridged horn antenna; the length of the waveguide extension is equal to the thickness of the three-dimensional impedance matching lens, which is used to fix the three-dimensional impedance matching lens to the double-ridged horn Antenna mouth surface, and completely cover the sides of the three-dimensional impedance matching lens.
  • the commercial full-wave simulation software CST was used for simulation verification.
  • the results show that the -10dB return loss bandwidth of the double-ridged pyramid horn antenna is 5.16-15.71GHz, as shown in Figure 4.
  • the bandwidth is 101.1%, which is an ultra-wideband antenna.
  • Three-dimensional impedance matching lens Considering the square mouth of the double-ridged pyramid horn antenna, set the three-dimensional impedance matching lens to be a rectangular parallelepiped shape. According to equations (7), (8), (9), the length and width of the three-dimensional impedance matching lens are set to be 195 mm (6.11 wavelengths), and the thickness is 30.396 mm (0.95 wavelengths).
  • the equivalent refractive index distribution of a three-dimensional matching lens shaped as a rectangular parallelepiped is shown in Figure 5. Its maximum equivalent refractive index is 3.2. Considering that the equivalent refractive index of the equivalent refractive index unit cannot be completely equal to air, the lens is The minimum equivalent refractive index is approximately 1.2.
  • the three-dimensional impedance matching lens includes several equivalent refractive index units.
  • the equivalent refractive index distribution of the lens is obtained according to formulas (7), (8), and (9), thereby obtaining a three-dimensional matrix of equivalent refractive index.
  • the refractive index value of is arranged corresponding to the units with equal equivalent refractive index, and finally a three-dimensional impedance matching lens is obtained.
  • the equivalent refractive index unit is composed of two types: one type includes a pair of perforated dielectric substrates, a dielectric substrate covered with a square metal patch on both sides, and the pair of perforated dielectric substrates are symmetrically attached to the double-sided covering metal.
  • one type On both sides of the dielectric substrate; one type includes three perforated dielectric substrates, of which two perforated dielectric substrates are fixed and equal in size, and the two fixed and equal-sized dielectric substrates are symmetrically attached to the remaining one. Hole dielectric substrate on both sides.
  • the two types of equivalent refractive index units include a pair of perforated dielectric substrates 8 and a dielectric substrate 9 covered with a square metal patch on both sides.
  • the aperture radius of the perforated dielectric substrate 8 is fixed at 1.25 mm. Adjust the size of the side length A of the two-layer square metal patch in the effective refractive index unit, and adjust the equivalent refractive index.
  • the schematic diagram of the structure is shown in Figure 6.
  • the simulation verifies that the equivalent refractive index range that it can cover is 1.35-3.2;
  • One type includes three perforated dielectric substrates, of which two perforated dielectric substrates 8 have a fixed and equal hole size, with a radius of 1.25 mm.
  • the equivalent refractive index is shown in Figure 7.
  • the equivalent refractive index range that it can cover is 1.2-1.35.
  • the dielectric substrate used is a Teflon plate with a dielectric constant of 2.2 and a loss tangent of 0.0001, and the metal patch is made of pure copper.
  • the equivalent refractive index units of different sizes are correspondingly arranged according to the equivalent refractive index three-dimensional matrix to form the three-dimensional impedance matching lens with a rectangular parallelepiped shape.
  • the three-dimensional impedance matching lens is processed in layers using the PCB process. There are 31 layers of the three-dimensional impedance matching lens along the z axis, and no gaps are left between the layers.
  • the thickness of the first and 31st dielectric substrates is 0.5mm (0.016 wavelengths), the thickness of the other dielectric substrates is 1mm (about 0.03 wavelengths), and the thickness of the metal patch is 0.018mm (0.00056 wavelengths).
  • a total of 31 layers are shown in Figure 8-15.
  • the arrangement pattern of each layer is determined according to the aforementioned lens design method. When the variables in formulas (7), (8), (9) are assigned fixed values, the corresponding unique arrangement pattern is determined.
  • the double-ridged horn antenna is a broadband horn antenna
  • the working bandwidth of the lens antenna depends on the working bandwidth of the double-ridged horn antenna
  • the double-ridged horn antenna can be replaced by other types of broadband horn antennas.
  • the shape of the three-dimensional impedance matching lens is the same as that of the double-ridged horn antenna.
  • the design only needs to limit the value range of the lens on the x and y axes to ensure that the value range is equal to the antenna aperture.
  • the x and y axes are taken The value range is (-97.5mm, 97.5mm).
  • the -10dB return loss bandwidth of the ultra-wideband high-gain lens antenna based on the three-dimensional impedance matching lens is 5.25-15.2GHz, as shown in Figure 16, the relative bandwidth is 97.3%, which is an ultra-wideband antenna, which verifies its wideband And the advantages of low return loss;
  • the uniqueness of the present invention is that it combines a new artificial electromagnetic medium with a lens antenna, and uses sub-wavelength equivalent refractive index units to construct a lens with a gradient distribution of refractive index.
  • the equivalent refractive index of the lens is orthogonal to x, y, and z. The directions show a gradual distribution from the center to both sides, especially in the electromagnetic wave propagation direction, the equivalent refractive index at both ends of the lens is 1, which is completely matched with the free space, no need to add a matching layer or use other techniques to reduce antenna echo loss.
  • the equivalent refractive index unit used has a flat refractive index curve, it can work in a very wide frequency band, and the working bandwidth of the lens antenna depends only on the bandwidth of the double-ridged horn antenna as the feed source.
  • the lens antenna can maintain high directivity and low return loss performance in the entire working frequency band, and has the advantages of easy design, simple structure, and low cost. It can replace traditional uniform dielectric lens antennas in satellite communications and millimeter wave radars. And microwave bioimaging and other fields have important application value.

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Abstract

本发明公开了一种基于三维阻抗匹配透镜的超宽带高增益透镜天线及其设计方法，包括三维阻抗匹配透镜、双脊喇叭天线馈源及波导延长段，双脊喇叭天线开口与波导延长段相连，三维阻抗匹配透镜被内嵌在波导延长段中，波导延长段长度与三维阻抗匹配透镜厚度相等，以完全覆盖三维阻抗匹配透镜侧边。从高频信号源发出的相干电磁波经双脊喇叭天线辐射类球面波，通过固定于喇叭天线口面波导延长段内的三维阻抗匹配透镜，转变为等相位面正交于传播方向的非均匀平面波，并向自由空间辐射。该透镜天线易于设计、结构简单、成本低廉、工作频带宽、增益高、回波损耗小，可以替代传统均匀介质透镜天线，在许多领域均具有很高的应用价值。

Description

一种基于三维阻抗匹配透镜的超宽带高增益透镜天线及其设计方法 技术领域
本发明涉及一种超宽带高增益三维阻抗匹配透镜天线及其设计方法，属于新型人工电磁器件领域。
背景技术
喇叭天线属于一种面天线，其特征在于馈电波导段终端以一定角度渐变张开，大多为圆形或矩形口面，整体形状呈喇叭状，是最为普遍、使用最为广泛的一类微波器件。喇叭天线之所以被广泛应用，原因在于其具有结构简单、工作频带宽、功率容量大、回波损耗小、插入损耗小等优点。但是，要想获得较好的定向性或较高的增益，其必定具有较大的尺寸，这也限制了其在许多场合的实际应用。为了在较小的尺寸内获得同等的性能，可以将介质材料基于几何光学理论制作成一定的形状，放置在喇叭天线的口面上组成透镜天线，以汇聚电磁波信号，形成较窄的波束，提高喇叭天线的定向性。然而现有的透镜大都采用均匀介质材料，经由机械加工呈现出既定的形状，其庞大的体积、较高的加工精度、高昂的成本均是限制其被广泛应用的短板。
发明内容
发明目的：本发明的目的是实现一种结构简单、成本低廉、工作频带宽、定向性好、回波损耗低的超宽带高增益透镜天线。
技术方案：为实现上述发明目的，本发明采用以下技术方案：
一种基于三维阻抗匹配透镜的超宽带高增益透镜天线，包括三维阻抗匹配透镜、双脊喇叭天线和波导延长段，双脊喇叭天线开口与波导延长段相连，三维阻抗匹配透镜被内嵌在波导延长段中，波导延长段长度与三维阻抗匹配透镜厚度相等，以完全覆盖三维阻抗匹配透镜侧边。
可选的，三维阻抗匹配透镜具有一定厚度，且形状与喇叭天线口面形状一致。
可选的，三维阻抗匹配透镜包括若干个等效折射率单元，所述等效折射率单元包括两类，其中，一类包括一对打孔介质基板和一块双面覆盖正方形金属贴片的介质基板，所述一对打孔介质基板对称紧贴于双面覆盖金属的介质基板两侧；另一类包括三块打孔介质基板，其中两块打孔介质基板打孔大小固定且相等，所述两块打固定且相等大小孔的介质基板对称紧贴于剩余一块打孔介质基板两侧。
可选的，三维阻抗匹配透镜的等效折射率分部在x、y、z三个正交方向均呈由中心向两侧递减的渐变分布，沿电磁波的传播方向，透镜两端的等效折射率为1，与自由空间完全匹配。
可选的，双脊喇叭天线为宽带喇叭天线，作为馈源辐射宽带类球面波，透镜天线工作带宽取决于双脊喇叭天线工作带宽。
本发明还提供了一种基于三维阻抗匹配透镜的超宽带高增益透镜天线的设计方法，包括以下步骤：
(1)设计双脊喇叭天线、波导延长段；
双脊喇叭天线选用正方形口面的双脊角锥喇叭天线，喇叭口面伸出部分为波导延长段，根据三维阻抗匹配透镜设计公式，设定喇叭口径面，为保证波导延长段完全覆盖三维阻抗匹配透镜侧边，设定波导延长段长度；
(2)设计三维阻抗匹配透镜；
考虑双脊角锥喇叭天线的正方形口面，设定三维阻抗匹配透镜为长方体形状，根据三维阻抗匹配透镜设计公式，设定三维阻抗匹配透镜长度、宽度和厚度；三维阻抗匹配透镜包括若干个等效折射率单元，所述等效折射率单元由两类构成：一类包括一对打孔介质基板，一块双面覆盖正方形金属贴片的介质基板，所述一对打孔介质基板对称紧贴于双面覆盖金属的介质基板两侧；一类包括三块打孔介质基板，其中两块打孔介质基板打孔大小固定且相等，所述两块打固定且相等大小孔的介质基板对称紧贴于剩余一块打孔介质基板两侧。
进一步的，等效折射率单元的具体设计步骤如下：
(21)使用Matlab软件计算并提取出三维匹配透镜的离散等效折射率分布，规定在x、y方向离散间隔约为0.1个波长，在z方向离散间隔约为0.06个波长，得到对应于透镜等效折射率分布的三维矩阵，此处波长指定为双脊喇叭天线的中心波长；
(22)考虑到三维匹配透镜在x、y方向离散间隔约为0.1个波长，在z方向离散间隔约为0.06个波长，设定等效折射率单元尺寸在x、y方向约为0.1个波长，在z方向约为0.06个波长；所述两种等效折射率单元，一类通过改变等效折射率单元中两层正方形金属贴片的边长，调整其等效折射率大小；一类通过改变等效折射率单元中间层打孔大小，调整其等效折射率大小；设计两类等效折射率单元时，采用的介质基板为介电常数2.2，损耗角正切为0.0001的Teflon板材，金属贴片采用纯铜材质；
(23)按照等效折射率三维矩阵对应排布不同尺寸的等效折射率单元，组成所述形为长方体的三维阻抗匹配透镜。
进一步的，整个透镜的等效折射率分布计算方法为：
根据费马定理，为保证出射波为等相位的平面波，则需保证从点源辐射的任意电磁波经由自由空间和透镜后总光程相等；因此，假定透镜中心为坐标轴原点，点源至透镜中心的连线方向为z方向，对于透镜上任一点(x,y,z),有：
Figure PCTCN2020083888-appb-000001
其中，n 1为自由空间折射率；t为透镜的厚度，f为点源距离透镜边缘的垂直距离；
不同于其他透镜，该三维阻抗匹配透镜的等效折射率在x、y、z三个正交方向均呈由中心向两侧递减的渐变分布，为方便起见，在这里我们假设其沿三个正交方向均呈线性变化，由此上式变化为：
Figure PCTCN2020083888-appb-000002
令
Figure PCTCN2020083888-appb-000003
上式简化为：
Figure PCTCN2020083888-appb-000004
对上式积分，方程变为：
Figure PCTCN2020083888-appb-000005
当z固定不变时，上式简化为：
Figure PCTCN2020083888-appb-000006
假设透镜的等效折射率在x、y方向拥有相同的线性变化趋势，则有：
Figure PCTCN2020083888-appb-000007
假设在z方向上，透镜两侧的等效折射率应为1，且透镜的等效折射率呈线性中心递减变化，因此：
Figure PCTCN2020083888-appb-000008
将上式带入公式(5)，则：
Figure PCTCN2020083888-appb-000009
其中，n m(0)为透镜等效折射率的最大值；
假设等效折射率为线性变化，因此：
n m(z)＝2n(x,y)-1               (9)；
因此，根据式(7)、(8)、(9)，得到整个透镜的等效折射率分布。
有益效果：与现有技术相比，本发明具有以下优点：
1、容易设计：本发明的三维阻抗匹配透镜依据现有公式进行快速设计，适应不同应用场景，只需针对不同应用场景对公式中参数进行调整。
2、结构简单，成本低廉：本发明的三维阻抗匹配透镜由微波介质板堆叠而成，可由PCB工艺进行加工，设计难度低，精度要求不高，成本低廉。
3、工作频带宽：本发明所采用的等效折射率单元具有平坦的折射率曲线，可以工作在非常宽的频带内，透镜天线的工作带宽只取决于作为馈源的双脊喇叭天线的带宽，且双脊喇叭天线可由其他类型宽带喇叭天线代替。
4、增益高、定向性好：本发明机理在于从高频信号源发出的相干电磁波经双脊喇叭天线辐射类球面波，通过固定于喇叭天线口面的波导延长段内的三维阻抗匹配透镜，转变为等相位面正交于传播方向的非均匀平面波向自由空间辐射，因此远场定向性好，增益高。
5、回波损耗低：本发明的三维阻抗匹配透镜的等效折射率在x、y、z三个正交方向均呈由中心向两侧递减的渐变分布，尤其在电磁波传播的z方向上，透镜两端的等效折射率为1，与自由空间完全匹配，不存在电磁波反射，因此不需要添加匹配层或者采用其他技术降低天线回波损耗。
附图说明
图1是基于三维阻抗匹配透镜的超宽带高增益透镜天线结构示意图；
图2是添加波导延长段的双脊角锥喇叭天线结构示意图；
图3是同轴-双脊波导转换结构示意图；
图4是添加波导延长段的双脊角锥喇叭天线-10dB回波损耗仿真结果图；
图5是形为长方体的三维阻抗匹配透镜的等效折射率分布图；
图6是含有双面覆盖正方形金属贴片的等效折射率单元结构示意图；
图7是包含三层打孔介质基板的等效折射率单元结构示意图；
图8是三维阻抗匹配透镜第1-3、5、7、9、11、13、15、17、19、21、23、25、27、29-31层结构示意图；
图9是三维阻抗匹配透镜第4、28层结构示意图；
图10是三维阻抗匹配透镜第6、26层结构示意图；
图11是三维阻抗匹配透镜第8、24层结构示意图；
图12是三维阻抗匹配透镜第10、22层结构示意图；
图13是三维阻抗匹配透镜第12、20层结构示意图；
图14是三维阻抗匹配透镜第14、18层结构示意图；
图15是三维阻抗匹配透镜第16层结构示意图；
图16是基于三维阻抗匹配透镜的超宽带高增益透镜天线-10dB回波损耗仿真结果图；
图17是基于三维阻抗匹配透镜的超宽带高增益透镜天线与未加载三维阻抗匹配透镜的双脊角锥喇叭天线的增益结果对比图。
具体实施方式
下面结合具体实施例和附图对本发明的技术方案作进一步的介绍。以下实施例仅是本发明的优选实施方式，应当指出：对于本技术领域的普通技术人员来说，在不脱离本发明原理的前提下，还可以做出若干改进和等同替换，如改变三维匹配透镜的尺寸与形状，改变三维阻抗匹配透镜的等效折射率分布规律，或将双脊角锥喇叭天线置换成其他宽带天线等，这些对本发明权利要求进行改进和等同替换后的技术方案，均落入本发明的保护范围。
一种基于三维阻抗匹配透镜的超宽带高增益透镜天线，如图1所示，包括形为长方体的三维阻抗匹配透镜1、正方形口面的双脊角锥喇叭天线馈源2及波导延长段3，双脊喇叭天线开口与波导延长段相连，三维阻抗匹配透镜被内嵌在波导延长段中，波导延长段长度与三维阻抗匹配透镜厚度相等，以完全覆盖三维阻抗匹配透镜侧边。
添加波导延长段的双脊角锥喇叭天线如图2所示。从高频信号源发出的相干电磁波经同轴馈入双脊角锥喇叭天线，经过同轴-双脊波导转换结构11转换为类球面波。同轴 -双脊波导转换结构的侧视图如图3所示，在双脊喇叭天线后端的波导段内壁上下以z轴为中心对称连接两个脊4，构成双脊波导结构，并在双脊波导末端沿y轴插入同轴结构5，同轴一端高于双脊波导，为方便馈电，另一端的探针6与双脊波导下侧的脊相连，为保证同轴与双脊波导的匹配，降低回波损耗，在波导后侧添加阶梯匹配结构7。
经由同轴-双脊波导转换结构得到的类球面电磁波通过固定于喇叭天线口面的波导延长段内的三维阻抗匹配透镜，转变为等相位面正交于传播方向的非均匀平面波，并向自由空间辐射。该透镜天线易于设计、结构简单、成本低廉，经仿真验证，其工作频带宽、增益高、回波损耗低。
三维阻抗匹配透镜天线设计原理如下，假定透镜的厚度为t，点源距离透镜边缘的距离为f。基于几何光学理论，从点源辐射出的电磁波，经由三维阻抗匹配透镜，出射波相位被修正，成为等相位面正交于传播方向的非均匀平面波。根据费马定理，为保证出射波为等相位的平面波，则需保证从点源辐射的任意电磁波经由自由空间和透镜后总光程相等。因此，假定透镜中心为坐标轴原点，点源至透镜中心的连线方向为z方向，对于透镜上任一点(x，y，z)，有：
Figure PCTCN2020083888-appb-000010
其中，n 1为自由空间折射率，一般取为1，
Figure PCTCN2020083888-appb-000011
为透镜在(x,y,z)处的折射率，Δx，Δy分别为沿x轴与y轴的位置变化。
不同于其他透镜，该三维阻抗匹配透镜的等效折射率在x、y、z三个正交方向均呈由中心向两侧递减的渐变分布，为方便起见，在这里我们假设其沿三个正交方向均呈线性变化，由此方程(1)变化为：
Figure PCTCN2020083888-appb-000012
令
Figure PCTCN2020083888-appb-000013
上式可简化为：
Figure PCTCN2020083888-appb-000014
对上式积分，方程变为：
Figure PCTCN2020083888-appb-000015
其中，n m(z)为透镜再垂直于z轴方向上的折射率最大值，n m(z)仅为变量z的函数。
当z固定不变时，方程可以简化为：
Figure PCTCN2020083888-appb-000016
为方便起见，我们假设透镜的等效折射率在x、y方向拥有相同的线性变化趋势，则有：
Figure PCTCN2020083888-appb-000017
假设在z方向上，透镜两侧的等效折射率应为1，且透镜的等效折射率呈线性中心递减变化，因此：
Figure PCTCN2020083888-appb-000018
将上式带入公式(5)，则：
Figure PCTCN2020083888-appb-000019
其中n m(0)为透镜等效折射率的最大值。
假设等效折射率为线性变化，因此：
n m(z)＝2n(x,y)-1              (9)；
因此，根据式(7)、(8)、(9)，可以得到整个透镜的等效折射率分布。
在本实施例中，基于三维阻抗匹配透镜的超宽带高增益透镜天线设计步骤说明如下：
1、双脊喇叭天线、波导延长段：为简化三维阻抗匹配透镜设计，双脊喇叭天线选用正方形口面的双脊角锥喇叭天线，如图2所示，喇叭口面伸出部分为波导延长段，波导延长段为正方形框架，其波导口面形状和尺寸与与双脊喇叭天线口面相等；波导延长段长度与三维阻抗匹配透镜厚度相等，用于将三维阻抗匹配透镜固定于双脊喇叭天线口面，并将三维阻抗匹配透镜侧边完全覆盖。设定双脊喇叭天线中心频率为9.4GHz，根据式(7)、(8)、(9)，设定喇叭口径面为195×195mm(6.11个波长×6.11个波长)；为保证喇叭相位中心与透镜焦距位置一致，设定焦距为299mm(9.37个波长)；为保证波导延 长段完全覆盖三维阻抗匹配透镜侧边，设定波导延长段长度为30.396mm(0.95个波长)。为拓展喇叭天线工作频段并方便馈电，采用同轴-双脊波导转换结构，如图3所示。为验证双脊角锥喇叭天线性能，采用商用全波仿真软件CST进行仿真验证，结果表明该双脊角锥喇叭天线的-10dB回波损耗带宽为5.16-15.71GHz，如图4所示，相对带宽101.1％，属于超宽带天线。
2、三维阻抗匹配透镜：考虑双脊角锥喇叭天线的正方形口面，设定三维阻抗匹配透镜为长方体形状。根据式(7)、(8)、(9)，设定三维阻抗匹配透镜长、宽均为195mm(6.11个波长)，厚度为30.396mm(0.95个波长)。形为长方体的三维匹配透镜的等效折射率分布如图5所示，其等效折射率最大值为3.2，考虑到等效折射率单元的等效折射率不能完全与空气相等，因此将透镜最小等效折射率近似至1.2。该三维阻抗匹配透镜包括若干个等效折射率单元，首先根据式(7)、(8)、(9)得出透镜的等效折射率分布，从而得到等效折射率三维矩阵，按照矩阵中的折射率数值对应排布具有相等等效折射率的单元，最终得到三维阻抗匹配透镜。所述等效折射率单元由两类构成：一类包括一对打孔介质基板，一块双面覆盖正方形金属贴片的介质基板，所述一对打孔介质基板对称紧贴于双面覆盖金属的介质基板两侧；一类包括三块打孔介质基板，其中两块打孔介质基板打孔大小固定且相等，所述两块打固定且相等大小孔的介质基板对称紧贴于剩余一块打孔介质基板两侧。
本发明中的等效折射率单元的具体设计步骤如下：
(1)使用Matlab软件计算并提取出三维匹配透镜的离散等效折射率分布，规定在x、y方向离散间隔为3mm(约0.1个波长)，在z方向离散间隔为2mm(约0.06个波长)，得到对应于透镜等效折射率分布的等效折射率三维矩阵。
(2)考虑到三维匹配透镜在x、y方向离散间隔为3mm(约0.1个波长)，在z方向离散间隔为2mm(约0.06个波长)，设定等效折射率单元尺寸在x、y方向为3mm(约0.1个波长)，在z方向为2mm(约0.06个波长)。所述两种等效折射率单元，一类包括一对打孔介质基板8和一块双面覆盖正方形金属贴片的介质基板9，打孔介质基板8的孔径半径固定为1.25mm，通过改变等效折射率单元中两层正方形金属贴片边长A的大小，调整其等效折射率大小，其结构示意图如图6所示，仿真验证其可以覆盖的等效折射率范围是1.35-3.2；一类包括三块打孔介质基板，其中两块打孔介质基板8打孔大小固定且相等，半径为1.25mm，通过改变等效折射率单元中间层10的打孔半径R的大小， 调整其等效折射率大小，其结构示意图如图7所示，仿真验证其可以覆盖的等效折射率范围是1.2-1.35。设计两类等效折射率单元时，采用的介质基板为介电常数2.2，损耗角正切为0.0001的Teflon板材，金属贴片采用纯铜材质。
(3)按照等效折射率三维矩阵对应排布不同尺寸的等效折射率单元，组成所述形为长方体的三维阻抗匹配透镜。为简化加工难度，对三维阻抗匹配透镜采用PCB工艺进行分层加工，沿z轴所述三维阻抗匹配透镜共计31层，层与层之间不留空隙。其中第1层与第31层介质基板厚度为0.5mm(0.016个波长)，其余层介质基板厚度均为1mm(约0.03个波长)，金属贴片厚度为0.018mm(0.00056个波长)，所述共计31层结构如图8-15所示。各层的排列模式根据前述透镜设计方法所确定，当公式(7)、(8)、(9)中的变量被赋予固定取值后，对应的唯一的排列模式被确定。
所述的双脊喇叭天线为宽带喇叭天线，透镜天线工作带宽取决于双脊喇叭天线工作带宽，双脊喇叭天线可由其他类型宽带喇叭天线代替。
所述三维阻抗匹配透镜形状与双脊喇叭天线口面相同，设计时只需限制透镜在x、y轴的取值范围，保证其取值范围等于天线口径大小，在这里x、y轴的取值范围均是(-97.5mm,97.5mm)。
为验证所述基于三维阻抗匹配透镜的超宽带高增益透镜天线的性能，我们采用商用全波仿真软件CST进行仿真验证，验证结果表明：
(1)所述基于三维阻抗匹配透镜的超宽带高增益透镜天线-10dB回波损耗带宽为5.25-15.2GHz，如图16所示，相对带宽97.3％，属于超宽带天线，验证了其宽频带与回波损耗低的优点；
(2)所述述基于三维阻抗匹配透镜的超宽带高增益透镜天线增益相较未加载三维阻抗匹配透镜的双脊角锥喇叭天线，在全频带内增益均有提升，增益最小提升1.2dB,增益最大提升15dB，如图17所示，验证了其高增益，高定向的优点。
本发明的独特之处在于将新型人工电磁媒质与透镜天线相结合，利用亚波长等效折射率单元构造折射率渐变分布的透镜，透镜的等效折射率在x、y、z三个正交方向均呈由中心向两侧递减的渐变分布，尤其是在电磁波传播方向上，透镜两端的等效折射率为1，与自由空间完全匹配，不需要添加匹配层或者采用其他技术降低天线回波损耗。由于所采用的等效折射率单元具有平坦的折射率曲线，因此可以工作在非常宽的频带内，透镜天线的工作带宽只取决于作为馈源的双脊喇叭天线的带宽。该透镜天线可以在整个 工作频带内保持高定向性以及低回波损耗的性能，并且具有容易设计、结构简单、成本低廉等优点，可以取代传统均匀介质透镜天线，在卫星通信、毫米波雷达测量以及微波生物成像等领域具有重要的应用价值。

Claims (8)

  1. 一种基于三维阻抗匹配透镜的超宽带高增益透镜天线，其特征在于：包括三维阻抗匹配透镜、双脊喇叭天线和波导延长段，双脊喇叭天线开口与波导延长段相连，三维阻抗匹配透镜被内嵌在波导延长段中，波导延长段长度与三维阻抗匹配透镜厚度相等，以完全覆盖三维阻抗匹配透镜侧边。
  2. 根据权利要求1所述的一种基于三维阻抗匹配透镜的超宽带高增益透镜天线，其特征在于：三维阻抗匹配透镜具有一定厚度，且形状与喇叭天线口面形状一致。
  3. 根据权利要求1所述的一种基于三维阻抗匹配透镜的超宽带高增益透镜天线，其特征在于：三维阻抗匹配透镜包括若干个等效折射率单元，所述等效折射率单元包括两类，其中，一类包括一对打孔介质基板和一块双面覆盖正方形金属贴片的介质基板，所述一对打孔介质基板对称紧贴于双面覆盖金属的介质基板两侧；另一类包括三块打孔介质基板，其中两块打孔介质基板打孔大小固定且相等，所述两块打固定且相等大小孔的介质基板对称紧贴于剩余一块打孔介质基板两侧。
  4. 根据权利要求1所述的一种基于三维阻抗匹配透镜的超宽带高增益透镜天线，其特征在于：三维阻抗匹配透镜的等效折射率分部在x、y、z三个正交方向均呈由中心向两侧递减的渐变分布，沿电磁波的传播方向，透镜两端的等效折射率为1，与自由空间完全匹配。
  5. 根据权利要求1所述的一种基于三维阻抗匹配透镜的超宽带高增益透镜天线，其特征在于：双脊喇叭天线为宽带喇叭天线，作为馈源辐射宽带类球面波，透镜天线工作带宽取决于双脊喇叭天线工作带宽。
  6. 一种权利要求1-5任一项所述基于三维阻抗匹配透镜的超宽带高增益透镜天线的设计方法，其特征在于，包括以下步骤：
    (1)设计双脊喇叭天线、波导延长段；
    双脊喇叭天线选用正方形口面的双脊角锥喇叭天线，喇叭口面伸出部分为波导延长段，根据三维阻抗匹配透镜设计公式，设定喇叭口径面，为保证波导延长段完全覆盖三维阻抗匹配透镜侧边，设定波导延长段长度；
    (2)设计三维阻抗匹配透镜；
    考虑双脊角锥喇叭天线的正方形口面，设定三维阻抗匹配透镜为长方体形状，根据三维阻抗匹配透镜设计公式，设定三维阻抗匹配透镜长度、宽度和厚度；三维阻抗匹配透镜包括若干个等效折射率单元，所述等效折射率单元由两类构成：一类包括一对打孔 介质基板，一块双面覆盖正方形金属贴片的介质基板，所述一对打孔介质基板对称紧贴于双面覆盖金属的介质基板两侧；一类包括三块打孔介质基板，其中两块打孔介质基板打孔大小固定且相等，所述两块打固定且相等大小孔的介质基板对称紧贴于剩余一块打孔介质基板两侧。
  7. 根据权利要求6所述的一种基于三维阻抗匹配透镜的超宽带高增益透镜天线的设计方法，其特征在于，等效折射率单元的具体设计步骤如下：
    (21)使用Matlab软件计算并提取出三维匹配透镜的离散等效折射率分布，规定在x、y方向离散间隔约为0.1个波长，在z方向离散间隔约为0.06个波长，得到对应于透镜等效折射率分布的三维矩阵，此处波长指定为双脊喇叭天线的中心波长；
    (22)考虑到三维匹配透镜在x、y方向离散间隔约为0.1个波长，在z方向离散间隔约为0.06个波长，设定等效折射率单元尺寸在x、y方向约为0.1个波长，在z方向约为0.06个波长；所述两种等效折射率单元，一类通过改变等效折射率单元中两层正方形金属贴片的边长，调整其等效折射率大小；一类通过改变等效折射率单元中间层打孔大小，调整其等效折射率大小；设计两类等效折射率单元时，采用的介质基板为介电常数2.2，损耗角正切为0.0001的Teflon板材，金属贴片采用纯铜材质；
    (23)按照等效折射率三维矩阵对应排布不同尺寸的等效折射率单元，组成所述形为长方体的三维阻抗匹配透镜。
  8. 根据权利要求6所述的一种基于三维阻抗匹配透镜的超宽带高增益透镜天线的设计方法，其特征在于，整个透镜的等效折射率分布计算方法为：
    根据费马定理，为保证出射波为等相位的平面波，则需保证从点源辐射的任意电磁波经由自由空间和透镜后总光程相等；因此，假定透镜中心为坐标轴原点，点源至透镜中心的连线方向为z方向，对于透镜上任一点(x,y,z),有：
    Figure PCTCN2020083888-appb-100001
    其中，n 1为自由空间折射率；t为透镜的厚度，f为点源距离透镜边缘的垂直距离；
    不同于其他透镜，该三维阻抗匹配透镜的等效折射率在x、y、z三个正交方向均呈 由中心向两侧递减的渐变分布，为方便起见，在这里我们假设其沿三个正交方向均呈线性变化，由此上式变化为：
    Figure PCTCN2020083888-appb-100002
    令
    Figure PCTCN2020083888-appb-100003
    上式简化为：
    Figure PCTCN2020083888-appb-100004
    对上式积分，方程变为：
    Figure PCTCN2020083888-appb-100005
    当z固定不变时，上式简化为：
    Figure PCTCN2020083888-appb-100006
    假设透镜的等效折射率在x、y方向拥有相同的线性变化趋势，则有：
    Figure PCTCN2020083888-appb-100007
    假设在z方向上，透镜两侧的等效折射率应为1，且透镜的等效折射率呈线性中心递减变化，因此：
    Figure PCTCN2020083888-appb-100008
    将上式带入公式(5)，则：
    Figure PCTCN2020083888-appb-100009
    其中，n m(0)为透镜等效折射率的最大值；
    假设等效折射率为线性变化，因此：
    n m(z)＝2 n(x,y)-1    (9)；
    因此，根据式(7)、(8)、(9)，得到整个透镜的等效折射率分布。
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CN114597667A (zh) * 2022-02-14 2022-06-07 西安科技大学 一种蜂窝状超宽带高增益涡旋波六边形介质柱阵列透镜
CN114597667B (zh) * 2022-02-14 2024-04-19 西安科技大学 一种蜂窝状超宽带高增益涡旋波六边形介质柱阵列透镜
CN115863995A (zh) * 2022-12-07 2023-03-28 深圳职业技术学院 一种宽带高增益喇叭天线
CN115863995B (zh) * 2022-12-07 2023-06-27 深圳职业技术学院 一种宽带高增益喇叭天线

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