Design method of gradient refractive index planar microwave lens based on equivalent medium

Abstract

The invention relates to a design method of a gradient refractive index planar microwave lens based on an equivalent medium, which is characterized in that the gradient refractive index planar microwave lens comprises a plurality of lens units, the plurality of lens units are arranged and combined to form a planar lens body, and each lens unit can perform phase regulation and control in a range of 0-360 degrees; during design, a measuring plane is arranged at the design position of the planar lens body on the radiation side of the feed source, wavefront phase distribution of radiation waves emitted by the feed source reaching the measuring plane is measured and recorded, discrete processing is carried out on the result of the measured wavefront phase distribution, and wavefront phases of all lens units on the planar lens body are obtained. And according to the wavefront phase and the target phase, calculating to obtain a phase regulation quantity required by each lens unit. Through the design method, the design error is reduced, the focusing and transmission performance of the plane lens body is improved, and a large gain is obtained.

Description

Technical Field

[0001] The present invention relates to the technical field of antenna lenses, and in particular to a design method of a gradient refractive index plane microwave lens based on an equivalent medium. Background Art

[0002] The existing antenna lens design method is to design the lens using the ideal spherical wave assumption, that is, the phase shift required at each position on the lens is calculated by treating the radiation wave of the feed source as a uniform spherical wave; for example, the Chinese invention patent with publication number CN112366458B, entitled "A low-profile gradient refractive index lens based on metamaterials", the lens of this patent is composed of several multi-layer metamaterial units, and the refractive index of each multi-layer metamaterial unit is Where: n(r) is the refractive index of the multilayer metamaterial unit at a distance r from the center of the low-profile gradient refractive index lens, n0 is the refractive index of the multilayer metamaterial unit at the center of the low-profile gradient refractive index lens, F is the distance from the low-profile gradient refractive index lens to the phase center of the feed source, and T is the thickness of the low-profile gradient refractive index lens. It can be seen from this that the refractive index of each multilayer metamaterial unit in this scheme is calculated based on the distance from the center of the lens, and each multilayer metamaterial unit in this scheme is designed based on the assumption of an ideal spherical wave. Since there is a certain deviation between the wavefront phase distribution of the actual radiation wave and the wavefront phase distribution of the ideal spherical wave, especially under near-field conditions, the deviation between the wavefront phase distributions of the two is even greater. For designs where the distance between the lens and the feed source is relatively close, such a design method will cause the actual performance of the lens to differ significantly from the expected effect, affecting the focusing accuracy and phase control effect of the lens. Summary of the Invention

[0003] The purpose of the present invention is to provide a design method for a gradient refractive index planar microwave lens based on an equivalent medium, thereby reducing design errors, improving the focusing and transmission performance of the lens, and obtaining a larger gain.

[0004] The technical solution adopted by the present invention to solve the technical problem is: a design method for a gradient refractive index planar microwave lens based on an equivalent medium, comprising a plurality of lens units, each of which is formed into a planar lens body by arrangement and combination. Each lens unit is composed of a plurality of transmission layers arranged and spliced in sequence. The plurality of transmission layers are symmetrically arranged in pairs with the center of the lens unit as a reference. The two symmetrically arranged transmission layers have the same structure, and the dielectric constant of each transmission layer gradually increases from the outermost layer to the center layer. Each lens unit achieves phase control within a range of 0° to 360° by controlling the parameters of its transmission layer.

[0005] During the design process, a measurement plane is set up at the design position of the planar lens body on the radiation side of the feed source. The wavefront phase distribution of the radiation wave emitted by the feed source reaching the measurement plane is measured and recorded. The measured wavefront phase distribution results are discretely processed to obtain the wavefront phase of each lens unit on the planar lens body. Based on the wavefront phase and the target phase, the phase control amount required for each lens unit is calculated.

[0006] Through this design method, since each lens unit is designed and regulated according to the actual wavefront information of the feed source, the planar lens body can more accurately match the radiation characteristics of the feed source, reduce design errors, improve the focusing and transmission performance of the planar lens body, and obtain greater gain.

[0007] Furthermore, in the aforementioned design method for a gradient refractive index planar microwave lens based on an equivalent medium, the transmission performance of the lens unit within the target operating frequency band is changed by adjusting its half-wavelength resonant frequency. The half-wavelength resonant frequency of the lens unit is iteratively optimized through an external algorithm. The workflow of the external algorithm is as follows:

[0008] Step S1: generating an initial external population, the external population including a number of external individuals, the parameter of each external individual being a value of a half-wavelength resonant frequency;

[0009] Step S2: Obtaining the structural parameters of each external individual lens unit at its half-wavelength resonant frequency through an algorithm; the internal algorithm may be an algorithm for calculating the dielectric constant and thickness of each transmission layer of the lens unit, or an algorithm for calculating the equivalent dielectric constant and thickness of the lens unit by treating the lens unit as a uniform medium;

[0010] Step S3: According to the structural parameters of the lens unit corresponding to each external individual, the forward transmission coefficient S of the scattering parameter of the lens unit corresponding to each external individual is obtained by simulation software. 21 (f k ), substitute the external fitness function Get the total fitness of the external population, |S 21 (f k )| is the fitness of each external individual;

[0011] Step S4: Determine whether the total fitness of the external population meets the external convergence condition, which is less than or equal to the external preset value; if the external convergence condition is met, select the half-wavelength resonant frequency corresponding to the individual with the smallest fitness as the optimal value, and stop the external algorithm; if the external convergence condition is not met, proceed to the next step;

[0012] Step S5: Perform crossover and mutation on the external individuals in the original external population to generate a new external population, substitute the new external population and return to step S2.

[0013] Furthermore, in the aforementioned design method for a gradient refractive index planar microwave lens based on an equivalent medium, the internal algorithm is a genetic algorithm, and the optimal structural parameters of each external individual corresponding lens unit at its half-wavelength resonant frequency are obtained through the internal algorithm. The workflow of the internal algorithm is as follows:

[0014] Step S21: generating an initial internal population, the internal population including a plurality of internal individuals, the parameters of each internal individual including the number i of transmissive layers on one half of the lens unit, the dielectric constant of each transmissive layer on one half of the lens unit, and the thickness of each transmissive layer on one half of the lens unit;

[0015] Step S22: Obtain the impedance of each transmission layer of the half side of the lens unit corresponding to each internal individual according to its parameters, and substitute it into the internal fitness function Z j is the impedance of the jth transmission layer from the outermost layer to the middle layer, and the fitness of each internal individual is obtained;

[0016] Step S23: summing the fitness of each internal individual in the internal population to obtain the total fitness of the internal population, and judging whether the total fitness of the internal population meets the internal convergence condition, which is less than or equal to the internal preset value; if the internal convergence condition is met, the internal individual with the smallest fitness in the internal population is selected as the optimal solution, and the internal algorithm is stopped; if the internal convergence condition is not met, proceeding to the next step;

[0017] Step S24: performing crossover and mutation on each internal individual of the internal population to form a new internal population;

[0018] Step S25: Substitute the new internal population and return to step S22.

[0019] Furthermore, in the aforementioned method for designing a gradient refractive index planar microwave lens based on an equivalent medium, step S24 of the internal algorithm includes the following sub-steps:

[0020] Step S241: selecting an internal individual from the original internal population as the parent generation through the roulette method, and selecting an internal individual from the original internal population as the parent generation through the roulette method;

[0021] Step S242: Randomly select the layer number i from the parent generation and the parent generation and incorporate it into the parameters of the offspring generation. The layer number i of the offspring generation is mutated with a preset probability and then incorporated into the parameters of the new internal individual.

[0022] Step S243: Randomly select a transmission layer from the parent generation as the first intersection point, and randomly select a transmission layer from the parent generation as the second intersection point. The sum of the number of layers from the outermost layer to the first intersection point in the parent generation and the number of layers from the second intersection point to the middle layer in the parent generation is equal to the value of the layer number i of the new internal individual. The dielectric constant and thickness of each transmission layer between the outermost layer and the first intersection point in the parent generation are incorporated into the parameters of the child generation. The dielectric constant and thickness of each transmission layer between the second intersection point to the middle layer in the parent generation are incorporated into the parameters of the child generation. The dielectric constant and thickness of each transmission layer of the child generation are mutated with a preset probability and then incorporated into the parameters of the new internal individual.

[0023] Step S244: Incorporate the new internal individuals into the new internal population. If the number of internal individuals in the new internal population is not equal to the number of internal individuals in the original internal population, return to step S241.

[0024] Furthermore, in the aforementioned design method of a gradient refractive index planar microwave lens based on an equivalent medium, the transmission parameters of each transmission layer are regulated by an equivalent medium, and the equivalent dielectric constant of each transmission layer is changed by distributing adjustment structures of different sizes on its dielectric substrate.

[0025] Furthermore, in the aforementioned design method of a gradient refractive index planar microwave lens based on an equivalent medium, the control process of the equivalent dielectric constant of each transmission layer is as follows:

[0026] Step S10: Perform simulation test on the transmission layer through the simulation program to obtain the input reflection coefficient S of the scattering parameter of the transmission layer. 11 , forward transmission coefficient S 21 ;

[0027] Step S20: Calculate the equivalent refractive index of the transmission layer Where k0 is the wave number of free space, h j is the thickness of the transmission layer; calculate the equivalent impedance of the transmission layer The equivalent dielectric constant of the transmission layer can be calculated from this

[0028] Step S30: Check whether the equivalent dielectric constant of the transmission layer matches the target value. If not, adjust the dielectric constant by changing the size of the adjustment structure on the dielectric substrate, and return to step S10.

[0029] Furthermore, in the aforementioned design method of a gradient refractive index planar microwave lens based on an equivalent medium, the adjustment structure may be a hole punched on a dielectric substrate or a metal patch attached thereto.

[0030] Furthermore, in the aforementioned design method of a gradient refractive index planar microwave lens based on an equivalent medium, the dielectric constant of each transmission layer of the lens unit is the product of the square roots of the dielectric constants of its two adjacent transmission layers.

[0031] The technical solution of the present invention has the following beneficial effects: reducing design errors, improving the focusing and transmission performance of the lens, and obtaining a larger gain. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 Schematic diagram of the assembly structure of the lens unit of the embodiment;

[0033] Figure 2 is a schematic structural diagram of one of the outermost transmissive layers of the lens unit of the embodiment;

[0034] Figure 3 FIG. 4 is a schematic structural diagram of a transmission layer of a lens unit except the outermost layer according to an embodiment of the present invention.

[0035] Description of reference numerals:

[0036] 1-lens unit; 2-transmission layer; 21-dielectric substrate; 22-via; 23-metal patch. DETAILED DESCRIPTION

[0037] In order to have a clearer understanding of the technical features, purposes and effects of the present invention, specific embodiments of the present invention are now described in detail with reference to the accompanying drawings.

[0038] A design method for a gradient refractive index planar microwave lens based on an equivalent medium includes a plurality of lens units 1, each of which is formed into a planar lens body by arrangement and combination. Each lens unit 1 is composed of a plurality of transmission layers 2 stacked and spliced in sequence. The transmission layers 2 are symmetrically arranged in pairs with the center of the lens unit 1 as a reference. The two symmetrically arranged transmission layers 2 have the same structure, and the dielectric constant of each transmission layer 2 gradually increases from the outermost layer to the center layer. Each lens unit 1 achieves phase control within a range of 0° to 360° by controlling the parameters of its transmission layers 2.

[0039] During the design process, a measurement plane is set up at the design position of the planar lens body on the radiation side of the feed source. The wavefront phase distribution of the radiation wave emitted by the feed source reaching the measurement plane is measured and recorded. The measured wavefront phase distribution results are discretely processed to obtain the wavefront phase of each lens unit 1 on the planar lens body. Based on the wavefront phase and the target phase, the phase control amount required for each lens unit 1 is calculated.

[0040] The design and manufacturing method of the lens unit 1 are as follows:

[0041] First, the lens unit 1 is equivalent to a uniform lens unit 1 with a non-magnetic resonance medium. The phase change caused by the lens unit 1 to the incident wave can be expressed as:

[0042]

[0043] Where λ is the wavelength of the incident wave, h is the thickness of the lens unit 1, and ε r is the relative permittivity of the homogeneous medium.

[0044] In order to achieve the design requirements of the planar lens, the lens unit 1 needs to meet the following conditions:

[0045] φ target =φ0+Δφ (2)

[0046] Where, φ target is the target phase of lens unit 1. The target phase of each lens unit 1 is equal, and the target phase is the design value of the plane lens body; φ0 is the initial phase, that is, the actual wavefront phase corresponding to lens unit 1; Δφ is the phase control amount of lens unit 1, and the maximum phase control amount is 2π and the minimum is 0.

[0047] According to equations (1) and (2), the dielectric constant ε of the lens unit 1 of the equivalent homogeneous medium is r The calculation formula is:

[0048]

[0049] Where ε0 is the initial dielectric constant, c is the speed of light, and f t is the target operating frequency.

[0050] Since an excessively high dielectric constant will lead to spatial impedance mismatch, the transmission performance will become very poor, so it is necessary to introduce half-wavelength resonance for optimization.

[0051] The half-wavelength resonant frequency of lens unit 1 is

[0052]

[0053] Where n is the frequency multiplication coefficient.

[0054] The lens unit 1 can obtain different transmission performance responses within a target frequency band by selecting and adjusting different half-wavelength resonant frequencies.

[0055] According to equations (3) and (4), the resonant frequency f at a specific half-wavelength can be obtained. half Under the condition that the thickness h of the lens unit 1 and the dielectric constant ε of the equivalent uniform medium r .

[0056] Then, a gradient refractive index design is performed on the lens unit 1. Each lens unit 1 is composed of a plurality of transmissive layers 2 stacked and spliced in sequence. The transmissive layers 2 are symmetrically arranged in pairs with the center of the lens unit 1 as the reference. The two symmetrically arranged transmissive layers 2 have the same structure, and the dielectric constant of each transmissive layer 2 gradually increases from the outermost layer to the center layer.

[0057] The number of transmissive layers 2 of the lens unit 1 is set to 2*i, i.e., i is the number of transmissive layers 2 on one half of the lens unit 1;

[0058] According to the impedance formula, we define the impedance of each transmission layer 2 as the geometric average of the impedances of the two adjacent transmission layers 2, that is,

[0059]

[0060] According to the conversion formula of impedance and dielectric constant The relationship between the dielectric constant of each transmission layer 2 and the dielectric constant of the adjacent two transmission layers 2 can be obtained as follows:

[0061]

[0062] Therefore, it can be seen that the dielectric constant of each transmissive layer 2 is the product of the square roots of the dielectric constants of two adjacent transmissive layers 2 .

[0063] The phase shift of the lens unit 1 designed with a gradient refractive index must be equal to the phase shift of the lens unit 1 with an equivalent homogeneous medium, that is, the optical path is consistent.

[0064] According to the optical path theory:

[0065]

[0066] Where, ε i is the dielectric constant of the middlemost transmission layer 2, ε1 is the dielectric constant of the outermost transmission layer 2, ε0 is the dielectric constant of free space, and h0 is the thickness of free space; is the optical path of lens unit 1 of the equivalent homogeneous medium, is the optical path in free space, Optical path of lens unit 1 designed for gradient refractive index.

[0067] At the same time, the thickness of the lens unit 1 is the sum of the thicknesses of the transmission layers 2, and it can be obtained that:

[0068] h=2·(h1+h2......+h i ) (8)

[0069] According to the limitations of equations (6), (7), and (8), the number i of the transmission layers 2 on one half of the lens unit 1 designed with a gradient refractive index, the dielectric constant of each transmission layer 2 on one half, and the thickness of each transmission layer 2 on one half cannot be uniquely solved. In order to achieve optimal impedance matching, it is necessary to find a solution with the minimum impedance difference between each adjacent two transmission layers 2.

[0070] In addition, according to equations (3) and (4), the thickness h of the lens unit 1 and the dielectric constant ε of the equivalent homogeneous medium are r The design requirement of a specific half-wavelength resonant frequency must be met. In order to optimize the transmission performance of the lens unit 1 , it is necessary to find the optimal solution for the half-wavelength resonant frequency.

[0071] Since the lens unit 1 has a centrosymmetrical structure, it is only necessary to design the transmission layers 2 on one half side of the lens unit 1 .

[0072] To this end, an external algorithm and an internal algorithm are introduced. Both the external algorithm and the internal algorithm are genetic algorithms. The external algorithm is used to obtain the optimal solution for the half-wavelength resonant frequency. The internal algorithm is nested within the external algorithm. The internal algorithm is used to obtain the optimal solution for the dielectric constant and thickness of each transmission layer 2 on one half side of the lens unit 1 corresponding to the half-wavelength resonant frequency in the external algorithm; thereby, the lens unit 1 with the optimal structure is obtained.

[0073] The specific workflow of the external algorithm and internal algorithm is as follows:

[0074] Step S1: Start the external algorithm to generate an initial external population, which includes a number of external individuals. The number of external individuals is in the range of 20 to 100. The parameter of each external individual is the value of the half-wavelength resonant frequency. The half-wavelength resonant frequency of each external individual should be near the target frequency point.

[0075] Step S2: Start the internal algorithm to obtain the structural parameters of each external individual corresponding lens unit 1 at its half-wavelength resonant frequency through the internal algorithm:

[0076] Step S21: Generate an initial internal population, which includes a number of internal individuals. The number of internal individuals is in the range of 20 to 100. The parameters of each internal individual include the number i of the transmission layer 2 on one half of the lens unit 1 (randomly selected from 4 to 20), the dielectric constant of each transmission layer 2 on one half of the lens unit 1 (randomly selected from 2.2 to 10), and the thickness of each transmission layer 2 on one half of the lens unit 1 (randomly selected from 0.1 mm to 3 mm). The dielectric constant and thickness of each transmission layer 2 on one half of the lens unit 1 should comply with the restrictions of formulas (6), (7), and (8).

[0077] Step S22: Obtain the impedance of each transmission layer 2 on one half of the lens unit 1 corresponding to each internal individual according to its parameters, and substitute it into the internal fitness function Z j is the impedance of the jth transmission layer 2 from the outermost layer to the middle layer, thereby obtaining the fitness of each internal individual;

[0078] Step S23: The fitness of each internal individual in the internal population is summed to obtain the total fitness of the internal population, and it is determined whether the total fitness of the internal population meets the internal convergence condition. The internal convergence condition is less than or equal to the internal preset value. In this embodiment, the internal preset value is set to 0. If the internal convergence condition is met, the internal individual with the smallest fitness in the internal population is selected as the optimal solution, the internal algorithm is stopped, and the process proceeds to step S3. If the internal convergence condition is not met, the process proceeds to the next step.

[0079] Step S24: Perform crossover and mutation on each internal individual of the internal population to form a new internal population:

[0080] Step S241: selecting an internal individual from the original internal population as the parent generation through the roulette method, and selecting an internal individual from the original internal population as the parent generation through the roulette method;

[0081] Step S242: Randomly select the layer number i from either the parent generation or the parent generation and incorporate it into the parameters of the offspring generation. The layer number i of the offspring generation is mutated with a preset probability and then incorporated into the parameters of the new internal individual. In this embodiment, the mutation probability of the layer number i is 5%, and the mutation range is ±1.

[0082] Step S243: Randomly select a transmission layer 2 from the parent generation as the first intersection point, and randomly select a transmission layer 2 from the parent generation as the second intersection point. The sum of the number of layers from the outermost layer to the first intersection point in the parent generation and the number of layers from the second intersection point to the middle layer in the parent generation is equal to the value of the number of layers i of the new internal individual. The dielectric constant and thickness of each transmission layer 2 between the outermost layer and the first intersection point in the parent generation are incorporated into the parameters of the child generation. The dielectric constant and thickness of each transmission layer 2 between the second intersection point to the middle layer in the parent generation are incorporated into the parameters of the child generation. The dielectric constant and thickness of each transmission layer 2 of the child generation are mutated with a preset probability and then incorporated into the parameters of the new internal individual. In this embodiment, the mutation probability of the number of layers, thickness, and dielectric constant of the transmission layer 2 is 5%.

[0083] Step S244: Incorporate the new internal individuals into the new internal population. If the number of internal individuals in the new internal population is not equal to the number of internal individuals in the original internal population, return to step S241.

[0084] Step S25: Substitute the new internal population and return to step S22.

[0085] Step S3: According to the structural parameters of the lens unit 1 corresponding to each external individual, the forward transmission coefficient S of the scattering parameter of the lens unit 1 corresponding to each external individual is obtained by simulation software. 21 (f k ), substitute the external fitness function Get the total fitness of the external population, |S 21 (f k )| is the fitness of each external individual;

[0086] Step S4: Determine whether the total fitness of the external population meets the external convergence condition, which is less than or equal to the external preset value. In this embodiment, the external preset value is 0. If the external convergence condition is met, the half-wavelength resonant frequency corresponding to the individual with the smallest fitness is selected as the optimal value, and the external algorithm is stopped. If the external convergence condition is not met, proceed to the next step.

[0087] Step S5: Cross the external individuals in the original external population, that is, randomly select two external individuals as the father and mother generations respectively, take the average of the half-wavelength resonant frequencies of the father and mother generations as the parameters of the offspring, and then mutate the parameters of the offspring and incorporate them into the new external individuals. In this embodiment, the mutation probability of the half-wavelength resonant frequency is 5%, and the mutation range is ±50MHz. Incorporate the new external individuals into the new external population, repeat the above-mentioned crossover and mutation operations until the number of external individuals in the new external population matches the number of external individuals in the original external population, substitute the new external population and return to step S2.

[0088] By repeatedly iterating the above external algorithm and internal algorithm, the optimal half-wave resonance frequency of each lens unit 1 and the optimal structural parameters under the half-wave resonance frequency are finally determined.

[0089] To ensure the ease and feasibility of manufacturing the lens unit 1, the transmission parameters of each transmission layer 2 of the lens unit 1 are regulated by an equivalent dielectric method. That is, the transmission layer 2 includes a dielectric substrate 21. The dielectric substrate 21 is provided with holes 22 or metal patches 23 to change the equivalent dielectric constant of the transmission layer 2. The equivalent dielectric constant of the transmission layer 2 is regulated by adjusting the size of the holes 22 or the metal patches 23, so that the equivalent dielectric constant of the transmission layer 2 matches the optimal dielectric constant obtained by the genetic algorithm.

[0090] The control process of the equivalent dielectric constant of each transmission layer 2 is as follows:

[0091] Step S10: Perform simulation test on the transmission layer 2 through the simulation program to obtain the input reflection coefficient S of the scattering parameter of the transmission layer 2 11 , forward transmission coefficient S21 ;

[0092] Step S20: Calculate the equivalent refractive index of the transmission layer 2 Where k0 is the wave number of free space, h j is the thickness of the transmission layer 2; calculate the equivalent impedance of the transmission layer 2 The equivalent dielectric constant of the transmission layer 2 can be calculated from this

[0093] Step S30: Check whether the equivalent dielectric constant of the transmission layer 2 matches the target value (optimal dielectric constant). If not, adjust the size of the via 22 or the metal patch 23 on the dielectric substrate 21 and return to step S10.

[0094] In this embodiment, Figure 2 As shown, the outermost transmission layer 2 of the lens unit 1 is punched to achieve the optimal dielectric constant, as shown in FIG. Figure 3 As shown, the transmission layer 2 of the lens unit 1 except the outermost layer is regulated by a metal patch 23 to achieve the optimal dielectric constant, as shown in FIG. Figure 1 As shown, the transmission layers 2 are finally spliced together to form the lens unit 1.

[0095] Through the above-mentioned design and manufacturing method, the lens unit 1 at each position of the planar lens body is regulated and designed to have an optimal structure according to the actual wavefront information of the feed source, so that the planar lens body can more accurately match the radiation characteristics of the feed source, reduce design errors, improve the focusing and transmission performance of the planar lens body, and obtain a larger gain.

Claims

1. A design method for a gradient refractive index planar microwave lens based on an equivalent medium, characterized by: The invention comprises a plurality of lens units, which are arranged and combined to form a planar lens body. Each lens unit is composed of a plurality of transmission layers arranged and spliced in sequence. The transmission layers are symmetrically arranged in pairs with the center of the lens unit as the reference. The two symmetrically arranged transmission layers have the same structure. The dielectric constant of each transmission layer gradually increases from the outermost layer to the center layer. Each lens unit can achieve phase control within the range of 0° to 360° by adjusting the parameters of each transmission layer. During the design process, a measurement plane is set up at the design position of the planar lens body on the radiation side of the feed source. The wavefront phase distribution of the radiation wave emitted by the feed source reaching the measurement plane is measured and recorded. The measured wavefront phase distribution results are discretely processed to obtain the wavefront phase of each lens unit on the planar lens body. Based on the wavefront phase and the target phase, the phase control amount required for each lens unit is calculated.

2. The method for designing a gradient refractive index planar microwave lens based on an equivalent medium according to claim 1, wherein: The transmission performance of the lens unit within the target operating frequency band is changed by adjusting its half-wavelength resonant frequency. The half-wavelength resonant frequency of the lens unit is iteratively optimized by an external algorithm, which is a genetic algorithm. The workflow of the external algorithm is as follows: Step S1: generating an initial external population, the external population including a number of external individuals, the parameter of each external individual being a value of a half-wavelength resonant frequency; Step S2: obtaining the structural parameters of each external individual corresponding lens unit at its half-wavelength resonant frequency through an internal algorithm; Step S3: According to the structural parameters of the lens unit corresponding to each external individual, the forward transmission coefficient S of the scattering parameter of the lens unit corresponding to each external individual is obtained by simulation software. 21 (f k ), substitute the external fitness function Get the total fitness of the external population, |S 21 (f k )| is the fitness of each external individual; Step S4: Determine whether the total fitness of the external population meets the external convergence condition, which is less than or equal to the external preset value; If the external convergence condition is met, the half-wavelength resonant frequency corresponding to the individual with the smallest fitness is selected as the optimal value, and the external algorithm is stopped; if the external convergence condition is not met, proceed to the next step; Step S5: Perform crossover and mutation on the external individuals in the original external population to generate a new external population, substitute the new external population and return to step S2.

3. The method for designing a gradient refractive index planar microwave lens based on an equivalent medium according to claim 2, wherein: The internal algorithm is a genetic algorithm, which is used to obtain the optimal structural parameters of each external individual lens unit at its half-wavelength resonant frequency. The working process of the internal algorithm is as follows: Step S21: generating an initial internal population, the internal population including a plurality of internal individuals, the parameters of each internal individual including the number i of transmissive layers on one half of the lens unit, the dielectric constant of each transmissive layer on one half of the lens unit, and the thickness of each transmissive layer on one half of the lens unit; Step S22: Obtain the impedance of each transmission layer of the half side of the lens unit corresponding to each internal individual according to its parameters, and substitute it into the internal fitness function Z j is the impedance of the jth transmission layer from the outermost layer to the middle layer, and the fitness of each internal individual is obtained; Step S23: summing the fitness of each internal individual in the internal population to obtain the total fitness of the internal population, and judging whether the total fitness of the internal population meets the internal convergence condition, which is less than or equal to the internal preset value; if the internal convergence condition is met, the internal individual with the smallest fitness in the internal population is selected as the optimal solution, and the internal algorithm is stopped; if the internal convergence condition is not met, proceeding to the next step; Step S24: performing crossover and mutation on each internal individual of the internal population to form a new internal population; Step S25: Substitute the new internal population and return to step S22.

4. The method for designing a gradient refractive index planar microwave lens based on an equivalent medium according to claim 3, wherein: Step S24 of the internal algorithm includes the following sub-steps: Step S241: selecting an internal individual from the original internal population as the parent generation through the roulette method, and selecting an internal individual from the original internal population as the parent generation through the roulette method; Step S242: Randomly select the layer number i from the parent generation and the parent generation and incorporate it into the parameters of the offspring generation. The layer number i of the offspring generation is mutated with a preset probability and then incorporated into the parameters of the new internal individual. Step S243: Randomly select a transmission layer from the parent generation as the first intersection point, and randomly select a transmission layer from the parent generation as the second intersection point. The sum of the number of layers from the outermost layer to the first intersection point in the parent generation and the number of layers from the second intersection point to the middle layer in the parent generation is equal to the value of the layer number i of the new internal individual. The dielectric constant and thickness of each transmission layer between the outermost layer and the first intersection point in the parent generation are incorporated into the parameters of the child generation. The dielectric constant and thickness of each transmission layer between the second intersection point to the middle layer in the parent generation are incorporated into the parameters of the child generation. The dielectric constant and thickness of each transmission layer of the child generation are mutated with a preset probability and then incorporated into the parameters of the new internal individual. Step S244: Incorporate the new internal individuals into the new internal population. If the number of internal individuals in the new internal population is not equal to the number of internal individuals in the original internal population, return to step S241.

5. The method for designing a gradient refractive index planar microwave lens based on an equivalent medium according to claim 1, wherein: The transmission parameters of each transmission layer are regulated by an equivalent medium method, and the equivalent dielectric constant of each transmission layer is changed by distributing adjustment structures of different sizes on its dielectric substrate.

6. The method for designing a gradient refractive index planar microwave lens based on an equivalent medium according to claim 5, wherein: The control process of the equivalent dielectric constant of each transmission layer is as follows: Step S10: Perform simulation test on the transmission layer through the simulation program to obtain the input reflection coefficient S of the scattering parameter of the transmission layer. 11 , forward transmission coefficient S 21 ; Step S20: Calculate the equivalent refractive index of the transmission layer Where k0 is the wave number of free space, h j is the thickness of the transmission layer; calculate the equivalent impedance of the transmission layer The equivalent dielectric constant of the transmission layer can be calculated from this Step S30: Check whether the equivalent dielectric constant of the transmission layer matches the target value. If not, adjust the dielectric constant by changing the size of the adjustment structure on the dielectric substrate, and return to step S10.

7. The method for designing a gradient refractive index planar microwave lens based on an equivalent medium according to claim 5 or 6, characterized in that: The adjustment structure can be punched on the dielectric substrate or affixed with a metal patch.

8. The method for designing a gradient refractive index planar microwave lens based on an equivalent medium according to claim 1, wherein: The dielectric constant of each transmission layer of the lens unit is the product of the square roots of the dielectric constants of the two adjacent transmission layers.

Images