CN113922099A - Method for realizing discretization of two-dimensional multilayer Luneberg lens by using modified equivalent medium theory - Google Patents
Method for realizing discretization of two-dimensional multilayer Luneberg lens by using modified equivalent medium theory Download PDFInfo
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- H—ELECTRICITY
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- H—ELECTRICITY
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Abstract
The invention discloses a method for realizing discretization of a two-dimensional multilayer Luneberg lens by using a modified equivalent medium theory. The method realizes the discretization work of the two-dimensional luneberg lens by correcting the radial equivalent medium parameters and by means of a pure medium structure. Compared with the classical equivalent medium theory, the method corrects the duty ratio parameter of the equivalent medium, and solves the problem that the classical model is not applicable to the structure; compared with the traditional continuous luneberg lens, the luneberg lens designed by the method has the advantages of plane wave excitation, ultra wide band, omnidirectional operation and the like, meanwhile, the breakthrough of radiation performance such as wave path reduction, low loss and the like is realized, and the engineering performance such as light weight, low cost, convenience in installation and the like is improved. The multilayer 3D printing pure medium material adopted by the invention completes the realization of corresponding equivalent medium electromagnetic parameters by punching design on the material, and achieves the effective radiation of plane waves under the condition of point source incidence.
Description
Technical Field
The invention relates to the field of optical devices (G02F) and antennas (H05B6/72), in particular to a method for realizing discretization of a two-dimensional multilayer luneberg lens by using a modified equivalent medium theory.
Background
The luneberg lens is an important research content in the fields of optics and electromagnetism, realizes the conversion from a point source to plane wave radiation by utilizing the design of radial nonuniform electromagnetic parameters, has the advantages of broadband, omnidirectional work and the like, and is widely applied to the researches of optical imaging, antenna directional radiation and scanning, electromagnetic wave beam self-backtracking and the like. In long-term related research, the design of the luneberg lens always has the problems of difficulty in realizing continuous electromagnetic parameters, large lens loss, poor designability and the like. In the existing research, although the realization difficulty of electromagnetic parameters can be reduced by using a continuous layering method, the processing difficulty of the lens is higher, and the loss is larger; based on a metamaterial theory, the design of the luneberg lens is completed by utilizing a printing micro-strip plate process, the electromagnetic parameter is reduced, the processing difficulty is reduced, the loss is reduced, and other performances are improved, but the working bandwidth of the lens is narrow, and the broadband work cannot be realized. In addition, in the theoretical aspect, the research of the luneberg lens is mainly based on optical variational calculation and the classical equivalent medium theory, however, the theories have strict applicable backgrounds and are not applicable to the electromagnetic model of the discretization of the lens. These problems directly limit the development of the theory and application of luneberg lenses, and have long limited the research on relevant electromagnetic and optical devices.
Disclosure of Invention
The invention aims to solve the problems in the prior art, provides a method for realizing two-dimensional multilayer Luneberg lens discretization by using a modified equivalent medium theory, overcomes the limitation that the classic equivalent medium theory is not suitable for lens discretization, and realizes the discretization Luneberg lens which obtains the breakthrough of radiation performances such as wave path reduction, loss reduction and the like on the premise of keeping the advantages of the traditional Luneberg lens and improves the engineering performances such as light weight, low cost, convenient installation and the like.
The invention provides a two-dimensional multilayer discretization luneberg lens, which comprises a radiation feed source and a discretization luneberg lens, wherein the radiation feed source is positioned on the central plane of the lens in the z direction and is positioned outside the lens; the discretization luneberg lens consists of a plurality of layers of discrete pure medium circular columns, and the circular columns are isolated by air.
The radiation feed source has the characteristic of quasi-two-dimension, and the radiation feed source radiates in an omnidirectional manner on an XOY plane; the feed source is positioned outside the cylindrical ring of the medium at the outermost layer of the lens, and specifically is the outer diameter position of the continuous luneberg lens before discretization.
The discretization luneberg lens is further improved, the discretization luneberg lens is composed of a plurality of layers of discretization pure medium circular columns, the circular columns are isolated by air, the wave path difference formed by the combination of single-layer air and medium in the radius direction is smaller than the single-time working wavelength, and therefore the outgoing wave is ensured not to have amplitude zero points.
Further improved, the pure medium circular column is made of medium materials with isotropy, non-magnetism and weak dispersion, wherein the isotropy and non-magnetism materials are selected according to the calculation requirement of equivalent dielectric constant, and the weak dispersion is selected according to the requirement of ultra-wideband operation; the dielectric constant of each layer is calculated according to a modified equivalent medium theory, and is determined by the material selected by the lens and the dispersion of the lens.
Further improved, the dielectric circular column is provided with uniformly distributed square via hole structures for realizing corresponding electromagnetic dielectric properties of each layer.
In a further improvement, the two-dimensional multilayer discretization luneberg lens is prepared by using a 3D printing technology, so that the preparation flow of the lens is simplified.
The invention also provides a method for realizing discretization of the two-dimensional multilayer Luneberg lens by using the modified equivalent medium theory, which comprises the following steps:
1) calculating parameters of the continuous layered luneberg lens to be discretized according to a classical luneberg lens formula, wherein the parameters comprise the overall dimension of the lens, the position of a radiation feed source and the refractive index of each layer; further obtaining the corresponding dielectric constant value of each layer of medium in a non-magnetic state;
2) discretizing the continuous layered luneberg lens, namely converting each layer of medium of the continuous layered lens into a combination of air and the medium, wherein the radial position of the medium layer is positioned at the radial center of the original continuous layered lens, and the dielectric constant of each layer of medium is calculated by using a modified equivalent medium theory;
3) and according to the dielectric constant of each layer of medium of the discrete luneberg lens obtained by calculation, independently perforating each layer to obtain the electromagnetic property required by each layer.
Further improved, the luneberg lens designed by the method has the discretization characteristic, the function of emitting plane waves fed by a point source can be realized, and compared with the traditional luneberg lens, the total wave path difference is reduced, so that the loss of the lens is reduced.
Further improved, the refractive index distribution parameters of the continuous layered luneberg lens are based on a classic luneberg lens formula, and the position of the radial midpoint of each layer is selected by the radius in calculation.
In a further improvement, the calculation of the dielectric constant of the continuous layered luneberg lens is based on isotropic and non-magnetic conditions to simplify the computational complexity of the equivalent medium, so that the dielectric constant of each layer is the square of the refractive index.
In a further improvement, the discretization of the continuous layered luneberg lens is to convert the luneberg lens filled with all media in each layer into a discrete lens form consisting of media and spacing air in each layer; in the radius direction, the center of each layer of medium is superposed with the center of the original continuous layered lens at the center of the layer, so as to ensure better medium equivalent effect.
In a further improvement, the dielectric constant of each layer of the medium of the discrete luneberg lens is calculated by a modified equivalent medium theory, and the equivalent is based on an equiphase condition along the radius direction with each layer of the medium of the continuous layered luneberg lens. For example, the method is more suitable for a lens discretization model compared with the circumferential equiphase-based condition of the traditional layered luneberg lens.
In a further development, the modified equivalent medium theory is modified by multiplying the ratio of medium to air thickness by a modification factor m in the equivalent calculation, the value of m being determined by the ratio of medium to air thickness, which decreases with increasing ratio of medium to air but is greater than 1.
The dielectric constant of each layer of medium of the discrete Luneberg lens is realized by designing a square hole structure on the medium, and the punching size is obtained according to the radial phase equivalence of the discrete Luneberg lens on the layer.
The invention has the beneficial effects that:
1. the method is suitable for the electromagnetic model of the discretization luneberg lens by adopting a radial phase condition and correcting an equivalent medium theory.
2. The method simplifies the calculation complexity of an equivalent medium theory by adopting a non-magnetic and isotropic medium, and reduces the processing difficulty of the lens.
3. The discretization luneberg lens has the advantages of light weight, low cost and convenience in installation.
4. The designed discretization luneberg lens has the beneficial effect of optical path reduction.
5. The discretization luneberg lens has the beneficial effect of low loss.
6. The designed discretization luneberg lens adopts a 3D printing technology suitable for discretization processing, so that the discretization luneberg lens can be produced in batches.
Drawings
Fig. 1 is a schematic diagram of an implementation of two-dimensional multi-layer luneberg lens discretization.
Fig. 2 is a discretized two-dimensional multilayer luneberg lens.
Fig. 3 is a comparison of the performance of a continuously layered luneberg lens, a discretized luneberg lens based on the classical equivalent medium theory, and a discretized luneberg lens based on the modified equivalent medium theory.
Detailed Description
The invention is further described with reference to the following figures and detailed description. As shown in fig. 1, in an embodiment of the method for realizing discretization of a two-dimensional multilayer luneberg lens by using a modified equivalent medium theory, discretization is performed on a traditional two-dimensional continuous layered luneberg lens, and the external dimension of the luneberg lens determines the relevant dimension of the discretized luneberg lens, that is, the overall outer diameter, the layering number, the lens height and the radiation feed source position of the luneberg lens are the same. The refractive index of each layer in the lens is determined by the classical continuous layered luneberg lens formula:
ηn＝(2-(rn/R)2)1/2 n∈(1,N) (1)
in the formula etanThe refractive index of the N-th layer increases from inside to outside, N is the total number of layers, rnIs the value of the central radius of the nth layer, and R is the integral radius of the lens. The thickness of each layer of the lens is selected to ensure that the wavelength range formed by the lens is not more than one wavelength, so that the emergent light can be emittedThe wave does not exhibit amplitude nulls. In the invention, all the layers of the continuously layered luneberg lens are made of isotropic and nonmagnetic materials, because the impedance change of the medium is not obvious at low refractive index, and simultaneously, the calculation complexity can be reduced, for example, the dielectric constant epsilon of each layer isnIs equal to etanSquare of (d). In this embodiment, the thickness of each layer of the lens is the same, i.e. rnIn other applications, the non-uniform continuous layered lens can be discretized, because the modification proposed by the present invention is only related to the ratio of the discretized medium to air, and not to the thickness of the layer, and therefore, the present invention shall also fall into the protection scope of the present invention. In the present embodiment, the discretization of the two-dimensional luneberg lens is performed, and in other applications, the invention is based on the equal phase condition of the lens radial direction, so that the invention can be used for discretization of the three-dimensional lens by proper adjustment. The specific method comprises the steps of adjusting the ratio of a medium to air in the discretization model of the two-dimensional lens and corresponding correction factors to enable the lens to have good effects on two orthogonal polarizations, and further inputting electromagnetic parameters of the two-dimensional lens into the three-dimensional model to obtain the discretized three-dimensional layered luneberg lens. Such design is based on the proposed method and shall also fall within the scope of protection of the present invention.
The discretization two-dimensional multilayer Luneberg lens related to the present embodiment, as shown in FIG. 2, includes a radiation feed source 1 and a discretization Luneberg lens 2. In order to ensure the omnidirectionality of input electromagnetic waves, the radiation feed source is XOY plane omnidirectional radiation. Discretizing the two-dimensional continuous layering luneberg lens, wherein the radial center of the discretized medium annular column is consistent with the original center in the continuous layering process, so that a better electromagnetic equivalent effect can be ensured. If the thickness of the annular column is d, the thickness of the layer of air is R/N-d, and the modified equivalent medium theory in the invention is expressed as the radial equiphase condition based on the radial equiphase condition
εn'1/2χd+(R/N-χd)＝εn 1/2R/N n∈(1,N) (2)
In the formula, epsilonn' is the dielectric constant of the discretized n-th layer, and x is a correction factor, the value of which is related only to the ratio of the thickness of the medium to the spacing air, i.e. tod/(R/N-d) are related. χ is an empirical parameter and decreases with increasing d/(R/N-d), but the values are all greater than 1. Compared with the prior art based on the circumferential equiphase condition, the method is more suitable for the discretization of the electromagnetic model of the Luneberg lens. In this embodiment, air is selected as the isolation medium of the dielectric annular column, and in other applications, other low-refractive-index materials or the lens is entirely disposed in a substrate with a specific refractive index, so as to realize a non-air-based luneberg lens design. The specific method is that the refractive index of the matrix is multiplied by the whole formula (1) to form the refractive index distribution of the corresponding continuous lens, and the distribution is corrected according to the formula (2) to obtain the discretized lens parameters. The method is a more conventional design idea, and the design can be easily obtained based on the method provided by the invention, so the method also belongs to the protection scope of the invention. In this embodiment, a discretization design of the luneberg lens is implemented, and in other applications, discretization correction can be performed on other types of lenses, such as fish eyes, meniscus lenses, and the like, by using the radial equal-phase equivalent method provided by the present invention. The specific method comprises the steps of obtaining corresponding electromagnetic distribution by utilizing a continuous layering formula of the lens to be discretized, and calculating the dielectric constant of the corresponding discretized lens by adjusting the correction factor according to a formula (2). The design is completely based on the equivalent medium correction method provided by the invention, and therefore, the design also belongs to the protection scope of the invention. In this embodiment, anisotropic or non-magnetic materials are selected for the multi-layer lens design, and in other applications, magnetic or anisotropic media materials may be used according to actual application requirements. If a magnetic material is used, obtaining corresponding parameters according to a relation between a refractive index and a dielectric constant/magnetic permeability through a formula (1), and solving a refractive index distribution obtained by reverse deduction through a formula (2) to obtain a dielectric constant/magnetic permeability value; if an anisotropic design is required, the polarization anisotropy parameters should be adapted according to the working polarization design. The method is obtained by utilizing the basic physical principle on the basis of the invention, and therefore, the method also belongs to the protection scope of the invention. It is worth mentioning that the method is also applicable to the condition that the thicknesses of each layer of media after discretization are different, and the specific method is that each layer of media is subjected toThe ring selects the corresponding correction factor.
According to the dielectric constant distribution of the discretization multilayer Luneberg lens, a proper material is selected, and the electromagnetic parameters required by each layer are realized by punching design on the material. Since the hole design can only reduce the dielectric constant of the material, the dielectric constant of the selected material should be larger than the maximum value of the dielectric constant required by the multilayer luneberg lens. The pore structure is uniformly distributed on each layer of medium, and the period distance is determined according to the size of the open pore of the layer so as to ensure the convenience of processing. The size of the perforations determines the equivalent dielectric constant epsilon of the layern_eff', and its equivalent dielectric constant is based on the radial equiphase condition, i.e.
εn'1/2d＝εn_eff'1/2d n∈(1,N) (3)
In the formula, epsilonn' is the dielectric constant of the discretized n-th layer obtained according to equation (2), and d is the thickness of the ring pillar. The larger the aperture of the hole, the smaller the equivalent dielectric constant. It is worth mentioning that the design of the periodically arranged hole structure mostly adopts a planar structure, and the dielectric constant obtained by planar calculation is slightly higher than that of the annular structure, so that the size of the opening of the annular medium is slightly larger than that of the plane. In this embodiment, the selected materials are the same, but in other applications, different materials may be selected. The specific method is that radial equivalence is completed based on the formula (3). Such design is a conventional design concept, and the design can be easily obtained based on the method provided by the present invention, and therefore, the present invention should also fall within the protection scope of the present invention.
For the processing of the discretization luneberg lens, the invention adopts a 3D printing technology. This is a result of considerations of processing convenience, processing cost and mass requirements. The material selection of 3D printing should be fully considered when designing the lens to ensure the smooth completion of processing. It is worth mentioning that the engineering realization of the lens can be also finished by utilizing the processing technologies of casting, cutting, milling and the like.
The design effect is shown in fig. 3, which compares the performances of a continuous layered luneberg lens, a discretized luneberg lens based on the classical equivalent medium theory and a discretized luneberg lens based on the modified equivalent medium theory in a phase mode. It is seen from the figure that compared with the traditional discretization luneberg lens based on the classical equivalent medium theory, the discretization luneberg lens based on the modified equivalent medium theory provided by the invention has better effect of point source to plane wave radiation, and even better effect than the traditional continuous luneberg lens antenna. In addition, the designed lens has obvious optical path reduction, and accordingly, the reduction of lens loss is realized.
While the invention has been described in terms of its preferred embodiments, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention.
Claims (15)
1. A two-dimensional multilayer discretization luneberg lens is characterized in that: the lens comprises a radiation feed source and a discretization luneberg lens, wherein the radiation feed source is positioned on the central plane of the lens in the z direction and is positioned outside the lens; the discretization luneberg lens consists of a plurality of layers of discrete pure medium circular columns, and the circular columns are isolated by air.
2. The two-dimensional multi-layered discretized luneberg lens of claim 1, wherein: the radiation feed source has the characteristic of quasi-two-dimension, and omnidirectional radiation is carried out on an XOY plane; the feed source is located outside the cylindrical ring of the medium on the outermost layer of the lens and is specifically determined by the input position of the luneberg lens point source.
3. The two-dimensional multi-layered discretized luneberg lens of claim 1, wherein: the lens consists of a plurality of layers of discrete pure medium circular columns, air exists among the circular columns, and the wave path difference formed by a single layer of air and a medium in the radius direction of the single layer of air is smaller than the single-time working wavelength.
4. The two-dimensional multi-layered discretized luneberg lens of claim 1, wherein: the pure medium circular cylinder is made of medium materials with isotropy, non-magnetism and weak dispersion, and the dielectric constant of the pure medium circular cylinder is determined by the material selected by the lens and the dispersion of the lens.
5. The two-dimensional multi-layer discretization luneberg lens of claims 1 and 3, wherein: the medium circular column is provided with uniformly distributed hole structures for realizing corresponding electromagnetic characteristics of each layer.
6. The two-dimensional multi-layered discretized luneberg lens of claim 1, wherein: the two-dimensional multilayer discretization luneberg lens is prepared by utilizing a 3D printing technology.
7. A method for realizing discretization of a two-dimensional multilayer Luneberg lens by using a modified equivalent medium theory is characterized by comprising the following steps:
(1) calculating parameters of the continuous layered luneberg lens to be discretized according to a classical luneberg lens formula, wherein the parameters comprise the overall dimension of the lens, the position of a radiation feed source and the refractive index of each layer; further obtaining the corresponding dielectric constant value of each layer of medium in a non-magnetic state;
(2) discretizing the continuous layered luneberg lens, namely converting each layer of medium of the continuous layered lens into a combination of air and the medium, wherein the radial position of the medium layer is positioned at the radial center of the original continuous layered lens, and the dielectric constant of each layer of medium is calculated by using a modified equivalent medium theory;
(3) and according to the dielectric constant of each layer of medium of the discrete luneberg lens obtained by calculation, independently perforating each layer to obtain the electromagnetic property required by each layer.
8. The method for realizing the discretization of the two-dimensional multilayer luneberg lens by utilizing the modified equivalent medium theory as claimed in claim 7, wherein: the luneberg lens designed by the method has the discretization characteristic, can realize the function of emitting plane waves fed by a point source, and has a reduced total wave path difference compared with the traditional luneberg lens.
9. The method for realizing the discretization of the two-dimensional multilayer luneberg lens by utilizing the modified equivalent medium theory as claimed in claim 7, wherein: the refractive index distribution parameters of the to-be-discretized continuous layered Luneberg lens are based on a classical Luneberg lens formula, and the position of the radial midpoint of each layer is selected by calculating the medium radius.
10. The method for realizing the discretization of the two-dimensional multilayer luneberg lens by utilizing the modified equivalent medium theory as claimed in claims 7 and 9, wherein the method comprises the following steps: the calculation of the dielectric constant of the continuous layered luneberg lens is based on isotropic, non-magnetic conditions, so the dielectric constant of each layer is the square of the refractive index.
11. The method for realizing the discretization of the two-dimensional multilayer luneberg lens by utilizing the modified equivalent medium theory as claimed in claim 7, wherein: the discretization of the continuous layered Luneberg lens is to convert the Luneberg lens filled with all the media in each layer into a discrete lens form composed of media and spacing air in each layer; in the radial direction, the center of each layer of medium coincides with the center of the original continuous layered lens in the layer.
12. The method for realizing the discretization of the two-dimensional multilayer luneberg lens by utilizing the modified equivalent medium theory as claimed in claims 7 and 11, wherein the method comprises the following steps: the wave path difference formed by the combination of the single-layer medium and the air in the radius direction of the discrete luneberg lens is not more than n times of the working wavelength, so that the emergent wave of the lens is ensured not to have an amplitude zero point, and the value of n is related to the ratio of the medium thickness to the air thickness of the discrete lens but not more than 1.
13. The method for realizing the discretization of the two-dimensional multilayer luneberg lens by utilizing the modified equivalent medium theory as claimed in claims 7 and 11, wherein the method comprises the following steps: the dielectric constant of each layer of medium of the discrete luneberg lens is calculated by a modified equivalent medium theory, and the equivalent is based on the equal phase condition of each layer of medium of the continuous layered luneberg lens along the radius direction.
14. The method for realizing the discretization of the two-dimensional multilayer luneberg lens by utilizing the modified equivalent medium theory as claimed in claims 7 and 13, wherein the method comprises the following steps: the correction method of the modified equivalent medium theory is that the ratio of the medium to the air thickness is multiplied by a correction coefficient m during equivalent calculation, and the value of m is related to the ratio of the medium to the air thickness and is larger than 1.
15. The method for realizing the discretization of the two-dimensional multilayer luneberg lens by utilizing the modified equivalent medium theory as claimed in claim 7, wherein: the dielectric constant of each layer of medium of the discrete Luneberg lens is realized by designing a hole structure on the medium, and the size of the hole is obtained according to the radial phase equivalence of the discrete Luneberg lens on the layer.
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| FR2582157A1 (en) * | 1985-05-15 | 1986-11-21 | Snecma | Antenna with reduced scanning step over a wide angular sector |
| CN105470659A (en) * | 2015-12-31 | 2016-04-06 | 电子科技大学 | Lightweight dielectric-filled multi-beam cylindrical Luneberg lens antenna |
| US20170162944A1 (en) * | 2014-07-24 | 2017-06-08 | Bae Systems Plc | Lens design method and radiation source substrate |
| RU174675U1 (en) * | 2017-07-25 | 2017-10-25 | Дмитрий Сергеевич Алиев | Luneberg Lens Antenna |
| CN109149122A (en) * | 2018-09-06 | 2019-01-04 | 西安电子科技大学 | A kind of lens and lens antenna based on 3D printing |
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- 2021-11-19 CN CN202111376294.4A patent/CN113922099A/en active Pending
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| FR2582157A1 (en) * | 1985-05-15 | 1986-11-21 | Snecma | Antenna with reduced scanning step over a wide angular sector |
| US20170162944A1 (en) * | 2014-07-24 | 2017-06-08 | Bae Systems Plc | Lens design method and radiation source substrate |
| CN105470659A (en) * | 2015-12-31 | 2016-04-06 | 电子科技大学 | Lightweight dielectric-filled multi-beam cylindrical Luneberg lens antenna |
| RU174675U1 (en) * | 2017-07-25 | 2017-10-25 | Дмитрий Сергеевич Алиев | Luneberg Lens Antenna |
| CN109149122A (en) * | 2018-09-06 | 2019-01-04 | 西安电子科技大学 | A kind of lens and lens antenna based on 3D printing |
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