CN104377452B - Design method for pure medium electromagnetic lens based on meta-surface - Google Patents
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Abstract
The invention discloses a design method for a pure medium electromagnetic lens based on a meta-surface. The method includes the following steps that firstly, according to medium materials of the lens and the wavelength of working electromagnetic waves, the relation between phase changes and medium thicknesses is obtained; secondly, according to requirements for the type and focal length of the lens (a convex lens or a concave lens or a reflecting mirror), needed distribution of phase jumps is worked out; thirdly, according to phase distribution requirements, the medium lens with the corresponding thickness is established in electromagnetic simulation software, is simulated and finely adjusted and then can be manufactured, wherein the phase distribution phi is obtained according to the requirement of the lens designed in the second step, distribution of the medium thicknesses is worked out, and modeling and simulating are conducted in the electromagnetic simulation software. The design method is simple and flexible; along with reduction of incidence wavelengths, the focal length of the lens will be increased; a lens set composed of the lens and a traditional lens can eliminate chromatic aberration.
Description
Technical Field
The invention relates to a pure medium electromagnetic lens based on an artificial electromagnetic surface, and belongs to the technical field of photoelectricity.
Background
Electromagnetic lenses are widely used in systems for transmitting and receiving radio waves or light waves. The conventional electromagnetic lens is generally a pure dielectric lens with an arc-shaped curved surface, and the principle of the conventional electromagnetic lens is continuous phase change, such as a convex lens, a concave lens and the like. The disadvantage is that it is bulky, thick and heavy.
After 2000, the development of the artificial electromagnetic materials (metamaterials) theory led to the appearance of several thin and light electromagnetic lenses. At present, such recent electromagnetic lens devices are basically constructed with so-called metamaterials. For example, the patent document with the application number of 201110080646.1 and the name of "a lens antenna with electromagnetic wave converging function" discloses a metamaterial electromagnetic lens, which is formed by combining and arraying metamaterial function plates, the device comprises a plurality of metamaterial bands with the refractive indexes distributed in a band shape in the middle, and the refractive indexes in the metamaterial bands continuously change towards the same direction. The patent document with the application number of 201110113906.0 and the name of 'an electromagnetic lens antenna' discloses an electromagnetic lens antenna, which comprises an anisotropic metamaterial panel with a convergence function and a radiation unit located on the focus of the metamaterial panel, wherein the metamaterial panel is formed by stacking metamaterial sheets, each metamaterial sheet comprises a substrate and a plurality of artificial microstructures attached to the substrate, the refractive index in each region is radially symmetrical relative to a central axis and gradually decreases along with the increase of the radius, the change rate gradually increases, and the refractive index at the junction of each region discontinuously changes. The patent document with the application number of 201110061811.9 and the name of 'a metamaterial electromagnetic lens antenna' discloses a metamaterial electromagnetic lens antenna, which comprises a feed source and a metamaterial, wherein the product of the equivalent dielectric constant and the equivalent magnetic permeability mu of each unit in the middle of the metamaterial is the highest value, and the product value of the equivalent dielectric constant and the equivalent magnetic permeability mu of other units is in a gradual change trend from small to large. The patent document with the application number of 2009102135055 and the name of 'a lens' comprises a metal horn provided with a feed source and a lens, wherein the lens is embedded at one end of the metal horn with the larger diameter; the lens comprises a core plate and a plane medium plate, wherein a plurality of core plate non-resonant basic units are arranged on one plane; and a core plate metal frame is printed in each core plate non-resonant basic unit.
In the searched documents, the electromagnetic lens is a metamaterial with a variable refractive index formed by printing various metal structures on a dielectric substrate, and the working principle of the lens is based on an electromagnetic resonance theory, so that the working bandwidth is narrow, the loss is large, and the design requirement of the metamaterial structure is high on the basis of the electromagnetic theory, and the technical popularization is difficult.
The existing electromagnetic lens manufacturing technology mainly utilizes the principle of continuous phase change to control electromagnetic waves, and the traditional realization scheme is that the phase is continuously changed through an arc-shaped curved surface of a dielectric lens, so that the electromagnetic lens has the advantages of mature technology, convenient processing and wide working frequency band, but has the defects of thickness and weight, and the volume and the weight are difficult to accept particularly in a low-frequency band; the latest metamaterial implementation scheme is to change the refractive index of the metamaterial through a specially designed metal resonance structure so as to realize continuous phase change. Huygens indicates three hundred years ago that each point on the wave front of the electromagnetic wave can be regarded as a secondary wave source in the process of propagating the electromagnetic wave, the shape of the wave front behind the point is obtained by coherent superposition of the electromagnetic waves radiated by all the secondary wave sources, and the later person refers to the huygens principle. The principle directly explains that the phase delay of a light path of a traditional medium optical lens is changed through a curved surface, so that the phase difference from each point on the emergent surface of the lens to a focus is integral multiple of 2 pi, the coherence enhancement of electromagnetic waves at the focus is realized, and the coherence of other points in space is counteracted. In recent two years of research on artificial electromagnetic surfaces (metasurfaces), it has been found that if a plurality of subwavelength (generally less than one-half wavelength) structures are artificially manufactured on the surface of a flat lens by using metal wires, the structures are subjected to phase jump of a secondary wave source, instead of realizing continuous phase change by means of a curved surface, and coherent superposition of electromagnetic waves at a focus can also be realized. However, such subwavelength structures are difficult to design and process, and have narrow operating bands, and most fatal problems are that strict requirements are imposed on the polarization direction of incident electromagnetic waves, and the loss is large, so that the subwavelength structures are difficult to be applied to practice. The present invention can solve the above problems well.
Disclosure of Invention
The invention aims to provide a design method of a pure medium electromagnetic lens based on an artificial electromagnetic surface, which can prepare the electromagnetic lens by using a pure medium and a simple processing method.
The technical scheme adopted by the invention for solving the technical problems is as follows: the method is characterized in that the lens is small in size, the total thickness is less than one medium internal wavelength (lambda/n), the working frequency band is wide, the design and the implementation are easy, and the processing cost is low.
Method flow
Step 1: and obtaining the relation between the phase change and the thickness of the medium according to the medium material used by the lens and the wavelength of the working electromagnetic wave.
According to the formula:determining the relationship between the phase change of the electromagnetic wave and the thickness of the medium, wherein rIs the dielectric constant, theta, of the dielectric material used for the lensiIs the incident angle of the electromagnetic wave, ω is the angular frequency, η0377 Ω is the free space wave impedance and h is the dielectric thickness.
Step 2: the required distribution of the phase jumps is calculated from the lens type (convex, concave, mirror) and the focal length requirements.
The phase distribution of the convex lens along the radial direction can be obtained by the aplanatic principle:wherein k is02 pi λ, f is the focal length of the lens, n is an arbitrary integer, and r is the distance from the center of the circle.
And for a concave lens, the phase distribution is:
the phase distribution of the mirror is:wherein,is the position vector of the lens surface when the phase center of the feed antenna is the origin of the rectangular coordinate system,is relative on the reflecting mirror surfaceAt the position vector of (0,0, f),is the unit direction vector of the desired reflected beam.
And step 3: constructing a dielectric lens with corresponding thickness in electromagnetic simulation software according to the phase distribution requirement, carrying out simulation and fine adjustment, and then processing and manufacturing; obtaining the phase distribution according to the requirement of the lens designed in the step 2According to the formulaAnd calculating the distribution of the thickness of the medium, and then modeling and simulating in electromagnetic simulation software.
Has the advantages that:
1. the design method of the invention is simple and particularly flexible.
2. The focal length of the lens is longer as the incident wavelength is reduced.
3. The invention can eliminate chromatic aberration by combining the lens with the traditional lens.
4. The lens has the advantages of small volume, total thickness less than one medium internal wavelength (lambda/n), wide working frequency band, easy design and realization and low processing cost.
Drawings
FIG. 1 is a schematic diagram of an incident surface and a two-port equivalent network model when electromagnetic waves are incident on a dielectric material according to the present invention.
And (3) identification and explanation: FIG. 1(a) shows an artificial electromagnetic surface medium element with oblique incidence of electromagnetic beams; fig. 1(b) shows an equivalent two-port transmission line circuit model.
FIG. 2 is a diagram showing the relationship between the phase change of the perpendicular incident electromagnetic field and the thickness of the polyimide dielectric film according to the present invention.
FIG. 3 is a schematic diagram of a pure dielectric electromagnetic lens constructed by using sub-wavelength dielectric blocks with different thicknesses and a full-wave simulation result diagram.
And (3) identification and explanation: FIG. 3(a) identifies a constructed pure medium THz lens based on the phase jump principle; FIG. 3(b) shows the field strength distribution in the y-z plane from a full-wave simulation; fig. 3(c) shows the power distribution in the x-axis direction on the focal plane.
FIG. 4 is a diagram of a pure dielectric electromagnetic lens constructed with concentric cylinders of different thicknesses and a full-wave simulation result.
And (3) identification and explanation: FIG. 4(a) a pure dielectric THz lens constructed of concentric cylinders of different thicknesses; FIG. 4(b) field intensity distribution in the y-z plane from full-wave simulation; FIG. 4(c) power distribution in the x-axis direction on the focal plane.
FIG. 5 is the field intensity distribution in the y-z plane obtained by full-wave simulation of the present invention: FIG. 5(a) shows a 0.9THz diagram; FIG. 5(b) shows a schematic 1.0THz diagram; FIG. 5(c) shows a schematic 1.1THz diagram.
FIG. 6 is a flow chart of a method of the present invention.
Detailed Description
The technical solution of the present invention will be described in detail below with reference to the accompanying drawings.
Example 1
The invention considers that the final purpose of the artificial electromagnetic surface of the metal structure is to realize the phase jump of the secondary Huygens source, and the realization of the phase jump also has a means of changing the thickness of an electromagnetic wave propagation medium, so that the invention designs a pure medium electromagnetic lens. The working principle is as follows: the present invention takes FIG. 1(a) as an example, and assumes a beam of TE electromagnetic waves is represented by θiThe angle is oblique incident on a certain unit of the lens, the unit can be seen as the mn-th unit in a two-dimensional plane, and the period length is half wavelength (L ═ lambda0/2), plane of incidence xz⊥mn. Assuming that each cell is a uniform planar dielectric layer, the present invention can obtain a two-port network model according to the transmission line theory, as shown in fig. 1(b), where z is 0 and h is above and belowmn) The TE wavefields of the surface may be related by an ABCD matrix,
wherein,omega is the angular frequency, η0377 Ω is the free space wave impedance. Since the tangential field must be continuous on the upper and lower surfaces of the media element, boundary conditions are obtained:
the transmission coefficient of the electromagnetic field through the unit can be obtained by combining the formula (1) and the formula (2):
the formula accurately gives the transmission field of the lower surface of the mn-th dielectric unit, and if the electric field of the lower surface is viewed as the mouth-to-face field distribution of the electromagnetic lens, the far-field directional diagram can be calculated. The invention easily derives from the equation (3) the phase variation of the transmission field:
from this equation, ifThe incident angle of the electromagnetic wave and the refractive index of the dielectric material are known, and the phase of the transmission field is completely determined by the thickness of the dielectric element. If the thickness of the dielectric element varies from 0 to λ0The phase shift of/n, which also ranges from 0 to 2 pi, is a necessary condition for complete control of the propagating electromagnetic wave. Fig. 2 shows the phase change of the polyimide dielectric thin film unit as a function of the thickness when the operating frequency is 1THz, wherein the solid black line is the theoretical calculation result of formula (4), and the line "+" is the electromagnetic field full-wave simulation result. The two are matched.
As mentioned earlier, the exit field at the bottom of each element of the lens can be seen as a Wheatstone secondary point source, and at any point in space in the propagation direction, if the phase difference caused by the spatial distance can be compensated by the phase change of each secondary field point, the transmission fields of each element can be coherently superposed to form a focus, and the total field at the focus isThe expression is as follows:
wherein EiIs a function of the incident field and,is the position vector of the mn-th cell. To obtain the electromagnetic wave transmission characteristics of the biconvex lens, the phase distribution of the dielectric lens along the radial direction can be obtained by the aplanatic principle:the thickness distribution of the dielectric layer in the radial direction can be obtained according to the formula (4):
FIG. 3(a) shows1THz focusing lens constructed by polyimide dielectric film, the dielectric constant of polyimide isr3.1, a loss tangent of 0.05 and an overall dimension of 5.25 × 5.25.25 mm2(17.5λ0×17.5λ0) Is divided into 35 × 35 units, and the size of each unit is 0.15 × 0.15.15 mm2(λ0/2×λ02), the maximum thickness is 0.17mm, the concentric circular array is sectioned from the inside to the outside into 15 desired phase jump zones, the f/D (focal length/lens diameter) is designed to be 1.0, although it is also possible to reduce the f/D by increasing the phase gradient of the lens surface or increasing the lens size. Fig. 3(b) is a full-wave electromagnetic simulation result, and fig. 3(c) shows the focal plane (z ═ 5mm) along the lineDirectional power distribution.
In order to further reduce the manufacturing process and increase the lateral focal spot resolution, the lens can be further modified as shown in fig. 4(a), which is composed of 22 concentric cylinders with different thicknesses, and the f/D (f is 5mm, D is 7.35mm) is designed to be 0.68. FIG. 4(b) is a full-wave electromagnetic simulation result from which the present invention clearly shows that more energy is concentrated to the focal point, which should be the cylindrical medium reduces the tangential (between cells) directionDirection) of the object. Fig. 4(c) shows the power distribution along the x-axis direction on the focal plane.
Fig. 5 further shows the electric field distribution of the broadband electromagnetic wave incident perpendicular to the lens surface, and as can be seen from fig. 5(a) - (c), as the operating frequency is increased from 0.9THz to 1.1THz, the focal length is increased from 4.6mm to 5.7mm, which is exactly opposite to the conventional curved dielectric lens, and therefore, the lens group formed by combining the lens and the conventional curved dielectric lens can eliminate the phase difference.
The pure medium lens based on the artificial electromagnetic surface is different from the traditional Fresnel lens, the Fresnel lens realizes weight reduction and volume reduction by removing the non-refraction part of the traditional medium lens, but the arc-shaped curved surface is reserved. The pure medium unit based on the artificial electromagnetic surface can be used for realizing the convex lens, the functions of the concave lens, the directional refractor and the like, and is quite flexible in design. The present invention can design a corresponding lens by obtaining a desired phase distribution according to the lens function and arranging the dielectric elements in a thickness according to the above formula (6).
Example 2
As shown in fig. 6, the present invention provides a method for designing a pure dielectric electromagnetic lens based on an artificial electromagnetic surface, the method includes the following steps:
step 1: obtaining the relation between the phase change and the medium thickness according to the medium material used by the lens and the wavelength of the working electromagnetic wave;
according to the formula:determining the relationship between the phase change of the electromagnetic wave and the thickness of the medium, wherein rIs the dielectric constant, theta, of the dielectric material used for the lensiIs the incident angle of the electromagnetic wave, ω is the angular frequency, η0377 Ω is the free space wave impedance, h is the dielectric thickness;
step 2: calculating the distribution of required phase jump according to the lens type (convex lens, concave lens and reflector) and the focal length requirement;
for example, the phase distribution of the convex lens in the radial direction can be obtained by the principle of aplanatism:wherein k is02 pi λ, f is the focal length of the lens, n is any integer, r is the distance from the center of the circle;
and for a concave lens, the phase distribution is:
the phase distribution of the mirror is:wherein,is the position vector of the lens surface when the phase center of the feed antenna is the origin of the rectangular coordinate system,is the position vector on the mirror surface relative to (0,0, f),is the unit direction vector of the desired reflected beam;
and step 3: constructing a dielectric lens with corresponding thickness in electromagnetic simulation software according to the phase distribution requirement, carrying out simulation and fine adjustment, and then processing and manufacturing; obtaining the phase distribution according to the requirement of the lens designed in the step 2According to the formulaAnd calculating the distribution of the thickness of the medium, and then modeling and simulating in electromagnetic simulation software.
Claims (1)
1. A design method of a pure medium electromagnetic lens based on an artificial electromagnetic surface is characterized by comprising the following steps:
step 1: obtaining the relation between the phase change and the medium thickness according to the medium material used by the lens and the wavelength of the working electromagnetic wave;
according to the formula:determining the relationship between the phase change of the electromagnetic wave and the thickness of the medium, wherein rIs the dielectric constant, theta, of the dielectric material used for the lensiIs the incident angle of the electromagnetic wave, ω is the angular frequency, η0377 Ω is the free space wave impedance, h is the dielectric thickness;
step 2: calculating the distribution of required phase jump according to the lens type (convex lens, concave lens and reflector) and the focal length requirement;
the phase distribution of the convex lens along the radial direction can be obtained by the aplanatic principle:wherein k is02 pi λ, f is the focal length of the lens, n is any integer, r is the distance from the center of the circle;
and for a concave lens, the phase distribution is:
the phase distribution of the mirror is:wherein,is the position vector of the lens surface when the phase center of the feed antenna is the origin of the rectangular coordinate system,is the position vector on the mirror surface relative to (0,0, f),is the unit direction vector of the desired reflected beam;
and step 3: constructing a dielectric lens with corresponding thickness in electromagnetic simulation software according to the phase distribution requirement, carrying out simulation and fine adjustment, and then processing and manufacturing; according to the aboveThe phase distribution of the reflector is obtained according to the requirements of the lens designed in the step 2According to the formulaAnd calculating the distribution of the thickness of the medium, and then modeling and simulating in electromagnetic simulation software.
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| CN105487145B (en) * | 2016-01-20 | 2017-12-29 | 浙江大学 | A kind of method for surpassing surface structure ultra thin optical lens based on artificial micro-structure |
| KR20170137364A (en) | 2016-06-03 | 2017-12-13 | 삼성전자주식회사 | Electromagnetic wave focusing device and optical apparatus including the same |
| CN106094066B (en) * | 2016-08-04 | 2018-09-07 | 浙江大学 | A method of the ultra-thin colour optics lens of surface structure are surpassed based on artificial micro-structure |
| CN108520994B (en) * | 2018-02-12 | 2019-12-13 | 中天宽带技术有限公司 | method for quickly designing impedance matching circuit of miniaturized broadband dielectric phase shifter |
| CN108318947A (en) * | 2018-04-08 | 2018-07-24 | 中山大学 | A kind of production method of low-refraction all dielectric planar lens |
| CN109037959B (en) * | 2018-07-17 | 2021-05-14 | 中国科学院光电技术研究所 | Ultra-large-caliber light-weight achromatic plane electromagnetic lens based on generalized catadioptric law |
| CN109346843B (en) * | 2018-10-31 | 2021-05-18 | 南京邮电大学 | Design method of space one-dimensional scanning lens antenna and beam scanning method |
| CN112234341B (en) * | 2019-06-30 | 2022-02-01 | Oppo广东移动通信有限公司 | Antenna assembly and electronic equipment |
| CN111786125B (en) * | 2020-06-28 | 2021-09-17 | 北京高信达通信科技股份有限公司 | Dielectric cylindrical lens, dielectric film and manufacturing method of dielectric cylindrical lens |
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| US5389943A (en) * | 1991-02-15 | 1995-02-14 | Lockheed Sanders, Inc. | Filter utilizing a frequency selective non-conductive dielectric structure |
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