CN111900545B - High-directionality plano-concave lens containing ENZ metamaterial sandwich layer with non-uniform thickness - Google Patents

High-directionality plano-concave lens containing ENZ metamaterial sandwich layer with non-uniform thickness Download PDF

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CN111900545B
CN111900545B CN202010822178.XA CN202010822178A CN111900545B CN 111900545 B CN111900545 B CN 111900545B CN 202010822178 A CN202010822178 A CN 202010822178A CN 111900545 B CN111900545 B CN 111900545B
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concave lens
enz metamaterial
metal plate
enz
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CN111900545A (en
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杨锐
贾艺铭
雷振亚
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Xidian University
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    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q15/00—Devices for reflection, refraction, diffraction or polarisation of waves radiated from an antenna, e.g. quasi-optical devices
    • H01Q15/0006—Devices acting selectively as reflecting surface, as diffracting or as refracting device, e.g. frequency filtering or angular spatial filtering devices
    • H01Q15/0086—Devices acting selectively as reflecting surface, as diffracting or as refracting device, e.g. frequency filtering or angular spatial filtering devices said selective devices having materials with a synthesized negative refractive index, e.g. metamaterials or left-handed materials
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q15/00—Devices for reflection, refraction, diffraction or polarisation of waves radiated from an antenna, e.g. quasi-optical devices
    • H01Q15/02—Refracting or diffracting devices, e.g. lens, prism
    • H01Q15/12—Refracting or diffracting devices, e.g. lens, prism functioning also as polarisation filter

Abstract

A high-directionality plano-concave lens containing an ENZ metamaterial sandwich layer with non-uniform thickness comprises a parallel slab waveguide, a metal reflecting surface and a plano-concave lens, wherein the metal reflecting surface and the plano-concave lens are integrally arranged in the parallel slab waveguide, the three-fourth metal reflecting surface and one fourth of the plano-concave lens form a closed circle, the plano-concave lens is formed by a concave ENZ metamaterial substrate, an intermediate layer and a plane ENZ metamaterial substrate are tightly attached to each other, the thicknesses of the concave ENZ metamaterial substrate and the plane ENZ metamaterial substrate are both l, the intermediate layer is formed by metal plates with equal widths and an ENZ metamaterial interlayer tightly attached between an upper metal plate and a lower metal plate which are symmetrical, the thickness a of the ENZ metamaterial interlayer shows non-linear reduced non-uniform change along with the increase of the width t of the metal plates, and a line source is arranged at the center of the circle of the closed circle and is parallel to the short side of the emergent surface of the.

Description

High-directionality plano-concave lens containing ENZ metamaterial sandwich layer with non-uniform thickness
Technical Field
The invention belongs to the technical field of electronic devices, and further relates to a high-directionality plano-concave lens containing an ENZ (amorphous-near-zero) metamaterial sandwich layer with non-uniform thickness and dielectric constant tending to zero in the technical field of microwave devices. The invention can be used for the high-efficiency transmission and the directional radiation of the electromagnetic wave of the line source.
Technical Field
In the fields of satellite communication, radar systems and the like, antennas with high gain and low sidelobes are widely applied, and metamaterial lens antennas have the advantages of high directionality, small sidelobes, small back lobes and the like and are widely used in the fields of microwave engineering, communication, military and the like. The metamaterial lens antenna generally uses artificial electromagnetic metamaterial units with different sizes which are regularly arranged to obtain the gradient refractive index required by the lens.
The patent document "broadband cylindrical lens antenna based on artificial electromagnetic material" (application number CN200910032139.3, application publication number CN 101587990 a) of the southeast university discloses a lens antenna based on artificial electromagnetic metamaterial. The lens structure in the antenna is formed by arranging the units with different sizes printed on the dielectric substrate according to a certain rule to obtain equivalent media with different refractive indexes, so that the directional radiation of the antenna is realized. The lens has the defects that the structure of the lens is complex and the manufacturing cost is high because the lens structure needs to design the unit structures which are arranged according to a certain rule according to different required refractive indexes.
The Shenzhen institute of high-tech engineering and engineering, Shenzhen, discloses a lens antenna composed of metamaterial sheets in the patent document 'metamaterial-based lens antenna' (application number CN201110338231.X, publication number CN 103094712A). The lens structure in the antenna is formed by a circular lens with the refractive index changing along with the radius and a metamaterial impedance converter formed by a plurality of layers of metamaterial units, and the purpose of converting spherical waves into plane waves is achieved by adjusting the phase of electromagnetic waves and matching impedance. The lens has the defects that the lens structure needs to use a multilayer metamaterial unit to form an impedance converter to realize impedance matching, the number of devices is large, integration is not easy, processing is complex, and manufacturing cost is high.
Disclosure of Invention
The invention aims to solve the problems in the prior art, and provides a high-directivity plano-concave lens with an ENZ metamaterial sandwich layer with non-uniform thickness, which is used for solving the problems that the lens antenna in the prior art is complex in design structure and difficult in realizing impedance matching.
The idea for realizing the purpose of the invention is as follows: the ENZ metamaterial serving as a novel artificial electromagnetic metamaterial has the characteristics of near-zero phase shift, zero refractive index and the like, can be used for lens design and can realize wave front shaping of electromagnetic waves, and has the advantage of simple structure. However, the intrinsic huge wave impedance of the ENZ metamaterial caused by the near-zero dielectric constant of the ENZ metamaterial is difficult to match, so that the reflection is enhanced, and one solution is to design the magnetic permeability of the ENZ metamaterial lens to be the same as the dielectric constant in numerical value to match with the impedance of free space, but the difficulty in implementation is greatly increased. The purpose of impedance matching between the lens and the free space is achieved by designing an ENZ metamaterial interlayer with non-uniform thickness, and efficient transmission of electromagnetic waves is achieved.
To achieve the above object, the present invention includes a parallel plate waveguide 1, a metal reflecting surface 2 and a plano-concave lens 3. The metal reflecting surface 2 and the concave lens 3 are both arranged in an upper metal flat plate 11 and a lower metal flat plate 12 of the parallel flat waveguide 1, and the metal reflecting surface 2 and the concave lens 3 form a structure with a radius of
Figure GDA0002964295520000021
λ is the wavelength of electromagnetic waves, the metal reflecting surface 2 occupies three quarters of the closed circle, the plano-concave lens 3 occupies one quarter of the closed circle, the incident surface of the plano-concave lens 3 is a concave surface, the exit surface is a plane, and the length of the long side of the exit surface is W ═ 10 λ; the metal reflecting surface 2 and the plano-concave lens 3 are equal in height and d in height, the plano-concave lens 3 is formed by tightly attaching a concave ENZ metamaterial substrate 4, an intermediate layer and a plane ENZ metamaterial substrate 5, the thicknesses of the concave ENZ metamaterial substrate 4 and the plane ENZ metamaterial substrate 5 are both l, and the intermediate layer is provided with an incident surface and an emergent surface which are the same as those of the plano-concave lens 3; the middle layer is composed of a metal plate 6 and an ENZ metamaterial interlayer 7 which are equal in width, the ENZ metamaterial interlayer 7 is tightly attached between an upper metal plate 61 and a lower metal plate 62 of the metal plate 6 to form a sandwich layer, the thickness a of the ENZ metamaterial interlayer 7 is non-uniformly changed, and the change of the thickness a of the ENZ metamaterial interlayer 7 is non-linearly reduced non-uniformly along with the increase of the width of the upper metal plate 61 of the metal plate 6 according to the following formula:
Figure GDA0002964295520000022
wherein, Y0Representing the differential characteristic admittance, Y, of free space0＝(W1/d)/η0，W1Representing an arbitrarily variable differential length, η, of the long side of the exit face of the plano-concave lens 30Representing the wave impedance, epsilon, of a free space of value 120 pirRepresents the dielectric constant, mu, of the ENZ metamaterial with the value of 0.01rThe magnetic permeability, theta, of an ENZ metamaterial with the value of 11The electrical length of the upper metal plate 61 of the metal plate 6 is shown,
Figure GDA0002964295520000023
k0representing wave number, k, in vacuum0ω denotes an angular frequency of the electromagnetic wave, ω 2 pi f denotes a frequency of the electromagnetic wave, and c denotes a value of 3 × 108m/s light velocity, t represents the width of the upper metal plate 61 of the metal plate 6, CTMRepresents the equivalent capacitance, C, between the upper metal plate 61 and the lower metal plate 62 of the metal plate 6TMAnd W1Proportional relation and increase with the increase of the frequency of the electromagnetic wave; the line source (8) is arranged at the center of the closed circle and is parallel to the short edge of the emergent surface of the plano-concave lens 3. When a line source 8 which is positioned at the center of the circle and is parallel to the plano-concave lens 3 is excited to generate TM polarized cylindrical waves, the transmitted waves are parallel to the emergent plane of the plano-concave lens 3, and high-directionality beams are formed.
Compared with the prior art, the invention has the following advantages:
firstly, the plano-concave lens 3 is formed by tightly attaching the concave ENZ metamaterial substrate 4, the middle layer and the plane ENZ metamaterial substrate 5, the unit structure of the plano-concave lens is not required to be designed, high-directivity radiation of electromagnetic waves is realized only by using a metal plate and the ENZ metamaterial and utilizing the wave front shaping effect of the ENZ metamaterial, the problem that the structure of the plano-concave lens in the prior art is complicated due to the fact that artificial metamaterial units which are regularly arranged according to the refractive index are formed into a belt, and the plano-concave lens has the advantages of being simple in structure, easy to process and low in cost.
Secondly, the intermediate layer composed of the metal plate 6 and the ENZ metamaterial interlayer 7 of the invention enables the intermediate layer to have the same characteristic impedance as the free space, realizes the impedance matching function, overcomes the problem of complex structure caused by the multi-layer unit structure of the impedance converter used for realizing the impedance matching in the prior art, and has the advantages of less devices, easy integration and low manufacturing cost.
Thirdly, the thickness a of the ENZ metamaterial interlayer 7 is nonlinearly reduced along with the increase of the width of the upper metal plate 61 of the metal plate 6, so that perfect tunnel transmission can be realized when incident waves pass through different transmission paths of the plano-concave lens 3, the problem of reflection enhancement caused by inherent huge wave impedance due to the near-zero dielectric constant of the ENZ metamaterial in the prior art is solved, and the ENZ metamaterial interlayer has the advantages of good transmission characteristic and high directionality.
Drawings
FIG. 1 is a schematic structural view of the present invention;
FIG. 2 is a top view of the present invention;
FIG. 3 is a side view of the present invention;
FIG. 4 is a schematic view of an ENZ metamaterial sandwich in accordance with the present invention;
FIG. 5 is a schematic diagram of an equivalent circuit of the plano-concave lens of the present invention;
FIG. 6 is a graph of thickness a of an ENZ metamaterial sandwich of examples 1 and 2 of the present invention as a function of metal plate width t;
FIG. 7 is a function F of the full transmission condition of the present invention1And F2Wherein FIG. 7(a) is a function F of example 11And F2FIG. 7(b) is a function F of example 21And F2The fitted curve graph of (1);
fig. 8 is the far field gain pattern of the plano-concave lens of the present invention, where fig. 8(a) is the yz plane far field gain pattern of example 1 and fig. 8(b) is the yz plane far field gain pattern of example 2.
Detailed Description
The invention is described in further detail below with reference to the figures and the specific embodiments.
The overall structure of the present invention will be described in further detail with reference to fig. 1 to 5.
The invention comprises a parallel flat waveguide 1, a metal reflecting surface 2 and a plano-concave lens 3. The metal reflecting surface 2 and the concave lens 3 are both arranged in an upper metal flat plate 11 and a lower metal flat plate 12 of the parallel flat waveguide 1, and the metal reflecting surface 2 and the concave lens 3 form a structure with a radius of
Figure GDA0002964295520000041
Wherein λ is the wavelength of the electromagnetic wave, and the metal reflecting surface 2 occupies a quarter of the closed circleThirdly, the plano-concave lens 3 occupies one fourth of the closed circle, the incident surface of the plano-concave lens 3 is a concave surface, the emergent surface is a plane, and the length of the long side of the emergent surface is W10 lambda. The metal reflecting surface 2 and the plano-concave lens 3 are equal in height and d in height, the plano-concave lens 3 is formed by tightly attaching a concave ENZ metamaterial substrate 4, an intermediate layer and a plane ENZ metamaterial substrate 5, the thicknesses of the concave ENZ metamaterial substrate 4 and the plane ENZ metamaterial substrate 5 are both l, and the intermediate layer is provided with an incident surface and an emergent surface which are the same as those of the plano-concave lens 3. The middle layer is composed of a metal plate 6 and an ENZ metamaterial interlayer 7 which are equal in width, the ENZ metamaterial interlayer 7 is tightly attached between an upper metal plate 61 and a lower metal plate 62 of the metal plate 6 to form a sandwich layer, the thickness a of the ENZ metamaterial interlayer 7 is non-uniformly changed, and the change of the thickness a of the ENZ metamaterial interlayer 7 is non-linearly reduced non-uniformly along with the increase of the width of the upper metal plate 61 of the metal plate 6 according to the following formula:
Figure GDA0002964295520000042
wherein, Y0Representing the differential characteristic admittance, Y, of free space0＝(W1/d)/η0，W1Representing an arbitrarily variable differential length, η, of the long side of the exit face of the plano-concave lens 30Representing the wave impedance, epsilon, of a free space of value 120 pirRepresents the dielectric constant, mu, of the ENZ metamaterial with the value of 0.01rThe magnetic permeability, theta, of an ENZ metamaterial with the value of 11The electrical length of the upper metal plate 61 of the metal plate 6 is shown,
Figure GDA0002964295520000043
k0representing wave number, k, in vacuum0ω denotes an angular frequency of the electromagnetic wave, ω 2 pi f denotes a frequency of the electromagnetic wave, and c denotes a value of 3 × 108m/s light velocity, t represents the width of the upper metal plate 61 of the metal plate 6, CTMRepresents the equivalent capacitance, C, between the upper metal plate 61 and the lower metal plate 62 of the metal plate 6TMAnd W1Proportional and increases with increasing frequency of the electromagnetic wave. The line source 8 is arranged at the center of the closed circle and is parallel to the plano-concave lensMirror 3 exit face short edge. When a line source 8 which is positioned at the center of the circle and is parallel to the plano-concave lens 3 is excited to generate TM polarized cylindrical waves, the transmitted waves are parallel to the emergent plane of the plano-concave lens 3, and high-directionality beams are formed.
The thicknesses of the high-directionality plano-concave lens containing the ENZ metamaterial sandwich layer with the non-uniform thickness, the upper metal flat plate 11, the lower metal flat plate 12 and the metal reflecting surface 2 of the parallel flat waveguide 1 are all 0.1 mm.
The width of the upper metal plate 61 of the metal plate 6 of the high-orientation plano-concave lens with the ENZ metamaterial sandwich layer with the non-uniform thickness is at the value t of the center of the plano-concave lens 31Minimum, value t at both ends of the plano-concave lens2And max.
The thickness a of the ENZ metamaterial interlayer 7 of the high-directionality plano-concave lens containing the ENZ metamaterial interlayer with non-uniform thickness is a value a at the center of the plano-concave lens 31Value a at both ends of the maximum, plano-concave lens2And minimum.
The working principle of the invention is that the concave ENZ metamaterial substrate 4 can extrude TM polarized waves vertically incident into the tunnel between the metal plates 6 for transmission, the plane ENZ metamaterial substrate 5 can release electromagnetic waves in the tunnel, and the ENZ metamaterial has near-zero phase shift characteristics, so that an emergent wave forms a high-directivity wave beam in parallel with an emergent surface, on the other hand, the thickness a of the ENZ metamaterial interlayer 7 is reduced along with the increase of the width t of the upper metal plate 61 of the metal plate 6, so that the incident wave can realize perfect tunnel transmission meeting the impedance matching with free space when passing through different transmission paths of the plano-concave lens 3, thereby realizing the full transmission and high-directionality radiation of the wave, an equivalent circuit of the plano-concave lens 3 can be constructed for the formula for calculating a, and the full transmission | S is satisfied neglecting the thin concave ENZ metamaterial substrate 4 and the planar ENZ metamaterial substrate 5.11The condition of | ═ 0 is:
Figure GDA0002964295520000051
let F1＝tanθ1，
Figure GDA0002964295520000052
Wherein Y is1For the differential characteristic admittance of the ENZ metamaterial sandwich 7,
Figure GDA0002964295520000053
solving to obtain Y satisfying the full transmission condition1Comprises the following steps:
Figure GDA0002964295520000054
the thickness a of the ENZ metamaterial interlayer 7 is determined for the width t of the upper metal plate 61 of the metal plate 6 at a certain operating frequency.
Referring to fig. 6 to 8, two embodiments are made to the overall structure of the present invention,
example 1 a highly directional plano-concave lens with a sandwich of ENZ metamaterial of non-uniform thickness with an operating frequency of 67 GHz.
The embodiment of the invention comprises the following steps: the equal-height metal reflecting surface 2 and the concave lens 3 are both arranged in the upper metal flat plate 11 and the lower metal flat plate 12 of the parallel flat waveguide 1, and the height d is 20 mm. The thicknesses of the metal reflecting surface 2 and the upper metal flat plate 11 and the lower metal flat plate 12 of the parallel slab waveguide 1 are both 0.1mm, the metal reflecting surface 2 and the concave lens 3 form a closed circle, the metal reflecting surface occupies three quarters of the closed circle, the concave lens occupies one quarter of the closed circle, and the radius r of the closed circle is 31.66 mm. The incidence surface of the plano-concave lens 3 is a concave surface, the emission surface is a plane, and the length W of the long side of the emission surface of the plano-concave lens 3 is 44.78 mm. The plano-concave lens 3 is formed by tightly attaching a concave ENZ metamaterial substrate 4, an intermediate layer and a plane ENZ metamaterial substrate 5, and the thicknesses of the concave ENZ metamaterial substrate 4 and the plane ENZ metamaterial substrate 5 are 0.5 mm. The middle layer has an incident surface and an emergent surface which are the same as the plano-concave lens 3, the middle layer is composed of a metal plate 6 and an ENZ metamaterial interlayer 7 which are equal in width, and the ENZ metamaterial interlayer 7 is tightly attached between an upper metal plate 61 and a lower metal plate 62 which are symmetrical to the metal plate 6 to form a sandwich layer. The width t of the upper metal plate 61 of the metal plate 6 is a value t at the center of the plano-concave lens 31Two of the smallest, plano-concave lensesValue t of terminal2Maximum, minimum width t15mm, maximum width t214.27 mm. The thickness a of the ENZ metamaterial interlayer 7 shows a non-linear decrease with the increase of the width of the upper metal plate 61 of the metal plate 6, the value a of the thickness a at the center of the plano-concave lens 31Value a at both ends of the maximum, plano-concave lens2Minimum, maximum thickness a13.08mm, minimum thickness a21.31 mm. Wherein in the formula for calculating a, the differential characteristic admittance Y of free space00.013, the differential length W of the long side of the exit surface of the plano-concave lens 31Dielectric constant epsilon of ENZ metamaterial with thickness of 10mmr0.01, permeability μ r1, the frequency f of the electromagnetic wave is 67GHz, and the differential equivalent capacitance C between the upper metal plate 61 and the lower metal plate 62 of the metal plate 6TM＝2.04×10-15F。
Example 2 a highly directional plano-concave lens with a non-uniform thickness ENZ metamaterial sandwich layer with an operating frequency of 92.5 GHz.
The structure of the embodiment of the present invention is the same as that of embodiment 1, and the height d of the metal reflecting surface 2 and the concave lens 3, the thickness of the metal reflecting surface 2 and the upper metal plate 11 and the lower metal plate 12 of the parallel plate waveguide 1, and the minimum width t of the upper metal plate 61 of the metal plate 6 are the same as those of embodiment 11Thickness l of the concave ENZ metamaterial substrate 4 and the planar ENZ metamaterial substrate 5, and dielectric constant epsilon of the ENZ metamaterialrAnd magnetic permeability murAnd in the formula for calculating a, the differential characteristic admittance Y of free space0Differential length W1These parameters remain unchanged and only the following parameters are changed:
the radius r of the closed circle is 22.93mm, the length W of the long side of the exit surface of the plano-concave lens 3 is 32.43mm, and the maximum width t of the upper metal plate 61 of the metal plate 62Maximum thickness a of the ENZ metamaterial sandwich 7 of 11.72mm12.16mm, minimum thickness a20.72mm, and 92.5GHz, and the differential equivalent capacitance C between the upper metal plate 61 and the lower metal plate 62 of the metal plate 6TM＝2.62×10-15F。
The technical effects of the present invention are further described in detail by simulation experiments.
1. Simulation conditions are as follows:
matlab and Ansoft HFSS v19 simulation software is adopted in the invention.
2. Simulation content:
the simulation experiments of the invention are three.
Simulation 1, calculating and simulating the variation of the thickness a of the ENZ metamaterial interlayer satisfying the full transmission condition at 67GHz and 92.5GHz along with the width t of the upper metal plate 61 of the metal plate 6, and the simulation result is shown in FIG. 6.
Simulation 2, function F at thickness a of corresponding ENZ metamaterial interlayer for width t of upper metal plate 61 of different metal plates 61And F2The fitting degree of (2) is calculated and simulated along with the frequency change, and the simulation result is shown in fig. 7.
Simulation 3 was performed on the yz plane far-field radiation characteristics of the plano-concave lenses of examples 1 and 2 of the present invention, and the simulation result is shown in fig. 8.
3. And (3) simulation result analysis:
the variation of the thickness a of the ENZ metamaterial interlayer according to embodiments 1 and 2 of the present invention with the width t of the metal plate is further described with reference to fig. 6 for the width t of the upper metal plate 61 of the metal plate 6 of the plano-concave lens 3 and the ENZ metamaterial interlayer 7. The abscissa in fig. 6 is the width t of the upper metal plate 61 of the metal plate 6 in millimeters (mm) and the ordinate is the thickness a of the ENZ metamaterial interlayer 7 in millimeters (mm). The solid line in fig. 6 is a width t versus thickness a curve at an operating frequency of 67GHz, and the dotted line is a width t versus thickness a curve at an operating frequency of 92.5 GHz. As can be seen from FIG. 6, when the operating frequency is 67GHz, the width t of the upper metal plate 61 of the metal plate 6 is increased from the minimum 5mm to 14.27mm, and the calculation formula of the invention that the thickness a varies with the width t calculates that the thickness a of the ENZ metamaterial interlayer 7 should be nonlinearly reduced from the maximum 3.08mm to the minimum 1.31mm so as to meet the full transmission condition. When the operating frequency is 92.5GHz, the width t of the upper metal plate 61 of the metal plate 6 is increased from the minimum 5mm to 11.72mm, and the thickness a of the ENZ metamaterial interlayer 7 is calculated to be reduced from the maximum 2.16mm nonlinearity to the minimum 0.72mm, so that the full transmission condition can be met.
Reference is made to FIG. 7(a) for function F of example 1 of the present invention1And F2Is fitted to the function F of the full transmission condition1And F2As will be further described. In FIG. 7(a), the abscissa is frequency in GHz and the ordinate is F1And F2The function value of (a) is in 1. The solid line with the width t of 5mm in fig. 7(a) is F when the width t is the minimum1The function value, the long dotted line with width t of 5mm, is F when width t is minimum2The dotted line with the function value of 14.27mm represents F at the maximum width t1The function value, the short dashed line with width t of 14.27mm, is F at the maximum width t2And (4) function values. As can be seen from FIG. 7(a), when the working frequency is 67GHz, the ENZ metamaterial interlayer designed according to FIG. 4 is calculated according to the function F of the equivalent circuit1And F2No matter the value of the curve along the axis in the z-axis direction of the plano-concave lens or the values of the two ends in the y-axis direction are intersected at 67GHz, the fact that the incident wave can be transmitted completely along all transmission paths of the whole lens profile under the design of the ENZ metamaterial interlayer with the non-uniform thickness is proved.
Reference is made to FIG. 7(b) for function F of example 2 of the present invention1And F2Is fitted to the function F of the full transmission condition1And F2As will be further described. The abscissa in FIG. 7(b) is frequency in GHz and the ordinate is F1And F2The function value of (a) is in 1. The solid line with the width t of 5mm in fig. 7(b) is F when the width t is the minimum1The function value, the long dotted line with width t of 5mm, is F when width t is minimum2The dotted line with the function value of 11.72mm represents F at the maximum width t1The function value, short dashed line with width t of 11.72mm, is F at maximum width t2And (4) function values. As can be seen from FIG. 7(b), at an operating frequency of 92.5GHz, the ENZ metamaterial interlayer designed according to FIG. 4 is calculated according to a function F of an equivalent circuit1And F2The curve intersects 92.5GHz at the axis of the plano-concave lens or at the positions of two ends of the plano-concave lens, and the fact that under the design of the ENZ metamaterial interlayer with the non-uniform thickness, incident waves can achieve full transmission along all transmission paths of the whole lens outline is proved.
The yz plane far field gain pattern versus plano-concave lens performance of example 1 of the present invention is further described with reference to fig. 8 (a). The abscissa in fig. 8(a) is the azimuth angle in degrees (deg), and the ordinate is the far-field gain in dbi. The solid line in fig. 8(a) is the far field gain in the yz plane of the plano-concave lens at an operating frequency of 67 GHz. As can be seen from fig. 8(a), at an operating frequency of 67GHz, the maximum gain of far-field radiation in yz plane of the plano-concave lens in embodiment 1 of the present invention is 20.22dBi, and the side lobe is low, so that efficient transmission and high-directivity radiation of TM polarized waves are achieved.
The yz plane far field gain pattern versus plano-concave lens performance of example 2 of the present invention is further described with reference to fig. 8 (b). The abscissa in fig. 8(b) is the azimuth angle in degrees (deg), and the ordinate is the far-field gain in dbi. The solid line in fig. 8(b) is the far field gain in the yz plane of the plano-concave lens at an operating frequency of 92.5 GHz. As can be seen from fig. 8(b), at an operating frequency of 92.5GHz, the maximum gain of far-field radiation in yz plane of the plano-concave lens in embodiment 2 of the present invention is 20.67dBi, and the side lobe is low, so that efficient transmission and high-directivity radiation of TM polarized waves are achieved.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and those skilled in the art can make various changes and modifications without departing from the innovative concept of the present invention, but these changes are all within the scope of the present invention.

Claims (4)

1. A high-directivity plano-concave lens with an ENZ metamaterial sandwich layer with non-uniform thickness comprises a parallel slab waveguide (1), a metal reflecting surface (2) and a plano-concave lens (3), and is characterized in that: the metal reflecting surface (2) and the plano-concave lens (3) are both arranged in an upper metal flat plate (11) and a lower metal flat plate (12) of the parallel flat waveguide (1), and the metal reflecting surface (2) and the plano-concave lens (3) form a structure with a radius of
Figure FDA0002964295510000013
Wherein lambda is the wavelength of the electromagnetic wave, the metal reflecting surface (2) occupies three quarters of the closed circle, and the plano-concave lens (3) occupies one quarter of the closed circleThe incidence surface of the planoconcave lens (3) is a concave surface, the emergent surface is a plane, and the length of the long side of the emergent surface is W which is 10 lambda; the metal reflecting surface (2) and the plano-concave lens (3) are equal in height, the height is d, the plano-concave lens (3) is formed by tightly attaching a concave surface ENZ metamaterial substrate (4), an intermediate layer and a plane ENZ metamaterial substrate (5), the thicknesses of the concave surface ENZ metamaterial substrate (4) and the plane ENZ metamaterial substrate (5) are both l, and the intermediate layer is provided with an incident surface and an emergent surface which are the same as those of the plano-concave lens (3); the middle layer is composed of metal plates (6) with equal width and an ENZ metamaterial interlayer (7), and the ENZ metamaterial interlayer (7) is tightly attached between an upper metal plate (61) and a lower metal plate (62) which are symmetrical to the metal plates (6) to form a sandwich layer; the thickness a of the ENZ metamaterial interlayer (7) is non-uniformly changed, and the change of the thickness a of the ENZ metamaterial interlayer is non-uniformly changed in a non-linear reduction mode along with the increase of the width of an upper metal plate (61) of the metal plate (6) according to the following formula:
Figure FDA0002964295510000011
wherein, Y0Representing the differential characteristic admittance, Y, of free space0＝(W1/d)/η0，W1Represents an arbitrarily variable differential length, eta, of the long side of the exit face of the plano-concave lens (3)0Representing the wave impedance, epsilon, of a free space of value 120 pirRepresents the dielectric constant, mu, of the ENZ metamaterial with the value of 0.01rThe magnetic permeability, theta, of an ENZ metamaterial with the value of 11Indicating the electrical length of the upper metal plate (61) of the metal plate (6),
Figure FDA0002964295510000012
k0representing wave number, k, in vacuum0ω denotes an angular frequency of the electromagnetic wave, ω 2 pi f denotes a frequency of the electromagnetic wave, and c denotes a value of 3 × 108m/s, t represents the width of the upper metal plate (61) of the metal plate (6), CTMRepresents the equivalent capacitance between the upper metal plate (61) and the lower metal plate (62) of the metal plate (6), CTMAnd W1Proportional relation and increase with the increase of the frequency of the electromagnetic wave; the line source (8) is arranged atThe center of the closed circle is parallel to the short edge of the emergent surface of the plano-concave lens (3).
2. The highly oriented plano-concave lens with a non-uniform thickness ENZ metamaterial sandwich layer as claimed in claim 1, wherein: the thicknesses of the upper metal flat plate (11), the lower metal flat plate (12) and the metal reflecting surface (2) of the parallel flat waveguide (1) are all 0.1 mm.
3. The highly oriented plano-concave lens with a non-uniform thickness ENZ metamaterial sandwich layer as claimed in claim 1, wherein: the width of the upper metal plate (61) of the metal plate (6) is at the value t of the center of the plano-concave lens (3)1Minimum, value t at both ends of the plano-concave lens2And max.
4. The highly oriented plano-concave lens with a non-uniform thickness ENZ metamaterial sandwich layer as claimed in claim 1, wherein: the thickness a of the ENZ metamaterial interlayer (7) has a value a at the center of the plano-concave lens (3)1Value a at both ends of the maximum, plano-concave lens2And minimum.
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