CN114976666B - Double-layer frequency multi-element reflection super-surface and design method - Google Patents
Double-layer frequency multi-element reflection super-surface and design method Download PDFInfo
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- H01Q15/0013—Devices acting selectively as reflecting surface, as diffracting or as refracting device, e.g. frequency filtering or angular spatial filtering devices said selective devices working as frequency-selective reflecting surfaces, e.g. FSS, dichroic plates, surfaces being partly transmissive and reflective
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Abstract
The invention relates to a reflective double-function super-surface which generates two different functions at two different frequencies under the vertical irradiation of circularly polarized electromagnetic waves. The unit structure comprises two complementary metal resonators, two dielectric plates and a metal floor. The double-C-shaped slotted resonator is printed on the first dielectric plate, the double-C-shaped metal resonator is printed on the second dielectric plate, and the metal floor is printed on the bottommost layer. According to the invention, the independent regulation and control of the geometric phases at two different resonant frequencies are realized by independently changing the rotation angles of the metal resonators on different dielectric plates of the unit, the geometric phase coverage of the reflected wave 2 pi is realized at the units at different resonant frequencies, and the reflection amplitude is close to 1. Based on the excellent performance of the units, the dual-function super-surface is formed by periodically arranging high-efficiency complementary resonator units and rotating resonators of different layers at two resonance frequencies of the units, and the focused OAM beam and the zero-order Bessel beam with the mode number of l=3 are realized at 9.2GHz and 11.2 GHz.
Description
Technical Field
The invention relates to the technical field of reflective super-surfaces, in particular to a double-layer frequency multi-element reflective super-surface and a design method.
Background
Along with the rapid development of communication systems, the multifunctional microwave device is widely applied to integrated equipment such as signal transmission and imaging systems, but the conventional multifunctional microwave device has the problems of large volume, high loss, low efficiency and the like, and does not meet the robustness and practicality of the microwave device. In comparison, a super surface with a sub-wavelength thickness has good regulatory capability for the amplitude, phase and polarization of electromagnetic waves. For the traditional optical lens, phase accumulation is obtained by means of distance transmission, the super surface can obtain abrupt phase through resonance coupling with incident electromagnetic waves, and strong control capability of the super surface on the electromagnetic waves is shown. Because of the superior electromagnetic regulation capability of the super-surface, the super-surface has important progress in the aspects of abnormal reflection/refraction of electromagnetic waves, radar cross section Reduction (RCS), holography, focusing, vortex beam generators and the like.
In order to improve the integration and compactness of the device, researchers have widely conducted researches on multifunctional super-surface devices. At present, the multifunctional is realized mainly by exciting information (such as frequency, polarization, direction and position) to the super surface by electromagnetic waves. The frequency is important information carried by electromagnetic waves, and frequency multiplexing enables the device to have high-efficiency frequency spectrum utilization rate, so that the frequency multifunctional super-surface is widely applied in electromagnetic regulation and control. The core of the design frequency multifunctional super-surface is to regulate and control the amplitude, polarization and phase of electromagnetic waves by means of asymmetric anisotropic units working in different frequency bands on the super-surface. The unit has good regulation and control capability on electromagnetic waves, so that the frequency multi-element super surface is widely applied, wherein the frequency multi-element phase regulation and control super surface is widely applied to a multifunctional microwave integrated device, such as a multi-frequency multi-channel super surface of vortex beams and holograms, an achromatic holographic super surface and a broadband spin-decoupled undistorted dual-phase super surface due to good transmission characteristics and full-space electromagnetic wave regulation and control capability. Although the frequency multifunctional super-surface unit can realize the integration of functions in a plurality of frequency bands to cope with different working environments, most of the frequency multifunctional super-surface units are realized by means of splicing a plurality of metal resonators on a single-layer medium or utilizing methods such as spatial multiplexing (transmission and reflection integration) on a multi-layer medium. This approach reduces efficiency because crosstalk inevitably exists from channel to channel. To avoid cross-talk, this requires that each operating band of the frequency multi-functional subsurface not be too closely spaced.
Disclosure of Invention
The invention provides a double-layer frequency multi-element reflection super-surface which is characterized by being formed by periodic arrangement of high-efficiency complementary resonator units, wherein the high-efficiency complementary resonator units comprise two layers of dielectric plates, and a double-C-shaped slotted resonator, a double-C-shaped metal resonator and a metal floor which are in complementary forms are constructed on the two layers of dielectric plates;
the double-layer frequency multi-element reflection super surface realizes a focused OAM beam with the mode number of l=3 and a zero-order Bessel beam under the condition of low frequency ratio.
Still further, the high efficiency complementary resonator unit includes a double-C-shaped slotted resonator, a first layer of dielectric plate, a double-C-shaped metal resonator, a second layer of dielectric plate, and a metal floor, which are arranged in structural order.
Further, the thickness H of the first dielectric plate 1 =1.5mm, second layer dielectric plate thickness H 2 =1.5mm, dielectric plate material is F4B;
the double-C-shaped slotted resonator, the double-C-shaped metal resonator and the metal floor are made of copper, and the conductivity of the double-C-shaped slotted resonator is sigma=5.8x10 7 S/m。
Still further, the high efficiency complementary resonator element period p=10.2 mm;
the double C-shaped slotted resonator has the following structural parameters: outer diameter r of outer ring 1 =4.75 mm, outer ring inner diameter r 2 =4.35 mm, middle groove width w 1 =0.3 mm, inner metal ring width w 2 =0.4mm, metal width g of the connection part of the outer ring and the inner ring 1 ＝0.9mm；
The structural parameters of the double C-shaped metal resonator are as follows: inner diameter width r of metal ring 3 =3.0 mm, metal ring width w 3 Metal ring gap width g =0.8mm 2 ＝0.3mm。
Further, the high efficiency complementary resonator unit is at two resonant frequencies f 1 And f 2 Independent geometric phase regulation and control of 100% cross circular polarized wave conversion are realized at all positions, wherein the double C-shaped slotted resonator works at the frequency f 1 The double C-shaped metal resonator works at the frequency f in charge of the geometric phase function regulation and control at the frequency 2 Responsible for the functional regulation of the geometric phase at this frequency, i.e. at the resonant frequency f 1 And f 2 The high-efficiency complementary resonator unit under the incidence condition of linear polarized waves meets the following conditions:
|r xx |＝|r yy |＝1
wherein r is xx R is the reflection coefficient at x polarization yy For the reflection coefficient at the y-polarization, the reflection phase is homopolar for the linearly polarized wave.
Further, the double-layer frequency multi-reflection super-surface is at the working frequency f 1 A focused OAM beam with mode number l=3 implemented at=9.2 GHz, which is decomposed into a focused phase part and a vortex phase part using the phase superposition principle, for which the efficient complementary resonator element satisfies the following phase distribution:
wherein f 0 214mm is its focal length, P is the unit period, lambda is the wavelength of the incident electromagnetic wave,is an arbitrary phase constant, m is the number of units from the origin along the x-direction, n is the number of units from the origin along the y-direction;
for the phase distribution of the vortex beam, the phase compensation of the incident wave by the unit needs to satisfy the following formula:
wherein l=3 is the number of modes of the OAM beam;
according to the phase superposition principle of electromagnetic waves, vortex phase and focusing phase are subjected to phase superposition, and the final unit phase distribution of the double-layer frequency multi-element reflection super surface meets the following formula:
indicating that the cell is at resonant frequency f 1 Final reflection phase at=9.2 GHz.
Further, the double-layer frequency multi-reflection super-surface is at the working frequency f 2 Implementing a zero order bessel beam at 11.2GHz, the high-efficiency complementary resonator element being at a resonant frequency f 2 The compensation phase of (2) satisfies the following formula:
where P is the period of the element, λ is the wavelength of the incident electromagnetic wave, β=30° is the diffraction half-angle of the bessel beam, m is the number of elements from the origin along the x-direction, and n is the number of elements from the origin along the y-direction.
The design method is characterized by comprising the following steps of:
step 1, designing a high-efficiency complementary resonator unit required by a double-layer frequency multi-element reflection super surface, so that the high-efficiency complementary resonator unit realizes the phase regulation and control of 100% crossed circularly polarized waves at two resonance frequencies;
step 2, forming a frequency multielement reflection super surface through aperiodic arrangement of high-efficiency complementary resonator units;
step 3, analyzing the performance of the multi-element reflective super-surface with double-layer frequency, and confirming that the multi-element reflective super-surface with double-layer frequency realizes the expected function;
in step 2, the double-layer frequency multiple reflection super-surface is finally constructed at f 1 =9.2 GHz and f 2 The frequency multiplexing multifunctional subsurface of the focused OAM beam and the zero-order bessel beam with the mode number l=3 is realized respectively with the operating frequency=11.2 GHz.
Further, in step 2, the double-layer frequency multiple reflection subsurface is at an operating frequency f 1 A focused OAM beam with mode number l=3 implemented at=9.2 GHz, which is decomposed into a focused phase part and a vortex phase part using the phase superposition principle, for which the efficient complementary resonator element satisfies the following phase distribution:
wherein f 0 214mm is its focal length, P is the unit period, lambda is the wavelength of the incident electromagnetic wave,is an arbitrary phase constant, m is the number of units from the origin along the x-direction, n is the number of units from the origin along the y-direction;
for the phase distribution of the vortex beam, the phase compensation of the incident wave by the unit needs to satisfy the following formula:
wherein l=3 is the number of modes of the OAM beam;
according to the phase superposition principle of electromagnetic waves, vortex phase and focusing phase are subjected to phase superposition, and the final unit phase distribution of the double-layer frequency multi-element reflection super surface meets the following formula:
indicating that the cell is at resonant frequency f 1 Final reflection phase at=9.2 GHz.
Further, in step 2, the double-layer frequency multiple reflection subsurface is at an operating frequency f 2 Implementing a zero order bessel beam at 11.2GHz, the high-efficiency complementary resonator element being at a resonant frequency f 2 The compensation phase of (2) satisfies the following formula:
where P is the period of the element, λ is the wavelength of the incident electromagnetic wave, β=30° is the diffraction half-angle of the bessel beam, m is the number of elements from the origin along the x-direction, and n is the number of elements from the origin along the y-direction.
The invention has the advantages that:
compared with the traditional frequency multifunctional super-surface, the frequency multi-element reflection super-surface provided by the invention has good independence at two resonance frequencies and strictly meets the principle of geometric phase.
The traditional frequency multifunctional super surface has the advantages of wide frequency band occupied spectrum range, low relative spectrum utilization rate, complex structure and difficult processing. The frequency multi-element reflection super-surface provided by the invention has the advantages of narrow frequency spectrum width, low frequency ratio, simple structure and easiness in processing.
Drawings
FIG. 1 is a block diagram of a dual-layer frequency multiple reflection subsurface;
FIG. 2 is a diagram of cell layout and structural parameters for a dual-layer frequency multiple reflection subsurface;
FIG. 3 f 1 And f 2 Electromagnetic response of the complementary resonator unit under incidence of x and y polarized waves at the resonance frequency;
FIG. 4 f 1 And f 2 Front and side view of surface current distribution of double C-shaped slotted resonator, double C-shaped metal resonator and metal floor at resonant frequency;
FIG. 5 shows a different alpha 1 (α 2 ) Dual C-shaped slotted resonator (dual C-shaped metal resonator) with alpha 2 (α 1 ) Varying reflection amplitude and phase;
FIG. 6 shows a different alpha 1 (α 2 ) The reflection amplitude and phase of the double-C-shaped slotted resonator (double-C-shaped metal resonator) with the change of frequency;
fig. 7 is a phase profile of a focused OAM beam element with mode number l=3;
fig. 8 is a zero-order bessel beam element phase distribution diagram;
fig. 9 is a zero-order bessel beamformed wave schematic diagram;
fig. 10, focusing OAM beam with mode number l=3 at focal plane f 0 Amplitude, phase simulation result plot at 214 mm;
fig. 11 different positions |e of zero-order bessel beam LCP |^ 2 Normalizing the distribution diagram;
fig. 12 shows the |e of the Bessel beam at different positions on the yoz plane LCP |^ 2 Normalized distribution curve graph.
Detailed Description
The technical scheme of the present invention will be described in more detail with reference to the accompanying drawings, and the present invention includes, but is not limited to, the following examples.
The invention provides a double-layer frequency multi-element reflection super-surface which is mainly formed by periodic arrangement of high-efficiency complementary resonator units. The high-efficiency complementary resonator unit is formed by constructing a double C-shaped slotted resonator, a double C-shaped metal resonator and a metal floor which are in complementary forms on two layers of dielectric plates, and the complementary resonators have very high Q values, so that the super surface formed by the unit can realize independent regulation and control of the phase under the condition of low frequency ratio.
For verification and exploration applications, the design works at f 1 =9.2 GHz and f 2 Multifunctional super-surface =11.2 GHz and at the working frequency f 1 And f 2 A focused OAM beam and a zero order bessel beam with a mode number of i=3 are implemented, respectively. By at f 1 And f 2 And (3) performing simulation test on the super surface at the working frequency to obtain a simulation result which is well matched with a theoretical result, and indicating that the super surface has good wave front phase regulation and control capability at the working frequency. Compared with the multifunctional super-surface reported in the past, the double-frequency working frequency ratio of the device provided by the patent is only 1.2, and the device is at f 1 、f 2 The efficiency is as high as 86.1% and 93%.
As shown in fig. 1-2, the high efficiency complementary resonator unit mainly comprises five parts: the double C-shaped slotted resonator, the first dielectric plate, the double C-shaped metal resonator, the second dielectric plate and the metal floor are sequentially formed. Wherein the thickness H of the first dielectric plate 1 =1.5mm, second layer dielectric plate thickness H 2 =1.5mm, dielectric plate material was F4B (ε r =2.65, tan δ=0.001), the material has the advantages of small tangent loss, small dispersion, low manufacturing difficulty, and the like. For the complementary metal resonator and the metal floor, copper is used as the material, and the conductivity of copper is sigma=5.8×10 7 S/m. The complementary resonator has a very high Q value, so that the unit can realize independent regulation and control of the phase under the condition of low frequency ratio, and crosstalk between channels caused by narrow frequency band is avoided. In order that the unit can have maximum reflection amplitude at two resonance frequencies, the following result is finally obtained by optimizing each parameter of the resonator in the unit. Wherein the unit period p=10.2 mm, the double C-shaped slotted resonator structure parameters are: outer diameter r of outer ring 1 =4.75 mm, outer ring inner diameter r 2 =4.35 mm, middle groove width w 1 =0.3 mm, inner metal ring width w 2 =0.4 mm. Wherein the outer ringMetal width g of portion connected with inner ring 1 =0.9 mm, the double C-shaped metal resonator structural parameters are: inner diameter width r of metal ring 3 =3.0 mm, metal ring width w 3 =0.8mm. Wherein the gap width g of the metal ring 2 =0.3 mm. For the rotation angle of the resonator, the double C-shaped slotted resonator takes the geometric center of the plane of the dielectric plate as the origin, and the counter-clockwise rotation angle of the double C-shaped slotted resonator on the plane of the dielectric plate is alpha 1 The double C-shaped metal resonator takes the geometric center of the plane of the dielectric plate as the origin and takes the anticlockwise rotation angle alpha as the plane of the dielectric layer 2 。
The units are periodically arranged according to the required functions to achieve the following point f 1 =9.2 GHz and f 2 A focused OAM beam and a zero order bessel beam with a mode number of l=3 are implemented at an operating frequency of =11.2 GHz, respectively.
For the realization of functions at different operating frequencies of a multifunctional subsurface, it is necessary to select suitable units. The unit is used for regulating and controlling the linear polarized electromagnetic wave, and the electromagnetic wave is controlled by changing the size of the metal patch to cause the reflected electromagnetic wave to generate abrupt change of transmission phase. For circularly polarized waves, the principle of geometric phase is applied by rotating the corresponding resonant frequency f 1 And f 2 The resonator of the device realizes the regulation and control of the phase of circularly polarized reflected electromagnetic waves. To further explain the efficient working principle of the unit under the normal incidence of circularly polarized waves, a Jones matrix under the reflection mode of linearly polarized waves is introducedWherein r is xx ，r yy The complex reflection coefficient of the x and y polarized waves comprises amplitude values and phase values of the reflected waves such as: />
Since the geometric phase principle is to generate a phase jump to a reflected wave of a resonance frequency corresponding to a unit by rotating a resonator in the unit, a coordinate system corresponding to the resonator is also changed when the resonator rotates by a fixed angle. When the resonator is rotated counterclockwise by an angle θ, the rotated uov coordinate system will have the following relationship with the xoy coordinate system.
Wherein the method comprises the steps ofDefined as a rotation matrix R (θ), which is the case when the resonator is left-handed about the central axis>0, opposite right-hand theta<0. Taking right-hand circular polarized wave normal incidence as an example, since the circular polarized wave energy is decomposed into two linear polarized waves which are mutually orthogonal, equal in amplitude and different in phase by 90 °, the right-hand circular polarized wave can be expressed as +.>
Wherein E is o Representing the amplitude of the incident wave.
After rotation of the resonator, the reflected wave is represented in the uov coordinate system as:
wherein r is uu To amplitude in u-direction, r vv For amplitude in the v-directionThen the phase shift introduced in the u-direction is phi vv Then a phase shift introduced in the v direction is introduced where θ is the rotation angle, whereby the generation of the cell geometry phase can be induced under circular polarized wave excitation.
Since the structure is a reflective supersurface, it is known from electromagnetic propagation theory: r is (r) uu ＝r xx ，r vv ＝r yy ，Whereby the reflected wave can be expressed as:
from the above results, it is found that the reflected wave has left-hand circularly polarized wave and right-hand circularly polarized wave, and is split into
Wherein,is right-hand circularly polarized wave, ">Is a left-hand circularly polarized wave;
from the results, it can be seen that the left-hand circularly polarized section carries e j2θ Phase factor, when The time result can be expressed as:
when right-hand circularly polarized waves are perpendicularly irradiated to the super surface, the reflected left-hand circularly polarized waves undergo polarization conversion with respect to the incident waves and there is a change in the geometric phase of 2θ. The high-efficiency complementary resonator unit has two resonant frequencies f 1 And f 2 Independent geometric phase regulation and control of 100% cross circular polarized wave conversion are realized at all positions, wherein the double C-shaped slotted resonator works at the frequency f 1 The double C-shaped metal resonator works at the frequency f in charge of the geometric phase function regulation and control at the frequency 2 Responsible for the functional regulation of the geometric phase at this frequency, i.e. at the resonant frequency f 1 And f 2 The high-efficiency complementary resonator unit under the incidence condition of linear polarized waves meets the following conditions:
|r xx |＝|r yy |＝1
wherein r is xx R is the reflection coefficient at x polarization yy For the reflection coefficient at the y-polarization, the unit is required to meet the above conditions for achieving 100% cross polarization conversion of circularly polarized waves for the homopolar reflection phase of linearly polarized waves.
To verify that the design unit satisfies the cross polarization reflection condition of the circularly polarized wave, simulation calculation is performed by a finite difference method (finite difference time domain, FDTD) of time domain. In the simulation process, the unit is perpendicularly irradiated by x and y orthogonal linear polarized waves, and two sides along the x and y directionsThe boundary is set as a period boundary condition, and the simulation result is shown in fig. 3. It can be seen that under the incidence of x and y polarized waves, the resonant frequency f 1 The part mainly comprises a double C-shaped slotted resonator and a metal floor to participate in resonance, and f 2 The resonance frequency is mainly that the double C-shaped metal resonator and the metal floor participate in resonance. At a different resonant frequency f 1 And f 2 R in the reflection field of (2) xx ，r yy The reflection amplitudes of (2) are all greater than 0.92, and can be regarded as being close to 1. At the same time, the reflection phase of the x, y polarized waveAnd->The phase difference value is kept to be uniformly changed in the frequency range of 8-10 GHz and 10-12 GHz, and the phase difference value is changed in f 1 And f 2 The position is stably kept at about 180 degrees, the amplitude and phase conditions of the x and y linear polarization reflected waves in the formula (6) are met, and the high-efficiency cross polarization reflection of the unit under the irradiation of the circular polarization wave is ensured.
In order to demonstrate that the cell has a good reflection effect at the resonance frequency, the cell is simulated by simulation software CST. By distributing the current of the cell in the reflection mode, as shown in FIG. 4, the resonant frequency f can be derived 1 When the circular polarized electromagnetic wave of 9.2GHz is vertically incident, closed resonant current exists in the double C-shaped slotted resonator which participates in regulating and controlling the circular polarized wave, and opposite current distribution is generated in a yoz plane with the bottom metal floor, so that the magnetic resonance phenomenon occurs. At the resonant frequency f 2 When the 11.2GHz circularly polarized electromagnetic wave is vertically incident, closed resonant current exists in the double-C-shaped metal resonator which participates in regulating and controlling the circularly polarized wave, and opposite current distribution is generated in a xoz plane with the bottom metal floor, so that a magnetic resonance phenomenon occurs.
To prove that under the incidence of circularly polarized waves, the high-efficiency complementary resonator unit can be at f 1 =9.2 GHz and f 2 Independent regulation and control of geometric phase can be realized at 11.2GHz, and cross polarization reflected wave energy can realize 2 pi geometric phase coverage, so that right-hand circularly polarized wave is perpendicularly incidentThe unit is simulated for example. Counterclockwise rotation of the double C-shaped slotted resonator from the initial position by alpha 1 Counter-clockwise rotation alpha of double-C-shaped metal resonator 2 The rotation step was 30 deg., and the simulation results were organized as shown in fig. 5-6.
As shown in FIG. 5, at the resonant frequency f 1 At=9.2 GHz, with the change of the rotation angle of the double C-shaped metal resonator, different α 1 The reflection amplitude of the double C-shaped slotted resonator is approximately 1 and the reflection phase is almost not along with alpha 2 Change, at the same time its reflection phase difference and rotation angle alpha 1 Satisfying a 2 times geometric phase relationship. In the same way at resonant frequency f 2 At =11.2 GHz, with the change of the rotation angle of the double C-shaped slotted resonator, different α 2 The reflection amplitude and phase of the double C-shaped metal resonator can be concluded the same. By aligning the double C-shaped slotted resonator with the double C-shaped metal resonator at the resonance frequency f 1 And f 2 The reflection phase errors at different angles are calculated to obtain that the reflection phase errors are smaller than 8 degrees, so that the reflection phase errors can be ignored, and the unit can have good independent phase control capability at different two resonance frequencies.
Whether the geometric phase for the complementary resonator element can be found at f 1 And f 2 The geometrical phase coverage at 2 pi is reached, as can be derived from figure 6. At resonant frequency f 1 And f 2 At the corner alpha with the double C-shaped slotted resonator 1 Corner alpha with double C-shaped metal resonator 2 Varying from 0 to 180, f 1 And f 2 The geometric phase of the reflected wave successfully realizes the coverage of the geometric phase of 2 pi, the phase changes of the resonators with different rotation angles at the working frequency meet the 2-time corner relation, the principle of the geometric phase is met, and the reflection amplitude is as high as 0.98 at the working frequency. The results fully show that the high-efficiency complementary resonator unit has the capability of independently regulating and controlling the circularly polarized electromagnetic waves with different frequencies, and the double C-shaped slotted resonator and the double C-shaped metal resonator are at the resonant frequency f 1 And f 2 The parts do not affect each other, which lays a solid foundation for designing the multifunctional super surface.
The double-layer frequency multi-element reflection super surface is designed on a singleThe cells have good mutual independence at different two resonance frequencies, and on the premise that the cells at the different two resonance frequencies realize geometric phase coverage of 2pi, the known cells are arranged aperiodically, so that the method is finally constructed at f 1 And f 2 For the working frequency, a frequency multiplexing multifunctional super surface of a focused OAM beam and a zero order bessel beam with a mode number of l=3 is respectively realized.
For the multifunctional super-surface at the working frequency f 1 A focused OAM vortex beam with mode number l=3 is implemented at=9.2 GHz, which is decomposed into a focused phase portion and a vortex phase portion using the phase superposition principle, as shown in fig. 7.
For the focus phase, the cell is required to satisfy the following phase distribution.
Wherein f 0 214mm is its focal length, P is the unit period, lambda is the wavelength of the incident electromagnetic wave,is an arbitrary phase constant, m (n) is the number of units from the origin in the x (y) direction. The focusing effect on the intended focal plane can be achieved as long as the reflection phase of each cell of the super surface is made to satisfy the formula.
Similarly, for the phase distribution of the vortex beam, the phase compensation of the unit on the incident wave needs to satisfy the following formula:
where l=3 is the number of modes of the vortex beam. According to the phase superposition principle of electromagnetic waves, the vortex phase and the focusing phase are subjected to phase superposition, so that the target function at the resonance frequency can be realized. The final phase distribution of the reflected electromagnetic wave for the target satisfies the following formula.
The double-layer frequency multi-element reflection super surface provided by the invention is at the working frequency f 2 Implementing a zero-order bessel beam at 11.2GHz requires bringing the super-surface element to resonance frequency f 2 The compensation phase of (c) satisfies the distribution shown in fig. 8, in which the unit specific phase values are as follows.
Where P is the period of the cell, λ is the wavelength of the incident electromagnetic wave, and β=30° is the diffraction half-angle of the bessel beam. According to the Bessel beam forming wave schematic diagram, as shown in fig. 9, it can be seen that the zero-order Bessel beam is mainly formed by overlapping the reflection parallel wave with an included angle beta with the positive direction of the Z-axis within a diffraction-free distance, so that the maximum diffraction-free distance Z can be known by the geometrical relationship in the diagram max Is shown below.
Wherein D is equal to the period of the reflective supersurface, and Z is calculated max =309 mm. From the equation, it can be seen that the Bessel beam energy generated by this method is mainly concentrated in a circle with radius D/4, where the energy is highest at Z max At/2, and the beam energy has a tendency to increase and decrease with increasing energy density as a function of distance from the subsurface location.
The double-layer frequency multi-element reflection super-surface provided by the invention carries out array arrangement and verification on units through joint simulation of CST-MATLAB, and comprises the following processes:
firstly, modeling structures such as a unit resonator, a dielectric plate, a metal floor and the like according to parameters in full-wave simulation software CST, and setting the anticlockwise rotation angles of a double-C-shaped slotted resonator and a double-C-shaped metal resonator respectively to be alpha by taking the geometric center of the plane of the dielectric plate as the circle center 1 And alpha is 2 。
Secondly for different operating frequencies f 1 And f 2 And the double C-shaped slotted resonator and the double C-shaped metal resonator in the unit are rotated through MATLAB according to the phase distribution of the function of the working frequency of the super surface. And through a geometric phase adjustment mechanism, the rotation angle of the unit resonator is adjusted, and the unit model is subjected to aperiodic arrangement, so that the modeling of the multifunctional super-surface is finally realized.
Finally, in the simulation software CST, the right-hand circularly polarized plane wave is subjected to time domain simulation on the vertical incidence super surface. At the working frequency f 1 The simulation data are arranged to obtain a focal plane f 0 The real part of the electric field at 214mm, the phase profile is shown in fig. 10. The real plot of the electric field in the figure shows that the electric field is significantly focused at the focus and the beam has a number of spiral arms equal to the number of modes i=3, while the electric field phase plot shows that the beam has a 1080 ° phase variation consistent with the number of modes i, which coincides with the wave forming characteristics of a theoretical focused OAM beam at the focus plane. For the focusing OAM beam efficiency of the near field simulation super surface with mode number l=3, the following method is adopted for calculation:
wherein the method comprises the steps ofDefined as the ratio of the total reflected wave power to the incident wave power, +.>The ratio of the focal power at the focal plane to the total power of the focal plane is the integral of the power of a circle surrounded by the focal point serving as the center and the half power width of the main lobe serving as the radius, and the integral area is shown as a black dotted line area in fig. 10. Calculated to get->Finally calculate and get the focus OThe simulation efficiency of the AM wave beam is eta f =87.5%. The main reason that the efficiency of the electromagnetic wave does not reach 100% is that part of the electromagnetic wave does not participate in focusing due to diffraction, so that the focusing efficiency is low.
At the working frequency f 2 The yoz surface and the Z surface are obtained by arranging the simulation data 1 ＝75、Z 2 ＝150、Z 3 =225 and Z 4 |e at four positions =309 mm LCP |^ 2 Normalized distribution as shown in fig. 11. The graph shows that the energy in the beam propagation direction is concentrated, the maximum energy intensity is provided at the center of the cross section at different positions, and the transverse energy gradually oscillates and decreases when the transverse energy deviates from the center position, so that the transverse energy accords with the oscillation trend of the Bessel function curve.
The wave forming effect of the super surface is verified through Bessel beam energy concentration efficiency, and Z is selected 1 ＝75、Z 2 ＝150、Z 3 =225 and Z 4 |e of four observation surfaces of 309mm LCP |^ 2 The energy distribution is calculated by the following formula.
Wherein P is 2 Is the diffraction beam-free area (circular area with the center of the plane as the center and the radius of D/4) in the same plane at the same position above the super surface, P 1 Is the caliber area of the super surface in the same plane (the square area with the side length of D is equal to the super surface in size); the energy of electromagnetic waves is determined by the poynting vector, i.e., s=e×h, where S is the poynting vector, E is the electric field strength, and H is the magnetic field strength.
Finally get at Z 1 ＝75、Z 2 ＝150、Z 3 =225 and Z 4 Longitudinal bessel beam energy concentration efficiency at four positions of 309mm is 82%,92%,85%, and 73% in order, which coincides with a diffraction-free transmission characteristic in which bessel beam energy increases slightly first and then decreases slightly with transmission distance. To further demonstrate the superior performance of the device, Z was extracted 1 ＝75、Z 2 ＝150、Z 3 =225 and Z 4 |e=0 at four positions of 309mm LCP |^ 2 The intensity distribution is normalized as shown in fig. 12. From the figure, it can be seen that |E in the main lobe LCP |^ 2 The intensity tends to increase and then decrease with increasing distance from the position Z, and the side lobes at different positions also have the same phenomenon. This is in perfect agreement with the wave-forming characteristics of the zero-order bessel beam. In conclusion, by simulating the double-layer frequency multi-reflection super-surface model, the method well realizes the frequency of the wave at f 1 =9.2 GHz and f 2 A focused OAM beam with mode number l=3 at 11.2GHz and a zero order bessel beam.
The invention also provides a design method of the double-layer frequency multi-element reflection super-surface, which specifically comprises the following steps:
step 1, designing a high-efficiency complementary resonator unit required by a double-layer frequency multi-element reflection super surface, so that the high-efficiency complementary resonator unit realizes the phase regulation and control of 100% crossed circularly polarized waves at two resonance frequencies;
to realize that the double-layer frequency multi-element reflection super surface is at different working frequencies f 1 And f 2 Beam forming at different resonant frequencies f 1 And f 2 The sub-wavelength size unit can realize the cross polarization high reflection and independent 2 pi phase regulation of the circularly polarized wave. The unit structure mainly comprises three layers of metal and two layers of dielectric plates, wherein a double-C-shaped slotted resonator with thickness H is printed on a first layer of dielectric plate 1 =1.5 mm, a second dielectric plate with a double C-shaped metal resonator printed thereon, the dielectric thickness H 2 =1.5 mm, the lowest layer was printed with a metal floor, all metal thickness h=0.036 mm. For the resonator and the metal floor, copper is used as the material, and the conductivity of copper is sigma=5.8×10 7 S/m, which aims to improve electromagnetic response effect and reduce insertion loss of the super surface. For resonators, the outer diameter r of the outer ring of the double C-shaped slotted resonator 1 =4.75 mm, outer ring inner diameter r 2 =4.35 mm, middle groove width w 1 =0.3 mm and inner metal ring width w 2 =0.4mm, wherein the metal width g of the connecting portion of the outer ring and the inner ring 1 =0.9 mm. The structural parameters of the double C-shaped metal resonator are as follows: inner diameter width r of metal ring 3 =3.0 mm, metal ring width w 3 =0.8 mm, where the metal ring gap width g 2 =0.3 mm. In order to verify that the unit can realize the phase regulation of 100% crossed circular polarized waves at two resonance frequencies, theoretical analysis is carried out on the unit structure condition based on geometric phase theory, and the following conclusion is drawn:
the high-efficiency complementary resonator unit has two resonant frequencies f 1 And f 2 Independent geometric phase regulation and control of 100% cross circular polarized wave conversion are realized at all positions, wherein the double C-shaped slotted resonator works at the frequency f 1 The double C-shaped metal resonator works at the frequency f in charge of the geometric phase function regulation and control at the frequency 2 Responsible for the functional regulation of the geometric phase at this frequency, i.e. at the resonant frequency f 1 And f 2 The high-efficiency complementary resonator unit under the incidence condition of linear polarized waves meets the following conditions:
|r xx |＝|r yy |＝1
wherein r is xx R is the reflection coefficient at x polarization yy For the reflection coefficient at the y-polarization, the reflection phase is homopolar for the linearly polarized wave.
Simulation verification is carried out on an x, y orthogonal linear polarization wave perpendicular incidence unit by a time domain finite difference method (finite difference time domain, FDTD), and finally a result is obtained to be highly coincident with a requirement, so that the unit can be considered to realize high-degree regulation and control of cross polarization of circular polarization waves at different two resonant frequencies.
Step 2, forming a frequency multielement reflection super surface through aperiodic arrangement of high-efficiency complementary resonator units;
unit-based independent regulation and control of circularly polarized electromagnetic waves with different frequenciesIs finally constructed at f 1 =9.2 GHz and f 2 The frequency multiplexing multifunctional subsurface of the focused OAM beam and the zero-order bessel beam with the mode number l=3 is realized respectively with the operating frequency of 11.2GHz, and the main process is as follows.
At f 1 A focused OAM beam with a super-surface implementation mode number of l=3 at 9.2GHz is decomposed into a focused phase portion and a vortex phase portion according to the phase superposition principle.
Wherein the focus phase distribution satisfies the formula:
wherein f 0 214mm is its focal length, P is the unit period, lambda is the wavelength of the incident electromagnetic wave,is an arbitrary phase constant, m is the number of units from the origin along the x-direction, n is the number of units from the origin along the y-direction;
for the phase distribution of the vortex beam, the phase compensation of the incident wave by the unit needs to satisfy the following formula:
wherein l=3 is the number of modes of the OAM beam;
according to the phase superposition principle of electromagnetic waves, vortex phase and focusing phase are subjected to phase superposition, and the final unit phase distribution of the double-layer frequency multi-element reflection super surface meets the following formula:
indicating that the cell is at resonant frequency f 1 Final reflection phase at=9.2 GHz.
Double-layer frequency multi-element reflection super surface at working frequency f 2 Implementing a zero order bessel beam at 11.2GHz, the high-efficiency complementary resonator element being at a resonant frequency f 2 The compensation phase of (2) satisfies the following formula:
where P is the period of the element, λ is the wavelength of the incident electromagnetic wave, β=30° is the diffraction half-angle of the bessel beam, m is the number of elements from the origin along the x-direction, and n is the number of elements from the origin along the y-direction.
To make the super surface energy better applied to engineering practice, the focal length f of the focused OAM beam can be controlled by changing array arrangement 0 And the number of modes, i, and the diffraction half angle beta of the Bessel beam to realize free control of the maximum diffraction-free distance of the Bessel beam.
And calculating the compensation phases required by the units at different positions at different two resonance frequencies through MATLAB, and carrying out joint array by using CST-MATLAB. Since the compensating phase and the rotation angle of the unit resonator satisfy a 2-fold relationship at different two resonance frequencies, MATLAB is set at f 1 And f 2 The rotation angles of the double-C-shaped slotted resonator and the double-C-shaped metal resonator obtained through calculation are written into VB commands in CST through an invoke function, and the super surface is modeled through the VB commands. In CST, the time domain simulation is carried out on the hypersurface obtained by modeling, wherein boundary conditions are set to open (add space) conditions, and ports are set to be vertically incident with right-hand circularly polarized plane waves.
Step 3, analyzing the performance of the multi-element reflective super-surface with double-layer frequency, and confirming that the multi-element reflective super-surface with double-layer frequency realizes the expected function;
to different working frequencies f 1 And f 2 The performance analysis of the super surface of the treatment part calculates the efficiency of two types of beams, and adopts the following steps for focusing the OAM beamThe method is as follows:
wherein the method comprises the steps ofDefined as the ratio of the total reflected wave power to the incident wave power, +.>The ratio of the focal power at the focal plane to the total power of the focal plane is the integral of the power of a circle surrounded by the focal point serving as the center and the half power width of the main lobe serving as the radius, and the integral area is shown as a black dotted line area in fig. 10. Calculated to get->Finally, the simulation efficiency of the focused OAM beam is calculated to be eta f =87.5%. The main reason that the efficiency of the electromagnetic wave does not reach 100% is that part of the electromagnetic wave does not participate in focusing due to diffraction, so that the focusing efficiency is low.
For zero-order Bessel beams, the subsurface is analyzed by calculating the beam energy concentration efficiency.
Wherein P is 2 Is the diffraction beam-free area (circular area with the center of the plane as the center and the radius of D/4) in the same plane at the same position above the super surface, P 1 Is the caliber area of the super surface in the same plane (the square area with the side length of D is equal to the super surface in size); the energy of electromagnetic waves is determined by the poynting vector, i.e., s=e×h, where S is the poynting vector, E is the electric field strength, and H is the magnetic field strength.
At the working frequency f 2 The simulation data of the zero-order Bessel beam is arranged at the position, and Z is taken 1 ＝75、Z 2 ＝150、Z 3 =225 and Z 4 |e of yoz face at four positions of 309mm LCP |^ 2 Energy distribution data and calculations are performed. Finally get at Z 1 ＝75、Z 2 ＝150、Z 3 =225 and Z 4 Longitudinal bessel beam energy concentration efficiency at four positions of 309mm is 82%,92%,85%, and 73% in order, which coincides with a diffraction-free transmission characteristic in which bessel beam energy increases slightly first and then decreases slightly with transmission distance.
In conclusion, the multifunctional super-surface simulation is better realized at f 1 =9.2 GHz and f 2 Focusing OAM wave beam with mode number l=3 at 11.2GHz and zero-order Bessel wave beam, and the design of the double-layer frequency multi-reflection super-surface energy is verified to well realize expected functions at two resonance frequencies and at the resonance frequency f 1 ，f 2 The experimental efficiency is up to 86.1% and 93%, which proves the superior performance of the multifunctional super surface and provides a new way for OAM wave beam generation and multifunctional integrated device design.
The present invention is not limited to the above embodiments, and those skilled in the art can implement the present invention in various other embodiments according to the examples and the disclosure of the drawings, so that the design of the present invention is simply changed or modified while adopting the design structure and concept of the present invention, and the present invention falls within the scope of protection.
Claims (8)
1. The double-layer frequency multi-element reflection super-surface is characterized by being formed by periodic arrangement of high-efficiency complementary resonator units, wherein the high-efficiency complementary resonator units comprise two layers of dielectric plates, and a double-C-shaped slotted resonator, a double-C-shaped metal resonator and a metal floor which are in complementary forms are constructed on the two layers of dielectric plates;
the double-layer frequency multi-element reflection super surface realizes focusing OAM wave beams and zero-order Bessel wave beams with the mode number of l=3 under the condition that the double-frequency working frequency ratio is 1.2;
the high-efficiency complementary resonator unit comprises a double-C-shaped slotted resonator, a first layer of dielectric plate, a double-C-shaped metal resonator, a second layer of dielectric plate and a metal floor which are arranged in structural sequence;
the high efficiency complementary resonator cell period p=10.2 mm;
the double C-shaped slotted resonator has the following structural parameters: outer diameter r of outer ring 1 =4.75 mm, outer ring inner diameter r 2 =4.35 mm, middle groove width w 1 =0.3 mm, inner metal ring width w 2 =0.4mm, metal width g of the connection part of the outer ring and the inner ring 1 ＝0.9mm；
The structural parameters of the double C-shaped metal resonator are as follows: inner diameter width r of metal ring 3 =3.0 mm, metal ring width w 3 Metal ring gap width g =0.8mm 2 ＝0.3mm；
The counter-clockwise rotation angle of the double-C-shaped slotted resonator is the same as that of the double-C-shaped metal resonator.
2. The dual-layer frequency multiple reflection supersurface of claim 1 wherein said first dielectric slab has a thickness H 1 =1.5mm, second layer dielectric plate thickness H 2 =1.5mm, dielectric plate material is F4B;
the double-C-shaped slotted resonator, the double-C-shaped metal resonator and the metal floor are made of copper, and the conductivity of the double-C-shaped slotted resonator is sigma=5.8x10 7 S/m。
3. The double-layer frequency multiple reflection supersurface of claim 1 wherein said high efficiency complementary resonator unit is at two resonant frequencies f 1 And f 2 Independent geometric phase regulation and control of 100% cross circular polarized wave conversion are realized at all positions, wherein the double C-shaped slotted resonator works at the frequency f 1 The double C-shaped metal resonator works at the frequency f in charge of the geometric phase function regulation and control at the frequency 2 Responsible for the functional regulation of the geometric phase at this frequency, i.e. at the resonant frequency f 1 And f 2 The high-efficiency complementary resonator unit under the incidence condition of linear polarized waves meets the following conditions:
|r xx |＝|r yy |＝1
wherein r is xx R is the reflection coefficient at x polarization yy For the reflection coefficient at the y-polarization, the reflection phase is homopolar for the linearly polarized wave.
4. The dual-layer frequency multiple reflection subsurface of claim 1, wherein the dual-layer frequency multiple reflection subsurface is at an operating frequency f 1 A focused OAM beam with mode number l=3 implemented at=9.2 GHz, which is decomposed into a focused phase part and a vortex phase part using the phase superposition principle, for which the efficient complementary resonator element satisfies the following phase distribution:
wherein f 0 214mm is its focal length, P is the unit period, lambda is the wavelength of the incident electromagnetic wave,is an arbitrary phase constant, m is the number of units from the origin along the x-direction, n is the number of units from the origin along the y-direction;
for the phase distribution of the vortex beam, the phase compensation of the incident wave by the unit needs to satisfy the following formula:
wherein l=3 is the number of modes of the OAM beam;
according to the phase superposition principle of electromagnetic waves, vortex phase and focusing phase are subjected to phase superposition, and the final unit phase distribution of the double-layer frequency multi-element reflection super surface meets the following formula:
indicating that the cell is at resonant frequency f 1 Final reflection phase at=9.2 GHz.
5. The dual-layer frequency multiple reflection subsurface of claim 1, wherein the dual-layer frequency multiple reflection subsurface is at an operating frequency f 2 Implementing a zero order bessel beam at 11.2GHz, the high-efficiency complementary resonator element being at a resonant frequency f 2 The compensation phase of (2) satisfies the following formula:
where P is the period of the element, λ is the wavelength of the incident electromagnetic wave, β=30° is the diffraction half-angle of the bessel beam, m is the number of elements from the origin along the x-direction, and n is the number of elements from the origin along the y-direction.
6. A method of designing a two-layer frequency multiple reflection subsurface based on the two-layer frequency multiple reflection subsurface of any one of claims 1-5, comprising the steps of:
step 1, designing a high-efficiency complementary resonator unit required by a double-layer frequency multi-element reflection super surface, so that the high-efficiency complementary resonator unit realizes the phase regulation and control of 100% crossed circularly polarized waves at two resonance frequencies;
step 2, forming a frequency multielement reflection super surface through aperiodic arrangement of high-efficiency complementary resonator units;
step 3, analyzing the performance of the multi-element reflective super-surface with double-layer frequency, and confirming that the multi-element reflective super-surface with double-layer frequency realizes the expected function;
in step 2, the double-layer frequency multiple reflection super-surface is finally constructed at f 1 =9.2 GHz and f 2 The frequency multiplexing multifunctional subsurface of the focused OAM beam and the zero-order bessel beam with the mode number l=3 is realized respectively with the operating frequency=11.2 GHz.
7. The method of claim 6, wherein in step 2, the double-layer frequency multiple reflection subsurface is at an operating frequency f 1 A focused OAM beam with mode number l=3 implemented at=9.2 GHz, which is decomposed into a focused phase part and a vortex phase part using the phase superposition principle, for which the efficient complementary resonator element satisfies the following phase distribution:
wherein f 0 214mm is its focal length, P is the unit period, lambda is the wavelength of the incident electromagnetic wave,is an arbitrary phase constant, m is the number of units from the origin along the x-direction, n is the number of units from the origin along the y-direction;
for the phase distribution of the vortex beam, the phase compensation of the incident wave by the unit needs to satisfy the following formula:
wherein l=3 is the number of modes of the OAM beam;
according to the phase superposition principle of electromagnetic waves, vortex phase and focusing phase are subjected to phase superposition, and the final unit phase distribution of the double-layer frequency multi-element reflection super surface meets the following formula:
indicating that the cell is at resonant frequency f 1 Final reflection phase at=9.2 GHz.
8. The method of claim 6, wherein in step 2, the double-layer frequency multiple reflection subsurface is at an operating frequency f 2 Implementing a zero order bessel beam at 11.2GHz, the high-efficiency complementary resonator element being at a resonant frequency f 2 The compensation phase of (2) satisfies the following formula:
where P is the period of the element, λ is the wavelength of the incident electromagnetic wave, β=30° is the diffraction half-angle of the bessel beam, m is the number of elements from the origin along the x-direction, and n is the number of elements from the origin along the y-direction.
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