CN114976666A - 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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Abstract
The invention relates to a reflection type dual-function super surface which can generate 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 layers of dielectric plates and a metal floor. The first layer of dielectric plate is printed with double C-shaped slotted resonators, the second layer of dielectric plate is printed with double C-shaped metal resonators, and the bottommost layer is printed with a metal floor. The invention realizes the independent regulation and control of the geometric phase at two different resonant frequencies by independently changing the rotation angles of the metal resonators on different dielectric slabs of the units, and the units at the different resonant frequencies realize the geometric phase coverage of the reflected wave 2 pi, and the reflection amplitude is close to 1. Based on the excellent performance of the unit, the dual-function super-surface is formed by periodically arranging high-efficiency complementary resonator units and rotating resonators of different layers at two resonant frequencies of the unit, and a focused OAM beam with a mode number l equal to 3 and a zero-order Bessel beam are realized at 9.2GHz and 11.2 GHz.
Description
Technical Field
The invention relates to the technical field of reflection super surfaces, in particular to a double-layer frequency multi-element reflection super surface and a design method thereof.
Background
With the rapid development of communication systems, multifunctional microwave devices are widely used in integrated devices such as signal transmission and imaging systems, but the traditional multifunctional microwave devices have the problems of large size, high loss, low efficiency and the like, and do not meet the robustness and practicability of microwave devices. In comparison, the super-surface with the sub-wavelength thickness has good regulation and control capability on the amplitude, the phase and the polarization of electromagnetic waves. For the traditional optical lens, phase accumulation is obtained by means of distance transmission, and the super surface can obtain an abrupt phase through resonance coupling with incident electromagnetic waves, so that the strong control capability of the super surface on the electromagnetic waves is shown. Due to the excellent electromagnetic regulation and control capability of the super-surface, the super-surface has made important progress in the aspects of electromagnetic wave abnormal reflection/refraction, radar scattering cross section Reduction (RCS), holography, focusing, vortex optical beam generators and the like.
In order to improve the integration level and compactness of the device, researchers have extensively conducted research on multifunctional super-surface devices. Currently, the multifunctional function is realized mainly by exciting information (such as frequency, polarization, direction and position) on the super surface through electromagnetic waves. The frequency is important information carried by electromagnetic waves, and the frequency reuse enables the device to have high-efficiency frequency spectrum utilization rate, so that the frequency multifunctional super surface is widely applied to the aspect of electromagnetic regulation. The core of designing the frequency multifunctional super surface lies in regulating and controlling 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 has good transmission characteristics and full-space electromagnetic wave regulation and control capability and is widely applied to multifunctional microwave integrated devices, such as a multi-frequency multi-channel super surface of vortex beams and holograms, an achromatic holographic super surface and a broadband spin decoupling distortionless two-phase super surface. Although the frequency multifunctional super-surface can realize the integration of functions in multiple frequency bands to deal with different working environments, most frequency multifunctional super-surface units rely on the splicing of multiple metal resonators on a single-layer medium or the realization of multiple functions on a multi-layer medium by using methods such as spatial multiplexing (transmission and reflection integration) and the like. This approach reduces efficiency due to inevitable channel-to-channel crosstalk. This requires that each operating band of the frequency multifunctional super-surface not be too close together to avoid cross-talk.
Disclosure of Invention
The invention provides a double-layer frequency multi-element reflection super surface which is characterized by being formed by periodically arranging high-efficiency complementary resonator units, wherein each high-efficiency complementary resonator unit comprises two layers of dielectric slabs, 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 slabs;
the double-layer frequency multi-element reflection super-surface realizes a focusing OAM wave beam with a mode number l of 3 and a zero-order Bessel wave beam under the condition of a low frequency ratio.
Furthermore, the efficient complementary resonator unit comprises a double-C-shaped slotted resonator, a first dielectric plate, a double-C-shaped metal resonator, a second dielectric plate and a metal floor which are arranged in sequence.
Further, the thickness H of the first dielectric plate 1 1.5mm, second layer dielectric plate thickness H 2 1.5mm, the 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 electrical conductivity of the double-C-shaped slotted resonator, the double-C-shaped metal resonator and the metal floor is 5.8 multiplied by 10 7 S/m。
Further, the period P of the high-efficiency complementary resonator unit is 10.2 mm;
the structural parameters of the double C-shaped slotted resonator are as follows: outer ring outer diameter r 1 4.75mm, inner diameter r of outer ring 2 4.35mm, and a middle groove width of w 1 0.3mm, width w of inner metal ring 2 0.4mm, the 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 3.0mm, width w of metal ring 3 0.8mm, metal ring gap width g 2 ＝0.3mm。
Furthermore, the highly efficient complementary resonator element has two resonant frequencies f 1 And f 2 Independent geometric phase control for 100% cross circularly polarized wave conversion is realized, wherein the double C-shaped slotted resonator works at a frequency f 1 The double C-shaped metal resonator works at the frequency f in charge of the function regulation and control of the geometric phase position of the frequency 2 Responsible for the control of the geometric phase function at that frequency, i.e. at the resonance frequency f 1 And f 2 The high-efficiency complementary resonator unit meets the following conditions under the incident condition of linearly polarized waves:
|r xx |＝|r yy |＝1
wherein r is xx Is the reflection coefficient at x polarization, r yy For the reflection coefficient in the y-polarization,
linearly polarized waves are in the same polarization reflection phase.
Furthermore, the double-layer frequency multi-element reflection super surface is at the working frequency f 1 A focused OAM beam with a mode number l of 3 realized at 9.2GHz is decomposed into a focus phase part and a vortex phase part using the phase superposition principle, for which the efficient complementary resonance is for the focus phaseThe unit satisfies the following phase distribution:
wherein f is 0 214mm is its focal length, P is the unit period, λ is the wavelength of the incident electromagnetic wave,
is an arbitrary phase constant, m is the number of cells from the origin along the x-direction, n is the number of cells 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 mode number of the OAM wave beam;
according to the phase superposition principle of electromagnetic waves, the vortex phase and the 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:
Furthermore, the double-layer frequency multi-element reflection super surface is at the working frequency f 2 Realizing a zero order Bessel beam at 11.2GHz, said highly efficient complementary resonator unit being at a resonance frequency f 2 Satisfies the following equation:
where P is the period of the elements, 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 in the x direction, and n is the number of elements from the origin in the y direction.
The double-layer frequency multi-element reflection super-surface design method is characterized by comprising the following steps:
step 1, designing an efficient complementary resonator unit required by a double-layer frequency multi-element reflection super surface, and enabling the efficient complementary resonator unit to realize phase regulation and control of 100% cross circularly polarized waves at two resonant frequencies;
step 3, analyzing the performance of the double-layer frequency multi-element reflection super-surface, and confirming that the double-layer frequency multi-element reflection super-surface realizes the expected function;
in step 2, a double-layer frequency multi-element reflection super surface is finally constructed at f 1 9.2GHz and f 2 The frequency multiplexing multifunctional super surface with the mode number l being 3 and the zero-order Bessel beam is realized by taking 11.2GHz as the working frequency.
Further, in step 2, the double-layer frequency multi-element reflecting super-surface is at the working frequency f 1 A focused OAM beam with a mode number l of 3 realized at 9.2GHz, which is decomposed into a focus phase part and a vortex phase part using the phase superposition principle, for the focus phase, the efficient complementary resonator unit satisfies the following phase distribution:
wherein f is 0 214mm is its focal length, P is the unit period, λ is the wavelength of the incident electromagnetic wave,
is an arbitrary phase constant, m is the number of cells from the origin along the x-direction, n is the number of cells 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 mode number of the OAM wave beam;
according to the phase superposition principle of electromagnetic waves, the vortex phase and the 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:
Further, in step 2, the double-layer frequency multi-element reflecting super-surface is at the working frequency f 2 Realizing a zero order Bessel beam at 11.2GHz, said highly efficient complementary resonator unit being at a resonance frequency f 2 Satisfies the following equation:
where P is the period of the elements, 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 in the x direction, and n is the number of elements from the origin in 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 resonant frequencies and strictly meets the principle of geometric phase.
The traditional frequency multifunctional super surface has wide frequency spectrum range occupied by the frequency band, low relative frequency spectrum utilization rate and complex structure and is difficult to process. The frequency multi-element reflection super-surface provided by the invention has the advantages of narrow occupied spectrum width, low frequency ratio, simple structure and easiness in processing.
Drawings
FIG. 1 is a block diagram of a two-layer frequency multi-element reflective super-surface;
FIG. 2 is a diagram of cell layout and structural parameters of a two-layer frequency multi-element reflective super-surface;
FIG. 3 is f 1 And f 2 Electromagnetic response of the complementary resonator unit under incidence of x and y polarized waves at the resonant frequency;
FIG. 4 is f 1 And f 2 The front view and the side view of the surface current distribution of the double C-shaped slotted resonator, the double C-shaped metal resonator and the metal floor at the resonance frequency;
FIG. 5 shows a variation of α 1 (α 2 ) Double C-shaped slotted resonator (double C-shaped metal resonator) along with alpha 2 (α 1 ) Varying reflected amplitude and phase;
FIG. 6 shows a variation of α 1 (α 2 ) The reflection amplitude and phase of the double C-shaped slotted resonator (double C-shaped metal resonator) along with the frequency change;
fig. 7 is a focused OAM beam cell phase profile with a pattern number l-3;
FIG. 8 is a phase distribution diagram of a zero-order Bessel beam unit;
FIG. 9 is a schematic diagram of zero order Bessel beamforming;
in fig. 10, the focused OAM beam with the pattern number l equal to 3 is in the focal plane f 0 214mm place amplitude, phase place simulation result chart;
FIG. 11 different positions | E of zero order Bessel beams LCP |^ 2 Normalizing the distribution map;
FIG. 12 is | E of Bessel beams at different positions of yoz plane LCP |^ 2 The distribution graph is normalized.
Detailed Description
The technical solution 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 embodiments.
The invention provides a double-layer frequency multi-element reflection super surface which is mainly formed by periodically arranging efficient complementary resonator units. The high-efficiency complementary resonator unit is composed of a double-C-shaped slotted resonator, a double-C-shaped metal resonator and a metal floor, wherein the double-C-shaped slotted resonator and the double-C-shaped metal resonator are constructed on two layers of dielectric plates in a complementary mode, and the complementary resonators have high Q values, so that the super surface formed by the unit can realize independent regulation and control of phases under the condition of low frequency ratio.
To validate and explore applications, the design works at f 1 9.2GHz and f 2 Multifunctional super-surface of 11.2GHz and at working frequency f 1 And f 2 A focused OAM beam with mode number l-3 and a zero order bessel beam are implemented, respectively. By passing at f 1 And f 2 And (3) carrying out simulation test on the super surface at the working frequency, and obtaining a simulation result which is well matched with a theoretical result, thereby showing 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 f 1 、f 2 The efficiency is as high as 86.1 percent and 93 percent.
As shown in fig. 1-2, the high efficiency complementary resonator unit mainly comprises five parts: the structure of the double-C-shaped slotted resonator, the first layer of dielectric plate, the double-C-shaped metal resonator, the second layer of dielectric plate and the metal floor is sequentially formed. Wherein the thickness H of the first dielectric plate 1 1.5mm, second layer dielectric plate thickness H 2 1.5mm, the dielectric plate material is F4B (ε r 2.65 and 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 electrical conductivity thereof is 5.8 × 10 ═ sigma 7 And (5) S/m. Because the complementary resonator has a very high Q value, the unit can realize independent regulation and control of the phase under the condition of low frequency ratio, and avoids frequency bandNarrow and cause cross talk between channels. In order to obtain the maximum reflection amplitude of the unit at the two resonance frequencies, the following results are obtained by optimizing the parameters of the resonator in the unit. Wherein unit period P is 10.2mm, and two C shape fluting resonator structural parameters are: outer ring outer diameter r 1 4.75mm, inner diameter r of outer ring 2 4.35mm, and a middle groove width of w 1 0.3mm, width w of inner metal ring 2 0.4 mm. Wherein the metal width g of the connection part of the outer ring and the inner ring 1 The structural parameters of the double-C-shaped metal resonator are as follows: inner diameter width r of metal ring 3 3.0mm, width w of metal ring 3 0.8 mm. Wherein the width g of the metal ring gap 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 slab as the origin and has an anticlockwise rotation angle alpha on the plane of the dielectric slab 1 The double C-shaped metal resonator takes the geometric center of the plane of the dielectric plate as the origin and rotates counterclockwise by an angle alpha on the plane of the dielectric layer 2 。
The units are arranged periodically according to the required function to achieve at f 1 9.2GHz and f 2 A focused OAM beam with a mode number l 3 and a zero order bessel beam are respectively realized at an operating frequency of 11.2 GHz.
For realizing the functions of the multifunctional super surface at different working frequencies, proper units need to be selected. The unit generally controls the linearly polarized electromagnetic wave by changing the size of the metal patch to make the reflected electromagnetic wave generate abrupt change of transmission phase. For circularly polarized waves, the principle of geometric phase is applied, by rotating the corresponding resonance frequency f 1 And f 2 The phase of the circularly polarized reflected electromagnetic wave can be regulated and controlled by the resonator. In order to further explain the high-efficiency working principle of the unit under the vertical incidence of circularly polarized waves, a Jones matrix under a linear polarized wave reflection mode is introduced
Wherein r is xx ，r yy Complex reflection coefficients of x and y polarized waves, including amplitude values and phase values of reflected waves as follows:
since the principle of geometric phase is to make the reflected wave of the unit corresponding to the resonant frequency have abrupt phase changes by rotating the resonator in the unit, the coordinate system corresponding to the resonator changes when the resonator rotates through a fixed angle. When the resonator is rotated counterclockwise by an angle θ, the rotated uov coordinate system has the following relationship with the xoy coordinate system.
Wherein
Defined as a rotation matrix R (theta), theta being defined when the resonator is rotated to the left about the central axis>0, opposite dextrorotation theta<0. Taking the right-hand circularly polarized wave as an example, the right-hand circularly polarized wave can be expressed as two mutually orthogonal linearly polarized waves with equal amplitude and 90 ° phase difference
Wherein E is o Indicating the amplitude of the incident wave.
After the resonator rotates, the reflected wave is expressed as follows under uov coordinate system:
wherein r is uu Amplitude in the u direction, r vv For amplitude in the v direction, and
then phi is the phase shift introduced in the u direction vv A phase shift is introduced in the v direction where θ is the rotation angle, thereby causing the generation of the geometric phase of the cell under circular polarized wave excitation.
Because the structure is a reflection-type super surface, the theory of electromagnetic propagation can be used to understand that: r is uu ＝r xx ，r vv ＝r yy ，
The reflected wave can thus be expressed as:
from the above results, it can be seen that the reflected wave has left-hand circular polarized wave and right-hand circular polarized wave, and is split into left-hand circular polarized wave and right-hand circular polarized wave
Wherein,
is a right-hand circularly polarized wave,
is a left-handed circularly polarized wave;
from the results, it can be seen that the left-handed circularly polarized part carriesE is j2θ Phase factor of
The time result can be expressed as:
so when a right-hand circularly polarized wave is perpendicularly irradiated to the super-surface, the reflected left-hand circularly polarized wave undergoes polarization conversion with respect to the incident wave and there is a geometric phase change of 2 θ. High efficiency complementary resonator unit at two resonance frequencies f 1 And f 2 Independent geometric phase control for 100% cross circularly polarized wave conversion, wherein the double C-shaped slotted resonator works at a frequency f 1 The double C-shaped metal resonator works at the frequency f in charge of the function regulation and control of the geometric phase position of the frequency 2 Is responsible for the geometric phase function control at this frequency, i.e. at the resonance frequency f 1 And f 2 The high-efficiency complementary resonator unit meets the following conditions under the incident condition of linearly polarized waves:
|r xx |＝|r yy |＝1
wherein r is xx Is the reflection coefficient at x polarization, r yy For the reflection coefficient in the y-polarization,
the unit is required to meet the conditions for realizing 100% cross polarization conversion of circularly polarized waves in the same polarization reflection phase of linearly polarized waves.
In order to verify that the design unit meets the cross polarization reflection condition of the circularly polarized wave, simulation calculation is carried out by a Finite Difference Time Domain (FDTD) method. In the simulation process, the unit is vertically irradiated by x and y orthogonal linear polarized waves, two boundaries along the x and y directions are set as periodic boundary conditions, and the simulation result is shown in fig. 3. It can be seen that the resonance frequency f is the incident x, y polarized wave 1 Where mainly the double C-shaped slotted resonator and the metal floor participate in resonance, and f 2 The double-C-shaped metal resonator and the metal floor are mainly in resonance at the resonance frequency. At different resonance frequencies f 1 And f 2 In the reflected field of (a) < r > xx ，r yy The reflection amplitudes of (a) are all greater than 0.92, and can be considered to be close to 1. At the same time, the reflection phase of the x, y polarized wave
And
the phase difference value keeps uniform change in the frequency ranges of 8-10 GHz and 10-12 GHz, and the phase difference value is maintained to be f 1 And f 2 The position is stably kept at about 180 degrees, the amplitude and phase conditions under the excitation of x and y linear polarization reflected waves of the formula (6) are met, and high-efficiency cross polarization reflection of the unit under the irradiation of the circular polarization waves is ensured.
In order to show the good reflection effect of the unit at the resonance frequency, the unit was simulated by simulation software CST. By the current distribution to the cell in the reflection mode, as shown in fig. 4, one can derive the resonant frequency f 1 When the circularly polarized electromagnetic wave with the frequency of 9.2GHz is vertically incident, closed resonant current exists in the double C-shaped slotted resonator which participates in the regulation and control of the circularly polarized wave, and the magnetic resonance phenomenon is generated due to the fact that the current distribution is opposite to that of the bottom layer metal floor in the yoz plane. When the resonant frequency f 2 Closed harmonics exist in double-C-shaped metal resonator participating in regulation and control of circularly polarized waves when circularly polarized electromagnetic waves with frequency of 11.2GHz are vertically incidentThe magnetic resonance phenomenon occurs due to the vibration current and the current distribution opposite to that of the bottom metal floor in the xoz plane.
To demonstrate that the complementary resonator element can be efficiently tuned at f for circularly polarized wave incidence 1 9.2GHz and f 2 The geometric phase can be independently regulated and controlled at 11.2GHz, the cross polarization reflected wave can realize the geometric phase coverage of 2 pi, and the unit is simulated by taking the vertical incidence of the right-hand circularly polarized wave as an example. Setting a double C-shaped slotted resonator to rotate from an initial position in a counterclockwise direction by alpha 1 Double C-shaped metal resonator rotating counterclockwise by alpha 2 The rotation step is 30 degrees, and the simulation result is collated as shown in the attached figures 5 to 6.
As shown in fig. 5, at a resonance frequency f 1 At 9.2GHz, the rotation angle of the double C-shaped metal resonator is changed, so that the alpha is different 1 The reflection amplitude of the double C-shaped slotted resonator approaches to 1 and the reflection phase hardly follows alpha 2 Change while its reflection phase difference and rotation angle alpha 1 Satisfying 2 times of geometric phase relation. At resonant frequency f for the same reason 2 At 11.2GHz, the angle of rotation of the double C-shaped slotted resonator is changed, so that the angle alpha is different 2 The reflection amplitude and phase of the double-C-shaped metal resonator can be concluded in the same way. By means of double C-shaped slotted resonators and double C-shaped metal resonators at resonant frequency f 1 And f 2 The reflection phase errors at different rotation angles are calculated to be less than 8 degrees, so that the reflection phase errors can be ignored, and the unit can be proved to have good independent phase control capability at different two resonance frequencies.
Whether or not the geometric phase for the complementary resonator element can be at f 1 And f 2 A geometrical phase coverage of up to 2 pi can be obtained from fig. 6. At the resonance frequency f 1 And f 2 At a rotation angle alpha with the double C-shaped slotted resonator 1 Angle of rotation alpha with double C-shaped metal resonator 2 From 0 DEG to 180 DEG f 1 And f 2 The geometric phase of the reflected wave is successfully covered by 2 pi, the phase change of the resonators with different rotation angles at the working frequency meets the 2-time corner relation, the geometric phase principle is met, and the reflection amplitude at the working frequency is as high as0.98. The results fully show that the high-efficiency complementary resonator unit has the capability of independently regulating and controlling circularly polarized electromagnetic waves with different frequencies, and the double-C-shaped slotted resonator and the double-C-shaped metal resonator have the resonant frequency f 1 And f 2 The parts are not mutually influenced, which lays a solid foundation for designing the multifunctional super surface.
The double-layer frequency multi-element reflection super-surface provided by the invention has good mutual independence at different resonant frequencies of the designed units, and finally constructs the design of the unit with f by non-periodic arrangement of the known units on the premise that the units at the different resonant frequencies realize the geometric phase coverage of 2 pi 1 And f 2 For the working frequency, the frequency multiplexing multifunctional super surface of the focused OAM wave beam with the mode number l being 3 and the zero-order Bessel wave beam is respectively realized.
For multifunctional super-surface at working frequency f 1 A focused OAM vortex beam with mode number l 3 realized at 9.2GHz 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 cells are required to satisfy the following phase distribution.
Wherein f is 0 214mm for its focal length, P for the unit period, λ for the wavelength of the incident electromagnetic wave,
is an arbitrary phase constant, and m (n) is the number of elements from the origin in the x (y) direction. The focusing effect on the desired focal plane can be achieved as long as the reflection phase of each cell of the super-surface satisfies the formula.
Similarly, for the phase distribution of the vortex beam, the phase compensation of the incident wave by the unit 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 target function at the resonant frequency can be realized by carrying out phase superposition on the vortex phase and the focusing phase. 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 Achieving a zero order bessel beam at 11.2GHz requires the super-surface element to be at the resonant frequency f 2 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 wave-forming principle diagram, as shown in FIG. 9, it can be known that the zero-order Bessel beam is mainly formed by overlapping the reflected parallel waves with the positive direction of the Z-axis at an angle of beta within the non-diffraction distance, and therefore the maximum non-diffraction distance Z can be known through the geometrical relationship in the diagram max As follows.
Where D is equal to the period of the reflecting super-surface, and Z is obtained by calculation max 309 mm. From the formula, the Bessel beam energy generated by the method is mainly concentrated in a circle with the radius of D/4, wherein the energy is highest at Z max And/2, the beam energy shows a trend of increasing energy density and then decreasing energy density with the change of the distance from the super-surface position.
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 is carried out on 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 the counterclockwise rotation angles of a double-C-shaped slotted resonator and a double-C-shaped metal resonator respectively taking the geometric center of the plane of the dielectric plate as the circle center are set to be alpha 1 And alpha 2 。
Secondly for different operating frequencies f 1 And f 2 And the phase distribution of the function at the working frequency of the super surface is realized by rotating the double-C-shaped slotted resonator and the double-C-shaped metal resonator in the unit through MATLAB. And through a geometric phase adjusting mechanism, the rotation angle of the unit resonator is adjusted, and the unit models are arranged in a non-periodic manner, so that the modeling of the multifunctional super surface is finally realized.
And finally, performing time domain simulation on the super surface by using the right-hand circularly polarized plane wave vertically incident in simulation software CST. At the operating frequency f 1 The simulation data are arranged to obtain the in-focus plane f 0 The phase profile is shown in fig. 10 for the real part of the electric field at 214 mm. The plot of the real part of the electric field shows that the electric field is clearly focused at the focal point and the beam has a number of spiral arms equal to the number of modes l-3, while the plot of the electric field phase shows that the beam has a 1080 ° phase change consistent with the number of modes l, which is consistent with the wave formation characteristics of a theoretically focused OAM beam at the focal plane. For the focusing OAM wave beam efficiency of the near-field simulation super surface with the mode number l being 3, the following method is adopted for calculation:
wherein
Defined 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 at the focal plane is shown, wherein the focal power is the integral of the power of a circle surrounded by the focal point as the center of the circle and the half power width of the main lobe as the radius, and the integral area is shown as the black dashed area in fig. 10. Can be calculated to obtain
Finally, the simulation efficiency of the focused OAM wave beam is calculated to be eta f 87.5%. The main reason why the efficiency of the electromagnetic wave does not reach 100% is that a part of the electromagnetic wave does not participate in focusing due to diffraction, so that the focusing efficiency is low.
At the operating frequency f 2 The yoz surface and the Z surface are obtained by sorting the simulation data 1 ＝75、Z 2 ＝150、Z 3 225 and Z 4 309mm | E at four positions LCP |^ 2 Normalized distribution, as shown in fig. 11. The figure shows that the energy in the beam propagation direction is more 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, and the oscillation trend of the Bezier function curve is met.
Verifying the wave forming effect of the super surface by Bessel beam energy concentration efficiency, and selecting Z 1 ＝75、Z 2 ＝150、Z 3 225 and Z 4 309mm | E for four viewing planes LCP |^ 2 The energy distribution is calculated by the following formula.
Wherein, P 2 Is a non-diffraction beam area (a circular area with the center of the plane as the circle center and the radius of D/4) in the same plane at the same position above the super surface, P 1 The area of the super surface aperture in the same plane (a square area with the side length of D, equal to the super surface size); the energy of the electromagnetic wave 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, result in Z 1 ＝75、Z 2 ＝150、Z 3 225 and Z 4 The longitudinal bessel beam energy concentration efficiency at four positions 309mm is 82%, 92%, 85% and 73% in this order, which coincides with the diffraction-free transmission characteristic that the bessel beam energy first slightly increases and then slightly decreases with the 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 309mm | E of x 0 at four positions LCP |^ 2 Normalized intensity distribution, as shown in fig. 12. As can be seen from the figure, | E in the main lobe LCP |^ 2 The intensity tends to increase and then decrease with increasing distance at position Z, and the same phenomenon occurs for side lobes at different positions. This is exactly in line with the wave forming properties of the zero order bessel beams. In conclusion, the simulation of the double-layer frequency multi-element reflection super-surface model is better realized at f 1 9.2GHz 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 double-layer frequency multi-element reflection super-surface design method, 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, and enabling the high-efficiency complementary resonator unit to realize phase regulation and control of 100% cross circular polarized waves at two resonant frequencies;
to realize double-layer frequency multi-element reflection super surface at different working frequencies f 1 And f 2 The formation of beams designed to be at different resonant frequencies f 1 And f 2 The sub-wavelength size unit can realize the cross polarization high reflection of circularly polarized waves and the independent 2 pi phase regulation. The unit structure mainly comprises three layers of metal and two layers of dielectric plates, wherein a double-C-shaped slotted resonator with a thickness H is printed on the first layer of dielectric plate 1 1.5mm, a double C-shaped metal resonator with a medium thickness H is printed on the second dielectric plate 2 1.5mm, the bottommost layer is printed with a metal floor, and all metal thicknesses H are 0.036 mm. For the resonator and the metal floor, the material used is copper, the electrical conductivity of which is 5.8 × 10 ═ c 7 S/m, for the purpose of increasingAnd the electromagnetic response effect reduces the insertion loss of the super surface. For the resonator, the outer ring outer diameter r of the double C-shaped slotted resonator 1 4.75mm, inner diameter r of outer ring 2 4.35mm, and a middle groove width of w 1 0.3mm and width w of inner metal ring 2 0.4mm, wherein the metal width g of the connecting part 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 3.0mm, width w of metal ring 3 0.8mm, wherein the metal ring gap width g 2 0.3 mm. In order to verify that the unit can realize the phase regulation and control of 100% cross circularly polarized waves at two resonant frequencies, theoretical analysis is carried out on the structural conditions of the unit on the basis of the geometric phase theory, and the following conclusion is obtained:
high efficiency complementary resonator unit at two resonance frequencies f 1 And f 2 Independent geometric phase control for 100% cross circularly polarized wave conversion, wherein the double C-shaped slotted resonator works at a frequency f 1 The double C-shaped metal resonator works at the frequency f in charge of the geometric phase function regulation and control of the frequency 2 Is responsible for the geometric phase function control at this frequency, i.e. at the resonance frequency f 1 And f 2 The high-efficiency complementary resonator unit meets the following conditions under the incident condition of linearly polarized waves:
|r xx |＝|r yy |＝1
wherein r is xx Is the reflection coefficient at x polarization, r yy For the reflection coefficient in the y-polarization,
linearly polarized waves are in the same polarization reflection phase.
Simulation verification is carried out by an x and y orthogonal linear polarized wave vertical incidence unit through a Finite Difference Time Domain (FDTD) method, and finally the obtained result is highly matched with the requirement so that the unit can realize high-degree regulation and control of cross polarization of circularly polarized waves at different resonant frequencies.
based on the ability of the unit to independently regulate and control circularly polarized electromagnetic waves with different frequencies, the double-layer frequency multi-element reflection super surface is finally constructed by f 1 9.2GHz and f 2 The frequency-multiplexed multifunctional super-surface with the mode number l of 3, namely the focused OAM beam and the zero-order bessel beam is respectively realized with the working frequency of 11.2GHz, and the main process is as follows.
Is at f 1 The focused OAM beam with the number of modes l-3 realized by the super-surface 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 is 0 214mm is its focal length, P is the unit period, λ is the wavelength of the incident electromagnetic wave,
is an arbitrary phase constant, m is the number of cells from the origin along the x-direction, n is the number of cells 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 mode number of the OAM wave beam;
according to the phase superposition principle of electromagnetic waves, the vortex phase and the 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:
Double-layer frequency multi-element reflection super surface at working frequency f 2 Realizing a zero order Bessel beam at 11.2GHz, said highly efficient complementary resonator unit being at a resonance frequency f 2 Satisfies the following equation:
where P is the period of the elements, 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 in the x direction, and n is the number of elements from the origin in the y direction.
To make the super-surface energy better applicable to engineering practice, the focal length f of the focused OAM beam can be controlled by changing the array arrangement 0 And the number of modes l, and the diffraction half angle β of the bessel beam to achieve free steering 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 performing joint arraying by utilizing CST-MATLAB. Since the compensation phase of the unit resonator satisfies a 2-fold relationship with the rotation angle at different two resonance frequencies, MATLAB was set at f 1 And f 2 And the rotating angles of the double C-shaped slotted resonator and the double C-shaped metal resonator obtained by calculation are written into a VB command in CST through an invoke function, and the super surface is modeled through the VB command. Performing time domain simulation on the super surface obtained by modeling in CST, setting boundary conditions as open (add space) conditions, and setting ports as portsIs arranged to be normally incident with a right-hand circularly polarized plane wave.
Step 3, analyzing the performance of the double-layer frequency multi-element reflection super-surface, and confirming that the double-layer frequency multi-element reflection super-surface realizes the expected function;
for different operating frequencies f 1 And f 2 The performance analysis of the super-surface calculates the efficiency of two types of beams, and the focused OAM beam is calculated in the following way:
wherein
Defined 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 at the focal plane is shown, wherein the focal power is the integral of the power of a circle surrounded by the focal point as the center of the circle and the half power width of the main lobe as the radius, and the integral area is shown as the black dashed area in fig. 10. Can be calculated to obtain
Finally, the simulation efficiency of the focused OAM wave beam is calculated to be eta f 87.5%. The main reason why the efficiency of the electromagnetic wave does not reach 100% is that a 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 super-surface is analyzed by calculating the beam energy concentration efficiency.
Wherein, P 2 Is a non-diffraction beam area (a circular area with the center of the plane as the circle center and the radius of D/4) in the same plane at the same position above the super surface, P 1 Is a super surface in the same planeArea of surface caliber (square area with side length of D, equal size to super surface); the energy of the electromagnetic wave 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 operating frequency f 2 The simulation data of the zero-order Bessel wave beam is arranged, and Z is taken 1 ＝75、Z 2 ＝150、Z 3 225 and Z 4 309mm | E of yoz plane at four positions LCP |^ 2 The energy distribution data is calculated. Finally, result in Z 1 ＝75、Z 2 ＝150、Z 3 225 and Z 4 The longitudinal bessel beam energy concentration efficiency at 309mm four positions is 82%, 92%, 85% and 73% in turn, which is consistent with the diffraction-free transmission characteristic that the bessel beam energy first slightly increases and then slightly decreases with transmission distance.
In summary, the multifunctional super-surface simulation is better realized at f 1 9.2GHz and f 2 The focusing OAM wave beam and the zero-order Bessel wave beam with the mode number l of 3 at 11.2GHz verify that the designed double-layer frequency multi-element reflection super surface can well realize the expected functions at two resonant frequencies and at the resonant frequency f 1 ，f 2 The experimental efficiency is as high as 86.1% and 93%, the superior performance of the multifunctional super surface is proved, and a new way is provided 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 other various embodiments according to the disclosure of the embodiments and the drawings, and therefore, all designs that can be easily changed or modified by using the design structure and thought of the present invention fall within the protection scope of the present invention.
Claims (10)
1. The double-layer frequency multi-element reflection super surface is characterized by being formed by periodically arranging high-efficiency complementary resonator units, wherein each high-efficiency complementary resonator unit comprises two layers of dielectric slabs, 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 slabs;
the double-layer frequency multi-element reflection super-surface realizes a focusing OAM wave beam with a mode number l of 3 and a zero-order Bessel wave beam under the condition of a low frequency ratio.
2. The double-layer frequency multi-element reflective super surface according to claim 1, wherein 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 arranged in a structural order.
3. The dual-layer frequency multi-element reflective super-surface of claim 2, wherein said first dielectric layer has a thickness H 1 1.5mm, second layer dielectric plate thickness H 2 1.5mm, dielectric sheet material F4B;
the double-C-shaped slotted resonator, the double-C-shaped metal resonator and the metal floor are made of copper, and the electrical conductivity of the double-C-shaped slotted resonator, the double-C-shaped metal resonator and the metal floor is 5.8 multiplied by 10 7 S/m。
4. The double-layer frequency multivariate reflective super-surface according to claim 2, wherein the high-efficiency complementary resonator element period P is 10.2 mm;
the structural parameters of the double C-shaped slotted resonator are as follows: outer ring outer diameter r 1 4.75mm, inner diameter r of outer ring 2 4.35mm, and a middle groove width of w 1 0.3mm, width w of inner metal ring 2 0.4mm, the 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 3.0mm, width w of metal ring 3 0.8mm, metal ring gap width g 2 ＝0.3mm。
5. The double-layer frequency multi-element reflective super surface of claim 4, wherein the high efficiency complementary resonator element is at two resonant frequencies f 1 And f 2 Independent for 100% cross circular polarized wave conversionVertical geometry phase regulation, in which a double C-shaped slotted resonator operates at frequency f 1 The double C-shaped metal resonator works at the frequency f in charge of the geometric phase function regulation and control of the frequency 2 Is responsible for the geometric phase function control at this frequency, i.e. at the resonance frequency f 1 And f 2 The high-efficiency complementary resonator unit meets the following conditions under the incident condition of linearly polarized waves:
|r xx |＝|r yy |＝1
wherein r is xx Is the reflection coefficient at x polarization, r yy For the reflection coefficient in the y-polarization,
linearly polarized waves are in the same polarization reflection phase.
6. The dual-layer frequency multivariate reflective super surface of claim 1, wherein the dual-layer frequency multivariate reflective super surface is at an operating frequency f 1 A focused OAM beam with a mode number l of 3 realized at 9.2GHz, which is decomposed into a focus phase part and a vortex phase part using the phase superposition principle, for the focus phase, the efficient complementary resonator unit satisfies the following phase distribution:
wherein f is 0 214mm for its focal length, P for the unit period, λ for the wavelength of the incident electromagnetic wave,
is of arbitrary phaseAmount, m is the number of elements from the origin in the x-direction, n is the number of elements from the origin in 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 mode number of the OAM wave beam;
according to the phase superposition principle of electromagnetic waves, the vortex phase and the 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:
7. The dual-layer frequency multivariate reflective super surface of claim 1, wherein the dual-layer frequency multivariate reflective super surface is at a working frequency f 2 Realizing a zero order Bessel beam at 11.2GHz, said highly efficient complementary resonator unit having a resonance frequency f 2 Satisfies the following equation:
where P is the period of the elements, 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 in the x direction, and n is the number of elements from the origin in the y direction.
8. A double-layer frequency multi-element reflection super-surface design method is characterized by comprising the following steps:
step 1, designing an efficient complementary resonator unit required by a double-layer frequency multi-element reflection super surface, and enabling the efficient complementary resonator unit to realize phase regulation and control of 100% cross circularly polarized waves at two resonant frequencies;
step 2, forming a frequency multi-element reflection super surface through non-periodic arrangement of the efficient complementary resonator units;
step 3, analyzing the performance of the double-layer frequency multi-element reflection super-surface, and confirming that the double-layer frequency multi-element reflection super-surface realizes the expected function;
in step 2, a double-layer frequency multi-element reflection super surface is finally constructed at f 1 9.2GHz and f 2 The frequency multiplexing multifunctional super surface with the mode number l being 3 and the zero-order Bessel beam is realized by taking 11.2GHz as the working frequency.
9. The method as claimed in claim 8, wherein in step 2, the double-layer frequency multi-element reflective super-surface is at an operating frequency f 1 A focused OAM beam with a mode number l of 3 realized at 9.2GHz, which is decomposed into a focus phase part and a vortex phase part using the phase superposition principle, for the focus phase, the efficient complementary resonator unit satisfies the following phase distribution:
wherein, f 0 214mm is its focal length, P is the unit period, λ is the wavelength of the incident electromagnetic wave,
is an arbitrary phase constant, m is the number of cells from the origin along the x-direction, n is the number of cells 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 mode number of the OAM wave beam;
according to the phase superposition principle of electromagnetic waves, the vortex phase and the 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:
10. The method as claimed in claim 8, wherein in step 2, the double-layer frequency multi-element reflective super-surface is at an operating frequency f 2 Realizing a zero order Bessel beam at 11.2GHz, said highly efficient complementary resonator unit being at a resonance frequency f 2 Satisfies the following equation:
where P is the period of the elements, 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 in the x direction, and n is the number of elements from the origin in the y direction.
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