CN114976666A - Two-layer frequency multi-reflection metasurface and its design method - Google Patents

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

Two-layer frequency multi-reflection metasurface and its design method

technical field

The invention relates to the technical field of reflection metasurfaces, and mainly relates to a double-layer frequency multivariate reflection metasurface and a design method.

Background technique

With the rapid development of communication systems, multi-functional microwave devices are widely used in integrated equipment such as signal transmission and imaging systems. However, traditional multi-functional microwave devices do not meet the Robustness and practicality of microwave devices. In contrast, metasurfaces with subwavelength thicknesses have good control capabilities for the amplitude, phase, and polarization of electromagnetic waves. For traditional optical lenses relying on distance transmission to obtain phase accumulation, metasurfaces can obtain abrupt phases through resonance coupling with incident electromagnetic waves, demonstrating the metasurface’s powerful ability to manipulate electromagnetic waves. Because of the superior electromagnetic control ability of metasurfaces, important progress has been made in electromagnetic wave anomalous reflection/refraction, radar cross section reduction (RCS), holography, focusing and vortex beam generators.

To improve the integration and compactness of devices, researchers have extensively carried out research on multifunctional metasurface devices. At present, multi-functionality is mainly achieved by electromagnetic waves on metasurface excitation information (such as frequency, polarization, direction, and position). Among them, frequency is an important information carried by electromagnetic waves, and frequency multiplexing enables devices to have efficient spectrum utilization, enabling frequency multifunctional metasurfaces to be widely used in electromagnetic regulation. The core of designing a frequency multifunctional metasurface lies in the regulation of the amplitude, polarization and phase of electromagnetic waves by asymmetric anisotropic units working in different frequency bands on the metasurface. Frequency multivariate metasurfaces are widely used because of their good ability to control electromagnetic waves. Among them, frequency multivariate phase control metasurfaces are widely used in multi-functional microwave integrated devices due to their good transmission characteristics and full-space electromagnetic wave control capabilities. Multi-frequency and multi-channel metasurfaces for vortex beams and holograms, achromatic holographic metasurfaces, and broadband spin-decoupled undistorted biphasic metasurfaces. Although frequency multifunctional metasurfaces can achieve functional integration in multiple frequency bands to cope with different working environments, most frequency multifunctional metasurface units rely on multiple metal resonators spliced on a single-layer dielectric or in a multi-layer dielectric. On the basis of spatial multiplexing (transmission, reflection integration) and other methods to achieve multi-function. This method reduces the efficiency due to the inevitable crosstalk between channels. In order to avoid crosstalk, it is required that each working frequency band of the frequency multifunctional metasurface cannot be too close.

SUMMARY OF THE INVENTION

The present invention provides a double-layer frequency multivariate reflection metasurface, which is characterized in that the double-layer frequency multivariate reflection metasurface is formed by periodic arrangement of high-efficiency complementary resonator units, and the high-efficiency complementary resonator unit includes two layers of dielectric plates , constructing complementary forms of double-C-shaped slotted resonators and double-C-shaped metal resonators and metal floors on the two-layer dielectric plate;

The double-layer frequency multivariate reflection metasurface realizes the focused OAM beam and zero-order Bessel beam with mode number l=3 under the condition of low frequency ratio.

Further, the high-efficiency complementary resonator unit includes a double C-shaped slotted resonator, a first layer of dielectric plates, a double C-shaped metal resonator, a second layer of dielectric plates, and a metal floor, which are arranged in structural order.

Further, the thickness of the first layer of dielectric plate H ₁ =1.5mm, the thickness of the second layer of dielectric plate H ₂ =1.5mm, and the material of the dielectric plate is F4B;

The material used for the double-C-shaped slotted resonator, the double-C-shaped metal resonator and the metal floor is copper, and the electrical conductivity thereof is σ=5.8×10 ⁷ S/m.

Further, the high-efficiency complementary resonator unit period P=10.2mm;

The structural parameters of the double C-shaped slotted resonator are: the outer diameter of the outer ring is r ₁ =4.75mm, the inner diameter of the outer ring is r ₂ =4.35mm, the width of the middle slot is w ₁ =0.3mm, and the width of the inner metal ring is w ₂ =0.4 mm, the metal width g ₁ =0.9mm of the connecting part of the outer ring and the inner ring;

The structural parameters of the double C-shaped metal resonator are: the inner diameter width of the metal ring r ₃ =3.0mm, the width of the metal ring w ₃ =0.8mm, and the gap width of the metal ring g ₂ =0.3mm.

Further, the high-efficiency complementary resonator unit achieves independent geometric phase modulation of 100% cross-circularly polarized wave conversion at both resonant frequencies f ₁ and f ₂ , wherein the double C-shaped slotted resonator operates at the frequency f ₁ , responsible for the functional regulation of the geometric phase at this frequency, the double C-shaped metal resonator works at the frequency f ₂ and is responsible for the functional regulation of the geometric phase at this frequency, that is, the linearly polarized waves are incident at the resonant frequencies f ₁ and f ₂ The high-efficiency complementary resonator unit satisfies:

|r _xx |=|r _yy |=1

为线极化波同极化反射相位。where r _xx is the reflection coefficient at x polarization, r _yy is the reflection coefficient at y polarization,

is the co-polar reflection phase of the linearly polarized wave.

Furthermore, the double-layer frequency multi-reflection metasurface realizes a focused OAM beam with a mode number of l=3 at the operating frequency f ₁ =9.2 GHz, which is decomposed into a focused phase part and a vortex phase part by using the principle of phase superposition, For focusing phase, the high-efficiency complementary resonator unit satisfies the following phase distribution:

是任意相位常量，m为沿x方向距原点的单元数目，n为沿y方向距原点的单元数目；Among them, f ₀ =214mm is the 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 away from the origin along the x direction, and n is the number of cells away 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:

Among them, l=3 is the mode number of OAM beam;

According to the phase superposition principle of electromagnetic waves, the phase superposition of the vortex phase and the focus phase is carried out. For the final unit phase distribution of the double-layer frequency multi-reflection metasurface, the following formula is satisfied:

表示单元在谐振频率f₁＝9.2GHz处最终的反射相位。

represents the final reflection phase of the cell at the resonant frequency f ₁ =9.2 GHz.

Furthermore, the double-layer frequency multi-element reflection metasurface realizes a zero-order Bessel beam at the operating frequency f ₂ =11.2 GHz, and the compensation phase of the high-efficiency complementary resonator unit at the resonant frequency f ₂ satisfies the following formula:

Among them, P is the period of the unit, 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 units away from the origin along the x direction, and n is the number of units away from the origin along the y direction.

A method for designing a double-layer frequency multi-element reflection metasurface is also proposed, wherein the method for designing a double-layer frequency multi-element reflection metasurface includes the following steps:

Step 1, designing a high-efficiency complementary resonator unit required for a multi-layer frequency multi-reflection metasurface, so that the high-efficiency complementary resonator unit can achieve 100% phase regulation of cross-circularly polarized waves at two resonance frequencies;

In step 2, a frequency multivariate reflection metasurface is formed by aperiodically arranging high-efficiency complementary resonator units;

Step 3, analyze the performance of the double-layer frequency multi-element reflection metasurface, and confirm that the double-layer frequency multi-element reflection metasurface realizes the expected function;

In step 2, the double-layer frequency multi-element reflective metasurface is finally constructed with f ₁ =9.2GHz and f ₂ =11.2GHz as the operating frequencies, and the focused OAM beam and zero-order Bessel with mode number l=3 are realized respectively. Frequency multiplexing of multifunctional metasurfaces for the Beer beam.

Further, in step 2, the double-layer frequency multi-element reflection metasurface realizes the focused OAM beam with mode number l=3 at the working frequency f ₁ =9.2GHz, and decomposes it into the focused phase part and the For the vortex phase part, for the focusing phase, the high-efficiency complementary resonator unit satisfies the following phase distribution:

是任意相位常量，m为沿x方向距原点的单元数目，n为沿y方向距原点的单元数目；Among them, f ₀ =214mm is the 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 away from the origin along the x direction, and n is the number of cells away 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:

Among them, l=3 is the mode number of OAM beam;

According to the phase superposition principle of electromagnetic waves, the phase superposition of the vortex phase and the focus phase is carried out. For the final unit phase distribution of the double-layer frequency multi-reflection metasurface, the following formula is satisfied:

表示单元在谐振频率f₁＝9.2GHz处最终的反射相位。

represents the final reflection phase of the cell at the resonant frequency f ₁ =9.2 GHz.

Further, in step 2, the double-layer frequency multi-element reflection metasurface realizes a zero-order Bessel beam at the operating frequency f ₂ =11.2GHz, and the high-efficiency complementary resonator unit compensates the phase at the resonant frequency f ₂ Satisfy the following formula:

Among them, P is the period of the unit, 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 units away from the origin along the x direction, and n is the number of units away from the origin along the y direction.

The advantages of the present invention are:

Compared with the traditional frequency multifunctional metasurface, the frequency multi-reflection metasurface provided by the present invention has good independence at two resonance frequencies and strictly satisfies the geometric phase principle.

The traditional frequency multi-function metasurface has a wide frequency spectrum, low relative spectrum utilization, complex structure and difficult processing. The frequency multi-reflection metasurface provided by the invention occupies narrow spectrum width, low frequency ratio, simple structure and easy processing.

Description of drawings

Figure 1 is a structural diagram of a double-layer frequency multi-reflection metasurface;

Figure 2 is a diagram of the cell layout and structural parameters of the double-frequency multi-reflection metasurface;

Fig. 3 is the electromagnetic response of the complementary resonator unit under the incident of x and y polarized waves at the resonant frequencies of f ₁ and f ₂ ;

Fig. 4 is the front view and 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 resonant frequencies _of f1 and f2 _;

Fig. 5 is the reflection amplitude and phase of the double C-shaped slotted resonator (double C-shaped metal resonator) with different α ₁ (α ₂ ) as a function of α ₂ (α ₁ );

Fig. 6 is the reflection amplitude and phase of the double C-shaped slotted resonator (double C-shaped metal resonator) with different α ₁ (α ₂ ) as a function of frequency;

Fig. 7 is the phase distribution diagram of the focused OAM beam unit of mode number 1=3;

Fig. 8 is a phase distribution diagram of zero-order Bessel beam unit;

Figure 9 is a schematic diagram of zero-order Bessel beam forming;

Figure 10 shows the simulation results of amplitude and phase of the focused OAM beam with mode number l=3 at the focal plane f ₀ =214 mm;

Figure 11 Normalized distribution of zero-order Bessel beams at different positions |E _LCP |^ ² ;

Fig. 12 is the normalized distribution curve of |E _LCP |^ ² of Bessel beams at different positions on the yoz plane.

Detailed ways

The technical solutions of the present invention will be described in more detail below with reference to the accompanying drawings. The present invention includes but is not limited to the following embodiments.

The invention provides a double-layer frequency multivariate reflection metasurface, wherein the metasurface is mainly constituted by the periodic arrangement of high-efficiency complementary resonator units. The high-efficiency complementary resonator unit is constructed by constructing complementary double C-shaped slotted resonators and double C-shaped metal resonators and metal floors on two-layer dielectric plates. Due to the high Q value of the complementary resonators, the The metasurface formed by the unit can realize the independent control of phase under the condition of low frequency ratio.

For verification and application exploration, multifunctional metasurfaces operating at f ₁ = 9.2 GHz and f ₂ = 11.2 GHz are designed, and focused OAM beams with mode numbers l=3 and f 2 are realized at the operating frequencies f ₁ and f ₂ , respectively. Zero order Bessel beam. Through the simulation test of the metasurface at the operating frequencies of f ₁ and f ₂ , the simulation results are in good agreement with the theoretical results, indicating that the metasurface has a good ability to control the wavefront phase at the operating frequency. Compared with previously reported multifunctional metasurfaces, the dual-frequency operating frequency ratio of the device proposed in this patent is only 1.2, and the device efficiency at f ₁ and f ₂ is as high as 86.1% and 93%.

As shown in Figures 1-2, the high-efficiency complementary resonator unit mainly includes five parts: double C-shaped slotted resonator - first layer of dielectric plate - double C-shaped metal resonator - second layer of dielectric plate - metal floor Structural order composition. The thickness of the first layer of dielectric plate H ₁ =1.5mm, the thickness of the second layer of dielectric plate H ₂ =1.5mm, the dielectric plate material is F4B (ε _r =2.65, tanδ = 0.001), the material has small tangent loss and small dispersion , the advantages of low manufacturing difficulty. For the complementary metal resonator and the metal floor, the material used is copper, the conductivity of which is σ=5.8×10 ⁷ S/m. Since the complementary resonator has a high Q value, the unit can achieve independent control of the phase under the condition of low frequency ratio, avoiding the crosstalk between channels caused by the narrow frequency band. In order that the unit can have the largest reflection amplitude at the two resonant frequencies, the following results are finally obtained by optimizing the parameters of the resonator in the unit. The unit period P=10.2mm, the structural parameters of the double C-shaped slotted resonator are: the outer diameter of the outer ring r ₁ =4.75mm, the inner diameter of the outer ring r ₂ =4.35mm, the width of the middle slot is w ₁ =0.3mm, the inner metal Ring width w ₂ =0.4 mm. The metal width g ₁ =0.9mm of the connecting part between the outer ring and the inner ring, and the structural parameters of the double C-shaped metal resonator are: the inner diameter width of the metal ring r ₃ =3.0mm, and the width of the metal ring w ₃ =0.8mm. Wherein the metal ring gap width g ₂ =0.3mm. For the resonator rotation angle, the double C-shaped slotted resonator takes the geometric center of the dielectric plate plane as the origin, and the counterclockwise rotation angle is α ₁ on the dielectric plate plane, and the double C-shaped metal resonator is located at the plane geometric center of the dielectric plate. As the origin, the angle of rotation is α ₂ counterclockwise in the plane of the dielectric layer.

The elements are periodically arranged according to the desired functions to achieve focused OAM beams and zero-order Bessel beams with mode number l=3 at operating frequencies f ₁ =9.2 GHz and f ₂ =11.2 GHz, respectively.

其中r_xx，r_yy为x、y极化波复反射系数，其中包含了反射波的振幅值与相位值如：

For the realization of functions at different operating frequencies of multifunctional metasurfaces, it is necessary to select appropriate units. The control of the linearly polarized electromagnetic wave by the unit generally adopts the change of the size of the metal patch to make the reflected electromagnetic wave undergo a sudden change in the transmission phase so as to realize the control of the electromagnetic wave. For the circularly polarized wave, the geometric phase principle is applied, and the phase control _of the circularly polarized reflected electromagnetic wave is realized by rotating the resonators corresponding to the resonant frequencies f1 and _f2 . In order to further explain the efficient working principle of the unit under the normal incidence of circularly polarized waves, the Jones matrix in the reflection mode of linearly polarized waves is introduced

Among them, r _xx and r _yy are the complex reflection coefficients of the x and y polarized waves, which include the amplitude and phase values of the reflected waves, such as:

Since the geometric phase principle is to make the reflected wave of the unit corresponding to the resonant frequency abruptly change the phase by rotating the resonator in the unit, when the resonator rotates through a fixed angle, the corresponding coordinate system will also change. When the resonator is rotated counterclockwise by the angle θ, the rotated uov coordinate system and the xoy coordinate system will have the following relationship.

定义为旋转矩阵R(θ)，当谐振器绕中心轴左旋则θ>0，相反右旋θ<0。这里以右旋圆极化波垂直入射为例，因圆极化波能分解为两个相互正交、幅值相等且相位相差90°的线极化波，故右旋圆极化波可表示为

in

Defined as the rotation matrix R(θ), when the resonator is left-rotated around the central axis, then θ>0, and the opposite is right-rotated θ<0. Here, the right-handed circularly polarized wave is vertically incident as an example. Since the circularly polarized wave can be decomposed into two mutually orthogonal linearly polarized waves with the same amplitude and 90° phase difference, the right-handed circularly polarized wave can be expressed as for

where E _o represents the amplitude of the incident wave.

After the resonator is rotated, the reflected wave is expressed in the uov coordinate system as:

则为在u方向引入的相移，而φ_vv则为在v方向引入的相移，其中θ是旋转角度，由此在圆极化波激励下可以引起单元几何相位的产生。where r _uu is the amplitude in the u direction, r _vv is the amplitude in the v direction, and

is the phase shift introduced in the u direction, and φ _vv is the phase shift introduced in the v direction, where θ is the rotation angle, which can cause the generation of the geometric phase of the unit under the excitation of circularly polarized waves.

由此反射波可以表示为：Because the structure is a reflective metasurface, it can be known from the electromagnetic propagation theory: r _uu =r _xx , r _vv =r _yy ,

The reflected wave can thus be expressed as:

From the above results, it can be seen that there are left-handed circularly polarized waves and right-handed circularly polarized waves in the reflected wave, which can be split into

为右旋圆极化波，

为左旋圆极化波；in,

is a right-handed circularly polarized wave,

is a left-handed circularly polarized wave;

时结果可以表示为：It can be seen from the results that the left-handed circularly polarized part carries the e ^j2θ phase factor, and when

The result can be expressed as:

Therefore, when the right-handed circularly polarized wave irradiates the metasurface vertically, the reflected left-handed circularly polarized wave undergoes polarization conversion with respect to the incident wave and has a geometric phase change of 2θ. The high-efficiency complementary resonator unit achieves independent geometric phase modulation of 100% cross-circularly polarized wave conversion at both resonant frequencies f ₁ and f ₂ , where the double C-shaped slotted resonator operates at frequency f ₁ , responsible for this frequency The geometric phase function regulation at , the double C-shaped metal resonator works at the frequency f ₂ and is responsible for the geometric phase function regulation at this frequency, that is, the high-efficiency complementary under the condition of linearly polarized wave incidence at the resonant frequencies f ₁ and f ₂ The resonator unit satisfies:

|r _xx |=|r _yy |=1

为线极化波同极化反射相位，为实现圆极化波100％交叉极化转换需要单元满足以上条件。where r _xx is the reflection coefficient at x polarization, r _yy is the reflection coefficient at y polarization,

In order to reflect the phase of the linearly polarized wave in the same polarization, in order to realize the 100% cross-polarization conversion of the circularly polarized wave, the unit needs to meet the above conditions.

与

在8～10GHz和10～12GHz的频段范围内相位差值保持均匀变化，并在f₁与f₂处稳定保持在180°左右，满足式(6)x、y线极化反射波激发下的幅度和相位条件，保证了圆极化波照射下单元的高效率交叉极化反射。In order to verify that the design unit satisfies the cross-polarization reflection conditions of circularly polarized waves, the simulation calculation is carried out by the finite difference time domain (FDTD) method. In the simulation process, the unit is irradiated vertically with x, y orthogonal linearly polarized waves, and the two boundaries along the x and y directions are set as periodic boundary conditions. The simulation results are shown in Figure 3. It can be seen that under the incidence of x and y polarized waves, the resonant frequency f ₁ is mainly the double C-shaped slotted resonator and the metal floor participate in the resonance, while the resonant frequency f ₂ is mainly the double C-shaped metal resonator and the metal floor. participate in resonance. In the reflection fields of different resonance frequencies f ₁ and f ₂ , the reflection amplitudes of r _xx and r _yy are all greater than 0.92, which can be regarded as close to 1. At the same time, the reflection phase of the x and y polarized waves

and

In the frequency range of 8-10GHz and 10-12GHz, the phase difference value keeps uniform change, and is stable at about 180° at f ₁ and f ₂ , which satisfies the equation (6) under the excitation of x and y linearly polarized reflected waves. The amplitude and phase conditions ensure high-efficiency cross-polarized reflection of the unit under the illumination of circularly polarized waves.

In order to show that the unit has a good reflection effect at the resonant frequency, the unit is simulated by the simulation software CST. According to the current distribution of the unit in the reflection mode, as shown in Fig. 4, it can be concluded that the double C-shaped slotted resonator memory that participates in regulating the circularly polarized wave when the circularly polarized electromagnetic wave is vertically incident at the resonant frequency f ₁ =9.2GHz The magnetic resonance phenomenon occurs in the closed resonant current and the opposite current distribution in the yoz plane with the underlying metal floor. When the resonant frequency f ₂ =11.2GHz circularly polarized electromagnetic wave is incident vertically, there is a closed resonant current in the double C-shaped metal resonator that participates in regulating the circularly polarized wave, and the current distribution is opposite to the underlying metal floor in the xoz plane. Magnetic resonance occurs.

In order to prove that under the incident circularly polarized wave, the high-efficiency complementary resonator unit can realize the independent control of the geometric phase at f ₁ =9.2GHz and f ₂ =11.2GHz, and the cross-polarized reflected wave can achieve 2π geometric phase coverage, The unit is simulated by taking the right-hand circularly polarized wave perpendicularly incident as an example. It is assumed that the double C-shaped slotted resonator rotates α ₁ counterclockwise from the initial position, and the double C-shaped metal resonator rotates α ₂ counterclockwise, and the rotation step is 30°. The simulation results are shown in Figures 5-6.

As shown in Fig. 5, at the resonant frequency f ₁ =9.2GHz, with the change of the rotation angle of the double C-shaped metal resonator, the reflection amplitude of the double C-shaped slotted resonator with different α ₁ approaches 1 and the reflection The phase hardly changes with α ₂ , and the reflection phase difference and the rotation angle α ₁ satisfy a 2-fold geometric phase relationship. Similarly, at the resonant frequency f ₂ =11.2GHz, with the change of the rotation angle of the double-C-shaped slotted resonator, the same conclusion can be drawn for the reflection amplitude and phase of the double-C-shaped metal resonator with different α ₂ . By calculating the reflection phase errors of the double-C-shaped slotted resonator and the double-C-shaped metal resonator at different rotation angles at the resonant frequencies f ₁ and f ₂ , it is concluded that they are both less than 8°, so they can be ignored, which proves that the unit can It has good independent phase control capability at two different resonant frequencies.

Whether the geometric phase of the complementary resonator unit can reach a geometric phase coverage of 2π at f ₁ and f ₂ can be obtained from FIG. 6 . At the resonant frequencies f1 and f2, as the rotation angle α1 _of the _double C-shaped slotted resonator and the rotation angle α2 _of the _double C-shaped metal resonator change from ₀ ° to ₁₈₀ °, the reflected waves at f1 and f2 The geometric phase of the resonator has successfully achieved 2π geometric phase coverage. The phase changes of resonators with different rotation angles between each other at the operating frequency satisfy the 2-fold rotation angle relationship, which conforms to the geometric phase principle, and the reflection amplitude is as high as 0.98 at the operating frequency. The above results fully show that the high-efficiency complementary resonator unit has the ability to independently control circularly polarized electromagnetic waves of different frequencies, and the double-C-shaped slotted resonator and the double-C-shaped metal resonator are mutually independent at the resonant frequencies f ₁ and f ₂ impact, which lays a solid foundation for the design of multifunctional metasurfaces.

The double-layer frequency multi-reflection metasurface proposed by the present invention has good mutual independence at two different resonant frequencies of the designed units, and under the premise that the units at different two resonance frequencies both achieve 2π geometric phase coverage , by arranging the known units aperiodically, the frequency reuse of the focused OAM beam and the zero-order Bessel beam with the mode number l=3 is finally constructed with f ₁ and f ₂ as the operating frequencies, respectively. Multifunctional metasurface.

For the multifunctional metasurface to realize the focused OAM vortex beam with mode number l=3 at the operating frequency f ₁ =9.2GHz, it is decomposed into the focused phase part and the vortex phase part by using the principle of phase superposition, as shown in Fig. 7 .

For the focusing phase, the unit is required to satisfy the following phase distribution.

是任意相位常量，m(n)为沿x(y)方向距原点的单元数目。只要使超表面的每个单元的反射相位满足公式，即可实现在预期焦平面上的聚焦效果。where f ₀ =214mm is the focal length, P is the unit period, λ is the wavelength of the incident electromagnetic wave,

is an arbitrary phase constant, and m(n) is the number of elements along the x(y) direction from the origin. As long as the reflection phase of each element of the metasurface satisfies the formula, the focusing effect on the expected focal plane can be achieved.

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 mode number of the vortex beam. According to the principle of phase superposition of electromagnetic waves, the target function at the resonance frequency can be achieved by superimposing the phase of the vortex phase and the focusing phase. Therefore, the final phase distribution of the electromagnetic wave reflected by the target satisfies the following formula.

The double-layer frequency multi-reflection metasurface proposed by the present invention realizes the zero-order Bessel beam at the operating frequency f ₂ =11.2GHz, and it is necessary to make the compensation phase of the metasurface unit at the resonant frequency f ₂ satisfy the distribution as shown in FIG. 8 , The specific phase values of the units are as follows.

In the formula, P is the period of the unit, λ is the wavelength of the incident electromagnetic wave, and β=30° is the diffraction half angle of the Bessel beam. According to the principle diagram of Bessel beam forming, as shown in Figure 9, it can be seen that the zero-order Bessel beam is mainly formed by the superposition of reflected parallel waves with an angle of β with the positive direction of the z-axis within the non-diffraction distance. From the geometric relationship, it can be known that the maximum non-diffraction distance Z _max is as follows.

Where D is equal to the period of the reflective metasurface, Z _max =309mm can be obtained by calculation. It can be seen from the formula that the energy of the Bessel beam generated by this method is mainly concentrated in a circle with a radius of D/4, of which the highest energy is at Z _max /2, and the beam energy varies with the distance from the metasurface. The energy density first increased and then decreased.

The double-layer frequency multi-element reflection metasurface proposed by the present invention is used to arrange and verify the unit through the co-simulation of CST-MATLAB, including the following processes:

Firstly, the unit resonator, dielectric plate, metal floor and other structures are modeled according to parameters in the full-wave simulation software CST, and the double C-shaped slotted resonator and double C-shaped metal resonator are set to the geometric center of the plane of the dielectric plate. The counterclockwise rotation angles for the center of the circle are α ₁ and α ₂ respectively.

Secondly, according to the phase distribution of different operating frequencies f ₁ and f ₂ and the function at the operating frequency of the metasurface, the double-C-shaped slotted resonator and the double-C-shaped metal resonator in the unit are rotated by MATLAB. Through the geometric phase adjustment mechanism, the rotation angle of the unit resonator is adjusted and the unit model is aperiodically arranged to finally realize the modeling of the multifunctional metasurface.

Finally, the time domain simulation is carried out in the simulation software CST with a right-handed circularly polarized plane wave perpendicularly incident on the metasurface. At the working frequency f ₁ , the real part of the electric field at the focal plane f ₀ =214 mm is obtained by sorting out the simulation data, and the phase distribution diagram is shown in FIG. 10 . The real part plot of the electric field in the figure shows that the electric field is clearly focused at the focal point and the beam has the same number of helical arms as the mode number l = 3, while the electric field phase plot shows that the beam has a 1080° phase change that is consistent with the mode number l. It is consistent with the wave-forming properties of the focused OAM beam in the focal plane processing theory. For the focused OAM beam efficiency of the near-field simulated metasurface with mode number l=3, the following method is used to calculate:

定义为完全反射波功率与入射波功率之比，

为焦平面处焦点功率与焦平面总功率之比，其中焦点功率为以焦点为圆心，主瓣半功率宽度为半径包围的圆功率积分，其积分区域如附图10黑色虚线区域。经计算可得

最终计算得到聚焦OAM波束的仿真效率为η_f＝87.5％。其效率未能达到100％的主要原因为部分电磁波因衍射未参与聚焦而使得聚焦效率较低。in

is defined as the ratio of the totally reflected wave power to the incident wave power,

is the ratio of the focal power at the focal plane to the total power of the focal plane, where the focal power is the power integral of the circle with the focal point as the center and the half-power width of the main lobe as the circle surrounded by the radius. can be calculated

The simulation efficiency of the focused OAM beam is finally calculated to be η _f =87.5%. The main reason why the efficiency cannot reach 100% is that the focusing efficiency of some electromagnetic waves is low because the diffraction does not participate in the focusing.

At the operating frequency f ₂ , by sorting out the simulation data, the |E _LCP |^ ² normalizations of the yoz plane and the four positions of Z ₁ =75, Z ₂ =150, Z ₃ =225 and Z ₄ =309mm are obtained. The normalized distribution is shown in Figure 11. The figure shows that the energy in the beam propagation direction is relatively concentrated, with the maximum energy intensity at the center of the cross section at different positions, and the lateral energy gradually oscillates and decreases when it deviates from the center position, which is in line with the oscillation trend of the Bessel function curve.

The wave forming effect of the metasurface is verified by the energy concentration efficiency of the Bessel beam, and the |E _LCP |^ ² of the four observation surfaces Z ₁ =75, Z ₂ =150, Z ₃ =225 and Z ₄ =309mm are selected The energy distribution is calculated by the following formula.

Among them, P ₂ is the non-diffraction beam area in the same plane at the same position above the metasurface (the center of the plane is the circular area with the center of the circle and the radius is D/4), and P ₁ is the aperture area of the metasurface in the same plane (the side length is D The energy of the electromagnetic wave is determined by the Poynting vector, that is, S=E×H, where S is the Poynting vector, E is the electric field strength, and H is the magnetic field strength.

Finally, the energy concentration efficiencies of longitudinal Bessel beams at the four positions of Z ₁ =75, Z ₂ =150, Z ₃ =225 and Z ₄ =309mm are 82%, 92%, 85% and 73%, respectively. This is consistent with the non-diffraction transmission characteristic that the Bessel beam energy increases slightly and then decreases slightly with the transmission distance. To further demonstrate the superior performance of the device, the |E _LCP |^ ² normalized intensity distributions at x=0 at four locations Z ₁ =75, Z ₂ =150, Z ₃ =225 and Z ₄ =309 mm were extracted, as shown in the appendix Figure 12. It can be seen from the figure that the |E _LCP |^ ² intensity in the main lobe increases first and then decreases with the increase of the 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 properties of zero-order Bessel beams. To sum up, through the simulation of the double-frequency multi-reflection metasurface model, it can better realize the focused OAM beam and zero-order Bessel with mode number l=3 at f ₁ =9.2GHz and f ₂ =11.2GHz er beam.

The present invention also proposes a method for designing a double-layer frequency multivariate reflection metasurface, which specifically includes the following steps:

Step 1, designing a high-efficiency complementary resonator unit required for a multi-layer frequency multi-reflection metasurface, so that the high-efficiency complementary resonator unit can achieve 100% phase regulation of cross-circularly polarized waves at two resonance frequencies;

In order to realize the beam formation of the double-layer frequency multi-reflection metasurface at different operating frequencies f ₁ and f ₂ , a cross-polarized circularly polarized wave with high reflection and independent 2π phase is designed at different resonant frequencies f ₁ and f ₂ . Tunable subwavelength size units. Its unit structure is mainly composed of three layers of metal and two layers of dielectric plates. Double C-shaped slotted resonators are printed on the first layer of dielectric plates, and its thickness H ₁ =1.5mm. The second layer of dielectric plates is printed with double C-shaped resonators. A metal resonator with a dielectric thickness H ₂ =1.5mm, the bottom layer is printed with a metal floor, and the thickness of all metals is H = 0.036mm. For the resonator and the metal floor, the material used is copper, and its conductivity is σ=5.8×10 ⁷ S/m. The purpose is to improve the electromagnetic response effect and reduce the insertion loss of the metasurface. For the resonator, the outer diameter of the double C-shaped slotted resonator is r ₁ =4.75mm, the inner diameter of the outer ring is r ₂ =4.35mm, the width of the middle slot is w ₁ =0.3mm, and the width of the inner metal ring is w ₂ =0.4 mm, wherein the metal width g ₁ of the connecting part between the outer ring and the inner ring is 0.9 mm. The structural parameters of the double C-shaped metal resonator are: the inner diameter width of the metal ring r ₃ =3.0mm, the width of the metal ring w ₃ =0.8mm, and the metal ring gap width g ₂ =0.3mm. In order to verify that the unit can achieve 100% cross-circularly polarized wave phase regulation at two resonant frequencies, based on the geometric phase theory, the unit structural conditions are theoretically analyzed and the following conclusions are drawn:

The high-efficiency complementary resonator unit achieves independent geometric phase modulation of 100% cross-circularly polarized wave conversion at both resonant frequencies f ₁ and f ₂ , where the double C-shaped slotted resonator operates at frequency f ₁ , responsible for this frequency The geometric phase function regulation at , the double C-shaped metal resonator works at the frequency f ₂ and is responsible for the geometric phase function regulation at this frequency, that is, the high-efficiency complementary under the condition of linearly polarized wave incidence at the resonant frequencies f ₁ and f ₂ The resonator unit satisfies:

|r _xx |=|r _yy |=1

为线极化波同极化反射相位。where r _xx is the reflection coefficient at x polarization, r _yy is the reflection coefficient at y polarization,

is the co-polar reflection phase of the linearly polarized wave.

Through the finite difference time domain (FDTD) method, the x, y orthogonal linearly polarized wave is vertically incident to the unit for simulation verification, and the final result is highly consistent with the requirements, so it is considered that the unit can operate at two different resonant frequencies. A high degree of circularly polarized wave cross-polarization control is achieved.

In step 2, a frequency multivariate reflection metasurface is formed by aperiodically arranging high-efficiency complementary resonator units;

Based on the unit's ability to independently control circularly polarized electromagnetic waves of different frequencies, the multi-layer frequency multi-reflection metasurface was finally constructed with f ₁ =9.2GHz and f ₂ =11.2GHz as the operating frequencies, respectively realizing the mode number l=3 The frequency multiplexing multifunctional metasurface of focused OAM beam and zero-order Bessel beam, the main process of which is shown below.

In order to realize the focused OAM beam with mode number l=3 on the metasurface at f ₁ =9.2 GHz, it is decomposed into a focused phase part and a vortex phase part according to the principle of phase superposition.

where the focus phase distribution satisfies the formula:

是任意相位常量，m为沿x方向距原点的单元数目，n为沿y方向距原点的单元数目；Among them, f ₀ =214mm is the 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 away from the origin along the x direction, and n is the number of cells away 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:

Among them, l=3 is the mode number of OAM beam;

According to the phase superposition principle of electromagnetic waves, the phase superposition of the vortex phase and the focus phase is carried out. For the final unit phase distribution of the double-layer frequency multi-reflection metasurface, the following formula is satisfied:

表示单元在谐振频率f₁＝9.2GHz处最终的反射相位。

represents the final reflection phase of the cell at the resonant frequency f ₁ =9.2 GHz.

The double-layer frequency multi-element reflective metasurface realizes the zero-order Bessel beam at the operating frequency f ₂ =11.2GHz, and the compensation phase of the high-efficiency complementary resonator unit at the resonant frequency f ₂ satisfies the following formula:

Among them, P is the period of the unit, 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 units away from the origin along the x direction, and n is the number of units away from the origin along the y direction.

In order to make the metasurface better applied to engineering practice, the focal length f ₀ and mode number l of the focused OAM beam can be controlled by changing the array arrangement, and the diffraction half-angle β of the Bessel beam can be controlled to maximize the Bessel beam. Free manipulation of diffraction-free distances.

The compensation phases required by the units at different positions at different two resonance frequencies are calculated by MATLAB, and the joint array is performed by CST-MATLAB. Because the compensation phase of the unit resonator and the rotation angle satisfy a 2-fold relationship at two different resonant frequencies, the double-C-shaped slotted resonator and the double-C-shaped metal resonator calculated by MATLAB at f ₁ and f ₂ are rotated The angle is written as a VB command in CST through the invoke function, and the hypersurface is modeled through the VB command. The time-domain simulation of the modeled metasurface is performed in CST. Here, the boundary conditions are all set to open (add space) conditions, and the ports are set to be vertically incident with right-handed circularly polarized plane waves.

Step 3, analyze the performance of the double-layer frequency multi-element reflection metasurface, and confirm that the double-layer frequency multi-element reflection metasurface realizes the expected function;

In order to analyze the performance of metasurfaces at different operating frequencies f ₁ and f ₂ , the efficiencies of two types of beams are calculated, and the following methods are used to calculate the focused OAM beam:

定义为完全反射波功率与入射波功率之比，

为焦平面处焦点功率与焦平面总功率之比，其中焦点功率为以焦点为圆心，主瓣半功率宽度为半径包围的圆功率积分，其积分区域如附图10黑色虚线区域。经计算可得

最终计算得到聚焦OAM波束的仿真效率为η_f＝87.5％。其效率未能达到100％的主要原因为部分电磁波因衍射未参与聚焦而使得聚焦效率较低。in

is defined as the ratio of the totally reflected wave power to the incident wave power,

is the ratio of the focal power at the focal plane to the total power of the focal plane, where the focal power is the power integral of the circle with the focal point as the center and the half-power width of the main lobe as the circle surrounded by the radius. can be calculated

The simulation efficiency of the focused OAM beam is finally calculated to be η _f =87.5%. The main reason why the efficiency cannot reach 100% is that the focusing efficiency of some electromagnetic waves is low because the diffraction does not participate in the focusing.

For zero-order Bessel beams, the metasurface is analyzed by calculating the beam energy concentration efficiency.

Among them, P ₂ is the non-diffraction beam area in the same plane at the same position above the metasurface (the center of the plane is the circular area with the center of the circle and the radius is D/4), and P ₁ is the aperture area of the metasurface in the same plane (the side length is D The energy of the electromagnetic wave is determined by the Poynting vector, that is, 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 , by sorting out the simulation data of the zero-order Bessel beam, take the |E of the yoz plane at four positions Z ₁ =75, Z ₂ =150, Z ₃ =225 and Z ₄ =309mm _LCP |^ ² energy distribution data and calculations. Finally, the energy concentration efficiencies of longitudinal Bessel beams at the four positions of Z ₁ =75, Z ₂ =150, Z ₃ =225 and Z ₄ =309mm are 82%, 92%, 85% and 73%, respectively. This is consistent with the non-diffraction transmission characteristic that the Bessel beam energy increases slightly and then decreases slightly with the transmission distance.

To sum up, the multifunctional metasurface simulation can well realize the focused OAM beam and zero-order Bessel beam with mode number l=3 at f ₁ =9.2GHz and f ₂ =11.2GHz, which verifies the design of double-layer The frequency multi-reflection metasurface can well achieve the desired function at two resonant frequencies, and the experimental efficiencies at the resonant frequencies f ₁ and f ₂ are as high as 86.1% and 93%, which proves the superior performance of the multifunctional metasurface. It also provides a new way for OAM beam generation and multifunctional integrated device design.

The present invention is not limited to the above-mentioned specific embodiments. Those skilled in the art can use other various specific embodiments to implement the present invention according to the disclosed content of the embodiments and the accompanying drawings. Simple transformations or modified designs fall within the protection scope of the present invention.

Claims (10)

1. a double-layer frequency multi-element reflection metasurface, is characterized in that, described double-layer frequency multi-element reflection metasurface is formed by the periodic arrangement of high-efficiency complementary resonator unit, and described high-efficiency complementary resonator unit comprises two-layer dielectric plates, constructing complementary forms of double C-shaped slotted resonators and double C-shaped metal resonators and metal floors on the two-layer dielectric plate; The double-layer frequency multivariate reflection metasurface realizes the focused OAM beam and zero-order Bessel beam with mode number l=3 under the condition of low frequency ratio. 2. The double-layer frequency multi-element reflection metasurface according to claim 1, wherein the high-efficiency complementary resonator unit comprises double-C-shaped slotted resonators, first-layer dielectric plates, double-C-shaped slotted resonators arranged in structural order Metal resonator, second dielectric plate and metal floor. 3 . The double-layer frequency multi-reflection metasurface according to claim 2 , wherein the thickness of the first layer of dielectric plate H ₁ =1.5mm, the thickness of the second layer of dielectric plate H ₂ =1.5mm, and the material of the dielectric plate is 3 . F4B; The material used for the double-C-shaped slotted resonator, the double-C-shaped metal resonator and the metal floor is copper, and the electrical conductivity thereof is σ=5.8×10 ⁷ S/m. 4. The multi-layer frequency multi-reflection metasurface according to claim 2, wherein the high-efficiency complementary resonator unit period P=10.2mm; The structural parameters of the double C-shaped slotted resonator are: the outer diameter of the outer ring is r ₁ =4.75mm, the inner diameter of the outer ring is r ₂ =4.35mm, the width of the middle slot is w ₁ =0.3mm, and the width of the inner metal ring is w ₂ =0.4 mm, the metal width g ₁ =0.9mm of the connecting part of the outer ring and the inner ring; The structural parameters of the double C-shaped metal resonator are: the inner diameter width of the metal ring r ₃ =3.0mm, the width of the metal ring w ₃ =0.8mm, and the gap width of the metal ring g ₂ =0.3mm. 5. The multi-layer frequency multi-reflection metasurface according to claim 4, wherein the high-efficiency complementary resonator unit achieves 100% independence of cross-circularly polarized wave conversion at the two resonant frequencies f ₁ and f ₂ Geometric phase control, wherein the double C-shaped slotted resonator works at frequency f ₁ and is responsible for the geometric phase function control at this frequency, and the double C-shaped metal resonator works at frequency f ₂ and is responsible for the geometric phase function control at this frequency , that is, the high _- efficiency complementary _resonator unit satisfies: |r _xx |=|r _yy |=1

where r _xx is the reflection coefficient at x polarization, r _yy is the reflection coefficient at y polarization,

is the co-polar reflection phase of the linearly polarized wave. 6. The double-layer frequency multi-element reflection metasurface according to claim 1, wherein the double-layer frequency multi-element reflection metasurface realizes the focused OAM beam of mode number 1=3 at the operating frequency f ₁ =9.2GHz, using The principle of phase superposition decomposes it into a focusing phase part and a vortex phase part. For the focusing phase, the high-efficiency complementary resonator unit satisfies the following phase distribution:

Among them, f ₀ =214mm is the 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 away from the origin along the x direction, and n is the number of cells away 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:

Among them, l=3 is the mode number of OAM beam; According to the phase superposition principle of electromagnetic waves, the phase superposition of the vortex phase and the focus phase is carried out. For the final unit phase distribution of the double-layer frequency multi-reflection metasurface, the following formula is satisfied:

represents the final reflection phase of the cell at the resonant frequency f ₁ =9.2 GHz. 7 . The double-layer frequency multi-element reflection metasurface according to claim 1 , wherein the double-layer frequency multi-element reflection metasurface realizes zero-order Bessel beams at the operating frequency f ₂ =11.2 GHz, and the highly efficient complementary The compensation phase of the resonator unit at the resonant frequency f ₂ satisfies the following formula:

Among them, P is the period of the unit, 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 units away from the origin along the x direction, and n is the number of units away from the origin along the y direction. 8. a double-layer frequency multi-element reflection metasurface design method, it is characterized in that, described double-layer frequency multi-element reflection metasurface design method comprises the following steps: Step 1, designing a high-efficiency complementary resonator unit required for a multi-layer frequency multi-reflection metasurface, so that the high-efficiency complementary resonator unit can achieve 100% phase regulation of cross-circularly polarized waves at two resonance frequencies; In step 2, a frequency multivariate reflection metasurface is formed by aperiodically arranging high-efficiency complementary resonator units; Step 3, analyze the performance of the double-layer frequency multi-element reflection metasurface, and confirm that the double-layer frequency multi-element reflection metasurface realizes the expected function; In step 2, the double-layer frequency multi-element reflective metasurface is finally constructed with f ₁ =9.2GHz and f ₂ =11.2GHz as the operating frequencies, and the focused OAM beam and zero-order Bessel with mode number l=3 are realized respectively. Frequency multiplexing of multifunctional metasurfaces for the Beamer beam. 9. The method for designing a double-layer frequency multi-element reflection metasurface according to claim 8, characterized in that, in step 2, the double-layer frequency multi-element reflection metasurface realizes the mode number l= at the operating frequency f ₁ =9.2GHz The focused OAM beam of 3 is decomposed into a focused phase part and a vortex phase part by using the principle of phase superposition. For the focused phase, the high-efficiency complementary resonator unit satisfies the following phase distribution:

Among them, f ₀ =214mm is the 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 away from the origin along the x direction, and n is the number of cells away 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:

Among them, l=3 is the mode number of OAM beam; According to the phase superposition principle of electromagnetic waves, the phase superposition of the vortex phase and the focus phase is carried out. For the final unit phase distribution of the double-layer frequency multi-reflection metasurface, the following formula is satisfied:

represents the final reflection phase of the cell at the resonant frequency f ₁ =9.2 GHz. 10 . The method for designing a double-layer frequency multi-element reflection metasurface according to claim 8 , wherein, in step 2, the double-layer frequency multi-element reflection metasurface realizes zero-order Bessel at the operating frequency f ₂ =11.2GHz. 11 . A beam, the compensation phase of the high-efficiency complementary resonator unit at the resonant frequency f ₂ satisfies the following formula:

Among them, P is the period of the unit, 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 units away from the origin along the x direction, and n is the number of units away from the origin along the y direction.

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