Metastructure surface broadband phase slope regulation and control method applied to invisible cloak

Through the multi-mode resonance model and the Lorentz resonance model, the geometric parameters of the superstructure unit are adjusted, and the problem of difficult to regulate the phase slope of the stealth cloak in the wide band is solved, broadband electromagnetic stealth is achieved, and the performance of the stealth cloak is improved.

CN119167614APending Publication Date: 2024-12-20AIR FORCE UNIV PLA
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Patent Information

Application Number
CN202411193016.9
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-08-28
Publication Date
2024-12-20

AI Technical Summary

Technical Problem

The phase slope of the existing stealth clothing is difficult to regulate in a wide band, resulting in bandwidth limitations of electromagnetic stealth technology.

Method used

Using multi-mode resonance model, the superstructure unit is constructed through the N-order Lorentz resonance model, TMM transmission matrix method and FDTD electromagnetic simulation software, and the geometric parameters are adjusted to realize the regulation of the wide-frequency phase slope. The specific steps include determining the phase distribution and establishing the Lorentz resonance model, construct the superstructure unit and adjust its geometric parameters to meet the required phase slope.

Benefits of technology

Effectively adjusting the phase slope within the broadband range, solving the broadband bottleneck problem of electromagnetic stealth, realizing the integration of multi-mode resonance models, expanding the range of reflected phase changes, and optimizing the resonance characteristics, improving the performance of electromagnetic stealth clothing.

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Abstract

The invention discloses a metasurface broadband phase slope regulation and control method applied to an invisible cloak, and belongs to the field of broadband phase slope regulation and control, and the method comprises the steps: determining the phase distribution which needs to be satisfied by a microstructure on the invisible cloak, and determining the metasurface broadband phase slope which needs to be satisfied based on the phase distribution; establishing an N-order Lorentz resonance model used for realizing metamaterial surface broadband phase slope regulation and control; constructing a superstructure unit based on a third-order Lorentz resonance model; according to the mapping relation between the geometric parameters of the super-structure units and the resonant frequency of the third-order Lorentz resonance model, the super-structure surface broadband phase slope needing to be met is achieved by adjusting the geometric parameters of the super-structure units, and regulation and control of the super-structure surface broadband phase slope applied to the invisible cloak are completed. According to the invention, the problem that the phase slope in the wide frequency band of the metamaterial for constructing the invisible cloak is difficult to regulate and control is solved.
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Description

Technical Field

[0001] The present invention belongs to the field of broadband phase slope control, and in particular relates to a method for broadband phase slope control of a metasurface applied to an invisible cloak. Background Art

[0002] Metasurfaces, as the planar structure of metamaterials, introduce the concept of "macroscopic order" on the basis of using structural parameters to control the electromagnetic properties of materials, further increasing the freedom of electromagnetic control, and at the same time compressing the anisotropic medium from a three-dimensional structure to a two-dimensional structure, cleverly solving the problems of material loss and structural complexity, and injecting new vitality into electromagnetic control. At present, metasurfaces have been used to prepare focusing lenses, beam deflectors, Airy beam generators, vortex light generators, electromagnetic invisibility cloaks and other devices, significantly improving the electromagnetic performance of the devices.

[0003] At the end of the 20th century, with the rise of metamaterials and the introduction of optical transformation theory, electromagnetic stealth technology has developed rapidly. At present, the mainstream stealth technologies mainly include optical transformation-based stealth cloaks, stealth cloaks, scattering cancellation stealth cloaks, metasurface stealth cloaks, and hybrid technology-based stealth cloaks, and their application areas have also expanded to electromagnetics, acoustics, thermal and optical fields. However, almost all stealth technologies are limited by bandwidth, which is mainly due to the difficulty in controlling the phase slope of the metamaterial used to construct the stealth cloak within a wide frequency band. Summary of the invention

[0004] In view of the above-mentioned deficiencies in the prior art, the present invention provides a method for controlling the broadband phase slope of a metasurface applied to an invisible cloak, which solves the problem that the phase slope of the metamaterial used to construct the invisible cloak is difficult to control within a broadband band.

[0005] In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is: a method for controlling broadband phase slope of a metasurface applied to an invisible cloak, comprising the following steps:

[0006] S1. Determine the phase distribution that the microstructure on the invisible cloak needs to satisfy, and determine the broadband phase slope of the metasurface that needs to be satisfied based on the phase distribution;

[0007] S2. Establish an N-order Lorentz resonance model for realizing broadband phase slope control of metasurface;

[0008] S3. Construct a superstructure unit based on the third-order Lorentz resonance model;

[0009] S4. According to the mapping relationship between the geometric parameters of the metastructure unit and the resonant frequency of the third-order Lorentz resonance model, the required broadband phase slope of the metasurface is achieved by adjusting the geometric parameters of the metastructure unit, thereby completing the regulation of the broadband phase slope of the metasurface applied to the invisibility cloak.

[0010] Furthermore, the expression of the phase distribution that the microstructure on the invisible cloak needs to satisfy in step S1 is:

[0011] g(f j ,p j )=π-2k j h(x)cos(α)

[0012] k j =2πf j / c

[0013] Among them, g(f j ,p j ) is the phase distribution that the microstructure on the invisible cloak needs to satisfy; f j is the operating frequency; p j is the polarization of the excitation electromagnetic wave; π is the circumference of a circle; k j is the propagation constant; h(·) is the height information function of the microstructure on the surface of the cloak; x is the coordinate corresponding to the projection of the microstructure on the surface of the cloak on the X-axis; cos(·) is the cosine function; α is the incident angle information; c is the speed of light.

[0014] Furthermore, the expression of the N-order Lorentz resonance model in step S2 is:

[0015]

[0016] Among them, μ 2eff is the N-order Lorentz resonance model; ω is the operating frequency; ω1 is the resonance frequency of the first resonance; i is the resonance order, γ1 is the damping frequency of the first resonance; ω 1p is the first resonant plasma frequency; ω i is the resonant frequency of the ith resonance; γ i is the i-th resonant damping frequency; ω ip is the plasma frequency of the ith resonance; ω n is the resonant frequency of the nth resonance; γ n is the nth resonant damping frequency; ω np is the plasma frequency of the nth resonance.

[0017] Furthermore, in step S3, the superstructure unit includes a first metal layer, a first F4B dielectric layer, a second metal layer, a second F4B dielectric layer, a third metal layer, a third F4B dielectric layer and a fourth metal layer connected in sequence from top to bottom.

[0018] Furthermore, the first F4B dielectric layer is 10 mm long, 10 mm wide, and has a thickness of d1=2 mm; the second F4B dielectric layer is 10 mm long, 10 mm wide, and has a thickness of d2=1 mm; and the third F4B dielectric layer is 10 mm long, 10 mm wide, and has a thickness of d3=0.5 mm.

[0019] Furthermore, the fourth metal layer is a square metal sheet with a thickness of 0.036 mm and a side length of 10 mm; the first metal layer, the second metal layer and the third metal layer are all square metal sheets with a thickness of 0.036 mm and a square hollow in the middle; the side length of the first metal layer is a1, and the side length of the square hollow is b1; the side length of the second metal layer is a2, and the side length of the square hollow is b2; the side length of the third metal layer is a3, and the side length of the square hollow is b3.

[0020] Furthermore, the geometric parameters of the super-unit in step S4 are a1, b1, a2, b2, a3 and b3.

[0021] Furthermore, the step S4 is specifically as follows: using the TMM transmission matrix method and the FDTD electromagnetic simulation software to construct a mapping relationship between the geometric parameters of the three-dimensional metastructure unit and the resonant frequency of the third-order Lorentz resonance model, and according to the mapping relationship between the geometric parameters of the metastructure unit and the resonant frequency of the third-order Lorentz resonance model, the required wide-band phase slope of the metasurface is achieved by adjusting the geometric parameters of the metastructure unit, thereby completing the regulation of the wide-band phase slope of the metasurface applied to the invisibility cloak.

[0022] The beneficial effects of the present invention are as follows: the present invention adopts a multi-mode resonance model to effectively integrate electromagnetic structures with different resonance numbers, resonance frequencies and resonance intensities, realizes effective regulation of the phase slope within a broadband range, and solves the broadband bottleneck problem of electromagnetic stealth. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 The figure is a flow chart of the method of the present invention.

[0024] Figure 2 Schematic diagram of the phase distribution that needs to be satisfied by stealth structures of different heights in an embodiment of the present invention.

[0025] Figure 3 Schematic diagram of the design of a superstructure unit based on the equivalent medium TMM model and FDTD simulation in an embodiment of the present invention.

[0026] Figure 4 Schematic diagram of structural parameters of the super-structure unit on the invisible cloak at different heights in an embodiment of the present invention.

[0027] Figure 5 Graph 1 shows the electromagnetic characteristics of the broadband invisible cloak when the electromagnetic wave is incident vertically in the embodiment of the present invention.

[0028] Figure 6 Schematic diagram of the electromagnetic characteristics of the broadband invisible cloak when the electromagnetic wave is incident obliquely in an embodiment of the present invention.

[0029] in, Figure 3 (a) is a schematic diagram of the composite superunit structure; Figure 3 (b) is f1 = 7.5 GHz, f3 = 12.9 GHz, and the three plasma frequencies are f p1 =5GHz, f p2 =4GHz and f p3 =6GHz, the curve of the reflection phase change of the triple resonance model calculated by TMM when f2 changes; Figure 4 (a) is the distribution diagram of structural parameters a1, a2 and a3; Figure 4 (b) is the distribution diagram of structural parameters b1, b2 and b3; Figure 4 (c) Schematic diagram of the absorption effect on the broadband invisible cloak obtained by FDTD simulation; Figure 4 (d) is a schematic diagram of the reflection amplitude spectrum of different super units obtained by FDTD simulation; Figure 5 (a) The E at different frequencies of 8-12 GHz tested when TM electromagnetic wave was used for excitation x Schematic diagram of electric field distribution; Figure 5 (b) is the E measured when the electromagnetic wave is incident at 45° polarization. x=y Schematic diagram of the electric field distribution at the xoz and yoz planes during polarization; Figure 5 (c) Schematic diagram of the electric field distribution of the target object at different frequencies on the xoz and yoz planes when the invisible cloak is not loaded; Figure 5 (d) is a schematic diagram of the scattered signals at different angles of the broadband invisible cloak with different frequencies in the tested reflection plane when excited by TM electromagnetic waves; Figure 5 (e) is a schematic diagram of the scattered signals at different angles of the broadband invisible cloak with different frequencies in the tested reflection plane when excited by TE electromagnetic waves; Figure 5 (f) is a schematic diagram of the scattering signals at different angles of the target object when the TE electromagnetic wave and the TM electromagnetic wave are simultaneously excited in the reflection plane under test without the invisible cloak; Figure 6 (a) Schematic diagram of the electric field distribution of the tested broadband invisible cloak when θ = 10°; Figure 6 (b) is a schematic diagram of the electric field distribution of the target object without the cloak when θ=10°; Figure 6 (c) is a schematic diagram of the electric field distribution of the tested broadband invisible cloak when θ = 20°; Figure 6 (d) is a schematic diagram of the electric field distribution of the target object without the cloak when θ=20°; Figure 6 (e) is a schematic diagram of the scattered signals at different angles of the broadband invisible cloak with different frequencies in the tested reflection plane when excited by electromagnetic waves at θ = 10°; Figure 6 (f) is a schematic diagram of the scattered signals at different angles of the broadband invisible cloak with different frequencies in the tested reflection plane when excited by electromagnetic waves at θ = 20°; Figure 6 (g) is a schematic diagram of the scattered signals at different angles of the target object without the invisible cloak at different frequencies in the tested reflection plane when excited by electromagnetic waves at θ = 10°; Figure 6 (h) is a schematic diagram of the scattered signals at different angles of the target object without the invisible cloak at different frequencies in the tested reflection plane when excited by electromagnetic waves at θ = 20°. DETAILED DESCRIPTION

[0030] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0031] like Figure 1 As shown, in one embodiment of the present invention, a method for controlling broadband phase slope of a metasurface applied to an invisible cloak comprises the following steps:

[0032] S1. Determine the phase distribution that the microstructure on the invisible cloak needs to satisfy, and determine the broadband phase slope of the metasurface that needs to be satisfied based on the phase distribution;

[0033] S2. Establish an N-order Lorentz resonance model for realizing broadband phase slope control of metasurface;

[0034] S3. Construct a superstructure unit based on the third-order Lorentz resonance model;

[0035] S4. According to the mapping relationship between the geometric parameters of the metastructure unit and the resonant frequency of the third-order Lorentz resonance model, the required broadband phase slope of the metasurface is achieved by adjusting the geometric parameters of the metastructure unit, thereby completing the regulation of the broadband phase slope of the metasurface applied to the invisibility cloak.

[0036] In this embodiment, in order to achieve broadband stealth requirements, the phase distribution of the microstructure on the invisible cloak needs to satisfy g(f j ,p j )=π-2k j h(x)cos(α), where f j is the operating frequency (f1 <f j <f3),p iis the polarization of the excitation electromagnetic wave, h(x) is the height information of the microstructure on the surface of the invisible cloak, and k j =2πf j / c is the propagation constant, α is the incident angle information, and the corresponding calculated phase distribution within the broadband range is shown in Figure 2 It can be found that the phase dispersion satisfies the linear distribution in the broadband range and has different slopes. Therefore, to realize broadband electromagnetic invisibility cloak, it is necessary to effectively control the phase slope of the electromagnetic structure. Figure 2 Where Frequency is the frequency and Reflection phase is the reflection phase.

[0037] The expression of the phase distribution that the microstructure on the invisible cloak needs to satisfy in step S1 is:

[0038] g(f j ,p j )=π-2k j h(x)cos(α)

[0039] k j =2πf j / c

[0040] Among them, g(f j ,p j ) is the phase distribution that the microstructure on the invisible cloak needs to satisfy; f j is the operating frequency; p j is the polarization of the excitation electromagnetic wave; π is the circumference of a circle; k j is the propagation constant; h(·) is the height information function of the microstructure on the surface of the cloak; x is the coordinate corresponding to the projection of the microstructure on the surface of the cloak on the X-axis; cos(·) is the cosine function; α is the incident angle information; c is the speed of light.

[0041] The expression of the N-order Lorentz resonance model in step S2 is:

[0042]

[0043] Among them, μ 2eff is the N-order Lorentz resonance model; ω is the operating frequency; ω1 is the resonance frequency of the first resonance; i is the resonance order, γ1 is the damping frequency of the first resonance; ω 1p is the first resonant plasma frequency; ω i is the resonant frequency of the ith resonance; γ i is the i-th resonant damping frequency; ω ip is the plasma frequency of the ith resonance; ω n is the resonant frequency of the nth resonance; γ n is the nth resonant damping frequency; ω npis the plasma frequency of the nth resonance.

[0044] In step S3, the superstructure unit includes a first metal layer, a first F4B dielectric layer, a second metal layer, a second F4B dielectric layer, a third metal layer, a third F4B dielectric layer and a fourth metal layer connected in sequence from top to bottom.

[0045] The first F4B dielectric layer is 10 mm long, 10 mm wide, and has a thickness of d1=2 mm; the second F4B dielectric layer is 10 mm long, 10 mm wide, and has a thickness of d2=1 mm; the third F4B dielectric layer is 10 mm long, 10 mm wide, and has a thickness of d3=0.5 mm.

[0046] The fourth metal layer is a square metal sheet with a thickness of 0.036 mm and a side length of 10 mm; the first metal layer, the second metal layer and the third metal layer are all square metal sheets with a thickness of 0.036 mm and a square hollow in the middle; the side length of the first metal layer is a1, and the side length of the square hollow is b1; the side length of the second metal layer is a2, and the side length of the square hollow is b2; the side length of the third metal layer is a3, and the side length of the square hollow is b3.

[0047] The geometric parameters of the super-unit in step S4 are a1, b1, a2, b2, a3 and b3.

[0048] The step S4 is specifically as follows: using the TMM transmission matrix method and the FDTD electromagnetic simulation software to construct a mapping relationship between the geometric parameters of the three-dimensional metastructure unit and the resonant frequency of the third-order Lorentz resonance model, and according to the mapping relationship between the geometric parameters of the metastructure unit and the resonant frequency of the third-order Lorentz resonance model, the required wide-band phase slope of the metasurface is achieved by adjusting the geometric parameters of the metastructure unit, thereby completing the regulation of the wide-band phase slope of the metasurface applied to the invisibility cloak.

[0049] In this embodiment, the present invention realizes broadband phase slope control by establishing a multi-resonance model. The interaction between multiple resonances can, on the one hand, expand the range of reflection phase variation, and on the other hand, adjust the phase slope by optimizing each resonance characteristic, such as resonance intensity, resonance frequency, and number of resonances. The Lorentz model with n resonances can be expressed as ω i ,ω ip and γ i are the resonant frequency, plasma frequency and damping frequency of the i-th resonance respectively. The Lorentz model with three resonances can be realized by using a three-layer ring structure. The structural diagram of the superstructure unit is shown in Figure 3As shown in (a), the meta-unit is composed of three F4B dielectric layers (total thickness is 3.5 mm) and four metal layers. The interaction between the four metal layers can excite three magnetic resonances. The third-order Lorentz model can describe the electromagnetic response of the real meta-unit by adjusting the corresponding resonant frequencies f1, f2 and f3. Through the Lorentz model, the corresponding resonant frequencies can be adjusted to independently control the phase distribution in different frequency ranges (low, medium and high frequency bands). Figure 3 In the example, the superstructure unit is composed of three F4B spacer layers and four metal layers, where ε r =2.65+0.01i, p=10mm, the first layer of dielectric thickness d1=2mm, the second layer of dielectric thickness d2=1mm and the third layer of dielectric thickness d3=0.5mm, the remaining b1, b2, b3 and a1, a2, a3 are used to control the electromagnetic properties of the meta-unit. Different resonant frequencies f calculated by TMM i The reflection phase spectra of the three-resonance meta-unit with different structural parameters are obtained by FDTD simulation.

[0050] Figure 3 (b) shows the effect of the resonant frequency f2 on the reflection phase. At this time, the reflection phase is only sensitive to the intermediate frequency band response. The phase control of low-frequency / high-frequency resonance is similar to that of the intermediate frequency. In short, the resonant frequency f1 realizes the phase control of the low-frequency band, while f3 determines the phase response of the high-frequency band. By changing the three resonant frequencies at the same time, any reflection phase slope can be obtained. The results are shown in Figure 3 (a) shows that the reflection phase is mainly controlled by f1 at 7 and 8 GHz, by f2 at 9, 10 and 11 GHz, and by f3 at 12 GHz. By adjusting these three resonant frequencies, a linear reflection phase spectrum with different slopes can be obtained. By introducing more resonators, the phase slope variation range can be further extended, but the widest upper and lower frequency ratio is about 2:1 due to the phase control freedom and the thickness of the meta-unit.

[0051] In this embodiment, a multi-resonance superstructure is used to achieve the regulation of phase slope in a broadband range, thereby compensating for target objects in different height ranges. The present invention designs a 3D pyramid-shaped broadband invisibility cloak, which is composed of 1200 superstructures with an overall size of 360mm×360mm×48mm. To extract the height information of the pyramid, the broadband invisibility cloak needs to meet 18 different phase slope distributions, see Figure 2 By adjusting the structural parameters a1, a2, a3 and b1, b2 and b3, the corresponding structural dimensions are obtained, see Figure 4(a) and (b), these superstructures are simulated by FDTD to obtain their reflection amplitude spectra. It can be found that in the broadband range, the reflection amplitude is higher than 0.8. The reduction of reflection amplitude in a specific frequency band is mainly caused by the absorption effect of the material. Figure 4 Where Size is the size, x / p is the number of units, and Absorption ratio is the absorption rate.

[0052] Adoption (where A is the reflection amplitude; N' is the number of sampling points; i' is the sampling point number; r i The absorption effect of different dispersion units was simulated by simulating the absorption rate of the designed broadband cloak in the range of 8-11GHz and less than 3.4% at 12GHz, which verified the high-efficiency electromagnetic control characteristics of the broadband cloak. The designed superstructure was loaded on the surface of the stealth target, and an ultra-wideband fully polarized cloak was designed. The cloak was processed using standard PCB technology, and the target object was processed using 3D printing technology. Then the cloak and the target object were assembled and bonded, thus forming a broadband cloak sample.

[0053] In this embodiment, the cloak is then experimentally tested in a microwave environment. To verify the broadband and full polarization characteristics of the cloak, linearly polarized waves of different modes (TE, TM and 45° polarization) and different frequencies are used to excite the cloak. Figure 5 The electric field and scattered field distribution obtained experimentally under vertical incidence are given. First, the target objects loaded and unloaded with the cloak are excited by TM polarized electromagnetic waves, and the electric field signal is detected in the xoz and yoz planes by the probe antenna. In order to clearly show the stealth effect, the incident field information is removed here, so that the obtained signal field only contains the scattered field. Figure 5 (a) It can be seen that after loading the broadband invisible cloak, when the electromagnetic wave is excited, the target object obtains a pure flat electric field signal in the range of 8-12GHz, verifying the perfect stealth effect in this frequency band. Figure 5 (c) Strong electromagnetic scattering occurs, so it is easy to detect. By rotating the transmitting antenna 45°, Figure 5 (b) and Figure 6 (c) shows the electric field distribution of the cloak and the target object under this polarization condition. Due to the symmetry of the cloak structure, we observed a similar flat electric field distribution, and some scattering is caused by the edge scattering effect of the cloak. Figure 5(df) shows the scattering field distribution at different angles and frequencies when the cloak is loaded and not loaded. In the working frequency range of 8-12GHz, when the cloak is loaded, almost all unnecessary scattering signals are effectively suppressed, leaving only vertical mirror reflection signals, which is completely consistent with the scattering of the plane metal plate, further verifying the perfect working characteristics of the cloak. For the target object without the cloak, strong scattering signals are observed in the ±30° direction. Figure 5 In the figure, E is the electric field vector; k is the transmission direction; f1, f2, f3, f4 and f5 are all resonant frequencies.

[0054] In this embodiment, the electromagnetic performance of the broadband invisible cloak at different oblique incident angles was tested. Figure 6 It can be seen that for oblique incident electromagnetic waves at θ = 10° and 20°, the broadband invisibility cloak has a scattering signal consistent with that of a flat metal plate, see Figure 6 (a) and Figure 6 (c) The scattering is completely different from when the cloak is not loaded. Figure 6 (eh) shows the scattering field when the cloak is loaded and not loaded under oblique incidence. When the broadband cloak is loaded, the main beam mainly appears at the mirror angles of θ=10° and 20°, while the target object without the cloak has a strong scattering effect in two signal directions. Therefore, under oblique incidence angles, the cloak can achieve broadband invisibility for the target object. The present invention adopts a multi-mode resonance model to propose a phase slope control method within a broadband range, thereby solving the problem of broadband electromagnetic stealth and preparing a pyramid cloak with good stealth effect, broadband and full polarization characteristics, which has favorably promoted the practical application of meta-structure cloaks. Figure 6 In the equation, H is the magnetic field vector; θ is the oblique incident angle; and Angle is the angle.

Claims

1. A method for controlling broadband phase slope of a metasurface used in an invisible cloak, characterized in that: The following steps are involved: S1. Determine the phase distribution that the microstructure on the invisible cloak needs to satisfy, and determine the broadband phase slope of the metasurface that needs to be satisfied based on the phase distribution; S2. Establish an N-order Lorentz resonance model for realizing broadband phase slope control of metasurface; S3. Construct a superstructure unit based on the third-order Lorentz resonance model; S4. According to the mapping relationship between the geometric parameters of the metastructure unit and the resonant frequency of the third-order Lorentz resonance model, the required broadband phase slope of the metasurface is achieved by adjusting the geometric parameters of the metastructure unit, thereby completing the regulation of the broadband phase slope of the metasurface applied to the invisibility cloak.

2. The method for controlling the broadband phase slope of a metasurface applied to an invisible cloak according to claim 1, characterized in that: The expression of the phase distribution that the microstructure on the invisible cloak needs to satisfy in step S1 is: g(f j ,p j )=π-2k j h(x)cos(a) k j =2πf j / c Among them, g(f j ,p j ) is the phase distribution that the microstructure on the invisible cloak needs to satisfy; f j is the operating frequency; p j is the polarization of the excitation electromagnetic wave; π is the circumference of a circle; k j is the propagation constant; h(·) is the height information function of the microstructure on the surface of the cloak; x is the coordinate corresponding to the projection of the microstructure on the surface of the cloak on the X-axis; cos(·) is the cosine function; α is the incident angle information; c is the speed of light.

3. The method for controlling broadband phase slope of a metasurface applied to an invisible cloak according to claim 1, characterized in that: The expression of the N-order Lorentz resonance model in step S2 is: Among them, μ 2eff is the N-order Lorentz resonance model; ω is the operating frequency; ω1 is the resonance frequency of the first resonance; i is the resonance order, γ1 is the damping frequency of the first resonance; ω 1p is the first resonant plasma frequency; ω i is the resonant frequency of the ith resonance; γ i is the i-th resonant damping frequency; ω ip is the plasma frequency of the ith resonance; ω n is the resonant frequency of the nth resonance; γ n is the nth resonant damping frequency; ω np is the plasma frequency of the nth resonance.

4. The method for controlling the broadband phase slope of a metasurface applied to an invisible cloak according to claim 1, characterized in that: In step S3, the superstructure unit includes a first metal layer, a first F4B dielectric layer, a second metal layer, a second F4B dielectric layer, a third metal layer, a third F4B dielectric layer and a fourth metal layer connected in sequence from top to bottom.

5. The method for controlling the broadband phase slope of a metasurface applied to an invisible cloak according to claim 4, characterized in that: The first F4B dielectric layer is 10 mm long, 10 mm wide, and has a thickness of d1=2 mm; the second F4B dielectric layer is 10 mm long, 10 mm wide, and has a thickness of d2=1 mm; the third F4B dielectric layer is 10 mm long, 10 mm wide, and has a thickness of d3=0.5 mm.

6. The method for controlling the broadband phase slope of a metasurface applied to an invisible cloak according to claim 4, characterized in that: The fourth metal layer is a square metal sheet with a thickness of 0.036 mm and a side length of 10 mm; the first metal layer, the second metal layer and the third metal layer are all square metal sheets with a thickness of 0.036 mm and a square hollow in the middle; the side length of the first metal layer is a1, and the side length of the square hollow is b1; the side length of the second metal layer is a2, and the side length of the square hollow is b2; the side length of the third metal layer is a3, and the side length of the square hollow is b3.

7. The method for controlling the broadband phase slope of a metasurface applied to an invisible cloak according to claim 6, characterized in that: The geometric parameters of the super-unit in step S4 are a1, b1, a2, b2, a3 and b3.

8. The method for controlling broadband phase slope of a metasurface applied to an invisible cloak according to claim 7, characterized in that: The step S4 is specifically as follows: using the TMM transmission matrix method and the FDTD electromagnetic simulation software, constructing a mapping relationship between the geometric parameters of the three-dimensional meta-structure unit and the resonant frequency of the third-order Lorentz resonance model; and The system achieves the required wide-band phase slope of the metasurface by adjusting the geometric parameters of the metacell. Completed the regulation of broadband phase slope of metasurface used in invisible cloaks.