Hinge type mechanical reconfigurable multifunctional transmission-reflection metasurface and design method

Abstract

The invention discloses a hinge type mechanical reconfigurable multifunctional transmission-reflection metasurface and a design method thereof. The metasurface is formed by arranging M * M metasurface units A and B in a staggered manner; the metasurface unit A and the metasurface unit B are each formed by stacking five layers including a metal structure, a dielectric plate, a resin plate, a dielectric plate and a metal structure from top to bottom, the first layer metal and the fifth layer metal of the unit A are double-ring symmetrical communicating groove resonators and metal floors, and the first layer metal and the fifth layer metal of the unit B are double-layer three-ring symmetrical communicating groove resonators. All metals are etched on the F4B dielectric plate; the third layer of resin plate is used for unit mechanical rotation to form phase and period regulation and control; a hinge structure assembly is designed through a 3D printing technology, and then M * M dielectric plates with etched metal structures are bonded with a resin plate to form a metasurface; the invention provides a hinge type mechanical reconfigurable multifunctional transmission-reflection metasurface, realizes circular polarization electromagnetic wave regulation and control and a variable wave beam and focus integrated device, and has the advantages of reconfigurability, high integration level and the like.

Description

Technical Field

[0001] The present invention belongs to the interdisciplinary field of the combination of novel artificial electromagnetic surfaces and microwave electromagnetic control technology, and relates to a reconfigurable transflective metasurface that simultaneously realizes beam changing and zooming functions through mechanical rotation. Background Art

[0002] Reconfigurable transflective metasurfaces mostly use electrically adjustable methods to change the physical properties or spatial distribution of their units. While this has promoted the widespread application of dynamic electromagnetic wave manipulation, it still faces challenges such as high cost, complex structural composition, difficulty in manufacturing, and complex control systems. Mechanical manipulation, on the other hand, allows for the manipulation of electromagnetic waves by reconfiguring the unit morphology within the metasurface. This technology has broader applicability because it does not rely on material properties. Inspired by the diverse deformation patterns found in nature, researchers have continuously attempted to reconfigure the geometric shape, spatial arrangement, and other dimensions of the basic units through mechanical manipulation, thereby regulating the electromagnetic response of the units. For example, early experiments have utilized stretchable materials (such as polydimethylsiloxane and silicone resin) to achieve reconfigurable metasurfaces. However, these materials can only withstand planar deformation under tensile strain, limiting their modulation capabilities to resonant frequency and amplitude. Furthermore, currently reported mechanically reconfigurable multifunctional metasurfaces are mostly confined to half-space, failing to maximize the powerful electromagnetic manipulation capabilities of reconfigurable metasurfaces and failing to meet the practical demand for devices that can flexibly manipulate electromagnetic waves across the entire space in applications such as communications. Summary of the Invention

[0003] Based on the above problems, the present invention proposes a hinged mechanical reconfigurable multifunctional transmissive-reflective metasurface and design method. The design method incorporates 3D printing technology and paper cutting method, and changes the unit period and phase by rotating the hinge structure. When the metasurface is stretched, the diagonal units rotate clockwise along the vertex, while the adjacent units rotate in the opposite direction. In this way, an interlaced structure is designed to construct two channels, reflection and transmission. At the same time, a connection is established between the rotation-related geometric phase and the rotation law, and a frequency-reused hinged mechanical reconfigurable multifunctional transmissive-reflective metasurface is designed. The variable beam function is realized in the reflection channel at f1 = 8 GHz, and the zoom function is realized in the transmission channel at f2 = 10.7 GHz.

[0004] The present invention discloses a hinged mechanically reconfigurable multifunctional transflective metasurface, wherein the hinged mechanically reconfigurable multifunctional transflective metasurface comprises a plurality of 2×2 unit modules;

[0005] The 2×2 unit module includes a hinged mechanical metasurface unit A and a hinged mechanical metasurface unit B, and the hinged mechanical metasurface unit A and the hinged mechanical metasurface unit B are arranged in a staggered manner;

[0006] The hinged mechanical metasurface unit A and the hinged mechanical metasurface unit B each include a first metal layer, a second dielectric layer, a third resin plate layer, a fourth dielectric layer, and a fifth metal layer stacked sequentially from top to bottom;

[0007] In hinged mechanical metasurface unit A, the first metal layer is a double-ring symmetrical connected slot resonator, and the fifth metal layer is a metal floor. In hinged mechanical metasurface unit B, the first and fifth metal layers have the same structure, both of which are triple-ring symmetrical connected slot resonators.

[0008] The first and fifth metal layers are both etched on the F4B dielectric plates of the second and fourth dielectric layers; the third resin plate layer is configured as a hinge structure and is connected to the third resin plate layer of the adjacent unit via the hinge structure;

[0009] The hinge structure can switch the metasurface period by rotating and unrotating the unit, where the period is p when the unit is not rotated and the period is α when the unit is rotated.

[0010] Furthermore, the hinge structure includes a resin body, a hinge, and a hinge rotation column;

[0011] Four hinge rotating columns are respectively set at the four corners of the resin body. Long holes matching the hinge rotating columns are opened at both ends of the hinge. One end of the hinge is connected to the hinge rotating column of the unit through the long hole, and the other long hole is connected to the hinge rotating column of the adjacent unit.

[0012] When the unit is not rotated, the hinge structure is in a closed state, and the edges of adjacent units are in contact. When the unit rotates, it is in a stretched state, and the units along the diagonal rotate α in the same direction, while the adjacent units rotate α in the opposite direction along the vertices, that is, the units rotate ±α, and the corner vertices of adjacent units are in contact.

[0013] Furthermore, the dual-ring symmetrical connecting groove resonator includes a dual-ring resonator inner ring groove, a dual-ring resonator outer ring groove, and two symmetrical dual-ring resonator connecting grooves connecting the dual-ring resonator inner ring groove and the dual-ring resonator outer ring groove, which are etched on the metal layer;

[0014] The two dual-ring resonator connecting slots are located on the same straight line. In the initial state, the angle β between the dual-ring resonator connecting slot and the x-axis is A is 0°;

[0015] The outer diameter of the outer ring slot of the double ring resonator r A4 =4.8mm, inner diameter of outer ring groove of double ring resonator r A3 =4.6mm, outer diameter of inner ring groove of double ring resonator r A2 =4.2mm, inner diameter of the ring groove of the double ring resonator r A1 =3.9mm, dual ring resonator connecting groove width g A =0.2mm.

[0016] Furthermore, the three-ring symmetrical connecting slot resonator includes a three-ring resonator inner ring slot, a three-ring resonator middle ring slot, a three-ring resonator outer ring slot, and two symmetrical three-ring resonator connecting slots connecting the inner ring of the three-ring slot resonator and the outer ring of the three-ring slot resonator, all etched on the metal layer;

[0017] The two three-ring resonator connecting slots are located on the same straight line. In the initial state, the angle β between the three-ring resonator connecting slot and the x-axis is B is 0°;

[0018] The outer diameter r of the outer ring groove of the three-ring resonator B6 =3.6mm, inner diameter r of the outer ring groove of the three-ring resonator B5 =3.4mm, the outer diameter of the ring groove in the three-ring resonator r B4 =3mm, inner diameter r of the ring groove in the three-ring resonator B3 =2.8mm, outer diameter of inner ring groove of three-ring resonator r B2 =2.4mm, inner diameter r of the inner ring groove of the three-ring resonator B1 =2.1mm, width of the connecting groove of the three-ring resonator g B =0.2mm.

[0019] A method for designing a hinged mechanically reconfigurable multifunctional transmissive-reflective metasurface is also provided. The method for designing a hinged mechanically reconfigurable multifunctional transmissive-reflective metasurface comprises the following steps:

[0020] Step 1: Based on the intrinsic connection between the internal rotation law of the hinged mechanical metasurface and the geometric phase, that is, the rotation of the metasurface unit vertex can be converted into the rotation of the metasurface unit central axis, a dual-unit staggered structure is constructed;

[0021] Step 2: Using frequency isolation, design a low-crosstalk hinged mechanical metasurface unit A and a hinged mechanical metasurface unit B, wherein the operating frequency of the hinged mechanical metasurface unit A is f1, and the operating frequency of the hinged mechanical metasurface unit B is f2;

[0022] Step 3: Predetermine the functions of the two channels, reflection and transmission, and design the initial phase distribution of the hinged mechanical reconfigurable multifunctional transmissive-reflective metasurface based on the staggered structure.

[0023] Step 4: Based on the principle of geometric phase control, a hinged mechanically reconfigurable multifunctional transmissive-reflective metasurface is constructed according to the initial phase distribution in step 3 at a certain rotation angle α.

[0024] Furthermore, in step 1, the hinged mechanical reconfigurable multifunctional transflective metasurface includes a hinged mechanical metasurface unit A and a hinged mechanical metasurface unit B, wherein the hinged mechanical metasurface unit A and the hinged mechanical metasurface unit B are arranged in an interlaced manner;

[0025] Both hinged mechanical metasurface unit A and hinged mechanical metasurface unit B include hinge structures, which are connected to adjacent units through the hinge structure. When the hinge structure rotates along the vertex by an angle α, the units along the diagonal rotate in the same direction by α, while the adjacent units rotate in the opposite direction by α along the vertex, resulting in a unit azimuth angle change ζ related to the structural rotation angle α, that is, α = ±ζ;

[0026] The hinge structure can be rotated at a period p and a period p When the unit rotates ±45°, the cycle is

[0027] According to the geometric phase characteristics, when a circularly polarized wave is incident, the geometric phase of its cross-polarized wave has a 2-fold relationship with the rotation angle of the metal structure of the metasurface unit;

[0028] Geometric phase change of hinged mechanical metasurface unit A Geometric phase change of hinged mechanical metasurface unit B “±” represents the handedness of the incident circularly polarized wave.

[0029] Furthermore, in step 2, the hinged mechanical metasurface unit A and the hinged mechanical metasurface unit B each include a first metal layer, a second dielectric layer, a third resin plate layer, a fourth dielectric layer, and a fifth metal layer stacked sequentially from top to bottom;

[0030] In hinged mechanical metasurface unit A, the first metal layer is a double-ring symmetrical connected slot resonator, and the fifth metal layer is a metal floor. In hinged mechanical metasurface unit B, the first and fifth metal layers have the same structure, both of which are triple-ring symmetrical connected slot resonators.

[0031] The first and fifth metal layers are both etched on the F4B dielectric plates of the second and fourth dielectric layers;

[0032] The third resin plate layer is arranged in a hinge structure and is connected to the third resin plate layer of an adjacent unit via the hinge structure.

[0033] Furthermore, in step 2, the dual-ring symmetrical connecting groove resonator includes a dual-ring resonator inner ring groove, a dual-ring resonator outer ring groove, and two symmetrical dual-ring resonator connecting grooves connecting the dual-ring resonator inner ring and the dual-ring resonator outer ring etched on the metal layer;

[0034] The three-ring symmetrical connecting groove resonator includes a three-ring resonator inner ring groove, a three-ring resonator middle ring groove, a three-ring resonator outer ring groove and two symmetrical three-ring resonator connecting grooves connecting the inner ring of the three-ring resonator and the outer ring of the three-ring resonator;

[0035] The structural parameters of the double-ring symmetrical connected slot resonator and the triple-ring symmetrical connected slot resonator were simulated and optimized respectively by using the parameter scanning method of CST software to determine the optimal structural parameters for the reflection amplitude of the double-ring symmetrical connected slot resonator and the transmission amplitude of the triple-ring symmetrical connected slot resonator.

[0036] Furthermore, in step 3, the initial phase distribution of the frequency-reused hinged mechanically reconfigurable multifunctional metasurface is designed according to the staggered dual-unit combination method;

[0037] The deflection angle is θ r Beam phase distribution as follows:

[0038]

[0039] y j represents the coordinate of the jth unit along the y-axis, λ1 represents the wavelength corresponding to the operating frequency f1, which is related to the operating frequency and satisfies that the speed of light c is equal to the wavelength λ1 multiplied by the operating frequency f1;

[0040] Focusing curved surface phase distribution with focal length F as follows:

[0041]

[0042] x i,j Indicates the coordinate of the (i, j)th unit on the x-axis, y i,j represents the coordinate of the (i, j)th unit on the y-axis, F is the focal length, λ2 represents the wavelength corresponding to the operating frequency f2, which is related to the operating frequency and satisfies that the speed of light c is equal to the wavelength λ2 multiplied by the operating frequency f2;

[0043] Initial phase distribution of the staggered structure Use the matrix method to connect the two:

[0044]

[0045] represents the phase distribution of the hinged mechanical metasurface unit A, Represents the phase distribution of the hinged mechanical metasurface unit B; the matrix M1(i,j)=(1+(-1) i+j ) / 2 and M2(i,j)=(1-(-1) i+j) / 2 represents two arrangements of the hinged mechanical metasurface unit A and the hinged mechanical metasurface unit B in the staggered structure. When M1(i,j) and M2(i,j) are equal to 1, it means that the hinged mechanical metasurface unit A or the hinged mechanical metasurface unit B is arranged in the metasurface structure; when M1(i,j) and M2(i,j) are equal to 0, it means that the metasurface structure does not arrange units; where i and j represent the number of rows and columns of the matrix M1 or M2, respectively.

[0046] Furthermore, in step 4, the initial phase distribution of the staggered structure Design the rotation angle β of the double-ring symmetrical connected slot resonator in hinged mechanical metasurface unit A and hinged mechanical metasurface unit B A and the rotation angle β of the three-ring symmetrical connected slot resonator B ,in,

[0047] The beneficial effects achieved by the present invention are:

[0048] The present invention is based on mechanical control of electromagnetic waves and combines 3D printing technology to disclose a hinged mechanically reconfigurable multifunctional transmissive-reflective metasurface. According to the rules of unit vertex rotation and center rotation, a topological configuration composite unit is designed. It consists of a reflective unit A and a transmissive unit B arranged in an alternating manner and rotating simultaneously, thereby realizing independent wavefront control of the two channels. The composite unit uses 3D printing technology to design a hinge structure and integrates it with a flexible paper-cutting method to further increase the degree of freedom of control of the structure. The above-mentioned hinged structure is used to assemble and manufacture a multifunctional transmissive-reflective metasurface, which not only improves the flexibility of the reconfigurable metasurface in controlling electromagnetic waves, but also expands the range of control space. Finally, to verify the feasibility of this method, a reflective variable beam and a transmissive variable focus integrated metasurface were produced, and its control capability was verified through experiments. The present invention can be used to realize reconfigurable metasurfaces under different materials / configurations and bands, providing new ideas and methods for the design of mechanically adjustable devices.

[0049] Compared with electrically controlled metasurfaces that use active components (such as switching diodes and varactor diodes), the present invention eliminates active devices and peripheral circuits and can be controlled simply by rotation, greatly reducing costs.

[0050] The electrically controllable metasurface of active components has a certain amount of static power consumption because it contains a large number of switching diodes or varactor diodes and peripheral circuits. However, the present invention has the unique advantage of zero static power consumption.

[0051] Compared with existing mechanically reconfigurable metasurfaces, the present invention can simultaneously achieve wavefront control of both reflection and transmission channels;

[0052] Compared with existing metasurface devices, the present invention is easy to transport because it can be stretched, compressed and assembled. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 Schematic diagram of a hinged mechanically reconfigurable multifunctional transflective-reflective metasurface.

[0054] Figure 2 The rotation patterns of hinged mechanically adjustable metasurface units. (a) Undeformed state (mode 1); (b) Deformed state with a rotation angle of a; (c) Deformed state with a rotation angle of 45° (mode 2); (d) Two-unit staggered structure.

[0055] Figure 3 This is the phase distribution after the 8×8 unit is rotated.

[0056] Figure 4 Schematic diagram of the metasurface unit. (a) Unit A and (b) Unit B.

[0057] Figure 5 Top view of metasurface unit A and the reflected amplitude and phase distributions at different rotation states. (a) and (c) Top view of unit A with no rotation and 45° rotation. (b) and (d) Reflected amplitude and phase distributions of unit A with no rotation and 45° rotation under circularly polarized wave incidence.

[0058] Figure 6 Top views of metasurface unit B and the transmission amplitude and phase distributions at different rotation states. (a) and (c) Top views of unit B with no rotation and -45° rotation. (b) and (d) Transmission amplitude and phase distributions of unit B with no rotation and -45° rotation under circularly polarized wave incidence.

[0059] Figure 7 The middle layer of the hinge structure. (a) Top view; (b) Transparent top view; (c) Top view after 3D printing.

[0060] Figure 8 Front views of unit A with a hinge structure and the reflected amplitude and phase distributions at different rotational states. (a) and (c) Front views of unit A with no rotation and with it rotated 45°. (b) and (d) Reflected amplitude and phase distributions of unit A with no rotation and with it rotated 45° under incident circularly polarized waves.

[0061] Figure 9 Front views of unit B containing a hinge structure and the transmission amplitude and phase distributions at different rotational states. (a) and (c) Front views of unit B with no rotation and -45° rotation. (b) and (d) Transmission amplitude and phase distributions of unit B with no rotation and -45° rotation under circularly polarized wave incidence.

[0062] Figure 10 The current distribution of the metasurface unit when not rotated. (a) Current distribution on the xy and xz planes under 8 GHz circularly polarized wave excitation; (b) Current distribution on the xy and xz planes under 10.7 GHz circularly polarized wave excitation.

[0063] Figure 11 The current distribution of the metasurface unit when rotated 45°. (a) Current distribution on the xy and xz planes under 8 GHz circularly polarized wave excitation; (b) Current distribution on the xy and xz planes under 10.7 GHz circularly polarized wave excitation.

[0064] Figure 12 Top view of the simulation model of the hinged mechanically reconfigurable multifunctional transflective-reflective metasurface. (a) Mode 1; (b) Mode 2.

[0065] Figure 13 Initial phase distribution of the hinged, mechanically reconfigurable, multifunctional transflective metasurface. (a) Metasurface phase distribution; (b) Phase distribution at a deflection angle of 30°; (c) Focus phase distribution at a focal point of 100 mm; (d) Arrangement of units A and B.

[0066] Figure 14 Design flow chart for hinged mechanically reconfigurable multifunctional transflective-reflective metasurface.

[0067] Figure 15 Schematic diagram of processing thin dielectric substrates for PCB technology. (a) Top view; (b) Bottom view.

[0068] Figure 16 Far-field simulation results of the deflected beam under 8 GHz circularly polarized wave incidence. (a) Mode 1 and (b) Mode 2.

[0069] Figure 17 It is the far-field experimental test environment.

[0070] Figure 18 Comparison of the experimental and simulated normalized electric field strength of the variable beam under 8 GHz circularly polarized wave incidence. (a) Mode 1 and (b) Mode 2.

[0071] Figure 19 Near-field simulation results of a zoom lens for a circularly polarized wave incident at 10.7 GHz. Normalized electric field intensity distributions for mode 1 in the (a) xz and (c) xy planes. Normalized electric field intensity distributions for mode 2 in the (b) xz and (d) xy planes.

[0072] Figure 20 It is the test environment for near-field experiments.

[0073] Figure 21Experimental test results of zoom transmission under 10.7 GHz circularly polarized wave incidence. Normalized electric field intensity distributions for mode 1 (a) in the xz plane and (c) in the xy plane. Normalized electric field intensity distributions for mode 2 (b) in the xz plane and (d) in the xy plane.

[0074] Figure 22 Figure 1 shows the normalized simulated and tested electric field intensity distributions of the focusing function at y = 0 under the incident 10.7 GHz circularly polarized wave. (a) Mode 1; (b) Mode 2. DETAILED DESCRIPTION

[0075] To facilitate understanding of the present invention, the hinged mechanically reconfigurable transflective metasurface and its design method are described in detail below using a specific example. As a principle prototype, in order to more clearly understand the above-mentioned objects, features, and advantages of this application, the present application is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that the embodiments of this application and the features therein can be combined with each other unless there is a conflict.

[0076] The present invention provides a hinged mechanically reconfigurable multifunctional transflective metasurface. Figure 1 As shown, a topological composite unit consisting of an alternating arrangement of units A and B was designed through a comprehensive phase control method that combines vertex rotation with center rotation. Units A and B are, respectively, a reflective structure with a metal backplane and a transmissive structure with a double-layer metal resonator. The metasurface array distribution was derived using a geometric phase control method. Subsequently, hinged structural units were designed by integrating origami and 3D printing technologies. These units were combined into a mechanically reconfigurable transmissive-reflective metasurface capable of independent and adjustable wavefront control in two circularly polarized channels. Simulation and experimental results show that when mode 1 is stretched to mode 2, a beamforming function is achieved in the 8 GHz reflection channel, with the deflection angle decreasing from 30° to 20.5°. In the 10.7 GHz transmission channel, a zoom function is achieved, with the focal point decreasing from 150 mm to 320 mm.

[0077] Specifically, a design method for a hinged mechanically reconfigurable multifunctional transmissive-reflective metasurface includes the following steps:

[0078] Step 1: construct a dual-unit staggered structure based on the rotation characteristics of the hinged metasurface;

[0079] First, the rotation characteristics of the structure are studied. Figure 2Figures (a) and (b) illustrate the deformation process of the designed metasurface's 2×2 unit module structure. When the structure is rotated by an angle α along its vertices, the diagonal square units all rotate in the same direction (clockwise or counterclockwise), while the adjacent square units rotate in the opposite direction along their vertices. This results in a change in the unit's azimuth angle (the angle of rotation of the unit around its central axis) by a factor of ζ, related to the structural rotation angle α, i.e., α = ±ζ. This mechanism can cleverly control the phase difference between adjacent units. Furthermore, due to the "rotating square" approach, the unit period can also be changed.

[0080] like Figure 2 As shown, during the conversion process Always equal to Its relationship with the structural rotation angle α is as follows:

[0081]

[0082] The subscript p indicates the direction, and the superscript p indicates the rotation state.

[0083] Further Figure 3 The phase arrangement is studied by taking the 8×8 unit module as an example. According to the geometric phase characteristics, when the circularly polarized wave is incident, the geometric phase of the cross-polarized wave is twice the rotation angle of the metal structure of the metasurface unit. Therefore, the geometric phase change of the unit in the blue square is Geometric phase change of the cell in the red square Here "±" represents the rotation direction of the incident circularly polarized wave. Combined with the subsequent unit design, the reflection unit A is located in the blue square and the transmission unit B is located in the red square. Therefore, the phase and unit cycle All of them can be flexibly controlled by rotating the paper-cut unit angle α. This comprehensive phase control method that combines vertex rotation and center rotation provides a special dynamic control method for reconfigurable metasurfaces. This paper will construct a metasurface through the direction-dependent PB phase and combine it with the paper-cut method for design. The paper-cut method in this design is to achieve regular transformation by cutting and rotating the pattern. Among them, the adjustable mechanism of the mechanically reconfigurable metasurface is to change the structural rotation angle α by synchronously stretching or contracting in two lateral directions, thereby regulating the electromagnetic response and spatial arrangement of the metasurface unit, and ultimately achieving flexible control of the wavefront.

[0084] The following will take the structure with a rotation angle of α = 45° as an example to illustrate the control mechanism of the hinged mechanical reconfigurable metasurface. Figure 2 As shown, the unit cycle becomes the original The undeformed structure is now called Mode 1, and the deformed structure after 45° rotation is called Mode 2.

[0085] Step 2: Using frequency isolation, design low-crosstalk hinged mechanical metasurface unit A and hinged mechanical metasurface unit B;

[0086] The metasurface is composed of M×M units A and B with different rotation angles, which are arranged periodically at equal intervals in a plane and are staggered; wherein unit A has the characteristics of high reflection amplitude at frequency f1 and low reflection amplitude at frequency f2, and unit B has the characteristics of low transmission amplitude at frequency f1 and high transmission amplitude at frequency f2.

[0087] like Figure 4 As shown, the two metasurface units A and B are both composed of a five-layer structure stack of "metal structure-dielectric plate-3D printed resin plate-dielectric plate-metal structure". In order to realize the integrated transmission-reflection metasurface, unit A is a reflective structure, in which the first metal layer is named a double-ring symmetrical connected slot resonator, and the fifth metal layer is designed to have a metal floor; while unit B is a reflective structure, in which the first and fifth metal layers are named double-layer three-ring symmetrical connected slot resonators, and the two layers are exactly the same; the first and fifth metal layers are both etched on the F4B dielectric plates (phase dielectric constant of 2.65, loss tangent of 0.001) of the second and fourth dielectric layers; the third resin plate layer uses a 3D printed resin plate (ABS-M30 material, relative dielectric constant of 2.7, loss tangent of 0.005) and is mainly designed as a hinge device to change the unit period;

[0088] According to the requirements of the above-mentioned metasurface unit characteristics, the structural parameters of units A and B are simulated and optimized using the scanning parameter method of CST software to determine the optimal structural parameters for the reflection amplitude of unit A and the transmission amplitude of unit B. The structural parameters of units A and B are optimized as follows: p = 10mm, r A1 =3.9mm, r A2 =4.2mm, r A3 =4.6mm, r A4 =4.8mm, g A =0.2mm, r B1 =2.1mm, r B2 =2.4mm, r B3 =2.8mm, r B4 =3mm, r B5 =3.4mm, r B6 =3.6mm, g B =0.2mm, h1=0.17mm, h2=6mm, the thickness of the metal structure is 0.018mm.

[0089] To investigate the electromagnetic properties of metasurface units A and B, CST full-wave simulation was used to further analyze the electromagnetic reflection and transmission of the units under circularly polarized wave incidence. The x and y directions were set as "unit cell" boundaries to simulate infinite boundaries, while the z direction was set to "open (odd space)."

[0090] According to the characteristics of the above-mentioned metasurface structure, when stretched from mode 1 to mode 2, unit A (B) is equivalent to the original unit rotating 45° counterclockwise (clockwise) along its central axis, which is recorded as ζ = 45° (-45°). Figure 5 (a) and (c) show the top view of the unit cell A when mode 1 is stretched to mode 2. 0° and 45° represent modes 1 and 2, respectively, and β A It represents the angle of the double-ring symmetrical connected slot resonator in unit A rotated counterclockwise on the xoy plane. Its initial state is that the opening slot of the resonator is along the x-axis. Figure 5 Figures (b) and (d) show the amplitude and phase responses for circularly polarized waves. For both α = 0° and 45°, the resonant mode of unit A appears at an operating frequency of 8 GHz, and the phase difference of the cross-polarized wave is twice the rotation angle. Because the bottom of unit A is entirely metal-floored in mode 1, its reflection amplitude is close to 1. However, in mode 2, due to the 50% duty cycle of the metal floor, the reflection amplitude drops to 0.8. Figure 6 (a) and (b) show the top view of the unit cell B when mode 1 is stretched to mode 2. B It represents the counterclockwise rotation angle of the double-layer three-ring symmetrical connected slot resonator in unit B on the xoy plane. Its initial state is that the opening slot of the resonator is along the x-axis. Figure 6 (b) and (d) show the amplitude and phase responses of unit B under circularly polarized wave incidence. When α = 0° and 45°, the resonant mode appears at an operating frequency of 10.7 GHz, and the phase difference of the cross-polarized wave is twice the rotation angle. Its transmission amplitude is above 0.8 in mode 1. However, in mode 2, due to the duty cycle of 50%, the transmission amplitude drops to 0.7. Most importantly, in both modes, the reflection amplitude of unit A at 10.7 GHz is less than 0.1, and the transmission amplitude of unit B at 8 GHz is less than 0.1, indicating that the two metasurface units can be independently controlled in the staggered structure.

[0091] In order to make the metasurface unit flexible, the hinge structure is designed by 3D printing technology, so it is necessary to integrate the structure into the unit for simulation. Figure 7 The middle hinge structure is used as the middle layer of the unit. Modeling is done using CST simulation software. Figure 7 (a) and (b) show the top view and transparent top view of the middle layer of the unit, respectively. Figure 7(c) shows the middle layer of the printed unit. The hinge structure consists of three parts: the resin body, the hinge, and the hinge pivot. When the hinge structure is stretched to 45°, the distance between the pivots of adjacent units increases, creating a gap between them. This ensures that adjacent units can close together when not rotating.

[0092] Figure 8 and Figure 9 The electromagnetic response characteristics of units A and B containing hinge structures under circularly polarized wave incidence are given. For the reflection unit A, the reflection amplitude remains basically unchanged, the phase changes, but the phase difference is maintained at the rotation angle β at 8GHz. A For unit B, when not deformed, due to the gap in the hinge structure, the transmission efficiency is Figure 6 The amplitude of (b) decreases by 0.1. When the deformation is 45°, the bandwidth with an amplitude of 0.7 or more becomes narrower, but the operating frequency band is still 10.7 GHz, and the phase difference between the two is basically the resonator rotation angle β B This indicates that the design is suitable for phase-controlled metasurfaces. Next, by analyzing the current distribution at two frequency points, we can further understand the electromagnetic effects under transflection conditions, thereby exploring the crosstalk of metasurface units in the staggered structure. Figure 10 As shown in (a) and (b), when a circularly polarized wave of 8 GHz is incident, a current is generated in the double-ring symmetrical connected slot resonator at the top of unit A, showing a strong local electric resonance effect. In sharp contrast, when a circularly polarized wave is incident at 10.7 GHz, the current is concentrated on the double-layer three-ring symmetrical connected slot resonator on the top and bottom surfaces of unit B, causing resonant transmission. At these two frequency points, the remaining current is very weak, indicating that they have almost no electromagnetic response. Therefore, it is shown that the use of this slot resonator can reduce internal mutual coupling, provide good isolation effect, and ensure that units A and B can achieve independent dual-channel wavefront control.

[0093] like Figure 11 As shown in (a) and (b), for mode 2, when an 8 GHz circularly polarized wave is incident on the unit, the current is also primarily concentrated in the top two-ring symmetrical connected slot resonator of unit A, indicating that the reflection channel is effective. In the 11.2 GHz transmission channel, strong current distribution is observed in the double-layer three-ring symmetrical connected slot resonator of unit B. The remaining current in both units is very weak, indicating minimal crosstalk between them and demonstrating that the two units can be independently controlled.

[0094] Step 3: Predetermine the functions of the two channels, reflection and transmission, and design the phase distribution of the hinged mechanically reconfigurable multifunctional transmissive-reflective metasurface based on the staggered structure;

[0095] Currently, reconfigurable array antennas have attracted much attention in the fields of microwave radar detection and adaptive communications due to their dynamic variable beam scanning capabilities. In comparison, although traditional array antennas can achieve variable beam scanning through electrically controlled phase shifters, they require a complex and costly phase shifter network and feeding system. In addition, focusing can achieve concentrated energy transmission, which helps to increase communication distance and is commonly used in satellite communications and ground base stations. Therefore, the present invention integrates two functions into a reconfigurable metasurface, with the reflection and transmission channels realizing the variable beam and zoom functions respectively, providing a new solution for mechanically reconfigurable multifunctional metasurface integrated devices.

[0096] The initial phase distribution of the frequency-reused hinged mechanical reconfigurable multifunctional metasurface is designed according to the staggered dual-unit combination in step 1.

[0097] According to the generalized Snell's law, the deflection angle is θ r Beam phase distribution as follows:

[0098]

[0099] y j represents the coordinate of the jth unit along the y-axis, λ1 represents the wavelength corresponding to the operating frequency f1, which is related to the operating frequency and satisfies that the speed of light c is equal to the wavelength λ1 multiplied by the operating frequency f1;

[0100] Focusing curved surface phase distribution with focal length F as follows:

[0101]

[0102] x i,j Indicates the coordinate of the (i, j)th unit on the x-axis, y i,j represents the coordinate of the (i, j)th unit on the y-axis, F is the focal length, λ2 represents the wavelength corresponding to the operating frequency f2, which is related to the operating frequency and satisfies that the speed of light c is equal to the wavelength λ2 multiplied by the operating frequency f2;

[0103] Phase distribution of staggered structures in hinged mechanically reconfigurable multifunctional transflective metasurface We use a matrix to link the two:

[0104]

[0105] represents the phase distribution of unit A, Represents the phase distribution of unit B; matrix M1(i,j)=(1+(-1) i+j ) / 2 and M2(i,j)=(1-(-1) i+j) / 2 represents the arrangement of the two units A and B in the staggered structure. When M1(i, j) and M2(i, j) are equal to 1, it means that the units A and B are to be arranged in the metasurface structure; when M1(i, j) and M2(i, j) are equal to 0, it means that the metasurface structure does not arrange the units; where i and j represent the number of rows and columns of the matrix M1 or M2, respectively, see Figure 12 .

[0106] Step 4: Based on the principle of geometric phase control, a hinged mechanically reconfigurable multifunctional transmissive-reflective metasurface is constructed;

[0107] In step 2, the rotation angle β of units A and B can be obtained A and β B It satisfies the principle of geometric phase control, that is, when a circularly polarized wave is incident, the reflection phase difference of the metasurface unit A is the rotation angle β A The transmission phase difference of metasurface unit B is 2 times the rotation angle β B Based on this control principle, the initial phase distribution of the staggered structure in step 3 is used. To design the rotation angle β of units A and B in the hinged mechanical reconfigurable multifunctional transflective metasurface A and β B ,in,

[0108] The present invention arranges the metasurface units A and B according to the initial phase distribution in step 3 above when they are not deformed. Next, the hinged mechanical reconfigurable multifunctional transmissive-reflective metasurface designed by stretching is discussed, so that α of each metasurface unit is 45°, that is, the rotation angles ζ of the metasurface units A and B around the central axis are 45° and -45° respectively. At this time, the phase difference between the deformed and undeformed unit A is 90°. Similarly, the phase difference between the deformed and undeformed unit B is -90°. Therefore, for the deformed mode 2, it still has the functions of beam deflection and focusing, but the reflection deflection angle θ r and the focal point F changes, so the reflection beam changing and transmission zoom functions can be achieved by stretching the metasurface.

[0109] like Figure 13 As shown in Figure 1, if the hinged mechanical reconfigurable multifunctional transflective metasurface consists of 30×30 units, including 15×30 units A and 15×30 units B, the size in the undeformed state (mode 1) is 300×300 mm. 2 After deformation of 45° (mode 2), the size is approximately 424×424mm 2 . Figure 13Simulation models of a hinged, mechanically reconfigurable, multifunctional transmissive-reflective metasurface were demonstrated in two states. Since the hinge structure has little effect on phase difference and only slightly affects amplitude, subsequent metasurface simulations were performed using a hingeless 3D-printed resin plate structure.

[0110] In order to verify the feasibility of the hinged mechanically reconfigurable multifunctional transmissive-reflective metasurface scheme, samples were made using 3D printing technology and paper cutting technology. Figure 14 The process flow chart of the hinged mechanically reconfigurable multifunctional transmissive-reflective metasurface is presented. First, the main body, hinge, and hinge rotating column are made of engineering resin using 3D printing technology. Second, they are assembled into a rotatable third dielectric plate. At the same time, the first (fifth) metal structure of the metasurface is etched onto the second (fourth) thin layer F4B dielectric plate using PCB technology. Figure 15 ), and cut it into 10×10mm pieces using laser cutting technology 2 After completing the above two steps, the small cubes were attached to the assembled 3D-printed resin plate, completing the hinged mechanically reconfigurable metasurface sample. The structure can be stretched or contracted to allow for repeated testing, and the processed sample consists of 30×30 units.

[0111] Step 5: Verify the integrated functions of reflection variable beam and transmission zoom

[0112] Further examples are given to verify the super surface design of the present invention. Figure 12 As shown in (b) and (c), when the metasurface is not deformed, if the preset deflection angle θ r is 30°, and the focal length F is 100mm. Figure 12 As shown in (a), the initial phase distribution of the metasurface can be obtained by formula (4): According to the phase distribution, unit A and unit B are arranged in the Figure 12 (d) Arrange the undeformed hinged mechanically reconfigurable multifunctional transmissive-reflective metasurface.

[0113] In order to demonstrate the reflection effect of the hinged mechanically reconfigurable multifunctional transflective-reflective metasurface in two modes, a CST full-wave simulation was first performed. Figure 16 As shown in the figure, for the reflection channel, when the circularly polarized wave is incident vertically, for the undeformed mode 1, a deflected beam with an angle of 30° is radiated at 8 GHz. When converted to mode 2, it is reflected at a deflection angle of 20.5°. The deformed reflection angle θ can be calculated using the generalized Snell's law. r ′ is about 21°. This is because the phase difference before and after the unit deformation remains basically unchanged, and the phase distribution of unit A increases by 45° compared to before deformation. Transforming the differential form of equation (2) yields: dy changes from period p to Therefore, the expression for vertical incidence can be obtained as:

[0114]

[0115] Next, we discuss the experimental effect of reflection. Figure 17 Far-field test platform. Figure 18 The experimental and simulated normalized electric field intensities for two modes in an 8GHz reflection channel are presented, with the two results showing close agreement, with only a slight angular error of 1°. For mode 1, when a right-handed circularly polarized wave is incident perpendicularly on the metasurface, a right-handed circularly polarized beam is reflected along a 30° angle. In mode 2, the reflected beam radiates along a 21° angle. In both modes, the simulated and tested sidelobe radiation electric field intensities are below 0.3. As expected, the simulation and experimental results agree well. The simulated efficiency for the two modes is 89.3% and 90.7%, respectively, while the experimental efficiency is 90.5% and 88.6%. The experimental error is mainly due to the 0.1-0.2mm machining error in 3D printing and the fact that the hinged mechanical metasurface cannot ensure that each unit rotates 45° when stretched. Therefore, this test strongly demonstrates that the designed hinged mechanical reconfigurable metasurface can achieve beam-changing functionality in both modes. This also proves the feasibility of the reflective function of the hinged mechanical reconfigurable multifunctional transflective metasurface designed in this invention.

[0116] Next, the transmission effect of the hinged mechanically reconfigurable multifunctional transflective metasurface in two modes was verified. Figure 19 As shown in (a) and (c), when a right-handed circularly polarized wave at 10.7 GHz is incident vertically on the undeformed mode 1, the normalized electric field intensity of the transmitted left-handed circularly polarized wave in the xz plane (center normal x = 0, y = 0) and the xy plane is obtained. It can be seen that the transmitted energy converges 150 mm below the center of the plane, achieving a good focusing effect. Figure 19 Figures (b) and (d) show the normalized electric field intensities in the xz and xy planes, respectively, for mode 2. It can be seen that the transmitted energy converges 320 mm below the center of the plane, significantly increasing the focal range compared to the undeformed state. Because the focusing phase is not linear, the specific focal position cannot be analyzed as with a deflected beam and can only be determined directly through testing. This analysis demonstrates that the hinged, mechanically reconfigurable transflective metasurface can achieve variable focus control.

[0117] Next, we discuss the test results under transmission conditions. Figure 20 Two-dimensional near-field scanning platform. When a 10.7GHz right-hand circularly polarized wave is incident vertically, Figure 21(a) and (c) show the electric field intensity distribution in the xz plane (center normal x = 0, y = 0) and the xy plane in mode 1, respectively. It can be seen that the transmitted energy converges 150 mm below the center of the plane, achieving a good focusing effect. Figure 21 (b) and (d) show the electric field intensity in the xz plane (center normal x = 0, y = 0) and the xy plane in mode 2, respectively. It can be seen that the transmitted energy is concentrated 320mm below the center of the plane. To further understand the focusing effect, Figure 22 The electric field intensity curves at y=0 in the two modes were plotted. Although there is a slight deviation in the center of the focus, the curve trends are basically the same. The focusing radiation efficiency (the ratio of the power of the focal spot of the circularly polarized channel to the total power of the transmitted beam) was calculated to be 92.5% and 94.2% in the simulation case, and the radiation efficiency was 90.1% and 89.2% in the experimental case. It can also be seen that the focus diameter is 40mm in mode 1 and 58mm in mode 2. The experimental test results are in good agreement with the numerical simulation results. The error mainly comes from the insufficient processing accuracy of the sample and the inability of the hinged metasurface to ensure that each unit rotates 45° when in a stretched state. In short, the above simulations and tests have proved that the mechanically reconfigurable metasurface can realize a zoom lens when a circularly polarized wave of 10.7GHz is incident. The feasibility of the transmission function of the hinged mechanically reconfigurable multifunctional transmissive-reflective metasurface designed in the present invention is proved.

[0118] The above are only specific steps of the present invention and do not constitute any limitation to the scope of protection of the present invention; any technical solutions formed by equivalent transformation or equivalent replacement fall within the scope of protection of the present invention; the parts not elaborated in detail in the present invention belong to the common knowledge of those skilled in the art.

Claims

1. A hinged mechanically reconfigurable multifunctional transflective metasurface, characterized in that: The hinged mechanically reconfigurable multifunctional transflective metasurface includes a plurality of 2×2 unit modules; The 2×2 unit module includes a hinged mechanical metasurface unit A and a hinged mechanical metasurface unit B, and the hinged mechanical metasurface unit A and the hinged mechanical metasurface unit B are arranged in a staggered manner; The hinged mechanical metasurface unit A and the hinged mechanical metasurface unit B each include a first metal layer, a second dielectric layer, a third resin plate layer, a fourth dielectric layer, and a fifth metal layer stacked sequentially from top to bottom; In the hinged mechanical metasurface unit A, the first metal layer is a double-ring symmetrical connected slot resonator, and the fifth metal layer is a metal floor; The first and fifth metal layers in the hinged mechanical metasurface unit B have the same structure, both of which are three-ring symmetrical connected slot resonators; The first and fifth metal layers are both etched on the F4B dielectric plates of the second and fourth dielectric layers; the third resin plate layer is configured as a hinge structure and is connected to the third resin plate layer of the adjacent unit via the hinge structure; The hinge structure can switch the metasurface period by rotating and unrotating the unit, where the period is p when the unit is not rotated and the period is α when the unit is rotated.

2. The hinged mechanically reconfigurable multifunctional transflective metasurface according to claim 1, characterized in that: The hinge structure includes a resin body, a hinge and a hinge rotating column; Four hinge rotating columns are respectively set at the four corners of the resin body. Long holes matching the hinge rotating columns are opened at both ends of the hinge. One end of the hinge is connected to the hinge rotating column of the unit through the long hole, and the other long hole is connected to the hinge rotating column of the adjacent unit. When the unit is not rotated, the hinge structure is in a closed state, and the edges of adjacent units are in contact. When the unit rotates, it is in a stretched state, and the units along the diagonal rotate α in the same direction, while the adjacent units rotate α in the opposite direction along the vertices, that is, the units rotate ±α, and the corner vertices of adjacent units are in contact.

3. The hinged mechanically reconfigurable multifunctional transflective metasurface according to claim 1, characterized in that: The dual-ring symmetrical connecting groove resonator includes a dual-ring resonator inner ring groove, a dual-ring resonator outer ring groove and two symmetrical dual-ring resonator connecting grooves connecting the dual-ring resonator inner ring groove and the dual-ring resonator outer ring groove, which are etched on the metal layer; The two dual-ring resonator connecting slots are located on the same straight line. In the initial state, the angle β between the dual-ring resonator connecting slot and the x-axis is A is 0°; The outer diameter of the outer ring slot of the double ring resonator r A4 =4.8mm, inner diameter of outer ring groove of double ring resonator r A3 =4.6mm, outer diameter of inner ring groove of double ring resonator r A2 =4.2mm, inner diameter of the ring groove of the double ring resonator r A1 =3.9mm, dual ring resonator connecting groove width g A =0.2mm.

4. The hinged mechanically reconfigurable multifunctional transflective metasurface according to claim 1, characterized in that: The three-ring symmetrical connecting slot resonator includes a three-ring resonator inner ring slot, a three-ring resonator middle ring slot, a three-ring resonator outer ring slot, and two symmetrical three-ring resonator connecting slots connecting the inner ring of the three-ring slot resonator and the outer ring of the three-ring slot resonator. The two three-ring resonator connecting slots are located on the same straight line. In the initial state, the angle β between the three-ring resonator connecting slot and the x-axis is B is 0°; The outer diameter r of the outer ring groove of the three-ring resonator B6 =3.6mm, inner diameter r of the outer ring groove of the three-ring resonator B5 =3.4mm, the outer diameter of the ring groove in the three-ring resonator r B4 =3mm, inner diameter r of the ring groove in the three-ring resonator B3 =2.8mm, outer diameter of inner ring groove of three-ring resonator r B2 =2.4mm, inner diameter r of the inner ring groove of the three-ring resonator B1 =2.1mm, width of the connecting groove of the three-ring resonator g B =0.2mm.

5. A design method for a hinged mechanically reconfigurable multifunctional transflective metasurface, characterized in that: The design method of the hinged mechanically reconfigurable multifunctional transflective-reflective metasurface comprises the following steps: Step 1: Based on the intrinsic connection between the internal rotation law of the hinged mechanical metasurface and the geometric phase, that is, the rotation of the metasurface unit vertex can be converted into the rotation of the metasurface unit central axis, a dual-unit staggered structure is constructed; Step 2: Using frequency isolation, design a low-crosstalk hinged mechanical metasurface unit A and a hinged mechanical metasurface unit B, wherein the operating frequency of the hinged mechanical metasurface unit A is f1, and the operating frequency of the hinged mechanical metasurface unit B is f2; Step 3: Predetermine the functions of the two channels, reflection and transmission, and design the initial phase distribution of the hinged mechanical reconfigurable multifunctional transmissive-reflective metasurface based on the staggered structure. Step 4: Based on the principle of geometric phase control, a hinged mechanically reconfigurable multifunctional transmissive-reflective metasurface is constructed according to the initial phase distribution in step 3 at a certain rotation angle α.

6. The design method of the hinged mechanically reconfigurable multifunctional transflective metasurface according to claim 5, characterized in that: In step 1, the hinged mechanical reconfigurable multifunctional transflective metasurface includes a hinged mechanical metasurface unit A and a hinged mechanical metasurface unit B, wherein the hinged mechanical metasurface unit A and the hinged mechanical metasurface unit B are arranged in an interlaced manner; Both hinged mechanical metasurface unit A and hinged mechanical metasurface unit B include hinge structures, which are connected to adjacent units through the hinge structure. When the hinge structure rotates along the vertex by an angle α, the units along the diagonal rotate in the same direction by α, while the adjacent units rotate in the opposite direction by α along the vertex, resulting in a unit azimuth angle change ζ related to the structural rotation angle α, that is, α = ±ζ; The hinge structure can be rotated at a period p and a period p When the unit rotates ±45°, the cycle is According to the geometric phase characteristics, when a circularly polarized wave is incident, the geometric phase of its cross-polarized wave has a 2-fold relationship with the rotation angle of the metal structure of the metasurface unit; Geometric phase change of hinged mechanical metasurface unit A Geometric phase change of hinged mechanical metasurface unit B "±" represents the handedness of the incident circularly polarized wave.

7. The design method of the hinged mechanically reconfigurable multifunctional transflective metasurface according to claim 5, characterized in that: In step 2, the hinged mechanical metasurface unit A and the hinged mechanical metasurface unit B each include a first metal layer, a second dielectric layer, a third resin plate layer, a fourth dielectric layer, and a fifth metal layer stacked sequentially from top to bottom; In the hinged mechanical metasurface unit A, the first metal layer is a double-ring symmetrical connected slot resonator, and the fifth metal layer is a metal floor; The first and fifth metal layers in the hinged mechanical metasurface unit B have the same structure, both of which are three-ring symmetrical connected slot resonators; The first and fifth metal layers are both etched on the F4B dielectric plates of the second and fourth dielectric layers; The third resin plate layer is arranged in a hinge structure and is connected to the third resin plate layer of an adjacent unit via the hinge structure.

8. The design method of the hinged mechanically reconfigurable multifunctional transflective metasurface according to claim 7, characterized in that: In step 2, the dual-ring symmetrical connecting groove resonator includes a dual-ring resonator inner ring groove, a dual-ring resonator outer ring groove, and two symmetrical dual-ring resonator connecting grooves connecting the dual-ring resonator inner ring and the dual-ring resonator outer ring, which are etched on the metal layer; The three-ring symmetrical connecting groove resonator includes a three-ring resonator inner ring groove, a three-ring resonator middle ring groove, a three-ring resonator outer ring groove and two symmetrical three-ring resonator connecting grooves connecting the inner ring of the three-ring resonator and the outer ring of the three-ring resonator; The structural parameters of the double-ring symmetrical connected slot resonator and the triple-ring symmetrical connected slot resonator were simulated and optimized respectively by using the parameter scanning method of CST software to determine the optimal structural parameters for the reflection amplitude of the double-ring symmetrical connected slot resonator and the transmission amplitude of the triple-ring symmetrical connected slot resonator.

9. The design method of the hinged mechanically reconfigurable multifunctional transflective metasurface according to claim 5, characterized in that: In step 3, the initial phase distribution of the frequency-reused hinged mechanically reconfigurable multifunctional metasurface is designed according to the staggered dual-unit combination method; The deflection angle is θ r Beam phase distribution as follows: y j represents the coordinate of the jth unit along the y-axis, λ1 represents the wavelength corresponding to the operating frequency f1, which is related to the operating frequency and satisfies that the speed of light c is equal to the wavelength λ1 multiplied by the operating frequency f1; Focusing curved surface phase distribution with focal length F as follows: x i,j Indicates the coordinate of the (i, j)th unit on the x-axis, y i,j represents the coordinate of the (i, j)th unit on the y-axis, F is the focal length, λ2 represents the wavelength corresponding to the operating frequency f2, which is related to the operating frequency and satisfies that the speed of light c is equal to the wavelength λ2 multiplied by the operating frequency f2; Initial phase distribution of the staggered structure Use the matrix method to connect the two: represents the phase distribution of the hinged mechanical metasurface unit A, Represents the phase distribution of the hinged mechanical metasurface unit B; the matrix M1(i,j)=(1+(-1) i+j ) / 2 and M2(i,j)=(1-(-1) i+j ) / 2 represents two arrangements of the hinged mechanical metasurface unit A and the hinged mechanical metasurface unit B in the staggered structure. When M1(i,j) and M2(i,j) are equal to 1, it means that the hinged mechanical metasurface unit A or the hinged mechanical metasurface unit B is arranged in the metasurface structure; when M1(i,j) and M2(i,j) are equal to 0, it means that the metasurface structure does not arrange units; where i and j represent the number of rows and columns of the matrix M1 or M2, respectively.

10. The design method of the hinged mechanically reconfigurable multifunctional transflective metasurface according to claim 9, characterized in that: In step 4, the initial phase distribution of the staggered structure Design the rotation angle β of the double-ring symmetrical connected slot resonator in hinged mechanical metasurface unit A and hinged mechanical metasurface unit B A and the rotation angle β of the three-ring symmetrical connected slot resonator B ,in,

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