Reflection and transmission integrated terahertz flexible metamaterial surface

Abstract

The invention provides a reflection and transmission integrated terahertz flexible metasurface which is used for solving the problems that an existing metasurface cannot have reflection and transmission functions at the same time, and the requirement for multiple functions and dynamic regulation and control in a complex application scene is difficult to meet. The design comprises a five-layer structure from top to bottom: a top-layer pattern layer is composed of two notch square copper sheets and two photosensitive silicon square sheets, a second layer and a fourth layer are polyimide flexible dielectric layers, a third layer is a vanadium dioxide regulation and control layer, and a bottom-layer pattern layer is obtained by clockwise rotating a top-layer pattern by 90 degrees. The metasurface utilizes the adjustable characteristics of vanadium dioxide and photosensitive silicon to regulate and control electromagnetic waves in two-way transmission, breaks through the application limitation of a traditional single reflection or transmission type metasurface, and can be widely applied to the fields of electromagnetic stealth, communication, near-field imaging and the like.

Description

Technical Field

[0001] The present invention belongs to the technical field of terahertz electromagnetic metasurfaces, and specifically relates to a reflective and transmissive integrated terahertz flexible metasurface. Background Art

[0002] In recent years, with rapid advances in semiconductor technology, optoelectronics, and other related fields, significant breakthroughs have been achieved in the development of terahertz (THz) wave radiation sources and related devices. With its unique physical properties and broad application prospects, THz technology is gradually demonstrating tremendous development potential. Due to its unique non-ionizing properties, high penetration, and sensitive response to material structure, THz wave technology exhibits broad application prospects in fields such as wireless communications, biomedicine, and security testing. However, due to the limitations of natural materials, the development of THz technology still faces numerous challenges. The emergence of electromagnetic metamaterials has effectively addressed this issue. Combining metamaterials with THz technology not only overcomes the limitations of traditional materials on the development of THz technology but also greatly enhances the feasibility of THz device design and application, opening up new possibilities for the research and application of multifunctional THz devices.

[0003] Metasurfaces demonstrate tremendous potential for light field manipulation, enabling flexible and efficient control of the amplitude, polarization, and phase of electromagnetic waves. Leveraging these properties, a range of terahertz devices with novel physical properties have been developed, including absorbers, polarization converters, asymmetric transmission devices, and superlenses. With the rapid miniaturization and integration of terahertz metasurface devices, achieving switchable multifunctional properties on a single metasurface has become a research hotspot, crucial for meeting complex and ever-changing application requirements. Furthermore, with continued breakthroughs in electromagnetic wave manipulation technology, the design of metasurface structures with both reflective and transmissive properties to achieve multifunctional dynamic control in complex application scenarios is becoming a key research direction in this field. Therefore, exploring a metasurface structure that simultaneously possesses tunable properties, bidirectional absorption, asymmetric transmission, and flexibility is crucial for enhancing its practical application in various fields. Summary of the Invention

[0004] To address the current difficulties of metasurfaces in achieving both reflective and transmissive transmission properties, this paper proposes a flexible terahertz metasurface that combines both reflection and transmission, enabling bidirectional electromagnetic wave control. This paper utilizes the phase transition properties of vanadium dioxide to transform the metasurface from a reflective to a transmissive structure. Dynamic control of the metasurface is achieved by adjusting the conductivity of photosensitive silicon.

[0005] To achieve the above object, the technical solution adopted by the present invention is:

[0006] A reflective and transmissive integrated terahertz flexible metasurface, comprising five layers: a top pattern layer consisting of two notched square copper sheets and two photosensitive silicon sheets, a second and fourth polyimide flexible dielectric layer, a third vanadium dioxide control layer, and a bottom pattern layer obtained by rotating the top pattern 90° clockwise.

[0007] The second and fourth polyimide flexible dielectric layers are consistent with the third vanadium dioxide control layer in length and width, but different in thickness;

[0008] According to the design method of the reflective and transmissive integrated terahertz flexible metasurface described in the present invention, the unit structures are periodically arranged along the x and y coordinate axes in the o-xyz spatial coordinate system, and are extended to form a multifunctional metasurface, where o is the origin of the coordinate axis.

[0009] According to the design method of the reflective and transmissive integrated terahertz flexible metasurface of the present invention, the dielectric constant of the second and fourth polyimide flexible dielectric layer materials is 3.50+0.00945i.

[0010] According to the design method of the reflective and transmissive integrated terahertz flexible metasurface of the present invention, the relative dielectric constant of the vanadium dioxide control layer is It is expressed as follows:

[0011]

[0012] Where ε represents the relative dielectric constant, VO2 represents vanadium dioxide, represents the relative dielectric constant of vanadium dioxide, ξ represents the volume fraction of vanadium dioxide in the metallic state, which changes with increasing temperature; ξ is approximately equal to 0 in the insulating state of vanadium dioxide, and its maximum value is 0.95; ξ is obtained from the Boltzmann function as follows:

[0013]

[0014] Where T is the ambient temperature, T0=68℃ is the phase transition temperature, ε i =9 and ε m are the dielectric constants of the insulating and metallic states of vanadium dioxide; ε in the terahertz band m Expressed using the Drude model:

[0015]

[0016] Where ε ∞ =9 is the high-frequency dielectric constant of vanadium dioxide, is the electrical conductivity of vanadium dioxide. When vanadium dioxide is in an insulating state, When vanadium dioxide is in the metallic state, ω represents the incident angular frequency, c = -0.6579 is the empirical coefficient related to backscattering, Γ = e / (m × μ) is the scattering coefficient, μ = 2 × 10 -4 m 2 / (V·s) is the carrier mobility, m*=2m=1.82×10 -30 kg represents effective mass, e=1.60×10 -19 C is the electron charge, i represents the imaginary unit, is with Related plasma frequencies.

[0017] According to the design method of the reflective and transmissive integrated terahertz flexible metasurface of the present invention, the conductivity of the photosensitive silicon is manipulated by pump light and expressed as follows:

[0018] s PSi =4.863×10 -4 ×A 2 +0.1856×A+1.569

[0019] Where σ represents conductivity, PSi represents photosensitive silicon, σ PSi Indicates the conductivity of photosensitive silicon. A is the energy flux of the pump beam. When there is no pump beam (no pump light flux), the photosensitive silicon is in an insulating state and its conductivity is 1S / m. At A, it is 294.6μJ / cm 2 When the pump light energy flux reaches the maximum, the photosensitive silicon is in a metallic state and its conductivity is 1×10 5 S / m.

[0020] According to the design method of the reflective and transmissive integrated terahertz flexible metasurface of the present invention, the bidirectional absorptivity A(ω) of the metasurface satisfies:

[0021] A(w)=1-R(w)-T(w)=a f (1-|S f11 | 2 -|S f21 | 2 )+a b (1-|S b11 | 2 -|S b21 | 2 )±t

[0022] Where R(ω) and T(ω) represent reflectivity and transmittance respectively, α f is the absorption coefficient of electromagnetic wave when incident in the forward direction, S f11 and S f21 are the reflection coefficient and transmission coefficient when the electromagnetic wave is incident in the forward direction; α bis the absorption coefficient of electromagnetic wave when it is incident in reverse direction, S b11 and S b21 are respectively the reflection coefficient and transmission coefficient when the electromagnetic wave is incident in the reverse direction; when the electromagnetic wave is incident in the forward direction, α f is 1, α b is 0; when the electromagnetic wave is incident in the reverse direction, α f is 0, α b is 1; τ is the error function of the bidirectional absorption rate:

[0023]

[0024] Where Z is the equivalent impedance of the absorber, Z0 represents the free space impedance, S 11 is the reflection coefficient of the entire metasurface, S 21 is the transmission coefficient of the entire metasurface.

[0025] According to the design method of the reflective and transmissive integrated terahertz flexible metasurface of the present invention, the transmission polarization conversion rate P of the metasurface is expressed as follows:

[0026]

[0027] Where P f and P b are the polarization conversion coefficients when the electromagnetic wave is incident in the forward direction and in the reverse direction, t xy and t yx represents the cross-polarization transmission coefficient, t yy and t xx Represents the co-polarization transmission coefficient. When the electromagnetic wave is incident in the forward direction, P f is 1, P b is 0, when the electromagnetic wave is incident in the reverse direction, P f is 0, P b =1; Transmission polarization conversion rate P error function K P It can be expressed as follows:

[0028]

[0029] Where Δφ represents the transmission phase difference, and the control function Φ of the transmission polarization conversion rate is further obtained:

[0030]

[0031] According to the design method of the reflective and transmissive integrated terahertz flexible metasurface of the present invention, the asymmetric transmission characteristics of the metasurface are expressed as follows:

[0032]

[0033] Where Δ lin (x) and Δlin (y) represents the asymmetric transmission parameters of the forward propagating x-polarized wave and y-polarized wave, and are the total transmittance of x and y polarized waves under normal incidence, T b x and T b y represent the total transmittance under reverse incidence of x and y polarized waves respectively; and is the transmission coefficient when the electromagnetic wave is incident in the normal direction, and is the transmission coefficient when the electromagnetic wave is incident in the reverse direction; the subscripts m and m+1 represent the numbers of any two adjacent frequency points within the working bandwidth, η x represents the relative error of the asymmetric transmission parameters of the x-polarization wave, η y It represents the relative error of the asymmetric transmission parameters of the y-polarization wave.

[0034] Beneficial effects of the present invention

[0035] (1) The present invention proposes a reflective and transmissive integrated terahertz flexible metasurface, which utilizes the phase change properties of vanadium dioxide to achieve the transformation of the metasurface from a reflective structure to a transmissive structure.

[0036] (2) The present invention proposes a reflective and transmissive integrated terahertz flexible metasurface. When vanadium dioxide is in a metallic state and photosensitive silicon is in an insulating state, the metasurface is a reflective structure. The middle vanadium dioxide layer separates the metasurface into two independent reflection systems, the top layer and the bottom layer. The metasurface can realize a bidirectional wave absorption function, and the bidirectional wave absorption characteristics can be applied to the field of near-field imaging.

[0037] (3) The present invention proposes a reflective and transmissive integrated terahertz flexible metasurface. When both vanadium dioxide and photosensitive silicon are in an insulating state, the designed metasurface is a transmissive structure. At this time, the metasurface exhibits good polarization conversion and asymmetric transmission characteristics.

[0038] (4) The present invention proposes a reflective and transmissive integrated terahertz flexible metasurface, which introduces the adjustable metamaterial photosensitive silicon into the metasurface. By adjusting the conductivity of the photosensitive silicon, the designed multifunctional metasurface can achieve dynamic regulation of the bidirectional wave absorption characteristics, the transmission polarization conversion characteristics and the asymmetric transmission characteristics.

[0039] (5) The present invention proposes a reflective and transmissive integrated terahertz flexible metasurface that maintains high bidirectional absorption and asymmetric transmission characteristics when conformally mounted on a cylinder, and can be widely used in practical engineering applications involving curved surfaces.

[0040] (6) The present invention proposes a reflective and transmissive integrated terahertz flexible metasurface that realizes switchable and multifunctional properties on a single metasurface. This structure not only enhances functional diversity while maintaining device miniaturization and integration, but also gives it stronger dynamic control capabilities to meet complex and changing application requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 Schematic diagram of the three-dimensional structure of a reflective and transmissive integrated terahertz flexible metasurface unit in an embodiment of the present invention;

[0042] Figure 2 Schematic diagram of the top pattern layer of a reflective and transmissive integrated terahertz flexible metasurface unit in an embodiment of the present invention;

[0043] Figure 3 Schematic side view of a reflective and transmissive integrated terahertz flexible metasurface unit according to an embodiment of the present invention;

[0044] Figure 4 Schematic diagram of the bottom pattern layer of the reflective and transmissive integrated terahertz flexible metasurface unit in an embodiment of the present invention;

[0045] Figure 5 This is a graph showing the absorptivity of the reflective and transmissive integrated terahertz flexible metasurface when electromagnetic waves are incident in the forward direction according to an embodiment of the present invention;

[0046] Figure 6 This is a graph showing the absorptivity of the reflective and transmissive integrated terahertz flexible metasurface when the electromagnetic wave is incident in the reverse direction in an embodiment of the present invention;

[0047] Figure 7 This is a graph showing the absorptivity of the reflective and transmissive integrated terahertz flexible metasurface conformally outside cylinders of different radii when electromagnetic waves are incident in the normal direction according to an embodiment of the present invention;

[0048] Figure 8 This is a graph showing the absorptivity of the reflective and transmissive integrated terahertz flexible metasurface conformally outside cylinders of different radii when electromagnetic waves are incident in the reverse direction according to an embodiment of the present invention;

[0049] Figure 9 This is a graph showing the absorptivity of different photosensitive silicon conductivities when the reflective and transmissive integrated terahertz flexible metasurface is incident in the forward direction of the x-polarized wave according to an embodiment of the present invention;

[0050] Figure 10 This is a graph showing the absorptivity of different photosensitive silicon conductivities when the reflective and transmissive integrated terahertz flexible metasurface is incident in the forward direction of the y-polarized wave according to an embodiment of the present invention;

[0051] Figure 11This is a graph showing the absorptivity of different photosensitive silicon conductivities when the reflective and transmissive integrated terahertz flexible metasurface is incident on an x-polarized wave in reverse direction in an embodiment of the present invention;

[0052] Figure 12 This is a graph showing the absorptivity of different photosensitive silicon conductivities when the reflective and transmissive integrated terahertz flexible metasurface is incident on the y-polarized wave in reverse direction in an embodiment of the present invention;

[0053] Figure 13 : is the transmission spectrum of the reflective and transmissive integrated terahertz flexible metasurface under normal incidence of electromagnetic waves in an embodiment of the present invention;

[0054] Figure 14 : is the transmission spectrum of the reflective and transmissive integrated terahertz flexible metasurface under reverse incidence of electromagnetic waves in an embodiment of the present invention;

[0055] Figure 15 This is the asymmetric transmission curve calculated for the reflective and transmissive integrated terahertz flexible metasurface in an embodiment of the present invention;

[0056] Figure 16 : is the polarization conversion rate curve of the reflective and transmissive integrated terahertz flexible metasurface in an embodiment of the present invention;

[0057] Figure 17 This is a graph showing the asymmetric transmission curves of the reflective and transmissive integrated terahertz flexible metasurface conformally outside cylinders of different radii in an embodiment of the present invention;

[0058] Figure 18 This is a graph showing the polarization conversion rate of the reflective and transmissive integrated terahertz flexible metasurface conformally outside cylinders of different radii when electromagnetic waves are incident in the forward direction according to an embodiment of the present invention;

[0059] Figure 19 This is a graph showing the polarization conversion rate of the reflective and transmissive integrated terahertz flexible metasurface conformally outside cylinders of different radii when electromagnetic waves are incident in the reverse direction in an embodiment of the present invention;

[0060] Figure 20 Graph showing asymmetric transmission curves of the reflective and transmissive integrated terahertz flexible metasurface under different photosensitive silicon conductivities in an embodiment of the present invention;

[0061] Figure 21 This is a graph showing the polarization conversion rate of the reflective and transmissive integrated terahertz flexible metasurface under different photosensitive silicon conductivities in an embodiment of the present invention. DETAILED DESCRIPTION

[0062] In order to make the main purpose, technical solutions and advantages of the present invention more clear, the following will be a more detailed and comprehensive description of the implementation method of the present invention with reference to the accompanying drawings in the embodiments of the present invention. It should be understood that the specific embodiments introduced here are only used to illustrate the present invention and are not intended to limit the present invention.

[0063] Combine Figures 1 to 4 The present invention designs a reflective and transmissive integrated terahertz flexible metasurface, which includes six layers: the first layer is a top pattern layer composed of two notched square copper sheets and two photosensitive silicon square sheets, the second layer is a polyimide flexible dielectric layer, the third layer is a vanadium dioxide regulation layer, the fourth layer is a polyimide flexible dielectric layer, and the fifth layer is a bottom pattern layer obtained by rotating the top pattern 90° clockwise.

[0064] The present invention uses the frequency domain solver in the CST electromagnetic simulation software to simulate and analyze the model. The unit structure is set to periodic boundary conditions along the x-axis and y-axis directions, and to open boundary conditions in the z-axis direction. When the electromagnetic wave is incident on the top layer of the metasurface along the -z direction, it is considered to be forward incident, and when it is incident on the bottom layer of the metasurface along the +z direction, it is considered to be reverse incident.

[0065] Taking into account the bidirectional wave absorption characteristics, polarization conversion characteristics and asymmetric transmission characteristics, the metasurface unit structure period of this embodiment is p = 50 μm, and the top pattern layer is composed of a conductivity of 5.80×10 7 S / m copper sheet and photosensitive silicon with a relative dielectric constant of 11.7.

[0066] The graphic range l1 of the square copper sheet with the outer notch of the top pattern layer is 48μm, l2 is 23μm, the graphic range l3 of the square copper sheet with the inner notch is 7μm, l4 is 6μm, the width w of the two photosensitive silicon square sheets is 5μm, the thickness t1 of the top pattern layer is 0.20μm, and the bottom pattern layer is obtained by rotating the top pattern layer 90° clockwise, and the thickness t3 of the bottom pattern layer is 0.20μm.

[0067] Taking into account the bidirectional wave absorption characteristics, polarization conversion characteristics and asymmetric transmission characteristics, the relative dielectric constants of the second and fourth polyimide flexible dielectric layers in this embodiment are ε PI =3.50+0.00945i, the thickness of the second dielectric layer h1 is 4 μm, the thickness of the fourth dielectric layer h2 is 4 μm, and the thickness t2 of the third vanadium dioxide control layer is 0.50 μm.

[0068] Furthermore, the relative dielectric constant of the vanadium dioxide control layer is It is expressed as follows:

[0069]

[0070] Where ε represents the relative dielectric constant, VO2 represents vanadium dioxide, represents the relative dielectric constant of vanadium dioxide, ξ represents the volume fraction of vanadium dioxide in the metallic state, which changes with increasing temperature; ξ is approximately equal to 0 in the insulating state of vanadium dioxide, and its maximum value is 0.95; ξ is obtained from the Boltzmann function as follows:

[0071]

[0072] Where T is the ambient temperature, T0=68℃ is the phase transition temperature, ε i =9 and ε m are the dielectric constants of the insulating and metallic states of vanadium dioxide; ε in the terahertz band m Expressed using the Drude model:

[0073]

[0074] Where ε ∞ =9 is the high-frequency dielectric constant of vanadium dioxide, is the electrical conductivity of vanadium dioxide. When vanadium dioxide is in an insulating state, When vanadium dioxide is in the metallic state, ω represents the incident angular frequency, c = -0.6579 is the empirical coefficient related to backscattering, Γ = e / (m × μ) is the scattering coefficient, μ = 2 × 10 -4 m 2 / (V·s) is the carrier mobility, m*=2m=1.82×10 -30 kg represents effective mass, e=1.60×10 -19 C is the electron charge, i represents the imaginary unit, is with Related plasma frequencies.

[0075] The conductivity of the photosensitive silicon described in the present invention is manipulated by pump light and is expressed as follows:

[0076] s PSi =4.863×10 -4 ×A 2 +0.1856×A+1.569

[0077] Where σ represents conductivity, PSi represents photosensitive silicon, σ PSi Indicates the conductivity of photosensitive silicon. A is the energy flux of the pump beam. When there is no pump beam (no pump light flux), the photosensitive silicon is in an insulating state and its conductivity is 1S / m. At A, it is 294.6μJ / cm 2 When the pump light energy flux reaches the maximum, the photosensitive silicon is in a metallic state and its conductivity is 1×10 5 S / m.

[0078] According to the design method of the reflective and transmissive integrated terahertz flexible metasurface of the present invention, the bidirectional absorptivity A(ω) of the metasurface satisfies:

[0079] A(w)=1-R(w)-T(w)=a f (1-|S f11 | 2 -|S f21 | 2 )+a b (1-|S b11 | 2 -|S b21 | 2 )±t

[0080] Where R(ω) and T(ω) represent reflectivity and transmittance respectively, α f is the absorption coefficient of electromagnetic wave when incident in the forward direction, S f11 and S f21 are the reflection coefficient and transmission coefficient when the electromagnetic wave is incident in the forward direction; α b is the absorption coefficient of electromagnetic wave when incident in reverse direction, S b11 and S b21 are respectively the reflection coefficient and transmission coefficient when the electromagnetic wave is incident in the reverse direction; when the electromagnetic wave is incident in the forward direction, α f is 1, α b When the electromagnetic wave is incident in the reverse direction, α f is 0, α b is 1; τ is the error function of the bidirectional absorption rate:

[0081]

[0082] Where Z is the equivalent impedance of the absorber, Z0 represents the free space impedance, S 11 is the reflection coefficient of the entire metasurface, S 21 is the transmission coefficient of the entire metasurface.

[0083] According to the design method of the reflective and transmissive integrated terahertz flexible metasurface of the present invention, the transmission polarization conversion rate P of the metasurface is expressed as follows:

[0084]

[0085] Where P f and P b are the polarization conversion coefficients when the electromagnetic wave is incident in the forward direction and in the reverse direction, t xy and t yx represents the cross-polarization transmission coefficient, t yy and t xx Represents the co-polarization transmission coefficient. When the electromagnetic wave is incident in the forward direction, Pf is 1, P b When the electromagnetic wave is incident in the reverse direction, P f is 0, P b =1; Transmission polarization conversion rate P error function K P It can be expressed as follows:

[0086]

[0087] Where Δφ represents the transmission phase difference, and the control function Φ of the transmission polarization conversion rate is further obtained:

[0088]

[0089] According to the design method of the reflective and transmissive integrated terahertz flexible metasurface of the present invention, the asymmetric transmission characteristics of the metasurface are expressed as follows:

[0090]

[0091] Where Δ lin (x) and Δ lin (y) represents the asymmetric transmission parameters of the forward propagating x-polarized wave and y-polarized wave, and are the total transmittance of x and y polarized waves under normal incidence, T b x and T b y represent the total transmittance under reverse incidence of x and y polarized waves respectively; and is the transmission coefficient when the electromagnetic wave is incident in the normal direction, and is the transmission coefficient when the electromagnetic wave is incident in the reverse direction; the subscripts m and m+1 represent the numbers of any two adjacent frequency points within the working bandwidth, η x represents the relative error of the asymmetric transmission parameters of the x-polarization wave, η y It represents the relative error of the asymmetric transmission parameters of the y-polarization wave. Specific embodiment:

[0093] 1) Design a reflective and transmissive metasurface unit structure such as Figure 1 As shown:

[0094] 2) Design of the top pattern layer: The period of the reflective and transmissive integrated metasurface unit structure in this embodiment is p = 50 μm, and the conductivity of the pattern layer is 5.80×10 7 S / m copper sheet and photosensitive silicon material with a relative dielectric constant of 11.7. When the photosensitive silicon is in a metallic state, its conductivity is 1×10 5S / m, when the photosensitive silicon is in an insulating state, its conductivity is 1S / m. The pattern range l1 of the outer notch square copper sheet is 48μm, l2 is 23μm, the pattern range l3 of the inner notch square copper sheet is 7μm, l4 is 6μm, the width w of the two photosensitive silicon square sheets is 5μm, and the thickness t1 of the top pattern layer is 0.20μm. Figure 2 As shown;

[0095] 3) Design of the second dielectric layer: The second layer of polyimide flexible dielectric material in this embodiment has a relative dielectric constant of ε PI =3.50+0.00945i, thickness h1 is 4μm, such as Figure 3 As shown;

[0096] 4) Design of the third regulating layer: The third vanadium dioxide regulating layer described in this embodiment has a conductivity of 2×10 5 S / m, the metasurface shows a reflective structure. When vanadium dioxide is in an insulating state, its conductivity is 10S / m, and the metasurface shows a transmissive structure. The thickness t2 is 0.50μm. Figure 3 As shown;

[0097] 5) Design of the fourth dielectric layer: The fourth layer of polyimide flexible dielectric material in this embodiment has a relative dielectric constant of ε PI =3.50+0.00945i, thickness h2 is 4μm, such as Figure 3 As shown;

[0098] 6) Designing the bottom pattern layer: The bottom pattern layer described in this embodiment is obtained by rotating the top pattern 90° clockwise, and the thickness t3 is 0.20 μm. Figure 4 As shown;

[0099] 7) The simulation operating frequency of the embodiment of the present invention is set to 0-3.5THz;

[0100] 8) The metasurface simulation conditions described in the embodiments of the present invention are set to open boundary conditions in the x-axis, y-axis, and z-axis directions. When the electromagnetic wave is incident on the top layer of the metasurface along the -z direction, it is considered to be forward incident. When it is incident on the bottom layer of the metasurface along the +z direction, it is considered to be backward incident.

[0101] 9) According to the method of the present invention, when the vanadium dioxide is in a metallic state and the photosensitive silicon is in an insulating state, the metasurface is a reflective structure. The middle vanadium dioxide layer separates the metasurface into two independent reflective systems, the top layer and the bottom layer. The metasurface can achieve a bidirectional wave absorbing function, such as Figure 5 and Figure 6 As shown:

[0102] When the electromagnetic wave is incident in the forward direction, the absorption peaks in the x and y polarization modes are located at 1.75 THz and 1.12 THz, respectively, and the absorption rates reach 93.33% and 97.32%, respectively. Figure 5 When the electromagnetic wave is incident in the reverse direction, the absorption peak positions in the x and y polarization modes are interchanged, and the absorption rates at 1.12THz and 1.75THz are 97.32% and 93.33%, respectively, as shown in Figure 6 This is because the bottom pattern layer is obtained by rotating the top pattern layer 90° clockwise, which is the same as the polarization angle between the x-polarized wave and the y-polarized wave. Therefore, the absorption characteristics of the x(y) polarized wave at reverse incidence are the same as the absorption characteristics of the y(x) polarized wave at forward incidence. The above analysis shows that the embodiment of the present invention can achieve two antisymmetric absorption peaks in the top and bottom layers, thereby forming a system with selective absorption characteristics.

[0103] 10) When vanadium dioxide is in a metallic state and photosensitive silicon is in an insulating state, the metasurface is conformally placed on the outside of a cylinder with a radius R increasing from 50 μm to 300 μm. The absorption rates of electromagnetic waves under forward and reverse incidence are as follows: Figure 7 and Figure 8 As shown:

[0104] When electromagnetic waves are incident in the forward direction, as R increases from 50μm to 300μm, the absorptivity of x-polarized waves increases from 86.93% to 99.40%, while the absorptivity under y-polarized wave incidence remains essentially unchanged. For electromagnetic waves incident in the reverse direction, the absorptivity under both x- and y-polarized wave incidences redshift, but the redshift trend under y-polarized wave incidence is more significant. The above results show that the embodiment of the present invention maintains a high absorption effect when conformally applied to a cylinder with a radius ranging from 50μm to 300μm, and can be widely used in practical engineering applications on curved surfaces.

[0105] 11) When vanadium dioxide is in a metallic state, the bidirectional absorption rate can be tuned by adjusting the conductivity of the photosensitive silicon, such as Figure 9 、 Figure 10 、 Figure 11 and Figure 12 As shown:

[0106] like Figure 9 As shown, when the x-polarized wave is incident in the forward direction, when σ PSi From 1S / m to 1×10 3 S / m, the absorption at 1.75THz first increases from 93.33% to 99.78% and then decreases to 67.97%. PSi =5×10 4 S / m, the absorption peak red-shifts to 1.14THz, and the absorption rate is 54.15%. PSi Increased to 1×105 S / m, the absorption rate at 1.14THz increases to 74.90%. When the y-polarized wave is incident in the forward direction, as σ PSi With the increase of , the absorption at 1.12 THz always maintains a high value, such as Figure 10 shown. Figure 11 and Figure 12 The absorption rate change curves of the reverse incident x- and y-polarized waves are respectively antisymmetric to the change trend at forward incidence.

[0107] 12) According to the method of the present invention, when both vanadium dioxide and photosensitive silicon are in an insulating state, the designed metasurface is a transmission structure, showing good polarization conversion and asymmetric transmission properties, such as Figure 13 、 Figure 14 、 Figure 15 and Figure 16 As shown:

[0108] like Figure 13 As shown, when the electromagnetic wave is incident in the forward direction, the transmission coefficient t yx is greater than 0.6 in the range of 1.52-1.71 THz and 2.70-3.06 THz, and t xy It is always less than 0.1 in the studied frequency band. This indicates that the forward incident electromagnetic wave realizes the conversion of x-polarized wave to y-polarized wave. When the electromagnetic wave is reversely incident, the transmission coefficient t yx and t xy In contrast to the transmission spectrum at normal incidence, Figure 14 This indicates that the reverse incident y-polarized wave is successfully converted into an x-polarized wave. The results show that the embodiment of the present invention achieves linear polarization conversion for both x- and y-polarized waves and has good asymmetric transmission characteristics. Figure 15 The calculated asymmetric transmission curve shows that when the electromagnetic wave is incident in the forward direction, the two bands mentioned above have a higher Δ lin (x) coefficient, which proves that only x-polarized waves are converted to y-polarized waves. When the electromagnetic wave is incident in the opposite direction, Δ lin (y) and Δ lin The result of (x) is opposite, indicating that the linear polarization conversion of y-polarized wave to x-polarized wave is allowed in both bands. Figure 16As shown, the forward incident x-polarized wave achieves a polarization conversion rate greater than 90% within 1.57-1.92THz and 2.32-3.37THz, and the corresponding relative bandwidths are 20.06% and 36.91%, respectively. The polarization conversion rates at the resonant frequencies of 1.86THz, 2.52THz, and 3.33THz are 99.41%, 99.90%, and 98.32%, respectively, which indicates that a complete conversion from x-polarization to y-polarization wave is achieved at the resonant frequency. The polarization conversion rate curve of reverse incidence completely coincides with the polarization conversion rate curve of forward incidence, which is consistent with the asymmetric transmission principle. The above results show that the embodiment of the present invention realizes the conversion from x-polarization to y-polarization wave when the electromagnetic wave is incident in the forward direction, and when the electromagnetic wave is incident in the reverse direction, the y-polarization wave can be converted into an x-polarization wave;

[0109] 13) When both vanadium dioxide and photosensitive silicon are in an insulating state, the polarization conversion rate curve and the asymmetric transmission curve of the metasurface conformally placed on the outside of a cylinder with a radius R increasing from 50 μm to 300 μm are as follows: Figure 17 、 Figure 18 and Figure 19 As shown:

[0110] exist Figure 17 In the first frequency band, Δ lin The maximum value of (x) increases from 0.40 (R = 50 μm) to 0.56 (R = 300 μm); in the second frequency band, Δ lin The maximum value of (x) increases from 0.49 to 0.63, indicating that the asymmetric transmission characteristics of the embodiment of the present invention are significantly improved with the increase of R. lin The change curve of (y) shows the same as Δ lin (x) Symmetrical trend characteristics. Figure 18 As shown in , with the increase of R, the polarization conversion rate of the forward incident electromagnetic wave in the first frequency band remains basically unchanged, while in the second frequency band, the bandwidth with the polarization conversion rate greater than 90% gradually widens. For the reverse incident electromagnetic wave, as shown in Figure 19 As shown, when R is 50μm, the frequency band with a polarization conversion rate greater than 90% is only in the range of 1.56-1.98THz and 2.32-2.90THz. As R increases, the bandwidth with a polarization conversion rate greater than 90% gradually widens; when R increases to 300μm, the bandwidth with a polarization conversion rate greater than 90% widens to 1.55-1.98THz and 2.35-3.36THz. In contrast, the flat surface can be regarded as a case where R is infinite, at which time it exhibits optimal polarization conversion and asymmetric transmission characteristics. Therefore, the metasurface of the same structure conformally on the surface of a cylinder with a gentler curvature will exhibit better asymmetric transmission characteristics and polarization conversion efficiency;

[0111] 14) When vanadium dioxide is in an insulating state, the asymmetric transmission and polarization conversion rate can be tuned by adjusting the conductivity of the photosensitive silicon, such as Figure 20 and Figure 21 As shown:

[0112] like Figure 20 As shown, with σ PSi As σ increases, the asymmetric transmission performance decreases. PSi Greater than 1×10 4 When S / m, the asymmetric transmission characteristics disappear. Figure 21 When the electromagnetic wave is incident in the forward direction, σ PSi From 1S / m to 1×10 3 When σ / m, the embodiment of the present invention has a higher polarization conversion rate and a wider working bandwidth, which means that good polarization conversion performance is achieved. PSi =1×10 4 When the polarization conversion efficiency of the first band decreases to 70.69%, the two operating frequency bands become narrower rapidly. PSi Increased to 5×10 4 When σ is less than 0.05, the polarization conversion efficiency of the first band disappears completely, and the polarization conversion efficiency of the second band decreases to 68.84%. PSi Continue to increase to 1×10 5 S / m, the polarization conversion rate of the second frequency band decreases from 68.84% to 19.90%. At this time, the embodiment of the present invention no longer has the polarization conversion function. In addition, when the electromagnetic wave is incident in the reverse direction, the polarization conversion rate curve coincides with that of the forward direction. The above results show that by adjusting σ PSi , the embodiments of the present invention can realize dynamic regulation of asymmetric transmission and polarization conversion rate.

[0113] The specific examples of the present invention are intended to illustrate the principles of the present invention in detail. Those skilled in the art should understand that while maintaining the core concepts and principles of the present invention, the functions and details achievable by the present invention may be subject to various changes and modifications. However, such changes based on the concepts of the present invention should fall within the scope of protection of the claims of the present invention.

Claims

1. A reflective and transmissive terahertz flexible metasurface, characterized by: Design a reflective and transmissive integrated terahertz flexible metasurface unit structure, comprising five layers: from top to bottom, a top pattern layer consisting of two notched square copper sheets and two photosensitive silicon sheets; the second and fourth layers are both polyimide flexible dielectric layers; the third layer is a vanadium dioxide regulation layer; and the bottom pattern layer is obtained by rotating the top pattern 90° clockwise. The second and fourth polyimide flexible dielectric layers are consistent with the third vanadium dioxide control layer in length and width, but different in thickness.

2. The method for designing a reflective and transmissive integrated terahertz flexible metasurface according to claim 1, characterized in that: The unit structures are periodically arranged along the x and y coordinate axes in the o-xyz space coordinate system, and are extended to form a multifunctional metasurface, where o is the origin of the coordinate axis.

3. The design method of the reflective and transmissive integrated terahertz flexible metasurface according to claim 2, characterized in that: The relative dielectric constant ε of the vanadium dioxide control layer VO2 It is expressed as follows: In the formula, ε represents the relative dielectric constant, VO2 represents vanadium dioxide, represents the relative dielectric constant of vanadium dioxide, ξ represents the volume fraction of vanadium dioxide in the metallic state, which changes with increasing temperature. ξ is approximately equal to 0 in the insulating state of vanadium dioxide, and its maximum value is 0.

95. ξ is obtained from the Boltzmann function as follows: Where T is the ambient temperature, T0=68℃ is the phase transition temperature, ε i =9 and ε m are the dielectric constants of the insulating and metallic states of vanadium dioxide, and ε in the terahertz band. m Expressed using the Drude model: Where, ε ∞ =9 is the high-frequency dielectric constant of vanadium dioxide, is the electrical conductivity of vanadium dioxide. When vanadium dioxide is in an insulating state, When vanadium dioxide is in the metallic state, ω represents the incident angular frequency, c = -0.6579 is the empirical coefficient related to backscattering, Γ = e / (m × μ) is the scattering coefficient, μ = 2 × 10 -4 m 2 / (V·s) is the carrier mobility, m*=2m=1.82×10 -30 kg represents effective mass, e=1.60×10 -19 C is the electron charge, i represents the imaginary unit, is with Related plasma frequencies.

4. The design method of the reflective and transmissive integrated terahertz flexible metasurface according to claim 3, characterized in that: The photosensitive silicon conductivity is manipulated by pump light and is expressed as follows: s PSi =4.863×10 -4 ×A 2 +0.1856×A+1.569 Where, σ represents conductivity, PSi represents photosensitive silicon, σ PSi Indicates the conductivity of photosensitive silicon. A is the energy flux of the pump beam. When there is no pump beam (no pump light flux), the photosensitive silicon is in an insulating state and its conductivity is 1S / m. At A, it is 294.6μJ / cm 2 When the pump light energy flux reaches the maximum, the photosensitive silicon is in a metallic state and its conductivity is 1×10 5 S / m.

5. The design method of the reflective and transmissive integrated terahertz flexible metasurface according to claim 4, characterized in that: The bidirectional absorptivity A(ω) of the metasurface satisfies: A(w)=1-R(w)-T(w)=a f (1-|S f11 | 2 -|S f21 | 2 )+a b (1-|S b11 | 2 -|S b21 | 2 )±t Where R(ω) and T(ω) represent reflectivity and transmittance respectively, α f is the absorption coefficient of electromagnetic wave when it is incident in the forward direction, S f11 and S f21 are the reflection coefficient and transmission coefficient when the electromagnetic wave is incident in the forward direction; α b is the absorption coefficient of electromagnetic wave when it is incident in reverse direction, S b11 and S b21 are respectively the reflection coefficient and transmission coefficient when the electromagnetic wave is incident in the reverse direction; when the electromagnetic wave is incident in the forward direction, α f is 1, α b When the electromagnetic wave is incident in the reverse direction, α f is 0, α b is 1; τ is the error function of the bidirectional absorption rate: Where Z is the equivalent impedance of the absorber, Z0 represents the free space impedance, S 11 is the reflection coefficient of the entire metasurface, S 21 is the transmission coefficient of the entire metasurface.

6. The method for designing a reflective and transmissive integrated terahertz flexible metasurface according to claim 5, characterized in that: The metasurface transmission polarization conversion rate P is expressed as follows: Where, P f and P b are the polarization conversion coefficients when the electromagnetic wave is incident in the forward direction and in the reverse direction, t xy and t yx represents the cross-polarization transmission coefficient, t yy and t xx Represents the co-polarization transmission coefficient; when the electromagnetic wave is incident in the forward direction, P f is 1, P b is 0; when the electromagnetic wave is incident in the reverse direction, P f is 0, P b =1; Transmission polarization conversion rate P error function K P It can be expressed as follows: Where Δφ represents the transmission phase difference, and the control function Φ of the transmission polarization conversion rate is further obtained:

7. The method for designing a reflective and transmissive integrated terahertz flexible metasurface according to claim 6, characterized in that: The asymmetric transmission characteristics of the metasurface are expressed as follows: Where, Δ lin (x) and Δ lin (y) represents the asymmetric transmission parameters of the forward propagating x-polarized wave and y-polarized wave, T f x and T f y are the total transmittance of x and y polarized waves under normal incidence, T b x and T b y represent the total transmittance under reverse incidence of x and y polarized waves respectively; and is the transmission coefficient when the electromagnetic wave is incident in the normal direction, and is the transmission coefficient when the electromagnetic wave is incident in the reverse direction; the subscripts m and m+1 represent the numbers of any two adjacent frequency points within the working bandwidth, η x represents the relative error of the asymmetric transmission parameters of the x-polarization wave, η y It represents the relative error of the asymmetric transmission parameters of the y-polarization wave.

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