Ultra-wideband and multi-frequency switchable terahertz absorber based on vo2 multilayer structure and preparation method thereof

By designing a multi-layer VO2 structure and utilizing the thermally induced phase transition of VO2, an ultra-wideband and multi-frequency switchable terahertz absorber was realized, solving the problems of narrow absorption bandwidth and narrow incident angle range in existing technologies, and meeting the application requirements of multi-band, wideband, and wide-angle absorption.

CN122370739APending Publication Date: 2026-07-10XIAN UNIV OF TECH

Patent Information

Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
XIAN UNIV OF TECH
Filing Date
2026-03-24
Publication Date
2026-07-10

AI Technical Summary

Technical Problem

Existing metamaterial terahertz absorbers suffer from narrow absorption bandwidth and narrow incident angle range, making it difficult to meet the application requirements of multi-band and broadband wide-angle absorption.

Method used

An ultra-wideband and multi-frequency switchable terahertz absorber based on a VO2 multilayer structure is adopted. By utilizing the reversible thermally induced phase transition of VO2, a synergistic structure of a metal substrate, multilayer dielectric layer and resonant layer is designed to enable the absorber to switch absorption modes at different temperatures, including ultra-wideband and multi-frequency absorption.

Benefits of technology

It achieves an ultra-wideband absorption rate of over 90% in the frequency range of 6.47 THz to 12.83 THz, and a multi-frequency absorption rate of over 90% at frequencies of 3.26 THz, 6.68 THz, 7.69 THz, 9.26 THz, 10.32 THz, and 13.09 THz. It also features polarization insensitivity and wide-angle absorption, making it suitable for broadband detection and multispectral imaging.

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Abstract

This invention relates to the terahertz field, specifically to an ultra-wideband and multi-frequency switchable terahertz absorber based on a VO2 multilayer structure and its fabrication method; it includes a metal substrate; a first dielectric layer covering the metal substrate; a double gold ring resonant layer formed by concentric ring structures distributed at the four corners of a square cross-section connected by a rectangular region; a VO2 spacer resonant layer covering the upper surface of the first dielectric layer and the top surface of the double gold ring resonant layer; a second dielectric layer covering the VO2 spacer resonant layer; a square ring VO2 resonant layer including an outer square ring and a circular structure at the center; a third dielectric layer covering the upper surfaces of the second dielectric layer and the square ring VO2 resonant layer; and an elliptical star-shaped VO2 resonant layer disposed on the third dielectric layer. This invention utilizes the reversible thermally induced phase transition characteristics of VO2 between its insulating and metallic states to achieve flexible switching between two distinct absorption modes in the same device.
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Description

Technical Field

[0001] This invention relates to the field of terahertz, specifically to an ultrawideband and multi-frequency switchable terahertz absorber based on a VO2 multilayer structure and its fabrication method. Background Technology

[0002] Terahertz (THz) waves generally refer to electromagnetic waves with frequencies ranging from 0.1 to 10 THz. Due to their low energy, strong penetrating power, and unique frequency and wavelength, terahertz waves and related technologies have become a research hotspot in various fields. Terahertz absorbers, as fundamental functional devices for terahertz applications, are widely used in detectors, spectral imaging, stealth, and other fields.

[0003] Terahertz absorbers based on metamaterials are devices that can efficiently absorb incident terahertz waves. The main principle is to utilize different loss mechanisms to convert terahertz waves into heat or other forms of energy, ultimately achieving the effect of terahertz wave absorption. Among various absorbers, metamaterial-based absorbers have received widespread attention from scholars both domestically and internationally in recent years. Compared with traditional absorbers, metamaterial absorbers have advantages such as small size, high absorption rate, and easy integration. Currently, the design, fabrication, and characterization of metamaterial terahertz absorbers have been extensively studied. Despite their high absorption rate, most existing metamaterial absorbers are single-band absorbers, exhibiting problems such as narrow absorption bandwidth and narrow incident angle range. This limits the application scenarios of metamaterial absorbers; for example, in spectral detection and phase imaging, there is an urgent need for multi-band, broadband wide-angle absorbers. Summary of the Invention

[0004] To address the problems mentioned in the prior art, this invention proposes an ultra-wideband and multi-frequency switchable terahertz absorber based on a VO2 multilayer structure and its fabrication method. Utilizing the reversible thermally induced phase transition of VO2, when VO2 is in the metallic state, it can achieve ultra-wideband absorption of 6.36 THz in the range of 6.47 THz to 12.83 THz. When VO2 is in the insulating state, it can simultaneously achieve multi-frequency absorption with an absorption rate exceeding 90% at six frequency points (3.26 THz, 6.68 THz, 7.69 THz, 9.26 THz, 10.32 THz, and 13.09 THz). Furthermore, this absorber features ultra-wideband and multi-frequency switchability, polarization insensitivity, wide-angle absorption, and a simple structure.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: This invention relates to an ultra-wideband and multi-frequency switchable terahertz absorber based on a VO2 multilayer structure, comprising multiple absorption units arranged in a periodic array. Each absorption unit has the following structure stacked sequentially from bottom to top: Metal substrate; A first dielectric layer covers the metal substrate; A double gold ring resonant layer is embedded inside the first dielectric layer, and the top surface of the double gold ring resonant layer is flush with the top surface of the first dielectric layer; the double gold ring resonant layer is formed by connecting concentric ring structures distributed at the four corners of a square cross section through a rectangular region; A VO2 spacer resonant layer covers the upper surface of the first dielectric layer and the top surface of the double gold ring resonant layer; A second dielectric layer covers the VO2 spacer resonant layer; A square ring VO2 resonant layer is disposed on the upper surface of the second dielectric layer. The square ring VO2 resonant layer includes an outer square ring and a circular structure disposed at the center. A third dielectric layer covers the upper surface of the second dielectric layer and the square ring VO2 resonant layer; An elliptical star-shaped VO2 resonant layer is disposed on the third dielectric layer.

[0006] As a further improvement of the present invention, the thickness of the double gold ring resonant layer is 1 to 3 µm, and includes two concentric rings, a rectangular region and a square frame. The two concentric rings, inner and outer, are located at the center of the square frame. The inner ring has an inner radius of 2–4 µm and an outer radius of 5–7 µm, while the outer ring has an inner radius of 8–9 µm and an outer radius of 10–12 µm. The rectangular regions are respectively located at the four corners of the square frame, and the side length of the rectangular regions is 1 to 3 µm.

[0007] As a further improvement of the present invention, the VO2 spacer resonant layer is a VO2 thin film, wherein the horizontal cross-sectional side length of the VO2 spacer resonant layer is the same as that of the first dielectric layer, and the thickness of the VO2 thin film is 0.2 to 0.6 μm.

[0008] As a further improvement of the present invention, the square ring VO2 resonant layer includes an outer square ring and a central circular structure disposed at the center of the outer square ring; The outer side length of the outer square ring is 30–32 μm, and the width is 3–6 μm; The radius of the central circular structure is 1–4 μm; The thickness of the square ring VO2 resonant layer is 0.03–0.07 μm.

[0009] As a further improvement of the present invention, the elliptical star-shaped VO2 resonant layer includes square units and a pattern disposed on the square units, the pattern being constructed as follows: At each of the four vertices of the square unit, a sector-shaped structure with a quarter circle centered at the vertex is formed; A circular structure is located at the center of the square unit; An arc-shaped substructure enclosed by an outer arc radius and an inner arc radius is prepared. The arc-shaped substructure is then arrayed by rotating 90° around the center of a square unit to obtain four identical arc-shaped substructures. Subtracting the circular structure from the four identical arc substructures results in an elliptical star pattern. The patterns include oval star shapes and quarter-circle fan-shaped structures.

[0010] As a further improvement of the present invention, the metal substrate is made of Au and has a thickness of 0.1–0.4 μm; The first dielectric layer, the second dielectric layer, and the third dielectric layer are all made of PDMS; wherein, the thickness of the first dielectric layer is 5-7 μm, the thickness of the second dielectric layer is 2-4 μm, and the thickness of the third dielectric layer is 2.8-3 μm.

[0011] As a further improvement of the present invention, the VO2 material of the VO2 spacer resonant layer, the square ring VO2 resonant layer and the elliptical star VO2 resonant layer undergoes a reversible phase transition under temperature control. Below 68℃, it is in an insulating state with a conductivity of 150 S / m; above 68℃, VO2 material is in a metallic state with a conductivity of 8 × 10⁻⁶. 4 S / m.

[0012] This invention proposes a method for fabricating an ultra-wideband and multi-frequency switchable terahertz absorber based on a VO2 multilayer structure, applicable to the aforementioned ultra-wideband and multi-frequency switchable terahertz absorber based on a VO2 multilayer structure, comprising the following steps: S1. Deposit and anneal the metal substrate on the substrate to form a metal substrate; S2. PDMS dielectric is deposited on the metal substrate using a spin coating process, and the first dielectric layer is formed after curing. S3. A metal film is deposited on the first dielectric layer using electron beam evaporation process, and then sequentially undergoes photoresist coating pre-baking, ultraviolet exposure, development, etching and shaping and photoresist removal and cleaning to form a double gold ring resonant layer embedded in the first dielectric layer. S4. A VO2 thin film is formed on the surface of the first dielectric layer and the top surface of the double gold ring resonant layer using a pulsed laser deposition process to form a VO2 spacer resonant layer. S5. PDMS dielectric is deposited on the VO2 spacer resonant layer using spin coating process, and a second dielectric layer is formed after curing. S6. A VO2 thin film is deposited on the second dielectric layer using pulsed laser deposition process, and then patterned and lifted by ultraviolet lithography to form a square ring VO2 resonant layer. S7. PDMS dielectric is deposited on the square ring VO2 resonant layer using pulsed laser deposition process, and a third dielectric layer is formed after curing. S8. A VO2 thin film is deposited on the third dielectric layer using pulsed laser deposition. After ultraviolet lithography patterning and lift-off shaping, an elliptical star-shaped VO2 resonant layer is obtained, thus completing the fabrication of the absorber.

[0013] As a further improvement to the present invention, the specific process of S3 includes: A gold thin film was deposited on the surface of the first dielectric layer using an electron beam evaporation method. Photoresist was spin-coated onto the surface of a gold thin film and then preheated on a hot plate at 95–100°C for 85–90 seconds. A concentric ring pattern is exposed using an ultraviolet lithography machine through a photomask; Use a developer solution to treat for 55–60 seconds to remove the photoresist from the exposed areas; The gold layer not protected by photoresist is selectively removed using a gold etching solution, and the adhesion layer is removed using a chromium etching solution. Residual photoresist was removed using acetone, and then the mixture was rinsed with ethanol and deionized water and dried with nitrogen to form a double gold ring resonant layer.

[0014] As a further improvement to the present invention, the specific process of S8 includes: A VO2 thin film was deposited on the third dielectric layer using a pulsed laser deposition process. Using ultraviolet lithography, an elliptical star pattern is defined at the center and quarter-circle fan-shaped patterns are located at the four corners; The photoresist and excess VO2 film were removed by a stripping method, leaving the elliptical star-shaped VO2 resonant layer formed by the central elliptical star pattern and the quarter-circle fan-shaped structures at the four corners.

[0015] Compared with the prior art, the present invention achieves the following technical effects: This invention utilizes the reversible thermo-induced phase transition characteristic of VO2 between its insulating and metallic states to achieve flexible switching between two distinct absorption modes within the same device, solving the problem of single-mode operation in existing absorbers. When the ambient temperature is above 68°C, VO2 transitions to the metallic state, and the square ring VO2 resonant layer and elliptical star VO2 resonant layer become strong resonant units. Through their interaction with the double gold ring resonant layer, they achieve ultra-wideband absorption with an absorption rate exceeding 90% in the frequency range of 6.47 THz to 12.83 THz, with an absorption bandwidth of 6.36 THz. This bandwidth is significantly superior to traditional single-band or multi-band absorbers, meeting the needs of applications such as broadband detection and stealth. When the ambient temperature is below 68°C, VO2 is in the insulating state, the response of the square ring VO2 resonant layer and elliptical star VO2 resonant layer weakens, and the absorption process is dominated by the double gold ring resonant layer. Through the patterned structure of the double gold ring resonant layer, absorption can be achieved at frequencies of 3.26 THz, 6.68 THz, 7.69 THz, 9.26 THz, and 10.32 THz. It achieves multi-frequency absorption with an absorption rate of over 90% at six frequency points including 13.09 THz and 13.09 THz, making it suitable for fields requiring multi-frequency response such as multispectral detection and spectral imaging.

[0016] This invention, through the synergistic design of a metal substrate, three dielectric layers, and three resonant layers, enables the absorber to achieve perfect matching with free-space impedance in both operating modes. The real part of the normalized equivalent impedance approaches 1, and the imaginary part approaches 0, ensuring minimal reflection of the incident terahertz wave at the device surface. Wave energy is effectively dissipated in the dielectric and resonant structure, thereby achieving a high absorption rate of over 90%. Simultaneously, the resonant layer patterns of this invention adopt a centrally symmetrical design, making the absorber insensitive to changes in the polarization angle of the incident wave. It maintains the same excellent absorption performance under perpendicular incidence conditions, greatly simplifying the alignment requirements in practical applications.

[0017] The preparation method of this invention is simple. The three dielectric layers are prepared using spin coating and curing processes, and the thickness is controllable. The double gold ring resonant layer is prepared using electron beam evaporation, photolithography, and etching processes, which can form complex metal patterns. The VO2 layers are grown using pulsed laser deposition, combined with ultraviolet photolithography and lift-off processes, avoiding the process difficulties of directly etching VO2. The entire preparation method has clear and accurate steps and good repeatability. Finally, this invention achieves the switching between ultra-wideband absorption mode and multi-frequency absorption mode on the same absorber by combining a multi-layer composite structure with VO2 material, which can be widely used in terahertz detectors, spectrum imaging, stealth technology, communications and other fields. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the absorption unit structure arranged periodically according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the absorption unit structure according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the structure of the double gold ring resonant layer in an embodiment of the present invention; Figure 4 This is a schematic diagram of the structure of the square ring VO2 resonant layer according to an embodiment of the present invention; Figure 5 This is a schematic diagram of the structure of the elliptical star-shaped VO2 resonant layer according to an embodiment of the present invention; Figure 6 This is the absorption spectrum of the terahertz absorber in an embodiment of the present invention when VO2 is in a metallic state; Figure 7 This is the absorption spectrum of the terahertz absorber in an embodiment of the present invention when VO2 is in an insulating state; Figure 8 This is the normalized equivalent impedance diagram of the terahertz absorber in an embodiment of the present invention when VO2 is in a metallic state; Figure 9 This is the normalized equivalent impedance diagram of the terahertz absorber when VO2 is in an insulating state according to an embodiment of the present invention; Figure 10 The electric field distribution of the absorber provided in the embodiments of the present invention is shown in (a)-(c), where (a)-(c) are the electric field distributions of the double gold ring resonant layer, the square ring VO2 resonant layer, the elliptical star VO2 resonant layer and the overall side view when VO2 is in the metallic state; (d)-(i) are the electric field distributions of the double gold ring resonant layer, the square ring VO2 resonant layer, the elliptical star VO2 resonant layer and the overall side view when VO2 is in the insulating state. Figure 11 This is a diagram showing the effect of VO2 conductivity on the absorption spectrum in the absorber of an embodiment of the present invention; Figure 12 This is a diagram illustrating the effect of the change in the incident wave polarization angle on the absorption spectrum according to an embodiment of the present invention. Figure 13 This is a diagram showing the effect of the change in incident angle on the absorption spectrum in TE mode in this embodiment of the invention; Figure 14 This is a schematic diagram of the pattern structure in the elliptical star-shaped VO2 resonant layer in an embodiment of the present invention; Figure 15 This is a schematic diagram of the thickness of the absorption unit structure according to an embodiment of the present invention.

[0019] Reference numerals: 1. Metal substrate; 2. First dielectric layer; 3. Double gold ring resonant layer; 4. VO2 spacer resonant layer; 5. Second dielectric layer; 6. Square ring VO2 resonant layer; 7. Third dielectric layer; 8. Elliptical star VO2 resonant layer. Detailed Implementation

[0020] In the following description, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments can be modified in various ways without departing from the spirit or scope of the invention. Therefore, the drawings and description are considered to be exemplary in nature and not restrictive.

[0021] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0022] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0023] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection, an electrical connection, or a communication connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0024] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can include direct contact between the first and second features, or contact between the first and second features through another feature between them. Furthermore, "above," "over," and "on top" of the second feature includes the first feature being directly above or diagonally above the second feature, or simply indicates that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature includes the first feature being directly above or diagonally above the second feature, or simply indicates that the first feature is at a lower horizontal level than the second feature.

[0025] It should be understood that, when used in this specification and the appended claims, the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0026] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0027] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0028] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0029] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0030] Example 1 This embodiment proposes an ultra-wideband and multi-frequency switchable terahertz absorber based on a VO2 multilayer structure, comprising multiple absorber units arranged in a periodic array, each absorber unit having the following structure stacked from bottom to top: Metal substrate 1; The first dielectric layer 2 covers the metal substrate 1; The double gold ring resonant layer 3 is embedded inside the first dielectric layer 2, and the top surface of the double gold ring resonant layer 3 is flush with the top surface of the first dielectric layer 2; the double gold ring resonant layer 3 is formed by connecting concentric ring structures distributed at the four corners of a square cross section through a rectangular region. A VO2 spacer resonant layer 4 covers the upper surface of the first dielectric layer 2 and the top surface of the double gold ring resonant layer 3; The second dielectric layer 5 covers the VO2 spaced resonant layer 4; A square ring VO2 resonant layer 6 is disposed on the upper surface of the second dielectric layer 5. The square ring VO2 resonant layer 6 includes an outer square ring and a circular structure disposed at the center. The third dielectric layer 7 covers the upper surface of the second dielectric layer 5 and the square ring VO2 resonant layer 6; An elliptical star-shaped VO2 resonant layer 8 is disposed on the third dielectric layer 7.

[0031] In this embodiment, the terahertz absorber is composed of multiple absorption units arranged in a two-dimensional periodic array in an M×N form. See [link to relevant documentation]. Figure 1 The diagram shows the structure of the absorption units arranged periodically. It can be seen that multiple absorption units are distributed in an array in the horizontal direction. The increase or decrease of the number of absorption units will not affect the overall absorption performance of the terahertz absorber. It can only be adjusted according to the size requirements of the actual application. In this embodiment, VO2 is vanadium dioxide.

[0032] Each absorption unit in the embodiment is a multilayer composite structure, see [link / reference]. Figure 2 The diagram shows the structure of a single absorption unit. Each absorption unit is composed of a metal substrate 1, a first dielectric layer 2, a double gold ring resonant layer 3, a VO2 spacer resonant layer 4, a second dielectric layer 5, a square ring VO2 resonant layer 6, a third dielectric layer 7, and an elliptical star-shaped VO2 resonant layer 8 stacked sequentially from bottom to top.

[0033] See Figure 2 and Figure 15 Specifically, the metal substrate 1, serving as the substrate for the absorption unit, is preferably made of Au material, with a preferred thickness t1 of 0.2 μm. The horizontal cross-section of the metal substrate 1 is square, and its side length p1 is consistent with the side lengths of the subsequent first dielectric layer 2, second dielectric layer 5, and third dielectric layer 7, which is 32–36 μm. Preferably, the thickness is 33μm; the metal substrate 1 utilizes the characteristics of Au material in the terahertz band, and its thickness is much greater than the skin depth of gold material in the terahertz band, which can effectively block the transmission of incident terahertz waves, making the transmittance of the absorber to terahertz waves 0, and ensuring that the energy of terahertz waves can be fully absorbed by the upper resonant structure and dielectric layer.

[0034] In this embodiment, the first dielectric layer 2 covers the upper surface of the metal substrate 1 and is bonded to the metal substrate 1. The material of the first dielectric layer 2 is PDMS, the thickness t2 is preferably 6μm, and the relative permittivity is stable at 2.25. The first dielectric layer 2 is used to support the double gold ring resonant layer 3, thereby providing a stable dielectric for the preparation and operation of the double gold ring resonant layer 3, and participating in the impedance matching adjustment of the entire absorber. In addition, PDMS material has low loss in the terahertz band and has good film formation and flexibility.

[0035] In this embodiment, the double gold ring resonant layer 3 is embedded inside the first dielectric layer 2, and the top surface of the double gold ring resonant layer 3 is flush with the top surface of the first dielectric layer 2. It will not form a protrusion or depression on the upper surface of the first dielectric layer 2, which ensures the surface flatness when the VO2 spacer resonant layer 4 is deposited, which is beneficial to improving the overall performance of the device. like Figure 3 The schematic diagram of the double gold ring resonant layer 3 shown indicates that it consists of two concentric rings (inner and outer), rectangular regions, and a square frame. Specifically, the overall thickness t3 of the double gold ring resonant layer 3 is 2 μm. The square frame surrounds and limits the rectangular regions and the two concentric rings. The width d1 of the square frame is 1–3 μm, preferably 1 μm. The two concentric rings are located at the center of the square frame and are the inner and outer rings, respectively. The inner radius r5 of the inner ring is 4 μm, and the outer radius r4 is 5 μm. The inner radius r6 of the outer ring is 9 μm, and the outer radius r7 is 10 μm. There are four rectangular regions, located at the four corners of the square frame, and the side length d2 of each rectangular region is 2 μm. The pattern features designed in this embodiment enable the double gold ring resonant layer 3 to generate independent resonant modes at multiple frequency points. When VO2 is in an insulating state, the absorption process is mainly dominated by the double gold ring resonant layer 3. Due to the designed pattern features, local electric field enhancement can be excited at different frequency points, thereby forming multi-frequency absorption peaks.

[0036] like Figure 15 As shown, the VO2 spacer resonant layer 4 covers the upper surface of the first dielectric layer 2 and the top surface of the double gold ring resonant layer 3. Specifically, it is a continuous VO2 thin film with the same side length of horizontal cross section as the first dielectric layer 2, which is 33 μm, and a thickness t4 of 0.4 μm. In this embodiment, the VO2 spacer resonant layer 4 is composed of VO2. Since VO2 has reversible thermal phase transition characteristics, the dielectric properties of the entire absorption unit change uniformly in the horizontal direction during the phase transition process, thereby achieving a smooth switching of absorption modes. When the temperature changes, the conductivity of VO2 will change significantly, thus affecting the electromagnetic response characteristics of the entire absorber. At the same time, the VO2 spacer resonant layer 4 also plays a transition role, separating the first dielectric layer 2, the double gold ring resonant layer 3 from the second dielectric layer 5 and the square ring VO2 resonant layer 6, avoiding energy loss caused by direct contact between different resonant layers, and optimizing the coupling effect of each resonant layer.

[0037] In this embodiment, the second dielectric layer 5 covers the upper surface of the VO2 spacer resonant layer 4. The material of the second dielectric layer 5 is also PDMS, with a relative permittivity of 2.25 and a thickness t5 of 2μm. The second dielectric layer 5 is used to support the square ring VO2 resonant layer 6 and to separate the VO2 spacer resonant layer 4 from the square ring VO2 resonant layer 6, forming an independent resonant cavity structure.

[0038] See Figure 4A square-ring VO2 resonant layer 6 is disposed on the upper surface of the second dielectric layer 5. The square-ring VO2 resonant layer 6 includes an outer square ring and a central circular structure located at the center of the outer square ring. The outer side length p2 of the outer square ring is 31 μm, the width d3 is 4 μm, the radius r8 of the central circular structure is 2 μm, and the overall thickness t6 of the square-ring VO2 resonant layer 6 is 0.05 μm. It should be noted that the outer side length of the outer square ring is 31 μm, which is smaller than the side length of the second dielectric layer 5 (33 μm), resulting in a gap. Both the outer square ring and the central circular structure are made of VO2 material. When VO2 is in a metallic state, it can interact with the top elliptical star-shaped VO2 resonant layer 8 to generate multiple mutually coupled resonant modes, thereby forming broadband absorption.

[0039] The third dielectric layer 7 covers the upper surface of the second dielectric layer 5 and the square ring VO2 resonant layer (6). The third dielectric layer 7 is also made of PDMS material with a relative permittivity of 2.25 and a thickness t7 of 2.95μm. The third dielectric layer 7 can also provide support for the elliptical star VO2 resonant layer 8.

[0040] See Figure 5 and Figure 14 In this embodiment, an elliptical star-shaped VO2 resonant layer 8 is disposed on the upper surface of the third dielectric layer 7. The elliptical star-shaped VO2 resonant layer 8 is made of VO2 with a thickness t8 of 0.05 μm, which is consistent with the thickness of the square ring VO2 resonant layer 6, thereby ensuring the consistency of the dielectric properties of VO2 in the metallic state. The elliptical star-shaped VO2 resonant layer 8 includes square units and patterns disposed on the square units. The pattern construction process is as follows: First, quarter-circle sector structures are fabricated with the four vertices of a square unit with a side length of 33 μm as centers, preferably with a radius r1 of 8 µm. Next, a circular structure with a radius r9 of 12 µm is placed at the center of the square unit. Then, an arc-shaped substructure is fabricated, enclosed by an outer arc radius r3 of 15.5 µm and an inner arc radius r2 of 17 µm. This arc-shaped substructure is then arranged in an array by rotating it 90° around the center of the square unit, resulting in four completely identical... The arc-shaped substructure is then processed. Finally, a subtraction operation is performed on the central circular structure and the four identical arc-shaped substructures to remove the area covered by the arc-shaped substructures, forming an elliptical star pattern. The elliptical star pattern consists of a central star pattern and four elliptical patterns around it. The width d4 of the outermost gap of the star pattern is 1.5 μm. Finally, a complete pattern is obtained, consisting of a quarter-circle fan-shaped structure at the four corners and a central elliptical star pattern. In this embodiment, the elliptical star VO2 resonant layer 8 can be co-coupled with the square ring VO2 resonant layer 6 to achieve ultra-wideband high absorption rate absorption.

[0041] In this embodiment, the VO2 spacer resonant layer 4, the square ring VO2 resonant layer 6, and the elliptical star-shaped VO2 resonant layer 8 are all made of VO2 material, ensuring the consistency of their phase transition characteristics. The phase transition critical point of VO2 material is 68℃. When the ambient temperature is below 68℃, the VO2 material of the three resonant layers is in an insulating state. At this time, the conductivity of the material is preferably adjusted to 150 S / m. When the ambient temperature is above 68℃, the VO2 material of the three resonant layers undergoes a thermally induced phase transition to a metallic state. At this time, the conductivity of the VO2 material is increased and adjusted to 80000 S / m. The reversible phase transition of VO2 material between the insulating state and the metallic state directly changes the impedance characteristics of the entire absorber, thereby realizing the switching of the absorption mode.

[0042] Example 2 This embodiment proposes a method for fabricating an ultrawideband and multi-frequency switchable terahertz absorber based on a VO2 multilayer structure, including the following steps: S1. Deposit and anneal the substrate to form a metal substrate 1. The substrate selected in this embodiment is a high-purity silicon substrate. First, the silicon substrate is ultrasonically cleaned with acetone, ethanol and deionized water for 10 min to 15 min in sequence to remove contaminants on the substrate surface. After being dried with nitrogen, it is placed in an oven at 110℃ to 120℃ for 30 min to 40 min to ensure that the substrate surface is dry and clean. Then, a gold film is deposited on the surface of the cleaned silicon substrate using an electron beam evaporation process, and the thickness of the gold film is controlled to be 0.2 μm. Finally, the silicon substrate with the gold film deposited is annealed at 300℃ to 350℃ for 30 min to 40 min to improve the crystal quality and conductivity of the gold film, and finally the metal substrate 1 is formed.

[0043] S2. PDMS dielectric is deposited on metal substrate 1 using spin coating process, and the first dielectric layer 2 is formed after curing treatment. PDMS is uniformly spin-coated on the upper surface of metal substrate 1. The spin coating speed is adjusted according to the specific process requirements to ensure the uniformity of PDMS dielectric thickness. After spin coating, it is placed in an oven at 120℃ for 1h to 2h to form a dense film of PDMS, ensuring the stability of its dielectric properties, and finally forming the first dielectric layer 2 with a thickness of 6μm.

[0044] S3. Fabrication of the double gold ring resonant layer 3 embedded in the first dielectric layer 2: First, a gold thin film is deposited on the upper surface of the first dielectric layer 2 using electron beam evaporation, with the thickness of the gold thin film controlled to 2 μm. Then, photoresist is spin-coated onto the surface of the gold thin film. After spin-coating, it is placed on a hot plate and pre-baked at 95–100°C for 85–90 seconds to allow the photoresist to initially cure. Subsequently, an ultraviolet lithography machine is used to expose the surface of the gold thin film with ultraviolet light through a mask. The pattern of the mask is the design pattern in the double gold ring resonant layer 3. After exposure... The photoresist is developed using a developer for 55-60 seconds to remove the photoresist in the exposed areas, exposing the underlying gold film. Then, a gold etchant is used to selectively remove the gold layer not protected by the photoresist, and a chromium etchant is used to remove the adhesion layer between the gold film and the first dielectric layer 2, forming the designed pattern. Finally, acetone is used to remove the residual photoresist, followed by rinsing with ethanol and deionized water in sequence. After drying with nitrogen, a double gold ring resonant layer 3 embedded in the first dielectric layer 2 with its top surface flush with the first dielectric layer 2 is obtained.

[0045] S4. A VO2 thin film is deposited on the surface of the first dielectric layer 2 and the top surface of the double gold ring resonant layer 3 using a pulsed laser deposition process. The laser energy density and deposition temperature are adjusted according to specific process requirements. The thickness of the deposited VO2 thin film is 0.4 μm, and no patterning is performed, directly forming the VO2 spacer resonant layer 4.

[0046] S5. This step is the same as S2. PDMS is deposited on the upper surface of the VO2 spacer resonant layer 4 using a spin coating process. After curing at 120℃ for 1 to 2 hours, a second dielectric layer 5 with a thickness of 2 μm is formed.

[0047] S6. First, a VO2 thin film with a thickness of 0.05 μm is deposited on the upper surface of the second dielectric layer 5 using pulsed laser deposition. Then, the VO2 thin film is patterned using ultraviolet lithography, and the pattern of the outer square ring and the central circular structure is defined by a mask. Finally, the photoresist and the excess VO2 thin film on it are removed by a stripping method, leaving the designed pattern to form the square ring VO2 resonant layer 6.

[0048] S7. This step is the same as S2 and S5. PDMS is deposited on the upper surface of the second dielectric layer 5 and the surface of the square ring VO2 resonant layer 6 using a spin coating process. After curing at 120℃ for 1 to 2 hours, a third dielectric layer 7 with a thickness of 2.95 μm is formed.

[0049] S8. First, a VO2 thin film with a thickness of 0.05 μm is deposited on the upper surface of the third dielectric layer 7 using pulsed laser deposition, which is the same as the thickness of the square ring VO2 resonant layer 6. Then, an ultraviolet lithography process is used to define the central elliptical star pattern and the quarter-circle fan-shaped structures at the four corners using a mask. Finally, the photoresist and excess VO2 film are removed by a lift-off method, leaving only the central elliptical star pattern and the quarter-circle fan-shaped structures to form the elliptical star VO2 resonant layer 8. This completes the fabrication of a single absorption unit.

[0050] Subsequently, multiple absorption units can be arranged in a periodic array in the form of M×N to obtain a complete terahertz absorber.

[0051] The operation of the terahertz absorber in this embodiment revolves around the phase transition of the VO2 material. By adjusting the ambient temperature to change the phase state of the VO2 material, the impedance characteristics of the entire absorber are altered, enabling switching between ultra-wideband absorption and multi-frequency absorption modes; see [link to relevant documentation]. Figure 6 and Figure 7 The absorption spectrum of the terahertz absorber in this example shows that, under normal incident conditions, VO2 in its insulating state exhibits multi-frequency absorption characteristics, displaying significant absorption peaks at six frequency points: 3.26 THz, 6.68 THz, 7.69 THz, 9.26 THz, 10.32 THz, and 13.09 THz, corresponding to absorptivity of 95%, 98%, 92%, 98%, 97%, and 99%, respectively. When the temperature increases, causing VO2 to transform into a metallic state, its conductivity can reach 8 × 10⁴ S / m, giving the absorber ultra-wideband absorption characteristics. Its absorption efficiency exceeds 90% in the frequency range of 6.47 THz to 12.83 THz, with an absorption bandwidth of 6.36 THz.

[0052] See Figure 8 and Figure 9 The diagram illustrates the normalized equivalent impedance of the terahertz absorber as a function of frequency, where the solid line represents the real part of the impedance and the dashed line represents the imaginary part. In the multi-frequency characteristics, at six frequency points (3.26 THz, 6.68 THz, 7.69 THz, 9.26 THz, 10.32 THz, and 13.09 THz), the real part of the impedance approaches 1, and the imaginary part approaches 0. In the ultra-wideband characteristics, within the frequency range of 6.47 THz to 12.83 THz, the real part of the impedance approaches 1, and the imaginary part approaches 0. In summary, the impedance of the terahertz absorber in this embodiment achieves a good match with the free-space impedance, i.e., perfect absorption.

[0053] To further investigate the physical mechanism of the terahertz absorber in this embodiment, the electric field distribution of the terahertz absorber at each center frequency was tested, and the results are as follows: Figure 10As shown, when VO2 is in the metallic state, Figure 10 The electric field distribution diagrams in (a)-(c) show that, within this frequency band, the energy is mainly concentrated in the gap region of the elliptical star-shaped VO2 resonant layer 8 and near the outer square ring of the square ring VO2 resonant layer 6. The energy distribution of the double gold ring resonant layer 3 is negligible. This indicates that the energy is significantly concentrated in the upper structure. The ultra-wideband absorption is mainly achieved by the elliptical star-shaped VO2 resonant layer 8 and the square ring VO2 resonant layer 6. The double gold ring resonant layer 3 effectively hinders the propagation of terahertz waves to the lower medium.

[0054] When VO2 is in an insulating state Figure 10 As shown in (d)-(i), the energy distribution of the elliptical star-shaped VO2 resonant layer 8 and the square ring VO2 resonant layer 6 is negligible. Furthermore, the electric field energy is mainly concentrated within the double gold ring resonant layer 3. The selective energy absorption in this region constitutes the core physical mechanism of the multi-frequency peak characteristic. The electric field corresponding to different frequency terahertz waves is concentrated in specific regions of this layer: at 3.26 THz, the energy is mainly focused on the upper side of the outer ring; at 6.68 THz, it is concentrated on the lower side of the inner ring; at 7.69 THz, the energy covers the outer ring and the four sides of the rectangular frame; at 9.26 THz, the energy is distributed in the double gold ring structure, the rectangular frame, and the four small rectangular regions; at 10.32 THz, the energy is focused on the inner ring; and at 13.09 THz, the energy is distributed on the left and right sides of the outer ring.

[0055] This embodiment aims to study the dynamic tuning capability of a terahertz absorber. Figure 11 The effect of VO2 conductivity on the absorption spectrum of the absorber is presented. The results show that when the conductivity of vanadium dioxide is in the metallic state of 200,000 S / m, 80,000 S / m, and 20,000 S / m, the terahertz absorber exhibits significant broadband absorption characteristics. Its absorption performance mainly comes from the synergistic coupling effect between metallic VO2 and each layer of the medium, and efficient energy capture and dissipation are achieved through a dual resonance mechanism.

[0056] When VO2 is in an insulating state with low conductivity, such as 20 S / m, 150 S / m, and 200 S / m, its absorption performance changes significantly. In this state, the absorption process is dominated solely by the structure of the double gold ring resonant layer 3, achieving multi-frequency absorption characteristics. In-depth analysis reveals that this conductivity-dependent change in absorption characteristics essentially stems from the physical properties of the VO2 dielectric constant. The VO2 dielectric constant has two important characteristics: its imaginary part is always significantly larger than its real part; and as conductivity increases, the real part of the dielectric constant exhibits a monotonically decreasing trend, while the imaginary part increases sharply, with the magnitude of change in the imaginary part far exceeding that of the real part. The dielectric response characteristics determine the two key performance parameters of the terahertz absorber: absorption frequency and absorption resonance. The absorption frequency is mainly determined by the real part of the dielectric constant, while the absorption intensity is mainly controlled by the imaginary part. In summary, the phase state of VO2 can be changed by controlling the temperature, thereby altering the conductivity and achieving the switching between ultra-wideband and multi-frequency absorption characteristics of the terahertz absorber.

[0057] In existing technologies, incident angle sensitivity and polarization angle sensitivity are the main performance indicators of absorbers. Under perpendicular incident conditions, Figure 12 Simulation results for the ultra-wideband and multi-frequency absorbance as a function of polarization angle are presented. The absorbance remains constant when the polarization angle changes continuously. This verifies that the absorbance is insensitive to the polarization angle, and the polarization angle insensitivity of the absorber is mainly determined by the lattice symmetry in the x and y directions.

[0058] Figure 13 The figure illustrates the effect of incident angle variations from 0° to 80° on the absorption spectrum. It shows that within the incident angle range of 0° to 60°, the terahertz absorber maintains stable absorption performance across both broadband and multi-frequency bands. However, the absorption efficiency begins to decrease when the incident angle exceeds 60°. Under multi-frequency absorption characteristics with a VO2 conductivity of 150 S / m, the angular sensitivity in the low-frequency band gradually increases with increasing incident angle. This is because the longer wavelengths at low frequencies lead to a decrease in the ratio of the resonant cavity geometry to the wavelength. Oblique incidence has a more significant impact on resonance, causing the multi-frequency absorption rate to gradually decrease when the incident angle exceeds 60°.

[0059] Under broadband absorption characteristics, when the conductivity of VO2 is 8×10 4 At an angle of S / m, the electric field energy excites resonance within the patterned surface of VO2, thereby enhancing absorption. When the incident angle exceeds 60°, the broadband region with absorption exceeding 90% gradually narrows. This weakening of the horizontal component of the electric field disrupts the resonance state, ultimately leading to a decrease in absorption efficiency. In summary, the terahertz absorber exhibits excellent polarization insensitivity and can adapt to an incident angle range of 0° to 60°.

[0060] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the scope of the invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0061] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can be appropriately combined to form other embodiments that can be understood by those skilled in the art. The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. An ultrawideband and multi-frequency switchable terahertz absorber based on a VO2 multilayer structure, characterized in that, It includes multiple absorption units arranged in a periodic array, and each absorption unit has the following structure stacked from bottom to top: Metal substrate (1); A first dielectric layer (2) covers the metal substrate (1); A double gold ring resonant layer (3) is embedded inside the first dielectric layer (2), and the top surface of the double gold ring resonant layer (3) is flush with the top surface of the first dielectric layer (2); the double gold ring resonant layer (3) is formed by connecting concentric ring structures distributed at the four corners of a square cross section through a rectangular region; A VO2 spacer resonant layer (4) covers the upper surface of the first dielectric layer (2) and the top surface of the double gold ring resonant layer (3); The second dielectric layer (5) covers the VO2 spaced resonant layer (4); A square ring VO2 resonant layer (6) is disposed on the upper surface of the second dielectric layer (5). The square ring VO2 resonant layer (6) includes an outer square ring and a circular structure disposed at the center. The third dielectric layer (7) covers the upper surface of the second dielectric layer (5) and the square ring VO2 resonant layer (6); An elliptical star-shaped VO2 resonant layer (8) is disposed on the third dielectric layer (7).

2. The ultra-wideband and multi-frequency switchable terahertz absorber based on a VO2 multilayer structure according to claim 1, characterized in that, The thickness of the double gold ring resonant layer (3) is 1 to 3 µm, and includes two concentric rings, a rectangular region and a square frame. The two concentric rings, inner and outer, are located at the center of the square frame. The inner ring has an inner radius of 2–4 µm and an outer radius of 5–7 µm, while the outer ring has an inner radius of 8–9 µm and an outer radius of 10–12 µm. The rectangular regions are respectively located at the four corners of the square frame, and the side length of the rectangular regions is 1 to 3 µm.

3. The ultra-wideband and multi-frequency switchable terahertz absorber based on a VO2 multilayer structure according to claim 1, characterized in that, The VO2 spacer resonant layer (4) is a VO2 thin film, wherein the horizontal cross-sectional side length of the VO2 spacer resonant layer (4) is the same as that of the first dielectric layer, and the thickness of the VO2 thin film is 0.2 to 0.6 μm.

4. The ultra-wideband and multi-frequency switchable terahertz absorber based on a VO2 multilayer structure according to claim 1, characterized in that, The square ring VO2 resonant layer (6) includes an outer square ring and a central circular structure located at the center of the outer square ring; The outer side length of the outer square ring is 30–32 μm, and the width is 3–6 μm; The radius of the central circular structure is 1–4 μm; The thickness of the square ring VO2 resonant layer (6) is 0.03 to 0.07 μm.

5. The ultra-wideband and multi-frequency switchable terahertz absorber based on a VO2 multilayer structure according to claim 1, characterized in that, The elliptical star-shaped VO2 resonant layer (8) includes square units and a pattern disposed on the square units, the pattern being constructed as follows: At each of the four vertices of the square unit, a sector-shaped structure with a quarter circle centered at the vertex is formed; A circular structure is located at the center of the square unit; An arc-shaped substructure enclosed by an outer arc radius and an inner arc radius is prepared. The arc-shaped substructure is then arrayed by rotating 90° around the center of a square unit to obtain four identical arc-shaped substructures. Subtracting the circular structure from the four identical arc substructures results in an elliptical star pattern. The patterns include oval star shapes and quarter-circle fan-shaped structures.

6. The ultra-wideband and multi-frequency switchable terahertz absorber based on a VO2 multilayer structure according to claim 1, characterized in that, The metal substrate (1) is made of Au and has a thickness of 0.1 to 0.4 μm; The first dielectric layer (2), the second dielectric layer (5) and the third dielectric layer (7) are all made of PDMS; wherein, the thickness of the first dielectric layer (2) is 5 to 7 μm, the thickness of the second dielectric layer (5) is 2 to 4 μm and the thickness of the third dielectric layer (7) is 2.8 to 3 μm.

7. The ultra-wideband and multi-frequency switchable terahertz absorber based on a VO2 multilayer structure according to claim 1, characterized in that, The VO2 materials of the VO2 spacer resonant layer (4), the square ring VO2 resonant layer (6) and the elliptical star VO2 resonant layer (8) undergo reversible phase transitions under temperature control. Below 68℃, it is in an insulating state with a conductivity of 150 S / m; above 68℃, VO2 material is in a metallic state with a conductivity of 8 × 10⁻⁶. 4 S / m.

8. A method for fabricating an ultrawideband and multi-frequency switchable terahertz absorber based on a VO2 multilayer structure, characterized in that, The ultrawideband and multi-frequency switchable terahertz absorber based on a VO2 multilayer structure as described in any one of claims 1 to 7 comprises the following steps: S1. A metal substrate is formed by deposition and annealing on the substrate (1). S2. PDMS medium is deposited on the metal substrate (1) by spin coating process, and the first dielectric layer (2) is formed after curing. S3. A metal film is deposited on the first dielectric layer (2) using an electron beam evaporation process. The film is then subjected to photoresist coating pre-baking, ultraviolet exposure, development, etching and shaping, and photoresist removal and cleaning to form a double gold ring resonant layer (3) embedded in the first dielectric layer (2). S4. A VO2 thin film is formed on the surface of the first dielectric layer (2) and the top surface of the double gold ring resonant layer (3) using pulsed laser deposition process to form a VO2 spacer resonant layer. S5. PDMS dielectric is deposited on the VO2 spacer resonant layer by spin coating process, and a second dielectric layer is formed after curing treatment (5). S6. A VO2 thin film is deposited on the second dielectric layer (5) using pulsed laser deposition process. After ultraviolet lithography patterning and lift-off shaping, a square ring VO2 resonant layer (6) is formed. S7. PDMS medium is deposited on the square ring VO2 resonant layer (6) using pulsed laser deposition process, and a third dielectric layer (7) is formed after curing. S8. A VO2 thin film is deposited on the third dielectric layer (7) using pulsed laser deposition process. After ultraviolet lithography patterning and lift-off shaping, an elliptical star-shaped VO2 resonant layer (8) is obtained, and the absorber is completed.

9. The method for fabricating an ultrawideband and multi-frequency switchable terahertz absorber based on a VO2 multilayer structure according to claim 8, characterized in that, The specific process of S3 includes: A gold film with a thickness of 2 µm was deposited on the surface of the first dielectric layer (2) using electron beam evaporation. Photoresist was spin-coated onto the surface of a gold thin film and then preheated on a hot plate at 95–100°C for 85–90 seconds. A concentric ring pattern is exposed using an ultraviolet lithography machine through a photomask; Use a developer solution to treat for 55–60 seconds to remove the photoresist from the exposed areas; The gold layer not protected by photoresist is selectively removed using a gold etching solution, and the adhesion layer is removed using a chromium etching solution. The residual photoresist was removed with acetone, and then the mixture was cleaned with ethanol and deionized water and dried with nitrogen to form a double gold ring resonant layer (3).

10. The method for fabricating an ultrawideband and multi-frequency switchable terahertz absorber based on a VO2 multilayer structure according to claim 8, characterized in that, The specific process of S8 includes: A VO2 thin film was deposited on the third dielectric layer (7) using a pulsed laser deposition process; Using ultraviolet lithography, an elliptical star pattern is defined at the center and quarter-circle fan-shaped patterns are located at the four corners; The photoresist and excess VO2 film were removed by a stripping method, leaving the elliptical star-shaped VO2 resonant layer (8) formed by the central elliptical star pattern and the quarter-circle fan-shaped structures at the four corners.