Device and method for enhancing Smith-Perot terahertz radiation based on metasurface

Abstract

The invention discloses an enhanced Smith-Perot terahertz radiation device and method based on a metasurface, and belongs to terahertz radiation. According to the enhanced Smith-Perot terahertz radiation device based on the metasurface provided by the invention, the penetrating composite hole digging unit is arranged on the metasurface structure, the cross section of the hole digging unit is of the cross structure formed by vertically intersecting the first rectangle and the second rectangle, and the center of the cross structure is the center of a circle, so that the specific hole digging structure can improve the radiation efficiency of the terahertz radiation device. Through cooperation with periodic arrangement of the whole metasurface in a two-dimensional array mode, the local field enhancement characteristic of the metasurface can be more effectively utilized, specifically, vertically-intersected rectangles form a hollow channel, charges are gathered due to the fact that no medium exists at the edge, and a high-strength electromagnetic field is formed in a cross area in combination with an evanescent field generated by electron beam glancing. The center of a circle coincides with the center of the cross structure, the electric field distribution symmetry is optimized, the scattering loss is reduced, the energy is further focused, and the radiation intensity is improved.

Description

Technical Field

[0001] The present invention relates to the field of terahertz radiation technology, and in particular to a metasurface-based enhanced Smith-Purcell terahertz radiation device and method. Background Art

[0002] Terahertz waves have significant applications in communications, imaging, spectral analysis, and other fields, but the development of efficient terahertz radiation sources has been a key bottleneck restricting technological development. Existing terahertz radiation sources are primarily categorized as electron, photon, and surface plasmon. Electron-based Smith-Purcell (SP) radiation offers significant potential due to its simple structure, low cost, and tunable frequency. It generates electromagnetic radiation through the interaction of a high-energy electron beam with a periodic metal grating. The frequency of this radiation is determined by the grating period and the electron beam velocity, theoretically covering a wide spectrum from ultraviolet light to the terahertz band.

[0003] However, traditional Smith-Purcell radiation mainly relies on the diffraction mechanism of a one-dimensional grating. When the electron beam passes through the grating, the excited electromagnetic energy needs to be radiated into free space through diffraction. The energy distribution of the grating diffraction follows the Fraunhofer diffraction law. Only a small amount of energy is concentrated in the direction of the main lobe, and most of the energy is diverged in the form of side lobes, causing the radiation intensity (|E|²) to decay rapidly with distance, resulting in low radiation intensity.

[0004] Therefore, how to enhance the intensity of Smith-Purcell terahertz radiation has become a technical problem that needs to be overcome urgently by those skilled in the art. Summary of the Invention

[0005] The object of the present invention is to provide a metasurface-based enhanced Smith-Purcell terahertz radiation device and method to overcome the problem of low radiation intensity of traditional Smith-Purcell radiation in the prior art caused by the one-dimensional grating diffraction mechanism.

[0006] The present invention solves the above technical problems through the following technical solutions: A metasurface-based enhanced Smith-Purcell terahertz radiation device includes a plurality of metasurface structures composed of a single layer of conductive flexible material. The metasurface structures are periodically arranged in a two-dimensional array. A penetrating composite hole unit is provided on the metasurface structure. The hole cross-section of the composite hole unit is composed of a first rectangle, a second rectangle and a circle. The first rectangle and the second rectangle intersect vertically to form a cross structure, and the center of the cross structure is the center of the circle.

[0007] A further improvement of the present invention is that the conductive flexible material is one of antimony tin oxide, graphene or carbon fiber.

[0008] A further improvement of the present invention is that the composite hole-digging unit is filled with gas, and the gas is at least one of air, oxygen or nitrogen.

[0009] A further improvement of the present invention is that the two-dimensional array includes a transverse array and a longitudinal array, the transverse array arranges no less than five metasurface structures, and the longitudinal array arranges no less than thirty metasurface structures.

[0010] A further improvement of the present invention is that the cross-section of the metasurface structure is a square with a side length of 30 μm to 3 mm.

[0011] A further improvement of the present invention is that the thickness of the super surface structure is 50-100 μm.

[0012] A further improvement of the present invention is that the first rectangle and the second rectangle are equal, have a length of 150 μm, and a width of 20 μm.

[0013] A further improvement of the present invention is that the radius of the circle is 11-50 μm.

[0014] The present invention also provides a working method of a metasurface-based enhanced Smith-Purcell terahertz radiation device, which grazes an electron beam at 0.1 to 0.9 times the speed of light onto the surface of the metasurface-based enhanced Smith-Purcell terahertz radiation device, thereby generating enhanced terahertz radiation within an observation angle range of 0 to 180°, wherein the movement direction of the electron beam is a 0° reference.

[0015] A further improvement of the present invention is that the observation angle range is 0-90°.

[0016] Compared with the prior art, the present invention has the following positive effects: The metasurface-based enhanced Smith-Purcell terahertz radiation device provided by the present invention is provided with a penetrating composite hole unit on the metasurface structure, and the hole cross-section is formed by the vertical intersection of a first rectangle and a second rectangle to form a cross structure, and the center of the cross structure is the center of a circle. This special hole structure, combined with the periodic arrangement of the metasurface as a whole in a two-dimensional array, can more effectively utilize the local field enhancement characteristics of the metasurface. Specifically, the vertically intersecting rectangles form a hollow channel, and charge accumulation occurs at the edge due to the absence of a medium. Combined with the evanescent field generated by the grazing electron beam, a high-intensity electromagnetic field is formed in the cross-intersection area, which directly enhances the radiation energy. The center of the circle coincides with the center of the cross structure, which optimizes the symmetry of the electric field distribution, reduces scattering loss, further focuses energy, and improves radiation intensity.

[0017] Furthermore, the use of a single layer of conductive flexible material to form a metasurface structure avoids the superposition of complex devices and makes the entire device structure simpler compared to the method of adding other devices to an ordinary grating to enhance the radiation intensity. It not only reduces the manufacturing difficulty and cost, but also reduces the energy loss and signal interference caused by the complex structure, thereby improving the stability and reliability of the device. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The drawings in the specification are used to provide further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0019] Figure 1 A top view of the metasurface structure of the metasurface-enhanced Smith-Purcell terahertz radiation device of the present invention; Figure 2 This is a front view of the metasurface structure of the metasurface-based enhanced Smith-Purcell terahertz radiation device of the present invention; Figure 3 Schematic diagram of the working principle of the metasurface-based enhanced Smith-Purcell terahertz radiation device of the present invention; Figure 4 This is a schematic diagram of a frequency of 0.58 THz detected in Example 1 of the present invention; Figure 5 Schematic diagram of frequencies corresponding to metasurface structures of different periods of the present invention; Figure 6 A schematic diagram showing the comparison of frequencies between the present invention and the grating structure; Figure 7 Schematic diagram of the frequency of different observation angles of the present invention.

[0020] Among them, 1 is the metasurface structure; 2 is the first rectangle; 3 is the second rectangle; 4 is the device body; 4-1 is the electron beam emission source; 4-2 is the direction of planar electron beam movement; 4-3 is the probe point. DETAILED DESCRIPTION

[0021] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0022] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort shall fall within the scope of protection of the present invention.

[0023] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.

[0024] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, which are intended to explain the present invention rather than to limit it.

[0025] See also Figure 1 and Figure 2 A metasurface-based enhanced Smith-Purcell terahertz radiation device includes a plurality of metasurface structures 1 composed of a single layer of conductive flexible material, wherein the metasurface structures 1 are periodically arranged in a two-dimensional array, and a penetrating composite hole unit is provided on the metasurface structure 1. The hole cross-section of the composite hole unit is composed of a first rectangle 2, a second rectangle 3 and a circle, wherein the first rectangle 2 and the second rectangle 3 intersect vertically to form a cross structure, and the center of the cross structure is the center of the circle.

[0026] The metasurface-based enhanced Smith-Purcell terahertz radiation device provided by the present invention is provided with a penetrating composite hole unit on the metasurface structure 1, and the hole cross-section is formed by the vertical intersection of a first rectangle 2 and a second rectangle 3 to form a cross structure, and the center of the cross structure is the center of a circle. This special hole structure, combined with the periodic arrangement of the metasurface as a whole in a two-dimensional array, can more effectively utilize the local field enhancement characteristics of the metasurface. Specifically, the vertically intersecting rectangles form a hollow channel, and charge accumulation occurs at the edge due to the absence of a medium. Combined with the evanescent field generated by the grazing electron beam, a high-intensity electromagnetic field is formed in the cross-intersection area, which directly enhances the radiation energy. The center of the circle coincides with the center of the cross structure, which optimizes the symmetry of the electric field distribution, reduces scattering loss, further focuses energy, and improves radiation intensity.

[0027] Specifically, the conductive flexible material is one of antimony tin oxide, graphene or carbon fiber.

[0028] The metasurface structure 1 is constructed using a single layer of conductive flexible material. Compared with the method of adding other devices to an ordinary grating to enhance the radiation intensity, this avoids the superposition of complex devices and makes the entire device structure simpler. It not only reduces the manufacturing difficulty and cost, but also reduces the energy loss and signal interference that may be caused by the complex structure, thereby improving the stability and reliability of the device.

[0029] Specifically, the composite hole-digging unit is filled with gas, and the gas is at least one of air, oxygen or nitrogen.

[0030] Specifically, the two-dimensional array includes a transverse array and a longitudinal array, the transverse array arranges no less than five metasurface structures 1, and the longitudinal array arranges no less than thirty metasurface structures 1.

[0031] Specifically, the cross section of the metasurface structure 1 is a square with a side length of 30 μm to 3 mm.

[0032] The metasurface structure 1 is periodically arranged in a two-dimensional array. Based on the Smith-Purcell radiation dispersion formula, the required period length is calculated to precisely control the terahertz wavelength. This design allows the device to flexibly adjust the radiation wavelength according to different application requirements, broadening its application range and meeting diverse terahertz radiation application scenarios.

[0033] The Smith-Purcell radiation dispersion formula is specifically:

[0034] where λ is the side length of the metasurface structure 1, p is the period length, n is the diffraction order, β is the ratio of the electron beam velocity to the speed of light, and cosθ is the cosine of the observation angle.

[0035] Specifically, the thickness of the supersurface structure 1 is 50-100 μm.

[0036] Specifically, the first rectangle 2 and the second rectangle 3 are equal, with a length of 150 μm and a width of 20 μm.

[0037] Specifically, the radius of the circle is 11-50 μm.

[0038] The present invention also provides a working method of a metasurface-based enhanced Smith-Purcell terahertz radiation device, which grazes an electron beam at 0.1 to 0.9 times the speed of light onto the surface of the metasurface-based enhanced Smith-Purcell terahertz radiation device, thereby generating enhanced terahertz radiation within an observation angle range of 0 to 180°, wherein the movement direction of the electron beam is a 0° reference.

[0039] Specifically, the observation angle range is 0~90°.

[0040] Example 1 A metasurface-based enhanced Smith-Purcell terahertz radiation device comprises a plurality of metasurface structures 1 formed of a single layer of conductive flexible material, the metasurface structures 1 being periodically arranged in a two-dimensional array. The metasurface structures 1 are provided with penetrating composite digging units, the digging cross-section of the composite digging units being composed of a first rectangle 2, a second rectangle 3, and a circle, wherein the first rectangle 2 and the second rectangle 3 intersect perpendicularly to form a cross structure, the center of the cross structure being the center of the circle; the conductive flexible material is antimony tin oxide, the composite digging units are filled with air, the two-dimensional array comprises a transverse array and a longitudinal array, wherein five metasurface structures 1 are arranged in the transverse array, and thirty metasurface structures 1 are arranged in the longitudinal array; the cross-section of the metasurface structure 1 is a square with a side length of 380 μm; the thickness of the metasurface structure 1 is 100 μm; the first rectangle 2 and the second rectangle 3 are equal, with a length of 150 μm and a width of 20 μm; and the radius of the circle is 50 μm.

[0041] See also Figure 3 When the device body 4 is working, the electron beam from the electron beam emission source 4-1 grazes the surface of the above-mentioned metasurface-based enhanced Smith-Purcell terahertz radiation device at 0.1 to 0.9 times the speed of light along the plane electron beam motion direction 4-2. The detection point 4-3 is set in the free space above the metasurface structure 1 to detect the frequency domain information of the point. Figure 4 , which is a schematic diagram of the device body 4 detecting a frequency of 0.58 THz.

[0042] The metasurface-based enhanced Smith-Purcell terahertz radiation device provided by the present invention can increase the radiation intensity by 20 times compared with ordinary gratings, and can achieve efficient enhancement without adding additional complex devices, with significant and stable effects. Compared with the traditional solution of enhancing radiation intensity by adding other devices, the present invention only realizes the function through the periodic arrangement of the metasurface and the composite hole-digging unit design, without the need for complex components, and the overall structure is simpler, easy to integrate and miniaturize. The Purcell radiation dispersion formula precisely calculates the side length of metasurface structure 1 and tailors its period to precisely control the wavelength of radiated terahertz radiation, meeting the wavelength requirements of various application scenarios. The geometric design of the composite hole-punching unit (a combination of a cross and a circle) further optimizes the local field distribution. Adjusting the size and shape of the hole cross-section allows for flexible modulation of electromagnetic field interactions, broadening the frequency tuning range. Utilizing the metasurface's local field enhancement properties, when the electron beam grazes, the evanescent field acts on metasurface structure 1. The absence of a dielectric medium creates charge accumulation and strong field regions at the edges of the hollowed-out regions, directly enhancing the radiation energy through the strong electric field effect. This results in high energy conversion efficiency and a clear physical mechanism. Through this innovative metasurface design, while enhancing terahertz radiation intensity, the structure is simplified, costs are reduced, and frequency is flexibly controlled. This provides an efficient, economical, and tunable solution for the practical application of Smith-Purcell radiation THz sources, with significant potential for applications in terahertz imaging, communications, spectral detection, and other fields.

[0043] Example 2 A metasurface-based enhanced Smith-Purcell terahertz radiation device comprises a plurality of metasurface structures 1 formed of a single layer of conductive flexible material, the metasurface structures 1 being periodically arranged in a two-dimensional array. A penetrating composite hole unit is provided on the metasurface structure 1, the hole cross-section of the composite hole unit being composed of a first rectangle 2, a second rectangle 3 and a circle, wherein the first rectangle 2 and the second rectangle 3 intersect perpendicularly to form a cross structure, the center of the cross structure being the center of the circle; the conductive flexible material is antimony tin oxide, the composite hole unit is filled with air, the two-dimensional array comprises a transverse array and a longitudinal array, wherein five metasurface structures 1 are arranged in the transverse array, and thirty metasurface structures 1 are arranged in the longitudinal array; the cross-section of the metasurface structure 1 is a square with a side length of 370 μm; the thickness of the metasurface structure 1 is 100 μm; the first rectangle 2 and the second rectangle 3 are equal, with a length of 150 μm and a width of 20 μm; and the radius of the circle is 50 μm.

[0044] Example 3 A metasurface-based enhanced Smith-Purcell terahertz radiation device comprises a plurality of metasurface structures 1 formed of a single layer of conductive flexible material, the metasurface structures 1 being periodically arranged in a two-dimensional array. A penetrating composite hole unit is provided on the metasurface structure 1, the hole cross-section of the composite hole unit being composed of a first rectangle 2, a second rectangle 3 and a circle, wherein the first rectangle 2 and the second rectangle 3 intersect perpendicularly to form a cross structure, the center of the cross structure being the center of the circle; the conductive flexible material is antimony tin oxide, the composite hole unit is filled with air, the two-dimensional array comprises a transverse array and a longitudinal array, wherein five metasurface structures 1 are arranged in the transverse array, and thirty metasurface structures 1 are arranged in the longitudinal array; the cross-section of the metasurface structure 1 is a square with a side length of 360 μm; the thickness of the metasurface structure 1 is 100 μm; the first rectangle 2 and the second rectangle 3 are equal, with a length of 150 μm and a width of 20 μm; and the radius of the circle is 50 μm.

[0045] Example 4 A metasurface-based enhanced Smith-Purcell terahertz radiation device comprises a plurality of metasurface structures 1 formed of a single layer of conductive flexible material, the metasurface structures 1 being periodically arranged in a two-dimensional array. A penetrating composite hole unit is provided on the metasurface structure 1, the hole cross-section of the composite hole unit being composed of a first rectangle 2, a second rectangle 3 and a circle, wherein the first rectangle 2 and the second rectangle 3 intersect perpendicularly to form a cross structure, the center of the cross structure being the center of the circle; the conductive flexible material is antimony tin oxide, the composite hole unit is filled with air, the two-dimensional array comprises a transverse array and a longitudinal array, wherein five metasurface structures 1 are arranged in the transverse array, and thirty metasurface structures 1 are arranged in the longitudinal array; the cross-section of the metasurface structure 1 is a square with a side length of 340 μm; the thickness of the metasurface structure 1 is 100 μm; the first rectangle 2 and the second rectangle 3 are equal, with a length of 150 μm and a width of 20 μm; and the radius of the circle is 50 μm.

[0046] Example 5 A metasurface-based enhanced Smith-Purcell terahertz radiation device comprises a plurality of metasurface structures 1 formed of a single layer of conductive flexible material, the metasurface structures 1 being periodically arranged in a two-dimensional array. A penetrating composite hole unit is provided on the metasurface structure 1, the hole cross-section of the composite hole unit being composed of a first rectangle 2, a second rectangle 3 and a circle, wherein the first rectangle 2 and the second rectangle 3 intersect perpendicularly to form a cross structure, the center of the cross structure being the center of the circle; the conductive flexible material is antimony tin oxide, the composite hole unit is filled with air, the two-dimensional array comprises a transverse array and a longitudinal array, wherein five metasurface structures 1 are arranged in the transverse array, and thirty metasurface structures 1 are arranged in the longitudinal array; the cross-section of the metasurface structure 1 is a square with a side length of 350 μm; the thickness of the metasurface structure 1 is 100 μm; the first rectangle 2 and the second rectangle 3 are equal, with a length of 150 μm and a width of 20 μm; and the radius of the circle is 50 μm.

[0047] See also Figure 5 , the peaks correspond from left to right to the frequencies detected by the device bodies 4 of Example 1, Example 2, Example 3, Example 4 and Example 5 respectively. The device bodies 4 of Examples 1 to 5 only change the side length (period) of the metasurface structure 1, and the internal structure dimensions are not changed. It can be seen that the device body 4 of Example 1 can detect a frequency of 0.58 THz; the device body 4 of Example 2 can detect a frequency of 0.59 THz; the device body 4 of Example 3 can detect a frequency of 0.61 THz; the device body 4 of Example 4 can detect a frequency of 0.62 THz; and the device body 4 of Example 5 can detect a frequency of 0.64 THz, which also proves that the enhanced Smith-Purcell terahertz radiation device based on the metasurface provided by the present invention can radiate terahertz waves of different frequencies by changing the size of the structural period.

[0048] See also Figure 6 The solid line represents the frequency curve detected by the first embodiment of the present invention, and the dotted line represents the frequency curve detected by the grating of the prior art, wherein the parameter period of the grating is 380 microns, the depth is 50 microns, and the duty cycle is 0.4. It can be seen that the intensity of the terahertz wave radiated by the enhanced Smith-Purcell terahertz radiation device based on the metasurface provided by the present invention is better than the intensity of the terahertz wave radiated by the ordinary grating. This is because the enhanced Smith-Purcell terahertz radiation device based on the metasurface provided by the present invention forms a ring-shaped displacement current distribution through the intersection area of ​​the composite hole-digging unit, which can form an optimal energy transfer with the longitudinal electric field of the electron beam, and the charge accumulation at each arm of the cross forms a strong field area. The generation of this strong field can enhance the electric field intensity of the radiation wavelength.

[0049] The device provided by the present invention can not only adjust the radiation frequency by reasonably adjusting the side length (period) of the metasurface structure 1, but also Figure 7 The device provided by the present invention can also adjust the frequency range of radiation by changing the observation angle.

[0050] Finally, it should be noted that the embodiments listed above are merely one or more specific manifestations of the technical solution of the present invention. Their purpose is to clearly illustrate the concept, principles, and application of the present invention through specific examples, and is in no way intended to limit the scope of protection of the present invention to these specific embodiments. In fact, the true value of this invention lies in its technical ideas and innovations, not in its form of expression or implementation.

[0051] For ordinary technicians in the relevant technical field, after thoroughly reading and understanding the technical solutions of the present invention, they are fully capable of making various forms of changes, modifications or equivalent replacements to the specific implementation methods of the invention based on their own professional knowledge and skills. These changes may include but are not limited to: adjusting the value range of technical parameters, optimizing algorithm processes to improve efficiency, replacing some technical components to achieve better compatibility or reduce costs, etc. As long as these modified technical solutions still substantially maintain the technical features claimed for protection by the original invention, that is, they can still achieve the core functions and effects of the present invention, then these changes should be deemed to fall within the scope of protection of the pending claims of the present invention.

[0052] Furthermore, with the continuous advancement and development of technology, new technical means and methods continue to emerge, providing ample room for further improvement and perfection of the present invention. Therefore, the scope of protection of the present invention should also include reasonably foreseeable improvements and extensions based on existing technologies. As long as these improvements and extensions do not deviate from the basic principles and core concepts of the present invention, they should be considered equivalent to the present invention and equally protected by patent rights.

Claims

1. A metasurface-based enhanced Smith-Purcell terahertz radiation device, characterized in that: The invention comprises a plurality of super surface structures (1) composed of a single layer of conductive flexible material, wherein the super surface structures (1) are periodically arranged in a two-dimensional array, and a composite hole-cutting unit is provided on the super surface structure (1), wherein the hole-cutting cross section of the composite hole-cutting unit is composed of a first rectangle (2), a second rectangle (3) and a circle, wherein the first rectangle (2) and the second rectangle (3) intersect vertically to form a cross structure, and the center of the cross structure is the center of the circle.

2. The metasurface-based enhanced Smith-Purcell terahertz radiation device according to claim 1, characterized in that: The conductive flexible material is one of antimony tin oxide, graphene or carbon fiber.

3. The metasurface-based enhanced Smith-Purcell terahertz radiation device according to claim 1, characterized in that: The composite hole-digging unit is filled with gas, which is at least one of air, oxygen or nitrogen.

4. The metasurface-based enhanced Smith-Purcell terahertz radiation device according to claim 1, characterized in that: The two-dimensional array includes a transverse array and a longitudinal array, wherein the transverse array is arranged with no less than five metasurface structures (1), and the longitudinal array is arranged with no less than thirty metasurface structures (1).

5. The metasurface-based enhanced Smith-Purcell terahertz radiation device according to claim 1, characterized in that: The cross section of the metasurface structure (1) is a square with a side length of 30 μm to 3 mm.

6. The metasurface-based enhanced Smith-Purcell terahertz radiation device according to claim 1, characterized in that: The thickness of the super surface structure (1) is 50-100 μm.

7. The metasurface-based enhanced Smith-Purcell terahertz radiation device according to claim 1, characterized in that: The first rectangle (2) and the second rectangle (3) are equal, with a length of 150 μm and a width of 20 μm.

8. The metasurface-based enhanced Smith-Purcell terahertz radiation device according to claim 1, characterized in that: The radius of the circle is 11-50 μm.

9. A method for operating a metasurface-based enhanced Smith-Purcell terahertz radiation device, characterized in that: An electron beam is glancing at the surface of the metasurface-enhanced Smith-Purcell terahertz radiation device according to any one of claims 1 to 8 at a speed of 0.1 to 0.9 times the speed of light to generate enhanced terahertz radiation within an observation angle range of 0 to 180°, wherein the moving direction of the electron beam is a 0° reference.

10. The method for operating a metasurface-based enhanced Smith-Purcell terahertz radiation device according to claim 9, characterized in that: The observation angle range is 0~90°.

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