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Metasurfaces have the characteristics of simple structure, easy fabrication, easy integration, etc., and can flexibly control electromagnetic waves. They are widely used in terahertz filters, lenses, polarization converters, wavefront adjustment and terahertz imaging and so on. By encoding and arranging unit cells with different amplitudes and phases according to a certain rule, the metasurfaces can achieve various functions such as imaging, focusing, beam splitting, and vortex beam. The reported coding metasurfaces are phase-modulated according to geometric phase or transmission phase theory. However, geometric phase has spin-locking property and transmission phase has single-frequency property, which hinder the applications of a unified metasurface in simultaneously regulating geometric phase and transmission phase. To address the above issues, in this work, we propose an radian and rotation co-induced phase modulation metasurface, whose unit cell independently modulates the cross-polarized reflection phases of LCP wave and RCP wave and has a certain bandwidth, which meets therequirement in a frequency region of 1–1.2 THz. Through the principle of phase convolution and shared aperture, the metasurface realizes the vortex beams with a topological charge of ±1, focusing with a focal length of 1500 μm, the deflected vortex beams with a topological charge of ±2, the quasi-perfect vortex beams, and the multichannel vortex beams. The structure has the advantages of simple structure, flexible and convenient regulation, and compact size, which improves the utilization of the electromagnetic space and has a broad application prospect in the future terahertz communication systems. 
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图 1 弧度与旋转共同诱导相位调控超表面及其功能示意图
Fig. 1. Schematic diagram of the proposed metasurface and its function induced by both arc and rotation co-induced phase modulation.
图 3 超表面单元的反射系数与相位 (a) LCP入射下超表面单元反射系数; (b) LCP入射下超表面单元反射相位; (c) RCP入射下超表面单元反射系数; (d) RCP入射下超表面单元反射相位
Fig. 3. Reflection coefficient and phase of the unit cells: (a) Reflection coefficients at LCP incidence; (b) reflection phases at LCP incidence; (c) reflection coefficients at RCP incidence; (d) reflection phases at RCP incidence.
图 4 (a) l = 1超表面相位分布; (b) l = 1的超表面排布; (c) l = –1超表面相位分布; (d) l = –1超表面排布
Fig. 4. (a) The phase distribution of the metasurfaces at l = 1; (b) metasurfaces arrangement at l = 1; (c) the phase distribution of the metasurfaces at l = –1; (d) metasurfaces arrangement at l = –1.
图 5 (a), (e) LCP波入射下, l = 1涡旋波束远场图和模式纯度; (b), (f) RCP波入射下, l = 1涡旋波束远场图和模式纯度; (c), (g) RCP波下, l = –1涡旋波束远场图和模式纯度; (d), (h) RCP波入射下, l = –1涡旋波束远场图和模式纯度
Fig. 5. (a), (e) Far-field patterns and mode purity of the vortex beam at l = 1 under LCP wave incidence; (b), (f) far-field patterns and mode purity of the vortex beam at l = 1 under RCP wave incidence; (c), (g) far-field patterns and mode purity of the vortex beam at l = –1 under LCP wave incidence; (d), (h) far-field patterns and mode purity of the vortex beam at l = –1 under RCP wave incidence.
图 6 (a) zf = 1500μm超表面聚焦相位排布; (b) 超表面结构
Fig. 6. (a) Focusing phase arrangement of zf = 1500 μm metasurfaces; (b) metasurface structure.
图 7 (a) LCP波入射, zf = 1500 μm处x-y截面的二维电场; (b) LCP波入射, y = 0 μm处x-z截面的二维电场; (c) RCP波入射, zf = 1500 μm处x-y截面的二维电场; (d) RCP波入射, y = 0 μm处x-z截面的二维电场
Fig. 7. (a) 2D electric field in x-y cross section at zf = 1500 μm under LCP wave incidence; (b) 2D electric field in x-z cross section at y = 0 under LCP wave incidence; (c) 2D electric field in x-y cross section at zf = 1500 μm under RCP wave incidence; (d) 2D electric field in the x-z cross section at y = 0 under RCP wave incidence.
图 8 (a) l = 2涡旋波束相位图; (b)“64206420…”偏折相位图; (c) l = 2偏折卷积涡旋波束相位图; (d) l = 2偏折涡旋波束超表面结构; (e) l = –2涡旋波束相位图; (f)“0022446600224466…”偏折相位图; (g) l = –2偏折卷积涡旋波束相位图; (h) l = –2偏折涡旋波束超表面结构
Fig. 8. (a) Vortex beam phase diagram at l = 2; (b) ‘64206420…’ deflection phase diagram; (c) deflection convolution vortex beam phase diagram at l = 2; (d) deflection vortex beam metasurfaces structure at l = 2; (e) vortex beam phase diagram at l = –2, (f) ‘0022446600224466…’ deflected phase diagram; (g) deflected convolved vortex beam phase diagram at l = –2; (h) deflected vortex beam metasurfaces structure at l = –2.
图 9 (a), (b) LCP波入射, l = 2偏折涡旋波束的远场和偏折角度; (c), (d) RCP波入射, l = 2偏折涡旋波束的远场和偏折角度; (e), (f) LCP波入射, l = –2偏折涡旋波束的远场和偏折角度; (g), (h) RCP波入射, l = -2偏折涡旋波束的远场和偏折角度
Fig. 9. (a), (b) Far field and deflection angle of l = 2 deflected vortex beam under LCP wave incidence; (c), (d) far field and deflection angle of l = 2 deflected vortex beam under RCP wave incidence; (e), (f) far field and deflection angle of l = –2 deflected vortex beam under LCP wave incidence; (g), (h) far field and deflection angle of l = -2 deflected vortex beam under RCP wave incidence.
图 10 (a) zf = 1500 μm超表面聚焦相位; (b)“02460246…”偏折相位; (c)卷积后偏折聚焦相位; (d)偏折聚焦超表面结构
Fig. 10. (a) zf = 1500 μm metasurfaces focusing phase, (b) ‘02460246.. ... .’ deflection phase, (c) deflection focusing phase after convolution, (d) deflection focusing metasurface structure
图 11 (a) LCP波入射, zf = 1500 μm处x-y截面的二维电场; (b) LCP波入射, y = 0 μm处x-z截面的二维电场; (c) RCP波入射, zf = 1500 μm处x-y截面的二维电场; (d) RCP波入射, y = 0 μm处x-z截面的二维电场
Fig. 11. (a) 2D electric field in x-y cross section at zf = 1500 μm under LCP wave incidence, (b) 2D electric field in x-z cross section at y = 0 under LCP wave incidence, (c) 2D electric field in x-y cross section at zf = 1500 μm under RCP wave incidence, (d) 2D electric field in the x-z cross section at y = 0 under RCP wave incidence.
图 12 (a), (e)拓扑荷数为l = 1和 l = 2的涡旋相位排布; (b), (f)负轴向产生的反向贝塞尔光束的傅里叶变换相位排布; (c), (g) 焦透镜的相位排布; (d), (h) 拓扑荷数为l = 1和l = 2的完美涡旋相位排布
Fig. 12. (a), (e) Vortex phase arrangement for the topological charges of l = 1 and l = 2; (b), (f) Fourier-transform phase arrangement of the inverted Bessel beam generated in the negative axial direction; (c), (g) phase arrangement of the focal lens; (d), (h) perfect vortex phase arrangement for the topological charges of l = 1 and l = 2.
图 13 (a) 拓扑荷数l = 1的完美涡旋波束电场强度分布; (b) 拓扑荷数l = 2的完美涡旋波束电场强度分布
Fig. 13. (a) Electric field strength distribution of a perfect vortex beam for the topological charge of l = 1; (b) electric field strength distribution of a perfect vortex beam for the topological charge of l = 2.
图 14 (a)左偏 (l = 2) 涡旋波束的相位排布; (b) 右偏 (l = –2) 涡旋波束的相位排布; (c) 横向双通道涡旋波束的相位排布
Fig. 14. (a) Phase arrangement of the left-biased vortex beam (l = 2); (b) phase arrangement of the right-biased vortex beam (l = –2); (c) phase arrangement of the transverse two-channel vortex beam.
图 15 (a) LCP波入射下, 频率1.1 THz处, l = ±2双通道涡旋波束的远场强度; (b) RCP波入射下, 频率1.1 THz处, l = ±2双通道涡旋波束的远场强度
Fig. 15. (a) Far-field intensity of two-channel vortex beam (l = ±2) at 1.1 THz under LCP wave incidence; (b) far-field intensity of two-channel vortex beam (l = ±2) at 1.1 THz under RCP wave incidence.
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