1.Department of Physics, Capital Normal University, Beijing 100048, China 2.Beijing Advanced Innovation Center for Imaging Theory and Technology, Beijing 100048, China 3.Key Laboratory of Terahertz Optoelectronics, Ministry of Education, Beijing 100048, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant No. 61575130).
Received Date:07 November 2018
Accepted Date:12 March 2019
Available Online:01 May 2019
Published Online:20 May 2019
Abstract:Terahertz vortex beam generators have potential applications in optical micro-manipulation, terahertz communications and many other fields. A broadband vortex beam generator in a terahertz frequency range is proposed based on the metasurface of double-split resonant rings’ array. The designed structure consists of two layers, i.e., the top layer, which is a metasurface of double-split resonant rings, and the bottom layer, which is the dielectric layer of polymide. The numerical simulation of the cell structure array is performed by using the CST microwave studio. In order to obtain the best performance, the structure parameters of metasurface are continuously optimized and a set of optimal geometric parameters is finally determined. The simulation results show that the circularly polarized incident light can be converted into corresponding cross-polarized transmitted light. By rotating the metal resonant ring on the top layer, the cross-polarized transmitted light can be controlled to have the same amplitude and correspondingly different phases. The relationship between the phase change and the angle of rotation conforms to the P-B phase principle. These cell structures are arranged according to a specific order and can form the vortex phase plates for generating the vortex beams with different topological charges. Taking the topological charge numbers 1 and 2 for example, two kinds of vortex phase plates are designed. The characteristics of the circularly cross-polarized vortex beams generated by a circularly polarized wave perpendicularly incident on the vortex phase plates are numerically analyzed. The results show that the ideal vortex beams with different topological charge numbers are generated. The characteristics of vortex beams appear to be consistent with those theoretical results. Moreover, the vortex beams can be generated in a frequency range from 1.39 THz to 1.91 THz. The operating bandwidth is much wider than the previously obtained result of the transmission terahertz vortex phase plates. The transmission is higher than 20%, and the maximum value of transmission can reach 24%, which is close to the theoretical limit value of the single-layered transmission-type metasurface. This work provides a reference for generating the terahertz vortex beams based on metasurface. It is expected to possess a practical application in generating the device of terahertz vortex beam. Keywords:terahertz/ metasurface/ broadband/ vortex beam generation
3.单元结构设计本文所设计的结构由金属-电介质两层结构构成, 顶层为双开口谐振环, 底层为介质层, 材料为聚酰亚胺(polymide, PI), 单元结构的组成和几何结构参数定义如图1所示. 设计的用于产生太赫兹涡旋光束的超表面是由若干个相同的顶层金属单元结构通过旋转不同角度布阵得到的. 图 1 单元结构示意图 Figure1. Schematic of the unit cell structure.
采用CST MICROWAVE STUDIO (2014)软件对其进行仿真, 同时考虑样品制备方面的条件, 经优化后最终选择的结构参数列于表1.
结构参数
结构参数意义
优化值/μm
p
单元结构周期
90
a
表层金属谐振环边长
58
d
开口谐振环的开口宽度
11
w
双开口谐振环的金属线宽
11
t1
顶层金属层厚度
0.2
t2
底层介质层厚度
50
表1双开口谐振环单元结构仿真优化后的结构参数 Table1.Optimized parameters of structure based on the double-split resonant rings.
确定几何结构参数后, 采用CST软件进行数值模拟, 分析顶层金属谐振环单元以其中心为原点, z轴为旋转轴, 旋转不同角度θr情况下的透射特性. 在模拟中, 对单元结构采用周期性边界条件, 采用左旋圆偏振波垂直于结构入射. 如图2(a)所示, 在1.39—1.98 THz的宽带范围内, 交叉偏振波的透射系数高于0.4且相近. 在1.7 THz处, 幅度最为相近且达到最高值0.49, 接近单层透射式超表面的理论极限值[18,19]. 在1.39—1.91 THz的宽带频率范围内, 交叉偏振波的透射系数高于0.45, 且随单元旋转基本没有变化. 也就是说, 透射率在0.52 THz的宽带频率范围内始终高于20%. 图 2 在左旋圆偏振波入射下不同旋转角度双开口谐振环单元结构的太赫兹透射特性模拟结果 (a)交叉偏振分量的透射系数; (b)交叉偏振分量的相位改变 Figure2. Transmission characteristic of the unit cells with different rotation angle of double-split resonant rings under the left circularly polarized incidence: (a) Transmission coefficients of the cross-polarized component; (b) phase shift of the cross-polarized component.
其中l为拓扑荷数, (x, y)描述了每个单元在超表面内的位置, θr为每个单元结构的旋转角. 改变l的值, 可以设计用于产生任意不同拓扑荷数涡旋光束的超表面, 这相比于之前八阶量化[22]等排布方式有了很大的改进. 本文以产生拓扑荷数为1和2的涡旋光束为例设计了两个涡旋相位板, 如图3所示. 每个超表面具有23 × 23个单元结构, 总大小为2.07 mm × 2.07 mm. 由于超表面产生涡旋光束的有效工作频率为1.39—1.98 THz, 对应波长为151.5—215.8 μm, 因此涡旋相位板有效层的厚度仅约为波长的1/1000. 当左旋圆偏振的太赫兹波束通过涡旋相位板时, 透射的交叉圆偏振太赫兹波束在每个单元上具有相同的强度和相应的相位调制, 因此产生了太赫兹涡旋场. 图 3 两种用于产生拓扑荷数分别为 (a) l = 1和(b) l = 2的涡旋光束超表面 Figure3. Schematic of two different designed metasurface for generating vortex beams with topological charges of (a) l = 1 and (b) l = 2
5.数值模拟结果及分析在CST MICROWAVE STUDIO软件中, 对上述两个超表面进行电磁仿真. 采用左旋圆偏振的高斯光束垂直入射到图3中的两个超表面上. 将高斯光束的频率设定为可产生涡旋光束的工作频率, 电场的x和y分量的振幅为1 V/m, 并且焦斑位于整个超表面的中心, 束腰半径设置为1500 μm(直径大于整个超表面, 图3中超表面的对角线为2927 μm). 可以认为光束是均匀入射到整个超表面上的. 对应于图3所示的涡旋相位板, 模拟产生了拓扑荷数分别为1和2的两种涡旋光束. 以1.7 THz为例, 给出了出射交叉圆偏振波的振幅和相应的相位分布图, 如图4所示. 图4(a)—图4(d)分别表示了左旋圆偏振波垂直入射到图3(a)所示的涡旋相位板上, 沿波束传播方向距超表面500 和1000 μm处的透射交叉偏振波的振幅和相位分布. 可以看出, 如我们所预期的, 出射光场产生了中心为暗环的振幅分布,并且相位呈现覆盖$ 2{\text{π}} $的螺旋分布. 图4(e)—图4(h)则分别表示了左旋圆偏振波垂直入射到图3(b)所示的涡旋相位板上, 沿波束传播方向距超表面500和1000 μm处的透射交叉偏振波的振幅和相位分布. 对比图4(a)和图4(c), 图4(e)和图4(g)可见, 随着传播距离的增加, 光束会有扩散, 但仍能够保持良好的涡旋光的特性. 对图4进行综合分析, 如我们所预期的, 出射光场产生了中心为暗环的振幅分布, 并且拓扑荷数越大, 中心暗环的半径越大. 同时, 相应的相位呈现$ l \cdot 2{\text{π}} $的螺旋分布, 很好地与理论值符合. 经过数值模拟, 也验证了在右旋圆偏振波入射到超表面的情况下, 出射的交叉圆偏振波具有中心为零的振幅分布以及与图4相反的相位分布, 证实了它也具有良好的涡旋光束的性质. 图 4 通过超表面产生拓扑荷数为1和2的涡旋光束的振幅和相位分布. 对于l = 1, 在z = –500 μm平面处的(a)振幅和(b)相位分布. 对于l = 1, 在z = –1000 μm平面处的(c)振幅和(d)相位分布. 对于l = 2, 在z = –500 μm平面处的(e)振幅和(f)相位分布. 对于l = 2, 在z = –1000 μm平面处的(g)振幅和(h)相位分布 Figure4. Distributions of the amplitude and phase of the two metasurfaces for generating vortex beams with topological charges of 1 and 2 at 1.7 THz: (a) Amplitude and (b) phase distributions at the plane of z = –500 μm for l = 1; (c) amplitude and (d) phase distributions at the plane of z = –1000 μm for l = 1; (e) amplitude and (f) phase distributions at the plane of z = –500 μm for l = 2; (g) amplitude and (h) phase distributions at the plane of z = –1000 μm for l = 2.
由于在1.39—1.91 THz的宽带范围内, 交叉圆偏振波的透射系数高于0.45且相近, 同时, 其相位变化满足P-B相位原理. 因此, 该结构在1.39—1.91 THz的宽带频率范围内能够产生涡旋光束, 且透过率高于20%. 如图5所示, 给出了1.4和1.9 THz的频率下, 左旋圆偏振波经过图3(a)所示的超表面后, 在距超表面500 μm处产生的交叉圆偏振涡旋光束的振幅和相位分布. 由图可见, 在1.4和1.9 THz频率下, 经过超表面出射的交叉圆偏振波具有中心为暗环的振幅分布和相位变化为$ 2{\text{π}} $的螺旋相位分布, 具有良好的涡旋光束的性质. 图 5 超表面产生拓扑荷数为1的涡旋光束的振幅和相位分布. 在1.4 THz下, 对于l = 1, 在z = –500 μm平面处的(a)振幅和(b)相位分布; 在1.9 THz下, 对于l = 1, 在z = –500 μm平面处的(c)振幅和(d)相位分布 Figure5. Distributions of the amplitude and phase of metasurface for generating vortex beam with topological charge of 1: (a) Amplitude and (b) phase distributions at the plane of z = –500 μm for l = 1 at 1.4 THz; (c) amplitude and (d) phase distributions at the plane of z = –500 μm for l = 1 at 1.9 THz.