Simulation study on tunable graphene metasurface focusing mirror based on flexible substrate
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摘要: 焦距范围可调的超薄聚焦反射镜在紧凑尤其是片上太赫兹光谱和成像系统中有重要应用价值。通过改变几何尺寸和调节化学势可以使石墨烯亚波长反射结构获得0-2π的相位，结合聚二甲基硅氧烷（PDMS）柔性基底的动态拉伸可以实现大动态范围的超薄太赫兹聚焦反射镜。本文设计了一个工作频率为1.0 THz，宽度为12 mm，焦距60 mm，厚度为75 μm的柔性基底动态调焦石墨烯超表面聚焦反射镜。首先在基底自然状态下通过掺杂调节单元石墨烯条的化学势和改变宽度使其反射相位覆盖0-2π相位，并按照预定设计的相位空间分布达到反射聚焦效果。然后通过横向拉伸柔性基底实现反射镜焦距的动态调节。仿真结果表明柔性基底长度在100%-140%内范围变化时，反射镜的焦距由53.4 mm增加到112.1 mm，动态调焦范围可达到最小焦距的109.7%，同时聚焦效率从69.7%减小到46.8%。此外，本文还研究了该反射镜在宽频带范围的工作性能，仿真结果表明其对于在0.85−1.0 THz范围内的入射平面波都能实现良好的动态聚焦。Abstract: Ultra-thin focusing mirror with adjustable focal length has important applicant value in compact systems, especially on-chip terahertz spectroscopy, imaging systems and communication systems. By changing the geometric size and adjusting the chemical potential, the graphene subwavelength reflective structure can achieve a phase of 0-2π. Combined with the above properties and the dynamic stretching of polydimethylsiloxane (PDMS) flexible substrate, the ultra-thin terahertz focusing reflector with large dynamic adjustment range can be realized. In this paper, a dynamic focusing graphene metasurface focusing reflector based on flexible substrate with a working frequency of 1.0 THz, a width of 12 mm, a focal length of 60 mm and a thickness of 75 μm is designed and investigated. Firstly, by adjusting the chemical potential and width of the graphene unit strips, the reflective phase covers the 0-2π, and the reflective focusing effect can be achieved according to the predesigned phase spatial distribution. Then, the dynamic adjustment of the focal length of the reflective mirror can be realized by laterally stretching the flexible substrate. The simulation results demonstrate that when the length of the flexible substrate varies from 100% to 140%, the focal length of the reflective mirror increases from 53.4 mm to 112.1 mm, the dynamic focus rage can reach 109.7% of the minimum focal length, and the focus efficiency decreases from 69.7% to 46.8%. In addition, the performance of the reflective mirror in a wide frequency range has also been investigated in this paper, and the simulation results demonstrate that the good dynamic focusing for incident plane waves in the frequency range of 0.85−1.0 THz can be achieved. The proposed tunable metasurface design is highly versatile in the development of ultra-thin, multifunctional and tunable terahertz devices for various applications.
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Key words:
- terahertz /
- graphene /
- metasurface /
- flexible substrate /
- dynamic focusing
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图 1 石墨烯反射超表面单元结构图。其中底层为导电聚合物，单层石墨烯条带嵌入PDMS，x方向周期p=150 μm，y方向的周期无限大，PDMS厚度上层d1=25 μm，下层厚度d2=50 μm，石墨烯宽度为w。
Figure 1. the structure of one unit cell graphene reflective metasurface. Which consists of a single-layer graphene strips embedded in PDMS and a conductive polymer ground plate. The graphene are ranged in the x direction with a period of p=150 um and the period in the y direction is infinite. The thickness of the upper and lower layers of PDMS is d1=25 um and d2=50 um respectively. The width of graphene is denoted by w.
图 2 柔性基底动态调焦石墨烯太赫兹超表面聚焦反射镜工作示意图。(a)为拉伸前反射镜，衬底横向长度为L，基底厚度为d，焦距为f；(b)为衬底PDMS沿x轴拉伸ε后反射镜，横向长度变为L(1+ε)，基底厚度为d/(1+ε)，焦距f'变为(1+ε)2f。
Figure 2. Schematic of the dynamic focusing graphene terahertz metasurface focusing on a flexible substrate. (a) is the encapsulated in a flexible polymer, the lateral length of the substrate is L, the thickness of the base is d, and the focal length is f; (b) is the reflector after the substrate PDMS stretches ε along the x axis, the lateral length becomes L(1+ε), the substrate thickness is d/(1+ε), and the focal length f' becomes (1+ε)2f.
图 3 柔性基底动态调焦石墨烯太赫兹超表面单元结构设计。(a)和(b)是单元结构的反射系数和相位随石墨烯的化学势μc和宽度w变化情况；(c)为经过优化计算得到的8个单元结构的反射系数和相位响应；(d)为拉伸前后PDMS衬底横向距原点距离与相位关系图。
Figure 3. The design of graphene terahertz metasurface unit structure for dynamic focusing on flexible substrate. (a) and (b) is the change of the reflection coefficient and phase of the unit structure with the chemical potential μc and width w of graphene;(c) is the reflection coefficient and phase response of the eight unit structure obtained through optimization calculation;(d) is a diagram of the relationship between the PDMS substrate lateral distance from the origin and the phase before and after stretching.
图 4 柔性基底动态调焦石墨烯太赫兹超表面聚焦反射镜在入射波频率为1.0 THz，衬底拉伸时归一化的电场分布。其中(a)−(e)对应衬底拉伸100%−140%。
Figure 4. The normalized electric field distribution of the dynamic focusing graphene terahertz metasurface focusing mirror on the flexible substrate when the incident wave frequency is 1.0 THz and the substrate is stretched. (a)−(e) correspond to 100%−140% of the substrate stretch.
图 5 柔性基底动态调焦石墨烯太赫兹超表面聚焦反射镜入射波频率为1.0 THz，衬底拉伸时理论焦距（黑色圆圈）与仿真计算焦距（红色方块）对比情况。
Figure 5. The frequency of the incident wave of the dynamic focusing graphene terahertz metasurface focusing mirror on the flexible substrate is 1.0 THz. The theoretical focal length (black circle) given by formula (4) when the substrate is stretched is compared with the simulated focal length (red square).
图 6 柔性基底动态调焦石墨烯太赫兹超表面聚焦反射镜在0.85−1.0 THz宽频工作频率下，PDMS拉伸幅度为100%到140%时，沿z轴(x=0)的电场强度分布图。其中(a)−(d)对应频率0.85 THz、0.90 THz、0.95 THz和1.0 THz。
Figure 6. The graphene terahertz super-surface focusing mirror with flexible substrate dynamic focusing is the electric field intensity distribution along the z-axis (x=0) when the PDMS stretching range is 100% to 140% at 0.85−1.0 THz broadband operating frequency. Among them (a)−(d) correspond to frequencies 0.85 THz, 0.90 THz, 0.95 THz and 1.0 THz, respectively.
图 7 柔性基底动态调焦石墨烯太赫兹超表面聚焦反射镜在0.85−1.0 THz宽频工作频率内，PDMS拉伸幅度为100%−140%的焦平面的电场强度分布图。其中(a)−(d)对应频率0.85 THz、0.90 THz、0.95 THz、1.0 THz。
Figure 7. The graphene terahertz super-surface focusing mirror with flexible substrate dynamic focusing is in the 0.85−1.0 THz broadband operating frequency, the PDMS stretching range is 100%−140% of the focal plane electric field intensiy distributiton map. (a)−(d) correspond to frequencies 0.85 THz, 0.90 THz, 0.95 THz, 1.0 THz.
图 8 石墨烯太赫兹超表面聚焦反射镜在0.85−1.0 THz宽频工作频率下的焦点位置(a, b)和聚焦效率(c, d)随柔性基底伸长100%−140%变化情况。
Figure 8. The focus position (a, b) and focus efficiency (c, d) of the graphene terahertz metasurface focusing mirror at 0.85−1.0 THz broadband operating frequency varies with the elongation of the flexible substrate by 100%−140%.
表 1 柔性基底动态调焦石墨烯太赫兹超表面单元结构参数设计结果
Table 1. The design results of structural parameters of graphene terahertz metasurface units for dynamic focusing on flexible substrates.
Cell(#) 
Parameter w=110 μm
uc = 1.00 eVw=140 μm
uc = 0.35 eVw=135 μm
uc = 0.14 eVw=75 μm
uc = 0.13 eVw=20 μm
uc = 0.03 eVw=37 μm
uc = 0.30 eVw=40 μm
uc = 0.45 eVw=85 μm
uc = 0.30 eVPhase(rad) −3.14 −2.31 −1.50 −0.76 0.02 0.74 1.56 2.37 Reflection 0.93 0.83 0.78 0.77 0.96 0.99 0.85 0.99 
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