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摘要:
近年来,超构表面(metasurface)作为一种人工二维结构由于其超薄的几何结构以及灵活的电磁调控能力受到了学界的广泛关注,如何进一步提高超构表面器件的性能成为了该领域的研究热点。悬链线电磁学(catenary electromagnetics)作为一类新兴的超构表面设计原理为设计高效率超构表面器件提供了新的思路和方法。本文提出了一种基于扭转悬链线结构的超构表面,其能够实现对不同旋向入射的圆偏振电磁波的高效选择性吸收。仿真结果表明所设计的器件在工作波长处对左旋圆偏振电磁波吸收率接近于1,而右旋圆偏振入射时吸收率小于22%,其对应的二向色性大于78%。同时,文章分析了产生高效率手性吸收的物理机制并且提出了一种基于该类结构的信息加密方法。该工作在手性成像与手性探测等领域具有一定的应用前景。
Abstract:As a kind of artificial two-dimensional material, metasurfaces have drawn wide attentions in recent years due to their ultra-thin profile and flexible electromagnetic manipulation capability. Therefore, how to further improve the working efficiency of metasurface devices has become a hotspot in this field. Catenary electromagnetics as an emerging metasurface design principle provides new ideas and methods for designing efficient metasurfaces. Here, we proposed a metasurface absorber based on twisted catenary structure that can achieve efficient spin-selective absorption. The simulated results indicate that the perfect absorption can be achieved for left-handed circularly polarized incidence at the working wavelength, while the absorption for right-handed circularly polarized incidence is below 22%. The corresponding circular dichroism is larger than 78%. Besides, the physical mechanism for the chiral absorption is analyzed and a promising application for information encryption is also discussed. This work may find potential applications in chiral imaging and chiral sensing.
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Key words:
- metasurface /
- catenary structure /
- chiral absorption /
- circular polarization
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Overview: Metasurface is a new kind of artificial two-dimensional material. Its working principle is to flexibly control the amplitude, phase and polarization of the incident electromagnetic wave by using the local interaction between the subwavelength scale unit cell and electromagnetic wave. Compared with traditional optical devices, devices based on metasurfaces have the advantages of compact structure, diverse functions, and easy integration. Therefore, metasurface has become a research hotspot in optics and photonics. At present, the electromagnetic manipulation devices based on the metasurfaces have achieved many novel functionalities, such as perfect absorption, anomalous deflection, focused imaging, electromagnetic cloak, and high efficiency holography. However, there are still some key problems to be solved in this field such as low working efficiency and narrow bandwidth. In recent years, the emergence of catenary electromagnetics provides new ideas and methods to solve these problems. In fact, catenary was first used in engineering and architecture to describe the shape of a soft rope suspended under the uniform gravitational force between two horizontal points. The use of catenary equations to solve problems in the field of electromagnetism has only recently been discovered by researchers. In this paper, we proposed a metasurface absorber based on a twisted catenary structure in the near-infrared band. The local electric field enhancement effect of the structure is different when the incident electromagnetic wave is with opposite spins, which can achieve efficient chiral selective absorption. The simulation results show that the circular dichroism is larger than 78% at the working wavelength. At the same time, the designed structure also has good angular stability, and can still get larger than 60% circular dichroism absorption in the case of oblique incidence at different azimuth angles. Besides, a possible method of information encryption using this kind of structure is proposed. Different information can be read by controlling the handedness of incident electromagnetic wave. This work further enriches the content of catenary electromagnetics, and has certain research value in the fields of chiral imaging and chiral sensing.
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1. 引 言
超构表面(Metasurface)是一类新兴的人工二维材料,其工作原理主要是利用亚波长尺度的单元结构与电磁波的局域相互作用实现对入射电磁波振幅、相位以及偏振等属性的灵活调控[1-4]。相较于传统光学器件,基于超构表面的器件具有结构紧凑、功能多样以及利于集成等优势,因此该领域已经成为当代光学与光子学的研究热点。目前,基于超构表面的电磁调控器件已经实现了许多新颖的功能,例如完美吸收[5-7]、异常偏折[8-11]、聚焦成像[12-15]、电磁隐身斗篷[16-18]以及高效率全息[19-22]等。然而,该领域仍然存在一些亟待解决的关键性问题。首先,由于超构表面与电磁波相互作用的距离受限(通常为亚波长尺度),导致部分器件的工作效率与带宽受到原理性的限制。其次,针对相位调控型超构表面,由于单元结构离散化引入的相位噪声会不可避免地影响器件的整体响应。最后,由于超构表面与电磁波相互作用的机理尚不完全明晰,还未能找到准确的数理模型描述超构表面的工作原理。
近年来,悬链线电磁学(catenary electromagnetics)的出现为解决上述问题提供了新的思路和方法[23]。事实上,悬链线最早的应用是在工程技术与建筑领域中,用于描绘悬在水平两点间均匀引力作用下软绳的形状。而利用悬链线方程解决电磁学领域的问题直到近年来才被研究人员发现。一方面,研究人员发现利用悬链线型单元结构能够设计出带宽与效率更高的超构表面器件。2015年,Pu等人在可见光波段利用悬链线型单元结构设计了一类轨道角动量光束产生器,相较于传统基于离散型单元结构的设计方法,悬链线型结构具有更大的工作带宽与效率,同时在理论上能够实现完美的相位匹配[24]。同年,Wang等人将该设计方法扩展到微波波段,进一步证实了该类结构的优越性[25]。2017年,Luo等人利用单个悬链线结构实现了宽带的自旋轨道相互作用[26]。2021年,Zhang等人利用悬链线型单元结构结合二次相位成像原理设计了一类宽带高效率的大视场成像透镜,视场角接近178°[27]。另一方面,利用悬链线方程可以计算一部分超构表面与电磁波相互作用后的等效阻抗,并且悬链线方程可以很好地描述结构内的电场分布。2018年,Pu等人首次提出利用悬链线方程准确描述电磁波与超构表面光栅之间的相互作用过程,并利用悬链线电磁模型设计了大角度带通滤波器[28]。2019年,Huang等人将悬链线电磁模型从一维光栅结构推广到二维阵列结构,并基于该原理设计了高效率平面薄膜天线与宽带电磁吸收器[29]。除此以外,悬链线电磁学在相干吸收[30]、偏振转换[31]与结构光场[32]等领域均有一系列应用。
在上述研究的基础上,本文设计并验证了一种基于扭转悬链线结构的手性超构表面,该结构能够对不同旋向入射的电磁波实现选择性吸收。该器件的工作示意图如图1(a)所示,当左旋圆偏振(left-handed circularly polarized,LCP)电磁波入射到器件上时将会被器件完全吸收,而当与之旋向相反的右旋圆偏振(right-handed circularly polarized,RCP)电磁波入射时,则只有一小部分被吸收。因此,该结构表现出较强的圆二向色性,该性质对于手性成像、手性光谱探测以及信息加密等领域均具有一定的应用价值。
图 1. 基于扭转悬链线结构的手性超构表面吸波器。(a) 器件工作示意图。当LCP电磁波入射到器件上时将会被器件完全吸收,而当RCP电磁波入射时,只有小部分被吸收;(b) 单元结构三维示意图(上)与俯视图(下)Figure 1. Chiral metasurface absorber based on twisted catenary structure. (a) The schematic image of the proposed metasurface. LCP incidence will be totally absorbed by the metasurface, while the RCP incidence will be largely reflected; (b) The 3D (top) and top view (bottom) schematic images of the unit cell2. 结果与讨论
如图1(b)所示为所设计超构表面的单元结构示意图。该单元结构由金属-介质-金属(metal-insulator-metal, MIM)结构排列而成,所选用的金属材料为金(Au),介质材料为硅(Si)。悬链线结构的表达式为[26]
{y=Λπln|sec(πxΛ)|x<0y=−Λπln|sec(πxΛ)|x≥0, (1) 其中:Λ为悬链线结构的周期,x和y分别为如图1(b)中标注的空间横纵坐标。在构建单元结构时,首先依据式(1)画出一条没有宽度的悬链线,再将该曲线沿着y轴方向平移δ
,最后根据实际加工制备的限制对该结构进行截断。利用参数扫描的方式通过商用电磁仿真软件CST Microwave Studio对该结构进行优化设计,得到了优化后的几何参数。三层结构自上而下的厚度分别为60 nm、310 nm和100 nm。单元结构的横向周期Px=560 nm,纵向周期Py=820 nm。悬链线在x轴方向的长度为Λ=600 nm,考虑到实际加工的限制对悬链线结构进行了截断处理,即实际的悬链线长度为Λ'=0.9Λ=540 nm,悬链线结构的宽度δ=80 nm。在仿真中x轴和y轴方向采用的边界条件为unit cell,z轴方向为open。Au和Si的材料参数取自参考文献[33]。 为了进一步说明该结构的性能,如图2所示为本文所提出的扭转悬链线与传统悬链线结构的对比。图2(a)为传统悬链线结构的示意图,该结构的表达式为[24]
图 2. 扭转悬链线结构与传统悬链线结构的对比。(a) 传统悬链线结构的示意图;(b) 不同旋向入射下的反射振幅;(c) 不同旋向入射下的吸收率;(d) 扭转悬链线结构的示意图;(e) 不同旋向入射下的反射振幅;(f) 不同旋向入射下的吸收率Figure 2. The comparison between the traditional catenary structure and the twisted catenary structure. (a) The schematic image of traditional catenary structure; (b) The reflected amplitude and (c) absorption under different circularly polarized incidence; (d) The schematic image of twisted catenary structure; (e) The reflected amplitude and (f) absorption under different circularly polarized incidencey=Λπln|sec(πxΛ)|. (2) 在仿真中采用的几何参数、选用材料以及仿真设置与上述扭转型悬链线结构相同。图2(b)和2(c)分别为传统悬链线结构在不同旋向电磁波入射下在1.4 μm~2 μm波段内的反射振幅与对应的吸收率。由图2(b)可知,不同旋向入射时的同极化反射振幅(rLCP→LCP、rRCP→RCP)始终相同,交叉极化反射振幅(rLCP→RCP、rRCP→LCP)的差异也很小(最大差值小于7%)。因此,如图2(c)所示对应的LCP吸收率ALCP与RCP吸收率ARCP在仿真的波长范围内基本相同(最大差值∆A<4%)。上述结果说明传统的悬链线结构不具有圆偏振选择性吸收的特点。有趣的是,如果将图2(a)中的传统悬链线结构在x>0部分进行扭转180°得到如图2(d)所示的扭转悬链线结构后,该类结构能够表现出优异的手性吸收性能。由图2(e)可知,当LCP入射时在1.7 μm附近扭转悬链线结构的同极化反射振幅rLCP→LCP与交叉极化反射振幅rLCP→RCP分别为9.3%与2.2%,而RCP入射时分别为rRCP→RCP=9.3%,rRCP→LCP=88%。因此对应的圆偏振吸收率ALCP与ARCP可以分别表示为[8]
ARCP=1−|rRCP→RCP|2−|rRCP→LCP|2, (3) ALCP=1−|rLCP→LCP|2−|rLCP→RCP|2. (4) 根据式(3)、式(4)可以得到ALCP=99.1%与ARCP=21.2%。因此,对应的圆偏振二向色性最大值∆A>78%。如图2(f)所示,该超构表面器件在仿真的波长范围内始终具有圆二向色性响应,从而证实了该器件能够在较宽的工作波段内工作。
由于器件的角度稳定性对于实际应用具有十分重要的意义,因此图3仿真了所设计的扭转型悬链线超构表面在不同方位角φ与入射角θ下的吸收率响应。关于方位角φ与入射角θ的定义如图1(a)所示。由图3(a)可知该器件在φ=0° LCP入射时的吸收率在θ处于0~60°范围内时基本没有明显的变化,仅表现为吸收峰的轻微蓝移,最大峰值仍然大于90%。而如图3(b)所示,φ=0° RCP入射时在1.7 μm附近的吸收率会随着入射角的增大而略微增大。因此,如图3(c)所示,当φ=0°,θ处于0~60°时,该结构在不同旋向圆偏振光入射时的最大吸收率差值∆A仍然大于60%。此外,由图3(d)和3(e)可知,在φ=90°时随着入射角θ的增大,LCP的吸收带宽也会增大而吸收峰值会降低,RCP的吸收率会增加并且在短波长处出现吸收峰。因此对应的二向色性吸收特性也会由高效窄带吸收谱变为宽带吸收谱,如图3(f)所示。由以上的分析可知,本文所设计的悬链线型手性吸收器具有较好的角度稳定性,能够在任意方位角与大入射角下工作,相较于部分已报导的超构表面器件具有明显的优势[34-37]。
为了进一步说明产生手性吸收的物理机理,图4(a)和4(b)分别给出了在工作波长与非工作波长时不同旋向电磁波入射下的归一化电场分布。由图4(a)可知,当LCP 入射时单元结构的边角处产生了极大的局域电场增强效果,而RCP入射时几乎不能观察到该效果。此外,图4(b)表明在非工作波长处该结构对LCP和RCP表现出几乎相同的电场响应,且几乎没有局域电场增强。由于在相同情况下超构表面对电磁波的吸收率正比于电场增强的倍数[38],因此图4(a)和4(b)说明产生手性吸收的原因主要是由于扭转型悬链线结构在工作波长处具有各向异性的电磁响应。同时,中间的Si作为介质层与上下两层金属形成了法布里波罗腔(Fabry–Pérot cavity),通过优化介质层的厚度可以进一步增加该器件的圆二向色性,从而实现高效的圆偏振选择性吸收。此外,二向色性响应产生的原因也可以从如图4(c)和4(d)所示的对线偏振(linearly polarized, LP)电磁波的响应来解释。由图4(c)可知,在工作波长附近(图中虚线所示),该器件对TE偏振电磁波和TM偏振电磁波有几乎相同的反射振幅,即rTE→TM=rTM→TE≈rTE→TE≈rTM→TM。而从图4(d)的反射相位可知rTE→TM与rTM→TE相位相同,而rTE→TE与rTM→TM相位相差π。对圆偏振电磁波的吸收可由对线偏振电磁波的吸收通过下式换算[39]:
图 4. 扭转悬链线结构手性吸收的物理机理。 (a) 工作波长处不同旋向电磁波入射的归一化电场分布;(b) 非工作波长处不同旋向电磁波入射的归一化电场分布;(c) 线偏振入射下的反射振幅;(d) 线偏振入射下的反射相位Figure 4. The physical mechanism for the chiral absorption of the twisted catenary structure. (a) The normalized electric field distribution under different circularly polarized incidence at the working wavelength; (b) The normalized electric field distribution under different circularly polarized incidence at the non- working wavelength; (c) The reflected amplitude under linearly polarized incidence; (d) The reflected phase under linearly polarized incidence(rRCP→RCPrRCP→LCPrLCP→RCPrLCP→LCP)=12×((rTE→TE+rTM→TM)+i(rTE→TM−rTM→TE)(rTE→TE−rTM→TM)−i(rTE→TM+rTM→TE)(rTE→TE−rTM→TM)+i(rTE→TM+rTM→TE)(rTE→TE+rTM→TM)−i(rTE→TM−rTM→TE)), (5) 由于在线偏振入射下交叉极化的振幅和相位均相同,而对于共极化的振幅相同相位相反,导致了式(5)左方矩阵中除右上角一项rRCP→LCP接近于1以外的其他项均接近于0,因此该结构表现出高效的手性吸收响应。
由于本文提出的扭转悬链线结构具有高效的手性吸收特性,因此该结构有望用于信息加密。图5(a)中的悬链线结构为图2(d)中的镜像结构,由于结构的对称性导致其手性响应也会发生翻转,因此能够实现对LCP入射光的高效反射以及对RCP入射光的高效选择性吸收。在此基础上对如图5(b)所示的超构表面进行了仿真验证,其中红色方框内部采用图2(d)中单元结构周期性排布而成,绿色方框内部由图5(a)中单元结构周期性排布而成,整个器件包含48个单元结构。利用CST Microwave Studio时域求解器进行仿真,如图5(c)~5(e)所示为入射电磁波波长等于1.7 μm时的近场图像(电场监视器位于距离超构表面120 nm处)。当入射电磁波为LP电磁波时,由于在该情况下两种悬链线结构的吸收率相同,因此观察到的近场电场分布均匀如图5(c)。而当入射电磁波为圆偏振电磁波时,如图5(d)和5(e)所示由于器件中不同区域由不同的悬链线结构排布而成,因此能够得到互补的近场图案。当入射光为LCP时,样品的左上角和右下角反射率明显大于另外两个区域,而当入射电磁波为RCP时,能够得到互补的近场图像。
图 5. 基于扭转悬链线结构的信息加密验证。(a) 将图2(d) 结构镜像后得到的单元结构及其吸收率;(b) 加密图像的原图像;在LP (c),LCP (d) 和RCP (e) 入射下的仿真近场图像Figure 5. The information encryption verification based on the twisted catenary structures. (a) The mirrored unit cell as that in Figure 2(d) and its absorption; (b) The original image for information encryption; The simulated near field image under LP (c), LCP (d) and RCP (e) incidence在验证了该方法能够实现圆偏振选择性吸收的基础上,图6进一步给出了利用该方法实现信息加密的应用举例。图6(a)为利用图2(d)与图5(a)中单元结构周期性排列得到的样品示意图,其中红色区域为图2(d)中单元结构排布而成,绿色区域由图5(a)中单元结构排布而成,灰色区域为金属膜层。当入射电磁波为波长等于1.7 μm的LP电磁波或无偏振(unpolarized)电磁波时,该样品的近场图像如图6(b)所示,由于在该情况下两种悬链线结构的吸收率相同,因此观察到的每个字母的亮度也相同。而当入射电磁波为圆偏振电磁波时,由于样品中的字母由手性相反的悬链线结构排布而成,因此能够得到互补的近场图案。如图6(c)和6(d)所示,当入射光为LCP时,得到的信息为“Canry Metur”,而当入射电磁波为RCP时,得到的信息为“tea as face”。事实上,如果在样品中加入偏振无关的吸波器时,该加密方法不仅能够得到互补的图像,也能得到相对独立的图像。
图 6. 基于扭转悬链线结构的信息加密应用举例。(a) 用于信息加密的样品示意图;在(b) LP或Unpolarized, (c) LCP和 (d) RCP入射下的近场图像Figure 6. The information encryption application based on the twisted catenary structure. (a) The sample image for information encryption; The calculated near field image under (b) LP or unpolarized, (c) LCP and (d) RCP incidence3. 总 结
综上所述,本文提出了一种工作在近红外波段基于扭转型悬链线结构的超构表面吸波器,利用该结构在不同旋向电磁波入射下的局域电场增强效果不同,能够实现高效的手性选择吸收。仿真结果表明,该结构在工作波长处得到的圆二向色性值大于78%。此外,所设计结构还具有较好的角度稳定性,在不同方位角斜入射情况下依然能够得到大于60%的二向色性吸收。文章同时提出了一种利用该类结构实现信息加密的可能方法,通过控制入射电磁波的旋向可以实现不同信息的读取。该工作进一步丰富了悬链线电磁学的内容,对手性成像、手性探测等领域具有一定的研究价值。
利益冲突:所有作者声明无利益冲突
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图 1 基于扭转悬链线结构的手性超构表面吸波器。(a) 器件工作示意图。当LCP电磁波入射到器件上时将会被器件完全吸收,而当RCP电磁波入射时,只有小部分被吸收;(b) 单元结构三维示意图(上)与俯视图(下)
Figure 1. Chiral metasurface absorber based on twisted catenary structure. (a) The schematic image of the proposed metasurface. LCP incidence will be totally absorbed by the metasurface, while the RCP incidence will be largely reflected; (b) The 3D (top) and top view (bottom) schematic images of the unit cell
图 2 扭转悬链线结构与传统悬链线结构的对比。(a) 传统悬链线结构的示意图;(b) 不同旋向入射下的反射振幅;(c) 不同旋向入射下的吸收率;(d) 扭转悬链线结构的示意图;(e) 不同旋向入射下的反射振幅;(f) 不同旋向入射下的吸收率
Figure 2. The comparison between the traditional catenary structure and the twisted catenary structure. (a) The schematic image of traditional catenary structure; (b) The reflected amplitude and (c) absorption under different circularly polarized incidence; (d) The schematic image of twisted catenary structure; (e) The reflected amplitude and (f) absorption under different circularly polarized incidence
图 4 扭转悬链线结构手性吸收的物理机理。 (a) 工作波长处不同旋向电磁波入射的归一化电场分布;(b) 非工作波长处不同旋向电磁波入射的归一化电场分布;(c) 线偏振入射下的反射振幅;(d) 线偏振入射下的反射相位
Figure 4. The physical mechanism for the chiral absorption of the twisted catenary structure. (a) The normalized electric field distribution under different circularly polarized incidence at the working wavelength; (b) The normalized electric field distribution under different circularly polarized incidence at the non- working wavelength; (c) The reflected amplitude under linearly polarized incidence; (d) The reflected phase under linearly polarized incidence
图 5 基于扭转悬链线结构的信息加密验证。(a) 将图2(d) 结构镜像后得到的单元结构及其吸收率;(b) 加密图像的原图像;在LP (c),LCP (d) 和RCP (e) 入射下的仿真近场图像
Figure 5. The information encryption verification based on the twisted catenary structures. (a) The mirrored unit cell as that in Figure 2(d) and its absorption; (b) The original image for information encryption; The simulated near field image under LP (c), LCP (d) and RCP (e) incidence
图 6 基于扭转悬链线结构的信息加密应用举例。(a) 用于信息加密的样品示意图;在(b) LP或Unpolarized, (c) LCP和 (d) RCP入射下的近场图像
Figure 6. The information encryption application based on the twisted catenary structure. (a) The sample image for information encryption; The calculated near field image under (b) LP or unpolarized, (c) LCP and (d) RCP incidence
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