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Mid-infrared large-angle high-efficiency retroreflector based on subwavelenght metallic metagrating

Wang Mei-Ou Xiao Qian Jin Xia Cao Yan-Yan Xu Ya-Dong

Mid-infrared large-angle high-efficiency retroreflector based on subwavelenght metallic metagrating

Wang Mei-Ou, Xiao Qian, Jin Xia, Cao Yan-Yan, Xu Ya-Dong
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  • How to effectively control the refraction, reflection, propagation and wavefront of dynamic waves or light has become one of hot research points in the field of optics. In the past few years, the concept of phase gradient metasurface has been proposed: it introduces a gradient of the phase discontinuity covering the entire angle 2π along the interface to provide an effective wave vector $\kappa $ and completely control the direction of outing wave. Therefore, the metasurface can possess many novel optical applications, such as holograms, metalenses, photonic spin Hall effect, etc. In this work, we design a simplified reflection-type optical metagrating. The results demonstrate that the metagrating can achive the function of two-channel retroreflection, that is, redirecting the incident wave back toward the source, with a nearly perfect conversion efficiency.The metagrating designed in this paper contains only two sub-cells with π reflection phase difference in period. The working wavelength (λ) of metagrating is fixed at 3 μm. The two sub-cells are filled with an impedance matching material (their material relative refractive indexes are n1 = 1 and n2 = 1.5 respectively and their thickness is d = 1.5 μm.).The period length range is 1.5 μm ≤ p ≤ 3 μm(considering reducing the reflection order). When the incident angle is ${\theta _{\rm{i}}}= \pm \arcsin [\lambda /(2p)]$, the absolute values of the incident angle and the reflected angle are equal, and then retroreflection occurs. When the wavelength is greater than the period ($\lambda \geqslant p$), the angle of retroreflection can be adjusted to any value ($\left| {{\theta _{\rm{i}}}} \right| \geqslant {\rm{3}}{{\rm{0}}^ \circ }$) by adjusting the period p. In this work, COMSOL MULTIPHYSICS software is used to simulate the retroreflection reflectivity and field pattern of the designed metagrating. The results verify the two-channel retroreflection property of the metagrating. In addition,as the angle of incidence changes from 30° to 60°, the efficiency of retroreflection at any incident angle can reach to more than 95%. When the incident angle is 75.4°, the metagrating still has an efficiency of 80% retroreflection. Therefore, the metagrating also achieves the function of high-efficiency retroreflection at a large-angle. Comparing with multiple sub-cells’ metasurface, the simplified metagrating with two sub-cells enables a similar function of retroreflection, but has many potential advantages, and can play an important role in high-efficiency sensing, imaging and communication.
      Corresponding author: Jin Xia, xjin@suda.edu.cn ; Cao Yan-Yan, yycao@stu.suda.edu.cn
    [1]

    Yu N, Genevet P, Kats M A, Aieta F, Tetienne J P, Capasso F, Gaburro Z 2011 Science 334 333

    [2]

    Kildishev A V, Boltasseva A, Shalaev V M 2013 Science 339 1232009

    [3]

    Yu N, Capasso F 2014 Nat. Mater. 13 139

    [4]

    Zhao Y, Liu X, Alù A 2014 J. Opt. 16 123001

    [5]

    Xu Y, Fu Y, Chen H 2016 Nat. Rev. Mater. 1 16067

    [6]

    Shi H Y, Zhang A X, Chen J Z, Wang J F, Xia S, Xu Z 2016 Chin. Phys. B 25 078105

    [7]

    Zhao J, Yang X, Dai J Y, Cheng Q, Li X, Qi N H, Ke J C, Bai G D, Liu S, Jin S, Alù A, Cui T J 2018 Natl. Sci. Rev. 6 231

    [8]

    Xu Y, Gu C, Hou B, Lai Y, Li J, Chen H 2013 Nat. Commun. 4 2561

    [9]

    Ni X, Ishii S, Kildishev A V, Shalaev V M 2013 Light Sci. Appl 2 e72

    [10]

    Yin X, Ye Z, Rho J, Wang Y, Zhang X 2013 Science 339 1405

    [11]

    Xu Y, Fu Y, Chen H 2015 Sci. Rep. 5 12219

    [12]

    Ra’di Y, Sounas D L, Alù A 2017 Phys. Rev. Lett. 119 067404

    [13]

    Chalabi H, Ra’di Y, Sounas D L, Alù A 2017 Phys. Rev. B 96 075432

    [14]

    Fu Y, Cao Y, Xu Y 2019 Appl. Phys. Lett. 114 053502

    [15]

    Qian E, Fu Y, Xu Y, Chen H 2016 Europhys. Lett. 114 34003

    [16]

    Ra’di Y, Alù A 2018 ACS Photonics 5 1779

    [17]

    Fu Y, Shen C, Cao Y, Gao L, Chen H, Chan C T, Cummer S A, Xu Y 2019 Nat. Commun. 10 2326

    [18]

    Ma Y, Ong C K, Tyc T, Leonhardt U 2009 Nat. Mater. 8 639

    [19]

    Jia Y, Wang J, Li Y, Pang Y, Yang J, Fan Y, Qu S 2017 AIP Adv. 7 105315

    [20]

    Yan L, Zhu W, Karim M F, Cai H, Gu A Y, Shen Z, Chong P H J, Kwong D L, Qiu C W, Liu A Q 2018 Adv. Mater. 30 e1802721

    [21]

    Lipuma D, Meric S, Gillard R 2013 Electron. Lett. 49 2

    [22]

    Zentgraf T, Liu Y, Mikkelsen M H, Valentine J, Zhang X 2011 Nat. Nanotechnol. 6 151

    [23]

    Nakagawa K, Sanada A 2017 ICMIM 978-1-5090-4354-5

    [24]

    Jiang W X, Bao D, Cui T J 2016 J. Opt. 18 044022

    [25]

    Fu Y, Li J, Xie Y, Shen C, Xu Y, Chen H, Cummer S A 2018 Phys. Rev. Mater. 2 105202

    [26]

    Song G, Cheng Q, Cui T J, Jing Y 2018 Phys. Rev. Mater. 2 065201

    [27]

    Shen C, Díaz-Rubio A, Li J, Cummer S A 2018 Appl. Phys. Lett. 112 183503

    [28]

    Shen C, Cummer S A 2018 Phys. Rev. Appl. 9 054009

    [29]

    Cao Y, Fu Y, Zhou Q, Ou X, Gao L, Chen H, Xu Y 2019 Phys. Rev. Appl. 12 024006

    [30]

    Zhang Z, Chu F, Guo Z, Fan J, Li G, Cheng W 2019 J. Lightwave Technol. 37 2820

  • 图 1  超构光栅的结构示意图 (a)逆向反射超构光栅的示意图, 其中红色和绿色箭头均表示回射, 蓝色箭头表示镜面反射; (b)超构光栅的结构单元示意图; (c)超构光栅入射和反射的等频图

    Figure 1.  The structute of the metagrating: (a) The schematic of the retroreflection metagrating, wherein red and green arrows indicate retroreflection and blue arrows indicate specular reflection; (b) the diagram of metagrating with two sub-cells; (c) the iso-frequency contours of the incident wave and reflection wave for the metagrating.

    图 2  设计的回射角为$ \pm {\rm{3}}{{\rm{0}}^ \circ }$时, 超构光栅的不同级次的反射效率以及高斯波入射到超构光栅的总磁场图 (a)超构光栅不同级次的反射效率随入射角度变化曲线; (b)高斯波入射到超构光栅, 双通道回射的总磁场图

    Figure 2.  The reflection efficiency of different orders and the total magnetic field pattern, while the designed retroreflection angle is $ \pm {\rm{3}}{{\rm{0}}^ \circ }$: (a) The reflection efficiency of different orders vary with incident angle; (b) the total magnetic field pattern of the two-channel retroreflector.

    图 3  设计的回射角为$ \pm {\rm{6}}{{\rm{0}}^ \circ }$时, 超构光栅的不同级次的反射效率以及高斯波入射到超构光栅的总磁场图 (a)超构光栅不同级次的反射效率随入射角度变化曲线; (b)高斯波入射到超构光栅, 双通道回射的总磁场图

    Figure 3.  The reflection efficiency of different orders and the total magnetic field pattern, while the designed retroreflection angle is $ \pm 6{{\rm{0}}^ \circ }$: (a) The reflection efficiency of different orders vary with incident angle; (b) the total magnetic field pattern of the two-channel retroreflector.

    图 4  逆向反射的效率和工作角度随周期长度的变化规律. 随$p$改变过程中, 金属槽的占空比和填充介质保持不变

    Figure 4.  The incident angle of retroreflection and retroreflectivity corresponding to different period lengths $p$. With the change of $p$, the duty cycle and filling medium of the metal slot remain unchanged.

  • [1]

    Yu N, Genevet P, Kats M A, Aieta F, Tetienne J P, Capasso F, Gaburro Z 2011 Science 334 333

    [2]

    Kildishev A V, Boltasseva A, Shalaev V M 2013 Science 339 1232009

    [3]

    Yu N, Capasso F 2014 Nat. Mater. 13 139

    [4]

    Zhao Y, Liu X, Alù A 2014 J. Opt. 16 123001

    [5]

    Xu Y, Fu Y, Chen H 2016 Nat. Rev. Mater. 1 16067

    [6]

    Shi H Y, Zhang A X, Chen J Z, Wang J F, Xia S, Xu Z 2016 Chin. Phys. B 25 078105

    [7]

    Zhao J, Yang X, Dai J Y, Cheng Q, Li X, Qi N H, Ke J C, Bai G D, Liu S, Jin S, Alù A, Cui T J 2018 Natl. Sci. Rev. 6 231

    [8]

    Xu Y, Gu C, Hou B, Lai Y, Li J, Chen H 2013 Nat. Commun. 4 2561

    [9]

    Ni X, Ishii S, Kildishev A V, Shalaev V M 2013 Light Sci. Appl 2 e72

    [10]

    Yin X, Ye Z, Rho J, Wang Y, Zhang X 2013 Science 339 1405

    [11]

    Xu Y, Fu Y, Chen H 2015 Sci. Rep. 5 12219

    [12]

    Ra’di Y, Sounas D L, Alù A 2017 Phys. Rev. Lett. 119 067404

    [13]

    Chalabi H, Ra’di Y, Sounas D L, Alù A 2017 Phys. Rev. B 96 075432

    [14]

    Fu Y, Cao Y, Xu Y 2019 Appl. Phys. Lett. 114 053502

    [15]

    Qian E, Fu Y, Xu Y, Chen H 2016 Europhys. Lett. 114 34003

    [16]

    Ra’di Y, Alù A 2018 ACS Photonics 5 1779

    [17]

    Fu Y, Shen C, Cao Y, Gao L, Chen H, Chan C T, Cummer S A, Xu Y 2019 Nat. Commun. 10 2326

    [18]

    Ma Y, Ong C K, Tyc T, Leonhardt U 2009 Nat. Mater. 8 639

    [19]

    Jia Y, Wang J, Li Y, Pang Y, Yang J, Fan Y, Qu S 2017 AIP Adv. 7 105315

    [20]

    Yan L, Zhu W, Karim M F, Cai H, Gu A Y, Shen Z, Chong P H J, Kwong D L, Qiu C W, Liu A Q 2018 Adv. Mater. 30 e1802721

    [21]

    Lipuma D, Meric S, Gillard R 2013 Electron. Lett. 49 2

    [22]

    Zentgraf T, Liu Y, Mikkelsen M H, Valentine J, Zhang X 2011 Nat. Nanotechnol. 6 151

    [23]

    Nakagawa K, Sanada A 2017 ICMIM 978-1-5090-4354-5

    [24]

    Jiang W X, Bao D, Cui T J 2016 J. Opt. 18 044022

    [25]

    Fu Y, Li J, Xie Y, Shen C, Xu Y, Chen H, Cummer S A 2018 Phys. Rev. Mater. 2 105202

    [26]

    Song G, Cheng Q, Cui T J, Jing Y 2018 Phys. Rev. Mater. 2 065201

    [27]

    Shen C, Díaz-Rubio A, Li J, Cummer S A 2018 Appl. Phys. Lett. 112 183503

    [28]

    Shen C, Cummer S A 2018 Phys. Rev. Appl. 9 054009

    [29]

    Cao Y, Fu Y, Zhou Q, Ou X, Gao L, Chen H, Xu Y 2019 Phys. Rev. Appl. 12 024006

    [30]

    Zhang Z, Chu F, Guo Z, Fan J, Li G, Cheng W 2019 J. Lightwave Technol. 37 2820

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  • Received Date:  26 July 2019
  • Accepted Date:  03 October 2019
  • Available Online:  07 December 2019
  • Published Online:  01 January 2020

Mid-infrared large-angle high-efficiency retroreflector based on subwavelenght metallic metagrating

    Corresponding author: Jin Xia, xjin@suda.edu.cn
    Corresponding author: Cao Yan-Yan, yycao@stu.suda.edu.cn
  • 1. College of Energy, Soochow University, Suzhou 215006, China
  • 2. Wenzheng College, Soochow University, Suzhou 215104, China
  • 3. School of Physical Science and Technology, Soochow University, Suzhou 215006, China

Abstract: How to effectively control the refraction, reflection, propagation and wavefront of dynamic waves or light has become one of hot research points in the field of optics. In the past few years, the concept of phase gradient metasurface has been proposed: it introduces a gradient of the phase discontinuity covering the entire angle 2π along the interface to provide an effective wave vector $\kappa $ and completely control the direction of outing wave. Therefore, the metasurface can possess many novel optical applications, such as holograms, metalenses, photonic spin Hall effect, etc. In this work, we design a simplified reflection-type optical metagrating. The results demonstrate that the metagrating can achive the function of two-channel retroreflection, that is, redirecting the incident wave back toward the source, with a nearly perfect conversion efficiency.The metagrating designed in this paper contains only two sub-cells with π reflection phase difference in period. The working wavelength (λ) of metagrating is fixed at 3 μm. The two sub-cells are filled with an impedance matching material (their material relative refractive indexes are n1 = 1 and n2 = 1.5 respectively and their thickness is d = 1.5 μm.).The period length range is 1.5 μm ≤ p ≤ 3 μm(considering reducing the reflection order). When the incident angle is ${\theta _{\rm{i}}}= \pm \arcsin [\lambda /(2p)]$, the absolute values of the incident angle and the reflected angle are equal, and then retroreflection occurs. When the wavelength is greater than the period ($\lambda \geqslant p$), the angle of retroreflection can be adjusted to any value ($\left| {{\theta _{\rm{i}}}} \right| \geqslant {\rm{3}}{{\rm{0}}^ \circ }$) by adjusting the period p. In this work, COMSOL MULTIPHYSICS software is used to simulate the retroreflection reflectivity and field pattern of the designed metagrating. The results verify the two-channel retroreflection property of the metagrating. In addition,as the angle of incidence changes from 30° to 60°, the efficiency of retroreflection at any incident angle can reach to more than 95%. When the incident angle is 75.4°, the metagrating still has an efficiency of 80% retroreflection. Therefore, the metagrating also achieves the function of high-efficiency retroreflection at a large-angle. Comparing with multiple sub-cells’ metasurface, the simplified metagrating with two sub-cells enables a similar function of retroreflection, but has many potential advantages, and can play an important role in high-efficiency sensing, imaging and communication.

    • 如何有效控制光的折射、反射、传播以及波前等, 一直是光学领域的热点研究之一. 在过去几年里, 科学家们提出了渐变超构表面的概念[1], 即通过在一个周期内沿着界面方向引入覆盖2π变化的突变相位, 进而在该方向引入有效波矢 $\kappa $. 根据切向方向动量守恒, 光在界面上发生反射和折射时满足广义的反射和折射定律: ${k_{\rm{i}}}\sin {\theta _{{\rm{in}}}} = {k_{\rm{i}}}\sin {\theta _{\rm{r}}} + \kappa $${k_{\rm{i}}}\sin {\theta _{{\rm{in}}}} = {k_{\rm{t}}}\sin {\theta _{\rm{t}}} + \kappa $, 从而可以实现对光的反射、折射以及波前进行有效调控. 局域突变相位概念为操控光的传播提供了新的维度, 基于这个概念和广义反射和折射定律, 随后科学家们提出了一系列超薄器件[2-7], 实现了不对称传输[8]、平面超构透镜[9]、光子自旋霍尔效应[10]等. 由于渐变超构表面存在阻抗不匹配的问题, 使得转化效率受到限制, 近年来人们考虑用一种非超薄的渐变超构表面来操控光的传播[11-13]. 与超薄超构表面类似, 这种渐变超构表面在结构上具有周期性, 由于较厚, 类似于传统的光栅; 但是与传统光栅不同的是, 这种渐变超构表面界面上带有覆盖2π突变相位, 可以对各个衍射级次进行调制, 我们把这种较厚的渐变超构表面简称为超构光栅. 研究显示: 渐变超构光栅具有超构表面中的各种异常光学特性[7,11-14], 不仅转化效率较高, 而且还具有超薄超构表面中观察不到的新光学现象, 蕴含新的物理机制[15-17], 例如奇偶性相关的异常折射/反射现象[17].

      在光学异常散射现象中, 逆向反射是一个很有趣的现象, 即反射波沿着入射波的方向原路返回[18]. 最近, 科学家们提出了多种结构用以实现逆向反射器件[19-24]. 例如, 利用Luneburg透镜可以实现大角度范围的逆向反射[25], 但其结构设计比较复杂包含多层结构. 另外该器件是非平面器件, 这就要求入射波理论上需完全对准透镜中心, 这给实际应用带来一些挑战. 因而研究如何构建平面器件实现逆向反射器件显的更有意义. 最近, 崔铁军课题组提出利用两层超构光栅实现平面的逆向反射器件[26], 对于0—70.0°的入射角均能实现逆向反射的效果. 但是对于大的入射角度, 逆向反射效率较低(60.0°入射时, 回射效率不到50%), 并且两层超构光栅之间存在的耦合也增加了系统的复杂性. 另外, Steven A. Cummer课题组, 利用超构光栅设计了三通道的平面逆向反射器件[27], 在大角度(60.0°)入射时能实现接近100%的逆向回射效率. 但是该超构光栅只能工作在单一的入射角度, 而且其一个周期内包含6个不同的结构单元, 几何结构比较复杂. 一般而言, 越多的结构单元可能会导致更多的电磁损耗[28], 从而降低逆向反射的效率.

      基于超构光栅中的异常衍射规律[17], 本文设计和研究了一个结构简单且易于制备的中红外平面超构光栅器件, 为了减少系统的复杂性和单元个数导致的损耗, 一个周期只包含2个单元. 理论研究表明: 该超构光栅可以实现几乎100%转化效率的逆向反射, 且在大角度时仍有接近完美的反射效率. 此外, 其逆向反射的工作角度可以通过几何结构调节, 理论上可以覆盖从0到90°.

    2.   逆向反射超构光栅设计原理
    • 图1是设计的超构光栅的结构示意图及原理. 如图1(a)所示, 超构光栅中的灰色区域表示金属银, 蓝色和粉色区域表示具有周期性重复的两个结构单元, 并且这两个单元具有π的反射相位差. 图1(b)表示超构光栅一个周期的结构, 周期长度为p, 包含两个结构单元. 两个单元宽度均为w, 厚度均为d, 单元内填充不同的阻抗匹配材料, 材料折射率分别为${n_1}$${n_{\rm{2}}}$, ${n_1}$${n_{\rm{2}}}$满足${n_2} - {n_1} = \lambda /(4 d)$的关系. 由于x方向上超构光栅界面处满足切向动量守恒, 因此入射角和反射角需满足以下关系式[29]:

      Figure 1.  The structute of the metagrating: (a) The schematic of the retroreflection metagrating, wherein red and green arrows indicate retroreflection and blue arrows indicate specular reflection; (b) the diagram of metagrating with two sub-cells; (c) the iso-frequency contours of the incident wave and reflection wave for the metagrating.

      其中${k_0} = 2{\text{π}}/\lambda $是空气中的波矢, $\lambda $是工作波长, ${\theta _{\rm{i}}}$是入射角, ${\theta _r}$是反射角, $G = 2{\text{π}}/p$是倒格矢, n是衍射级次. 在该超构光栅中, 为简单起见, 只考虑$n = \pm {\rm{1}}$$n = 0$的情况, 即$\lambda \geqslant p$. 我们采用图1(c)的等频图来更直观地说明该超构光栅的入射和反射角度. 图中黑色实线圆圈和蓝色虚线圆圈分别表示空气中入射和反射的等频圆, 它们的圆心都在${k_y}$轴上并且半径都为${k_0}$. 当超构光栅界面上引入了周期性的突变相位之后, 蓝色虚线圆就往下(上)平移了倒格矢G的长度, 由红色(绿色)实线圆表示, 同时也是衍射级次为$n = - {\rm{1}}$($n = {\rm{1}}$)的反射等频圆. 当波从空气中照射到超构光栅上时, 黑色等频圆处的红色(绿色)箭头表示波的入射方向, 由于需满足切向动量守恒条件(图中两条平行的黑色虚线所示), 因此对应的反射方向由红色(绿色)等频圆处的箭头表示. 当入射角等于${\theta _{\rm{i}}} = - \arcsin [\lambda /(2 p)]$时, 反射波只能耦合到$n = - {\rm{1}}$级次(红色圆圈), 满足$\left| {{\theta _{\rm{i}}}} \right| = {\theta _{\rm{r}}}$, 发生逆向反射, 并且由于不能耦合到其它反射级次, 理论上此时的逆向反射具有完美的反射效率. 同理, 当入射角等于${\theta _{\rm{i}}} = \arcsin [\lambda /(2 p)]$时, 反射波只能耦合到$n = {\rm{1}}$级次(绿色圆圈), 满足${\theta _{\rm{i}}} = \left| {{\theta _{\rm{r}}}} \right|$, 发生逆向反射且具有完美的反射效率. 因此该超构光栅可以同时实现两个通道的高效率逆向反射功能, 由图中的红色和绿色箭头表示. 并且当$\lambda \geqslant p$时, 只需改变周期p的大小, 就可以得到任意想要的回射角度($\left| {{\theta _{\rm{i}}}} \right| \geqslant {\rm{3}}{{\rm{0}}^ \circ }$). 图中蓝色箭头代表电磁波正入射时发生的镜面反射, 由于当电磁波以回射角度入射时, 均不会耦合到镜面反射的级次($n = 0$, 蓝色虚线圆圈), 因此本文不考虑超构光栅的镜面反射. 由分析可知, 通过设计两个单元为周期的超构光栅, 理论上可以实现高效率、大角度、双通道的回射器件.

    3.   数值计算结果
    • 为了证明上述超构光栅的回射特性, 本文使用COMSOL MULTIPHYSICS软件进行相关的数值仿真模拟. 设入射的电磁波波长为λ = 3 μm, 单元厚度为d = 1.5 μm, 单元宽度为w = 0.9p/2. 设置左侧蓝色单元的材料折射率为${n_1} = 1$, 右侧粉色单元材料的折射率为${n_2} = {n_1} + \lambda /(4 d) = 1.5$, 即可满足两个单元的反射相位差π. 金属的介电常数为真实数据 [30]. 当设计的回射角为$\left| {{\theta _{\rm{i}}}} \right|= $ 30°时, 相应的超构光栅周期为p = 3 μm. 数值模拟得到该超构光栅不同级次的反射效率随入射角度变化的结果, 由图2(a)所示. 图中横轴为电磁波的入射角度, 纵轴为相应的反射效率, 蓝色曲线表示n = 0级次的反射效率(镜面反射), 红色和绿色曲线分别表示n = –1和n = 1级次的反射效率(异常反射). 图上还有两条细长的粉色和绿色区域, 分别代表该超构光栅实现双通道回射功能的入射角度: ${\theta _{\rm{i}}}= \pm 30^ \circ $. 由模拟的结果可知, 在设计的回射角度下, 超构光栅对应的回射效率可以达到接近100%. 同样, 通过解析计算也可以得到超构光栅不同级次的反射效率随入射角度变化的曲线, 与本文数值模拟的结果保持一致[15]. 为了更清楚地展示超构光栅的双通道回射路径和回射效率, 我们模拟高斯波入射到该超构光栅, 画出总的磁场图, 如图2(b)所示. 上面(下面)的场图表示高斯波以30°(–30°)的入射角度照射到超构光栅上的情况, 图中的斜向下的绿色箭头(红色箭头)表示入射波的路径, 斜向上的绿色箭头(红色箭头)表示反射波的路径. 由图可知, 当入射角为30°时, 反射波只能耦合到 n =1级次, 对应的反射角度为–30°, 入射的高斯波和反射的高斯波的路径完美的重合在一起, 并且基本没有其他角度的反射, 实现了效率接近100%的回射效果. 同样地, 当入射角为–30°时, 反射波只能耦合到n = –1级次, 对应的反射角度为30°, 此时对于入射的高斯波也具有完美的回射效果. 由模拟的场图可知, 该超构光栅的回射角度和效率均符合上述的理论分析, 其确实可以同时实现两个通道的高效率回射功能.

      Figure 2.  The reflection efficiency of different orders and the total magnetic field pattern, while the designed retroreflection angle is $ \pm {\rm{3}}{{\rm{0}}^ \circ }$: (a) The reflection efficiency of different orders vary with incident angle; (b) the total magnetic field pattern of the two-channel retroreflector.

      另外, 对于大的入射角度, 该超构光栅仍然能实现较高效率的回射. 例如设计回射角为$\left| {{\theta _{\rm{i}}}} \right|= 60^ \circ$, 则相应的周期长度变为p = 1.732 μm, 入射波长和超构光栅其余的尺寸参数保持不变. 与图2的分析类似, 模拟得到此时超构光栅的不同级次的反射效率, 以及高斯波入射到超构光栅的总磁场图, 验证其大角度回射的效果, 如图3所示. 图3(a)中红色(绿色)曲线表示n = –1 (n = 1)级次的反射率和入射角度的关系曲线, 蓝色曲线表示n = 0级次的反射效率和入射角度的关系曲线. 图上粉色和绿色的细长区域代表实现回射功能的角度: $ \pm {\rm{6}}{{\rm{0}}^ \circ }$. 同样地, 可以看到当入射角度为–60°(60°)时, 衍射级n = –1 (n = 1)级次占据主导, 其反射角度为60°(–60°), 反射效率可以达到95%; 同时存在微弱的n = 0级次的反射(镜面反射), 反射角度为–60°(60°), 反射效率只有5%. 通过模拟高斯波以回射角度$ \pm {\rm{6}}{{\rm{0}}^ \circ }$入射到超构光栅的总磁场图, 可以直观地展现大角度回射的效果, 如图3(b)所示. 图中绿色箭头表示入射角度为60°时入射波和反射波的方向; 红色箭头表示入射角度为–60°时入射波和反射波的方向. 场图清楚地表明了对于设计的大回射角度$ \pm {\rm{6}}{{\rm{0}}^ \circ }$, 入射波的路径和回射波的路径仍然很好的重叠在一起. 此时虽然存在一部分微弱的镜面反射波, 但是和回射波比起来, 可以忽略不计. 由此可证明当电磁波以较大的入射角入射时, 该超构光栅依然具有高效率逆向反射特性.

      Figure 3.  The reflection efficiency of different orders and the total magnetic field pattern, while the designed retroreflection angle is $ \pm 6{{\rm{0}}^ \circ }$: (a) The reflection efficiency of different orders vary with incident angle; (b) the total magnetic field pattern of the two-channel retroreflector.

      对于其他的入射角度, 只需通过改变超构光栅周期长度p, 即可实现不同角度的高效率回射, 如图4所示. 蓝色点线代表不同的回射角度, 红色点线代表相应的回射效率. 为了保证只有三个反射级次(n = –1, 0, 1)且能实现双通道回射功能, 选取周期p的范围为1.5 μm ≤ p ≤ 3 μm. 在此范围内选取六个不同周期p分别为1.55 μm, 1.8 μm, 2.05 μm, 2.3 μm, 2.55 μm和2.8 μm, 对应的回射角度分别为75.4°, 56.4°, 47.0°, 40.7°, 36.0°和32.4°, 回射效率分别为80%, 96%, 98%, 97%, 97%和98%. 由此证明当改变周期p时, 可以得到任意想要的回射角度($\left| {{\theta _{\rm{i}}}} \right| \geqslant {\rm{3}}{{\rm{0}}^ \circ }$). 并且这些回射角度都具有较高的回射效率, 对于75.4°这样的大角度, 仍然具有80%的高效率回射. 毋庸置疑, 本文提出的简化设计的电磁超构光栅实现了高效率、大角度、双通道回射功能.

      Figure 4.  The incident angle of retroreflection and retroreflectivity corresponding to different period lengths $p$. With the change of $p$, the duty cycle and filling medium of the metal slot remain unchanged.

    4.   结论和展望
    • 综上所述, 对比周期内包含多个单元的超构光栅, 本文设计的超构光栅不仅具有同样的回射效果, 而且有较少的单元个数, 几何结构简单、易制备, 更重要的是, 由于越多的单元个数会导致越多的电磁损耗, 简化结构设计能够减少超构光栅的电磁损耗从而提高效率. 需要强调的是, 本文设计的超构光栅以两个单元为周期且满足两个单元具有π的反射相位差, 使反射波具有理想的波前相位分布. 在本文研究中, 为了便于讨论我们假设金属槽中填充的材料是阻抗匹配; 对于阻抗不匹配的情况, 通过几何结构参数优化, 我们可以得到与本文类似的逆向反射结果且效率较高. 进一步理论研究揭示: 通过超构光栅的不同级次的反射曲线和高斯波入射的总场图, 表明当周期长度小于工作波长($p \leqslant \lambda $)时, 超构光栅可以实现高效率的双通道回射功能. 另外, 改变超构光栅的周期长度p可以得到任意想要的回射角度($\left| {{\theta _{\rm{i}}}} \right| \geqslant {\rm{3}}{{\rm{0}}^ \circ }$). 选取多个不同的周期p, 研究了相应的回射角度和回射效率, 证明了该超构光栅大角度回射的高效性, 可以在高效率的传感探测、成像和通信等领域发挥重要的作用. 提出的超构光栅概念也可以为简化平面光学器件提供新的思路, 使其在光学器件的集成化和小型化方面实现更多的应用.

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