Arbitrarily shaped retro-reflector by optics surface transformation

The geometric shapes of the retro-reflectors are (a) an isosceles triangle, (b) a flat triangle, (c), (d) irregular surfaces, and (e) an array of isosceles triangles.

A retro-reflector can create reflected wave that is always parallel to, but in the opposite direction of, the incoming wave. Previous retro-reflector can be classified into two types: one is bulk device, including corner-cube reflector, cat's eyes reflector and Eaton lens, which cannot be integrated with planar modulators; the other is thin meta-surface retro-reflector, whose efficiency drops quickly as the viewing angle changes. To achieve planar thin retro-reflector with high efficiency and wide working angles, optical surface transformation (OST) can be used to design arbitrarily shaped retro-reflector.

Optical surface transformation is a new branch of transformation optics, of which advantages can be summarized as: 1) it provides a much simpler way to make designs (i.e., geometrical projection method without complex mathematical calculations); 2) all devices with various functions, geometrics and sizes designed by OST only need one kind of materials (i.e., optic-null medium with different shapes and main axes to realize); 3) it can be easily extended to other physical fields or even multi-physics controlling simultaneously.

Recently, research groups led by Prof. Fei Sun and Prof. Yichao Liu from Taiyuan University of Technology, and Sailing He from Zhejiang University introduced a new type of retro-reflector in Chinese Optics Letters Volume 18, No. 10, 2020 (Fei Sun, Yichao Liu, Yibiao Yang et al., Arbitrarily shaped retro-reflector by optics surface transformation). Based on OST, retro-reflector is designed by a surface-projecting manner in this study. The designed retro-reflector may have applications in planar integrated systems, compact sensors, navigation, and communication systems.

Based on OST, the retro-reflector can be designed as a thin planar slab with thickness 2λ₀/3, whose efficiency is above 98% with incident angles from -50 degrees to +50 degrees, and is still above 50% even as the incident angle increases to 80 degree. All retro-reflectors designed by OST only require one kind of homogeneous anisotropic media (optic-null medium) to realize (the orientation of the homogeneous ONMs' main axes may be different).

In this work, the authors use an ultra-thin metamaterial to realize the retro-reflection effect. This is a big improvement compared with the traditional space-consuming retro-reflectors. What's more, the required materials are quite simple, i.e., near-zero-index metamaterials and metal plates, which meet the requirements of mass production. One unique feature of the designed retro-reflector is the shaped can be tuned at will, and this flexibility provides more choices in some special applications. In conclusion, this work provides more flexible shapes of the retro-reflector, and at the same time keep an excellent retro-reflection efficiency.

There are two limitations of our work for real application, one is the introduction of near-zero-index materials and the other is the restriction to only one polarization. Therefore, our follow-up work is the replacing of the near-zero-index materials by normal dielectrics. Also, the retro-reflector should also be extended to work for both TE waves and TM waves. The direction of incident beam should also be extended for the whole upper half plane. After solving the above problem, we plan to extend the retro-reflector to work for multi-physics, e.g., one device works for both electromagnetic and acoustic waves.

超薄超构材料实现任意形状、大入射范围角反射器

多种形状的角反射器件仿真图 (a)等腰直角三角形、(b)压扁的三角形，(c)任意的一个反对称形状、(d)源从左侧入射到(c)中反对称形状、(e)三角阵列，(f)亚波长平板

导语： 始于50年前的“阿波罗登月”工程在月面上相继安放了三台激光反射镜，这三台“魔镜”一直以厘米级别的精度，帮助人类精准地测量地月距离。除了科学前沿的应用，角反射器逐渐以小巧灵动的“反射单元”形式，存在于我们身边如路标、车牌这样的小型器件中。

角反射器可以使一束光线原路返回。过去的角反射器可以分为两类：一类因体积较大，无法做成集成元件，比如锥体棱镜、猫眼反射器和Eaton透镜;另外一类为基于超表面的薄平面角反射器，但反射效率随视角变化降低。为了得到高效率、宽工作角度的薄平板型角反射器，可使用光学表面变换的方法设计任意形状的角反射器。

光学表面变换是由变换光学理论扩展得到的，其优点包括：1）设计过程简单，仅需通过几何表面投影的方式即可设计，无需复杂的数学计算；2）所有基于光学表面变换设计得到的器件，无论功能、形状和尺寸如何改变，都只需要一种光学零空间介质材料即可实现（零空间介质的形状和主轴选取不同方向）；3）设计方法很容易扩展到其他物理场甚至是多物理场同时调控。

太原理工大学孙非和刘一超副研究员以及浙江大学何赛灵教授领导的研究团队借助光学表面变换理论的特性， 通过表面投影的方法合作设计研发了一款新型角反射器,该工作发表在Chinese Optics Letters 2020年第18卷第10期（Fei Sun, Yichao Liu, Yibiao Yang et al., Arbitrarily shaped retro-reflector by optics surface transformation）。该反射器使用超薄超构材料实现了返射效果，克服了传统器件体积庞大的缺点，可以广泛应用于平板集成系统、紧凑型传感器、导航和通信系统。

基于光学表面变换理论，角反射器可以被设计为超薄的平板结构（厚度为波长的2/3），在入射角范围从-50°到+50°时效率高达98%。即使入射角达到80°，设计得到的角反射器效率仍然大于50%。所有基于光学表面变换设计得到的角反射器都只需要一种均匀的各向同性材料（光学零空间介质）即可实现。

在这项工作中，研究人员使用超薄超构材料实现了返射效果，相较于传统体积庞大的角反射器是一个很大的进步，在材料的应用上亦实现了简单化：具有近零折射率的超构材料和金属板即可满足批量生产要求。文中设计的角反射器还有一个独特功能就是可以随意调整形状，这种灵活性为某些特殊应用场合提供了更多选择。总之，这项工作为角反射器提供了更加灵活的形状，同时保持了出色的回反射效率。

该工作在实际应用中尚有一定的局限性，一方面是需要引入接近零折射率的材料，另一方面是单极化。因此，其后续工作是用普通电介质代替近零折射率的材料，同时扩展角反射器到既适用于TE波又适用于TM波，入射光束的方向也应拓展到整个上半平面。解决了上述问题后，进一步的计划是将该角反射器扩展到多物理场应用，比如只使用一种设备便可同时对电磁波和声波起到回反射作用。