光学共形变换在二维光学设计中的新应用

Since its introduction in 2006, transform optics has become a research topic in the fields of physics, optics, materials science and information science due to its powerful control capability on electromagnetic waves. As a branch of transformation optics, two-dimensional optical conformal mapping is mainly used to design some theoretical invisibility cloaks and imaging devices, but still faces difficulties in practical applications. The main reason is that the Zhukovski transformation has a high and large range of refractive index in the circular branch cut. In order to solve this problem, this project uses special devices or medium(resonant cavity, null-space medium, etc.) to replace the medium inside the branch cut to realize an omnidirectional cloak with simplified parameters. At the same time, we will study how to realize the near-zero refractive index material by optical conformal mapping. By utilizing the high refractive index background to "neutralize" the near-zero refractive index with a small value, it is possible to obtain a near-zero refractive index by using an ordinary graded index medium. We will further design near-zero refractive index directional emitters and zero-phase-advance waveguides. Finally, we will study the application of optical conformal transformation in super-resolution imaging to design a super-resolution magnifying glass that can break the diffraction limit.

变换光学自从2006年被提出以来，由于其强大的电磁操控能力，已成为物理学、光学、材料学和信息科学等领域的研究前沿和热点。其中对于二维光学共形变换的研究主要用来设计一些理论的隐身和成像方案，而在实际应用方面仍面临困难。最主要的原因是Zhukovski变换的支割线圆内折射率高且变化剧烈。本项目以解决这一难题为出发点，使用特殊器件（谐振腔、零空间介质等）替换掉支割线圆内的部分，实现参数简化的全方向隐身器件。同时研究如何通过光学共形变换来实现近零折射率材料，通过合理利用高折射率背景来“中和”数值很小的近零折射率，实现了用普通的渐变介质来获得近零折射率材料的性能，并进一步设计近零折射率定向辐射器和无相位延迟波导。最后我们将研究光学共形变换在超分辨成像方面的应用，设计一个不受衍射极限的超分辨放大镜。

通过二维光学共形变换的深入研究，设计了一系列新型电磁器件。(1)在隐身设计方面，通过在下层黎曼面中引入零空间介质解决了Zhukovski变换的支割线圆内折射率高且变化剧烈的问题，并且提出了消除几何色散的思路。在此基础上提出了进一步的优化策略，比如简化下层黎曼面的设计过程。(2)在实现近零折射率材料方面，通过变换消除参数的奇异性，等效获得具有“近零折射率特征”的材料，并用“近零折射率特征”材料实现了电磁波隧穿波导，理论推导了隧穿波导反射率随各个参数的变化公式，并提出微波段实验方案；实现了可以在空气区域增强电磁波能量的光学漏斗，分析了能量增强的均匀性、器件的带宽以及漏斗宽度对增强性能的影响，并提出微波段实验方案；实现了增强效率的高定向辐射器，分析了Q值和Purcell因子增强机理。(3)在超分辨成像方面，提出了一个无像差超分辨放大镜，并在微波段进行了验证。本项目的预期目标已经充分实现，且在近零折射率材料设计方面有了进一步的研究和突破。