Exact transformation optics by using electrostatics  

静电场精确设计变换光学

作　　者：Pengfei Zhao Guoxiong Cai Huanyang Chen 赵鹏飞;蔡国雄;陈焕阳(Institute of Electromagnetics and Acoustics and Department of Physics,College of Physical Science and Technology,Xiamen University,Xiamen 361005,China)

机构地区：[1]Institute of Electromagnetics and Acoustics and Department of Physics,College of Physical Science and Technology,Xiamen University,Xiamen 361005,China

出　　处：《Science Bulletin》2022年第3期246-255,共10页科学通报（英文版）

基　　金：the National Natural Science Foundation of China(92050102);the National Key Research and Development Program of China(2020YFA0710100);the National Natural Science Foundation of China(11874311);the FundamentalResearch Funds for the Central Universities(20720200074 and20720190049)。

摘　　要：We present a novel method for designing transformation optical devices based on electrostatics.An arbi-trary transformation of electrostatic field can lead to a new refractive index distribution,where wave-fronts and energy flux lines correspond to equipotential surfaces and electrostatic flux lines,respectively.Owing to scalar wave propagating exactly following an eikonal equation,wave optics and geometric optics share the same solutions in the devices.The method is utilized to design multipole lenses derived from multipoles in electrostatics.The source and drain in optics are considered as corre-sponding to positive charge and negative charge in the static field.By defining winding numbers in vir-tual and physical spaces,we explain the reason for some multipole lenses with illusion effects.Besides,we introduce an equipotential absorber to replace the drain to correspond to a negative charge with a grounded conductor.Therefore,it is a very general platform to design intriguing devices based on the combination of electrostatics and transformation optics.本文提出了一种通过静电学中电荷分布场来求解电动力学中含源介质传播场的新方法,定义了变换光学中的一种拓扑不变量——环绕数,并且发现一种新的幻象效应.变换前后不同分布的光源保持环绕数不变。电磁场在远场永远保持相似性,从而实现对光源幻象的准确调控,实现光学“高斯定理”.文中主要列举了多个多光源幻象透镜,通过精确计算发现,电磁场的等相位面与静电场等势面保持一致,且坡印廷矢量与电场线保持一致,此时得到的传播电磁场可根据静电场来分析其特性,光源可被视为相对等量的静电荷.由此实现的多光源不干涉幻象,远场看起来就像是一个大光源形成的电磁场.该工作为利用简单静电场设计光学器件提供了新思路,在变换光学中提出了以更本质的拓扑不变量来研究光学现象,在天线设计、大功率照明系统构造和军事伪装制造等方面具备潜在的应用价值.

关 键 词：Transformation optics ELECTROSTATICS Multipole lenses Winding number 

分 类 号：O441.1[理学—电磁学] O43[理学—物理]