利用保角变换实现环形光栅的Talbot效应  

Realizing Talbot effect of circular grating with conformal transformation

作　　者：杨哲宁 乐阳阳[1] 洪煦昊 赵瑞智 陆蓉儿 冯霞 许亚光 袁旭东 张超[1] 秦亦强[1] 朱永元[2] Yang Zhe-Ning;Yue Yang-Yang;Hong Xu-Hao;Zhao Rui-Zhi;Lu Rong-Er;Feng Xia;Xu Ya-Guang;Yuan Xu-Dong;Zhang Chao;Qin Yi-Qiang;Zhu Yong-Yuan(College of Engineering and Applied Sciences,Nanjing University,Nanjing 210023,China;School of Physics,Nanjing University,Nanjing 210023,China)

机构地区：[1]南京大学现代工程与应用科学学院,南京210023 [2]南京大学物理学院,南京210023

出　　处：《物理学报》2020年第3期108-112,共5页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11874214,11774165,11574146);江苏省自然科学基金(批准号:BK20150563)资助的课题~~

摘　　要：Talbot效应是一种近场自成像效应,通常只有周期光栅可以产生Talbot效应,而环形光栅无法产生.本文通过引入保角变换,发现可以在环形光栅外部设计适当的折射率渐变层介质,使得其中也能够产生严格的Talbot效应,并计算了对应的自成像半径表达式.本文利用FDTD软件分别将一个环形光栅放置在真空中以及人工设计的折射率渐变层中进行了模拟,并对二者的结果进行了比较分析,发现这种折射率渐变层介质确实对点光源入射的环形光栅的自成像情况有着很好的改善.希望这一工作能够推广Talbot效应的应用范围.The Talbot effect is a near-field diffraction effect that occurs in periodic structures.In a circular periodic structure with a point source as incident light,it has been found that there is no self-imaging effect of the grating at a certain propagation distance.In this paper,we combine the conformal transformation with the Talbot effect and work out a special medium in the physical space,which allows the circular grating to have a Talbot effect within it.The refractive index distribution generated by conformal transformation is calculated and the corresponding self-imaging radius expression is obtained.Lumerical product is used for simulation verification,and the applicable condition of the method is summarized.We separately carry out the simulations of a circular grating with and without the designed medium.Light field distributions in the two simulations differ from each other.The light field in the second situation shares more similarities with the light field of a plane grating than the first simulation.What is more,in the second situation,we can work out a certain Talbot radius,and the light field distribution at the calculated Talbot radius is quite similar to that at the circular grating.But for the first situation,we cannot calculate a certain Talbot radius and can obtain only the radius of the ring with highest self-imaging accuracy by comparing light field at each distance with the grating structure.We find that the small period of the circular grating we used in the second situation makes the light field at Talbot radius furcate.So we carry out a third simulation of a circular grating with a large period compared with the incident wavelength.The self-imaging result matches the grating structure quite well.However,there are some limits in this method.According to the conformal transformation,the refractive index near the center tends to be infinite,so we have to remove the medium near the center.Also,when the radius is big enough,refractive index there can be smaller than 1,so the Talbot effect should

关 键 词：TALBOT效应 自成像 环形光栅 保角变换 

分 类 号：O436[机械工程—光学工程]