一种设计环形汇聚光栅反射镜的新方法

马长链; 黄永清; 段晓峰; 任晓敏; 王琦; 王俊; 张霞; 蔡世伟

doi:10.7498/aps.63.240702

摘要

提出了一种利用数学变换来快速设计环形汇聚光栅反射镜的方法. 通过分析具体的物理场景, 抽象出已有条形汇聚光栅的“线”汇聚特性与所要设计的“点”汇聚特性在数学上对应的变换关系, 然后用该数学变换对条形汇聚光栅进行外形上的变换, 外形变换后的条形光栅即为可以实现“点”汇聚的环形光栅. 用有限元算法对设计的环形汇聚光栅进行仿真, 仿真证明采用该方法设计的环形光栅可以很好地实现高反、高汇聚. 采用这一方法, 设计了直径为29.788μm的环形光栅反射镜, 当垂直入射的径向偏振光从设计的环形光栅表面反射回来后将发生汇聚, 汇聚焦点位于环形光栅表面10μm处. 经计算, 反射镜的数值孔径为0.8302, 反射率为0.9163, 在焦点所在的汇聚面上, 汇聚光栅电场分布的半高宽为1.5548μm.

关键词:

Abstract

A new approach to designing planar, high numerical aperture, low loss, focusing reflectors using circular subwavelength high contrast gratings is presented. Through analyzing particular physical scene, a mathematical transformation from existing “focus line” convergent beam, which can be achieved by bar grating reflector, to the convergent beam with a “focus point”, is obtained. By changing the shape of the bar grating reflector with the mathematical transformation obtained, a circular grating reflector, which can achieve “focus point” convergent beam, is obtained. The focusing properties and reflection characteristic of the circular grating reflector are numerically studied with the finite element method. After the radially polarized light reflected from circular grating reflector with a diameter of 29.788 μm, the beam will focus at 10 μm away from the reflector, resulting in a numerical aperture of 0.8302 and a reflectivity of 0.9163. In the focal plane, the numerical simulation results present a field distribution with a full width half maximum value of 1.5548μm, which is extremely close to diffraction limit.

Keywords:

作者及机构信息

1.
北京邮电大学, 信息光子学与光通信国家重点实验室, 北京 100876

基金项目: 国家自然科学基金(批准号: 61274044, 61077049)、国家重点基础研究发展计划(批准号: 2010CB327600)、高等学校博士学科点专项科研基金(批准号: 20130005130001)、北京市自然科学基金(批准号: 4132069)、高等学校学科创新引智计划(批准号: B07005)、教育部新世纪优秀人才支持计划(批准号: NCET-13-0686)和国际科技合作项目(批准号: 2011DFR11010)资助的课题.

Authors and contacts

1.
State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61274044, 61077049), the National Basic Research Program of China (Grant No. 2010CB327600), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20130005130001), the Natural Science Foundation of Beijing, China (Grant No. 4132069), the 111 Project, China (Grant No. B07005), the Program for New Century Excellent Talents in University of Ministry of Education of China (Grant No. NCET-13-0686), and the International Science Cooperation Program, China (Grant No. 2011DFR11010).

参考文献

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施引文献

[1]	Karagodsky V, Sedgwick F G, Chang-Hasnain C J 2010 Opt. Express 18 16973
[2]	Chase C, Rao Y, Hofmann W, Chang-Hasnain C J 2010 Opt. Express 18 15461
[3]	Karagodsky V, Chang-Hasnain C J 2012 Opt. Express 20 10888
[4]	Li S, Guan B L, Shi G Z, Guo X 2012 Acta Phys. Sin. 61 184208 (in Chinese) [李硕, 关宝璐, 史国柱, 郭霞 2012 61 184208]
[5]	Luo Q, Huang L H, Gu N T, Rao C H 2012 Chin. Phys. B 21 094201
[6]	Wang Z L, Gao K, Chen J, Ge X, Zhu P P, Tian Y C, Wu Z Y 2012 Chin. Phys. B 21 118703
[7]	Zhao H J, Peng Y J, Tan J, Liao C R, Li P, Ren X X 2009 Chin. Phys. B 18 5326
[8]	Zheng G G, Wu Y G, Xu L H 2013 Chin. Phys. B 22 104212
[9]	Rastani K, Marrakchi A, Habiby S F, Hubbard W M, Gilchrist H, Nahory R E 1991 Appl. Opt. 30 1347
[10]	Fujita T, Nishihara H, Koyama J 1982 Opt. Lett. 7 578
[11]	Shiono T, Kitagawa M, Setsune K, Mitsuyu T 1989 Appl. Opt. 28 3434
[12]	Chang-Hasnain C J, Yang W J 2012 Adv. Opt. Photon. 4 379
[13]	Lu F, Sedgwick F G, Karagodsky V, Chase C, Chang-Hasnain C J 2010 Opt. Express 18 12606
[14]	Zhou Y, Huang M C Y, Chang-Hasnain C J 2008 IEEE Photon. Technol. Lett. 20 434
[15]	Fattal D, Peng Z, Tran T, Vo S, Fiorentino M, Brug J, Beausoleil R G 2013 Nature 495 348
[16]	Katsidis C C, Siapkas D I 2002 Appl. Opt. 41 3978
[17]	Zhan Q W, Leger J R 2002 Opt. Express 10 324
[18]	Carletti L, Malureanu R, Mrk J, Chung I S 2011 Opt. Express 19 23567
[19]	Fattal D, Li J J, Peng Z 2010 Nat. Photon. 4 466
[20]	Moharam M G, Gaylord T K 1981 J. Opt. Soc. Am. 71 811
[21]	Wen Z X 2010 Analytic Geometry and Linear Algebra (Beijing: Science Press) pp22-55 (in Chinese) [文志雄 2010 解析几何与线性代数 (北京: 科学出版社) 第22–55页]
[22]	Vanbrabant P J M, Beeckman J, Neyts K, James R, Fernandez F A 2009 Opt. Express 17 10895

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