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

[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

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

[1]	关建飞, 俞潇, 丁冠天, 陈陶, 陆云清. 金属光栅覆盖分布式布拉格反射镜结构的透射增强效应. , 2024, 73(11): 117301. doi: 10.7498/aps.73.20240357
[2]	杨哲宁, 乐阳阳, 洪煦昊, 赵瑞智, 陆蓉儿, 冯霞, 许亚光, 袁旭东, 张超, 秦亦强, 朱永元. 利用保角变换实现环形光栅的Talbot效应. , 2020, 69(3): 034201. doi: 10.7498/aps.69.20191340
[3]	祁云平, 张雪伟, 周培阳, 胡兵兵, 王向贤. 基于十字连通形环形谐振腔金属-介质-金属波导的折射率传感器和滤波器. , 2018, 67(19): 197301. doi: 10.7498/aps.67.20180758
[4]	邬融, 田玉婷, 赵东峰, 李大为, 华能, 邵平. 透射衍射光栅内全反射级次. , 2016, 65(5): 054202. doi: 10.7498/aps.65.054202
[5]	李宝, 杜炳政, 朱京平. Bragg反射齿型平面凹面衍射光栅性能研究. , 2015, 64(15): 154211. doi: 10.7498/aps.64.154211
[6]	魏政鸿, 云峰, 丁文, 黄亚平, 王宏, 李强, 张烨, 郭茂峰, 刘硕, 吴红斌. 低接触电阻率Ni/Ag/Ti/Au反射镜电极的研究. , 2015, 64(12): 127304. doi: 10.7498/aps.64.127304
[7]	刘华松, 刘丹丹, 姜承慧, 王利栓, 姜玉刚, 孙鹏, 季一勤. 周期结构薄膜在折射率色散下反射区特性研究. , 2014, 63(1): 017801. doi: 10.7498/aps.63.017801
[8]	熊水东, 徐攀, 马明祥, 胡正良, 胡永明. 掺铒光纤环形激光器中饱和吸收光栅瞬态特性引发跳模的实验研究. , 2014, 63(13): 134206. doi: 10.7498/aps.63.134206
[9]	刘颖刚, 车伏龙, 贾振安, 傅海威, 王宏亮, 邵敏. 微纳光纤布拉格光栅折射率传感特性研究. , 2013, 62(10): 104218. doi: 10.7498/aps.62.104218
[10]	翁永超, 况龙钰, 高南, 曹磊峰, 朱效立, 王晓华, 谢常青. 反射式单级衍射光栅. , 2012, 61(15): 154203. doi: 10.7498/aps.61.154203
[11]	周仁来, 鞠有伦, 杨超, 王巍, 王月珠. 一种对双包层大芯径光纤光栅反射率和纤芯折射率调制估算的方法. , 2012, 61(24): 244205. doi: 10.7498/aps.61.244205
[12]	王静, 张晨芳, 康泽新, 孙将, 郑斯文, 林桢, 王春灿, 简水生. 多偏振控制高双折射光纤环形镜输出特性的理论和实验研究. , 2011, 60(12): 124215. doi: 10.7498/aps.60.124215
[13]	傅正平, 林峰, 朱星. 一维金属光栅的光学反射吸收. , 2011, 60(11): 114213. doi: 10.7498/aps.60.114213
[14]	梁瑞冰, 孙琪真, 沃江海, 刘德明. 微纳尺度光纤布拉格光栅折射率传感的理论研究. , 2011, 60(10): 104221. doi: 10.7498/aps.60.104221
[15]	王振德, 刘念华. 正负折射率材料组成的半无限一维光子晶体的反射率. , 2009, 58(1): 559-564. doi: 10.7498/aps.58.559
[16]	徐敏, 张月蘅, 沈文忠. 半导体远红外反射镜中反射率和相位研究. , 2007, 56(4): 2415-2421. doi: 10.7498/aps.56.2415
[17]	薛力芳, 赵启大, 刘建国, 郭团, 黄桂岭, 刘丽辉. 基于圆环形薄壁截面梁的光纤光栅传感研究. , 2006, 55(6): 2804-2808. doi: 10.7498/aps.55.2804
[18]	郑晴, 赵晓鹏, 付全红, 赵乾, 康雷, 李明明. 左手材料的反射特性与负折射率行为. , 2005, 54(12): 5683-5687. doi: 10.7498/aps.54.5683
[19]	徐新华, 崔一平. 矩形折射率调制型长周期光纤光栅传输谱的理论分析及数值计算. , 2003, 52(1): 96-101. doi: 10.7498/aps.52.96
[20]	傅克祥, 张大跃, 王植恒, 张奇志, 张靖. 位相光栅的严格模式理论及其全反射特性. , 1998, 47(8): 1278-1288. doi: 10.7498/aps.47.1278

计量

文章访问数: 5827
PDF下载量: 498
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板