基于轴棱锥产生近似无衍射Mathieu光束的新方法

李冬; 吴逢铁; 谢晓霞

doi:10.7498/aps.63.152401

摘要

提出了一种基于轴棱锥产生零阶近似无衍射Mathieu光束的新方法，利用轴棱锥聚焦具有椭圆高斯振幅调制的平面波，得到近似零阶无衍射Mathieu 光束. 根据椭圆高斯平面波经轴棱锥衍射的衍射积分公式，对光强分布进行了数值模拟，依据几何光学模型计算了近似无衍射Mathieu光束的最大无衍射距离，并设计了实验对理论模拟的结果进行了验证. 实验采用柱透镜和准直扩束系统变换圆高斯光束产生具有椭圆高斯振幅调制的平面波，用轴棱锥聚焦该平面波后得到近似无衍射Mathieu光束，实验结果与理论模拟和计算相符.

关键词:

Abstract

A novel method of generating zero order non-diffracting Mathieu beam with an axicon is proposed. To create quasi non-diffracting Mahtieu beam, an axicon is used to focus a plane wave modulated by elliptical Gaussian amplitude. Based on the formula of diffraction integral of a plane wave modulated by elliptical Gaussian amplitude propagating through the axicon, the intensity of quasi non-diffracting beam is simulated numerically. The maximum propagation distance of the quasi-non-diffracting Mathieu beam is calculated according to a geometrical optical model. To verify the results of the theory, an experimental setup is designed.Using a cylindrical lens and a collimating and expanding system, a circular Gaussian beam can be converted in to a plane wave modulated by elliptical Gaussian amplitude. Focusing the plane wave using an axicon, a qausi-non-diffracting Mathieu beam can be generated. The exoerimental results are consistent with theoretical calcuations and numerical simulations.

Keywords:

non-diffracting Mathieu beam /
plane wave modulated by elliptical Gaussian amplitude /
axicon /
cylindrical lens

作者及机构信息

1.
华侨大学信息科学与工程学院, 福建省光传输与变换重点实验室, 厦门 361021

基金项目: 国家自然科学基金资助（批准号：61178015）和福建省自然科学基金（批准号：2012J01278）资助的课题.

Authors and contacts

1.
College of Information Science and Engineering, Huaqiao University, Fujian Key Laboratory of Optical Beam Transmission and Transformation, Xiamen 361021, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 611780515), and the Natural Science Foundation of Fujian Province, China(Grant No. 2012J01278).

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施引文献

[1]	Durnin J, Miceli J J, Eberly J 1987 Phys. Rev. Lett. 58 1499
[2]
[3]
[4]	Fan D D, Wu F T, Cheng Z M, Zhu J Q 2013 Acta Phys. Sin. 62 104219 (in Chinese) [范丹丹, 吴逢铁, 程治明, 朱健强 2013 物理学报 62 104219br>
[5]
[6]	Zhang Q A, Wu F T, Zheng W T, Pu J X 2011 Scientia Sininca Physica, Mechanica & Astronomica 41 1131 (in Chinese) [张前安, 吴逢铁, 郑维涛, 蒲继雄 2011 中国科学: 41 1131]
[7]	Zhao J, Zhang P, Deng D, Lou C, Song D, Liu J, Chen Z 2013 Chin. Opt. Let. 11 110701
[8]
[9]	Gutiérrez-Vega J C, Bandres M A 2005 J. Opt. Soc. Am. A 22 289
[10]
[11]
[12]	Wen W 2007 Ph. D. Dissertation (Changsha: Centeal South University) (in Chinese) [文伟 2007 博士学位论文(长沙: 中南大学)]
[13]	Gutierrez-Vega J C, Iturbe-Castillo M D, Chavez-Cerda S 2000 Opt. Lett. 25 1493
[14]
[15]
[16]	Fleischer J W, Segev M, Efremidis N K, Christodoulides D N 2003 Nature 422 147
[17]	Ye F, Mihalache D, Hu B 2009 Phys. Rev. A 79 053852
[18]
[19]	Jin X, Shui M, Wang Y X, Li C W, Yang J Y, Zhang X R, Yang K, Song Y L 2010 Chin. Phys. B 19 074203
[20]
[21]	Dholakia K, Čižmár T 2011 Nat. Photonics 5 335
[22]
[23]	Zheng J, Yao B, Yang Y, Lei M, Gao P, Li R, Ye T 2013 Chin. Opt. Lett. 11 112601
[24]
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[34]
[35]	Belafhal A, Hricha Z 2004 Phys. Chem. News 16 33
[36]
[37]	Cheng Z M, Wu F T, Fan D D, Fang X 2012 Scientia Sininca Physica, Mechanica & Astronomica 42 805 (in Chinese) [程治明, 吴逢铁, 范丹丹, 方翔 2012 中国科学: 42 805]
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[53]	Chafiq A, Hricha Z, Belafhal A 2006 Opt. Commun. 265 594

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