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谐振腔内的高质量圆对称艾里光束的产生方法

朱一帆 耿滔

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谐振腔内的高质量圆对称艾里光束的产生方法

朱一帆, 耿滔

Generation of high-quality circular Airy beams in laser resonator

Zhu Yi-Fan, Geng Tao
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  • 本文提出一种在谐振腔内产生高质量圆对称艾里光束的方法, 通过使用针对特定参数光束设计的衍射光学元件替代反射腔镜, 可在腔内获得所需的特定参数光束. 研究结果表明, 该方法产生的圆对称艾里光束的参数可控; 模式能量损耗低, 接近高斯基模光束; 光束质量高, 明显优于目前常用的傅里叶空间纯相位全息编码法. 接着, 讨论了组装系统时产生的腔长误差和同轴度误差, 以及加工衍射元件时产生的刻蚀误差对产生光束的影响. 结果表明, 现有的机械调节技术和微纳加工技术, 完全能满足系统误差的精度要求, 显示该方法对误差有较好的容差性.
    A scheme for forming high-quality circular Airy beams inside the laser resonator is presented theoretically. The desired circular Airy beam can be generated when the common reflective mirror is replaced by a designed diffractive optical element. The mode generated in the proposed cavity can be stimulated by using the so-called eigenvector method. The calculated results show that the parameters of the beams can be controlled by changing the phase distribution of the diffractive optical element. The loss of the generated mode is very low, which is close to that of the fundamental Gaussian mode. The purity of the generated mode is very high, which is much better than that from the phase-only encoding method in Fourier space. The phase distribution of the diffractive optical element needs designing for a fixed resonator length. In practice, the real resonator length may not be equal to the designed resonator length. Thus, the influence of the alignment error of the resonator length is discussed in detail. The results show that the diffraction loss of the proposed system is still very small even when the error reaches up to 2 mm. Meanwhile, the purity of the generated mode decreases little. Then, the influence of etching depth errors and the decenter of the reflective mirrors are discussed in detail. Here we assume that the fluctuations are randomly distributed. The value of the maximum fluctuation is used to represent the etching depth error degree. The results show that the diffraction loss of the proposed system is more sensitive to production error, and the purity of the generated mode is more sensitive to alignment error. Thus, we estimate that the maximum etching depth error should be less than six percent of the wavelength, and the vertical distance between the centers of the two reflective mirrors should be less than 7 μm if one wants to obtain high-quality CAB with high efficiency. The requirements for precision are acceptable for existing microfabrication and operation technologies.
      通信作者: 耿滔, Tao_Geng@hotmail.com
    • 基金项目: 国家重点基础研究发展计划(973计划) (批准号: 2015CB352001)、国家重大科学仪器设备开发专项(批准号: 2017YFB0503100)和上海市自然科学基金(批准号: 16ZR144600)资助的课题
      Corresponding author: Geng Tao, Tao_Geng@hotmail.com
    • Funds: Project supported by the National Basic Research Program of China (Grant No. 2015CB352001), the Special Funds of the Major Scientific Instruments Equipment Development of China (Grant No. 2012YQ17000408), and the Natural Science Foundation of Shanghai, China (Grant No. 16ZR144600)
    [1]

    Siviloglou G A, Broky J, Dogariu A, Christodoulides D N 2007 Phys. Rev. Lett. 99 213901Google Scholar

    [2]

    Minovich A E, Klein A E, Neshev D N, Pertsch T, Kivshar Y S, Christodoulides D N 2014 Laser. Photon. Rev. 8 221Google Scholar

    [3]

    Qian J, Liu B Y, Sun H X, Yuan S Q, Yu X Z 2017 Chin. Phys. B 26 114304Google Scholar

    [4]

    崔省伟, 陈子阳, 胡克磊, 蒲继雄 2013 物理学报 62 094205Google Scholar

    Cui S W, Chen Z Y, Hu K L, Pu J X 2013 Acta Phys. Sin. 62 094205Google Scholar

    [5]

    张泽, 刘京郊, 张鹏, 倪培根, Prakash J, 胡洋, 姜东升, Christodoulides D N, 陈志刚 2013 物理学报 62 034209Google Scholar

    Zhang Z, Liu J J, Zhang P, Ni P G, Prakash J, Hu Y, Jiang D S, Christodoulides D N, Chen Z G 2013 Acta Phys. Sin. 62 034209Google Scholar

    [6]

    Guo Y H, Huang Y J, Li X, Pu M B, Gao P, Jin J J, Ma X L, Luo X G 2019 Adv. Opt. Mater. 7 1900503Google Scholar

    [7]

    Li Z, Cheng H, Liu Z, Chen S, Tian J 2016 Adv. Opt. Mater. 4 1230Google Scholar

    [8]

    Fan Q, Zhu W, Liang Y, Huo P, Zhang C, Agrawal A, Huang K, Luo X, Lu Y, Qiu C, Lezec H J, Xu T 2019 Nano Lett. 19 1158Google Scholar

    [9]

    Efremidis N K, Christodoulides D N 2010 Opt. Lett. 35 4045Google Scholar

    [10]

    Papazoglou D G, Efremidis N K, Christodoulides D N, Tzortzakis S 2011 Opt. Lett. 36 1842Google Scholar

    [11]

    Liu K, Koulouklidis A D, Papazoglou D G, Tzortzakis S, Zhang X C 2016 Optica 3 605Google Scholar

    [12]

    Manousidaki M, Papazoglou D G, Farsari M, Tzortzakis S 2016 Optica 3 525Google Scholar

    [13]

    Manousidaki M, Fedorov V Y, Papazoglou D G, Farsari M, Tzortzakis S 2018 Opt. Lett. 4 3

    [14]

    Zhang P, Prakash J, Zhang Z, Mills M S, Efremidis N K, Christodoulides D N, Chen Z 2011 Opt. Lett. 36 2883Google Scholar

    [15]

    Davis J A, Cottrell D M, Zinn J M 2013 Appl. Opt. 52 1888Google Scholar

    [16]

    Davis J A, Cottrell D M, Sand D 2012 Opt. Express 20 13302Google Scholar

    [17]

    刘正楠, 耿滔, 邓攀 2019 中国激光 46 0209001

    Liu Z N, Geng T, Deng P 2019 Chin. J. Lasers 46 0209001

    [18]

    Fox A G, Li T 1961 Bell System Techical Journal 40 453Google Scholar

    [19]

    Chao J, Li B, Cheng Y, Wang Y 2007 Opt. Laser Technol. 39 490Google Scholar

    [20]

    Cheng Y Y, Wang Y Q, Hu J, Li J R 2004 Opt. Commun. 234 1Google Scholar

    [21]

    Bélanger P A, Paré C 1991 Opt. Lett. 16 1057Google Scholar

    [22]

    Leger J R, Chen D, Wang Z 1994 Opt. Lett. 19 108Google Scholar

    [23]

    Jiang Y, Zhu X, Yu W, Shao H, Zheng W, Lu X 2015 Opt. Express 23 29834Google Scholar

    [24]

    Li N, Jiang Y, Huang K, Lu X 2014 Opt. Express 22 22847Google Scholar

    [25]

    Zhou W, Bovik A C, Sheikh H R, Simoncelli E P 2004 IEEE Trans. Image Process 13 600Google Scholar

  • 图 1  (a) CAB初始面的光强分布; (b) CAB初始面的相位分布; (c) CAB的侧面光强分布

    Fig. 1.  (a) Intensity distributions of the CAB at the initial plane; (b) phase distributions of the CAB at the initial plane; (c) intensity distributions of the CAB during propagation in the r-z plane.

    图 2  谐振腔示意图

    Fig. 2.  Schematic of the laser resonator configuration for CAB generation.

    图 3  不同参数条件下, 使用Fox-Li方法计算获得的腔内光场模式分布 (a) r0 = 1 mm, w = 0.2 mm和a = 0.15; (b) r0 = 1.1 mm, w = 0.22 mm和a = 0.17; (c) r0 = 1.2 mm, w = 0.25 mm和a = 0.2

    Fig. 3.  Calculation results of the intensity distributions of the modes by using Fox-Li method with different parameters: (a) r0 = 1 mm, w = 0.2 mm and a = 0.15; (b) r0 = 1.1 mm, w = 0.22 mm and a = 0.17; (c) r0 = 1.2 mm, w = 0.25 mm and a = 0.2.

    图 4  理想CAB和使用不同方法产生的光束的径向光强分布 (a) r0 = 1 mm, w = 0.2 mm和a = 0.15; (b) r0 = 1.1 mm, w = 0.22 mm和a = 0.17; (c) r0 = 1.2 mm, w = 0.25 mm和a = 0.2

    Fig. 4.  Radial intensity distributions of the ideal CAB and the beams produced by different methods: (a) r0 = 1 mm, w = 0.2 mm and a = 0.15; (b) r0 = 1.1 mm, w = 0.22 mm and a = 0.17; (c) r0 = 1.2 mm, w = 0.25 mm and a = 0.2.

    图 5  理想CAB和使用不同方法产生的光束的光轴光强分布 (a) r0 = 1 mm, w = 0.2 mm和a = 0.15; (b) r0 = 1.1 mm, w = 0.22 mm和a = 0.17; (c) r0 = 1.2 mm, w = 0.25 mm和a = 0.2

    Fig. 5.  On-axis intensity contrast of the ideal CAB and the beams produced by different methods: (a) r0 = 1 mm, w = 0.2 mm and a = 0.15; (b) r0 = 1.1 mm, w = 0.22 mm and a = 0.17; (c) r0 = 1.2 mm, w = 0.25 mm and a = 0.2.

    图 6  光束参数为${r_0} = 1\;{\rm{mm}}$, $w = 0.2\;{\rm{mm}}$$a = 0.15$时, 系统对准误差对产生光束质量的影响 (a)基模的$\left| \gamma \right|$以及S与腔长误差${\delta _{\rm{l}}}$的关系; (b)基模的$\left| \gamma \right|$以及S与同轴度误差${\delta _{\rm{d}}}$的关系

    Fig. 6.  The influence of the alignment errors on formation of the fundamental mode with ${r_0} = 1\;{\rm{mm}}$, $w = 0.2\;{\rm{mm}}$ and $a = 0.15$: (a) $\left| \gamma \right|$ and S of the fundamental mode as a function of $\delta_{\rm l}$; (b) $\left| \gamma \right|$ and S of the fundamental mode as a function of $\delta _{\rm d}$

    图 7  基模的$\left| \gamma \right|$以及S${\delta _{\rm{h}}}$的关系

    Fig. 7.  $\left| \gamma \right|$ and S of the fundamental mode as a function of ${\delta _{\rm{h}}}$.

    表 1  不同参数条件下的衍射光学元件上的相位分布和计算获得的最大3个$\left| \gamma \right|$对应模式的光强分布

    Table 1.  The phase distributions of the diffractive optical elements, the three largest $\left| \gamma \right|$ and the calculated intensity distributions of corresponding modes with different parameters.

    CAB的参数衍射光学元件上的相位分布/rad$\left| \gamma \right|$光强分布
    r0 = 1 mm
    w = 0.2 mm
    a = 0.15
    0.9972
    0.9898
    0.9898
    r0 = 1.1 mm
    w = 0.22 mm
    a = 0.17
    0.9970
    0.9845
    0.9845
    r0 = 1.2 mm
    w = 0.25 mm
    a = 0.2
    0.9960
    0.9804
    0.9804
    下载: 导出CSV
  • [1]

    Siviloglou G A, Broky J, Dogariu A, Christodoulides D N 2007 Phys. Rev. Lett. 99 213901Google Scholar

    [2]

    Minovich A E, Klein A E, Neshev D N, Pertsch T, Kivshar Y S, Christodoulides D N 2014 Laser. Photon. Rev. 8 221Google Scholar

    [3]

    Qian J, Liu B Y, Sun H X, Yuan S Q, Yu X Z 2017 Chin. Phys. B 26 114304Google Scholar

    [4]

    崔省伟, 陈子阳, 胡克磊, 蒲继雄 2013 物理学报 62 094205Google Scholar

    Cui S W, Chen Z Y, Hu K L, Pu J X 2013 Acta Phys. Sin. 62 094205Google Scholar

    [5]

    张泽, 刘京郊, 张鹏, 倪培根, Prakash J, 胡洋, 姜东升, Christodoulides D N, 陈志刚 2013 物理学报 62 034209Google Scholar

    Zhang Z, Liu J J, Zhang P, Ni P G, Prakash J, Hu Y, Jiang D S, Christodoulides D N, Chen Z G 2013 Acta Phys. Sin. 62 034209Google Scholar

    [6]

    Guo Y H, Huang Y J, Li X, Pu M B, Gao P, Jin J J, Ma X L, Luo X G 2019 Adv. Opt. Mater. 7 1900503Google Scholar

    [7]

    Li Z, Cheng H, Liu Z, Chen S, Tian J 2016 Adv. Opt. Mater. 4 1230Google Scholar

    [8]

    Fan Q, Zhu W, Liang Y, Huo P, Zhang C, Agrawal A, Huang K, Luo X, Lu Y, Qiu C, Lezec H J, Xu T 2019 Nano Lett. 19 1158Google Scholar

    [9]

    Efremidis N K, Christodoulides D N 2010 Opt. Lett. 35 4045Google Scholar

    [10]

    Papazoglou D G, Efremidis N K, Christodoulides D N, Tzortzakis S 2011 Opt. Lett. 36 1842Google Scholar

    [11]

    Liu K, Koulouklidis A D, Papazoglou D G, Tzortzakis S, Zhang X C 2016 Optica 3 605Google Scholar

    [12]

    Manousidaki M, Papazoglou D G, Farsari M, Tzortzakis S 2016 Optica 3 525Google Scholar

    [13]

    Manousidaki M, Fedorov V Y, Papazoglou D G, Farsari M, Tzortzakis S 2018 Opt. Lett. 4 3

    [14]

    Zhang P, Prakash J, Zhang Z, Mills M S, Efremidis N K, Christodoulides D N, Chen Z 2011 Opt. Lett. 36 2883Google Scholar

    [15]

    Davis J A, Cottrell D M, Zinn J M 2013 Appl. Opt. 52 1888Google Scholar

    [16]

    Davis J A, Cottrell D M, Sand D 2012 Opt. Express 20 13302Google Scholar

    [17]

    刘正楠, 耿滔, 邓攀 2019 中国激光 46 0209001

    Liu Z N, Geng T, Deng P 2019 Chin. J. Lasers 46 0209001

    [18]

    Fox A G, Li T 1961 Bell System Techical Journal 40 453Google Scholar

    [19]

    Chao J, Li B, Cheng Y, Wang Y 2007 Opt. Laser Technol. 39 490Google Scholar

    [20]

    Cheng Y Y, Wang Y Q, Hu J, Li J R 2004 Opt. Commun. 234 1Google Scholar

    [21]

    Bélanger P A, Paré C 1991 Opt. Lett. 16 1057Google Scholar

    [22]

    Leger J R, Chen D, Wang Z 1994 Opt. Lett. 19 108Google Scholar

    [23]

    Jiang Y, Zhu X, Yu W, Shao H, Zheng W, Lu X 2015 Opt. Express 23 29834Google Scholar

    [24]

    Li N, Jiang Y, Huang K, Lu X 2014 Opt. Express 22 22847Google Scholar

    [25]

    Zhou W, Bovik A C, Sheikh H R, Simoncelli E P 2004 IEEE Trans. Image Process 13 600Google Scholar

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出版历程
  • 收稿日期:  2019-07-16
  • 修回日期:  2019-09-16
  • 上网日期:  2019-12-05
  • 刊出日期:  2020-01-05

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