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当高功率激光通过Kerr非线性介质传输时, Kerr效应会严重影响激光的传输特性. 实际应用中常遇到像散光束. 迄今为止, 像散光束传输特性的研究大都局限于在线性介质中的传输, 而在非线性介质中传输的研究较少, 且还未涉及像散激光束通过含光学系统的Kerr非线性介质传输变换的研究. 本文主要研究Kerr效应对聚焦光束像散特性和焦移特性的影响, 以及聚焦像散高斯光束的自聚焦焦距和光束焦点调控. 在光束扩展情况下, 推导出了聚焦像散高斯光束在Kerr非线性介质中传输的束宽、束腰位置和焦移的解析公式, 研究表明: 在自聚焦介质中, 随着自聚焦作用增强(如光束功率增强), 光束像散越强, 但焦移越小; 在自散焦介质中, 随着自散焦作用增强(如光束功率增强), 光束像散越弱, 但焦移越大. 另一方面, 在光束自聚焦情况下, 推导出了自聚焦焦距的解析公式, 研究表明利用光束像散可以调控光束焦点个数.When a powerful laser beam propagates in a Kerr nonlinear medium, the Kerr effect on the beam propagation characteristics is very significant. The astigmatic laser beams are often encountered in practice. Until now, much work has been carried out on the propagation characteristics of astigmatic laser beams in linear media, but a few researches have been reported about the propagation of astigmatic laser beams through nonlinear media. To the best of our knowledge, the propagation or the transformation of astigmatic laser beams through an optical system in a Kerr nonlinear medium has not been investigated. In this paper, the propagation characteristics of focused astigmatic Gaussian beams in a nonlinear Kerr medium are studied. The Kerr effect on the beam astigmatism and the focal shift of focused astigmatic Gaussian beams are investigated in detail, and the self-focusing focal length and focus control of focused astigmatic Gaussian beams in the Kerr nonlinear medium are also studied. For the beam spreading case, the analytical formula for each of the beam width, the beam waist position, and the focal shift of focused astigmatic Gaussian beams in the Kerr nonlinear medium is derived. It is shown that in the self-focusing medium, as the beam power increases (i.e. the self-focusing effect becomes stronger), the beam astigmatism becomes stronger, but the focal shift decreases. However, in a self-defocusing medium, as the beam power increases (i.e. the self-defocusing effect becomes stronger), the beam astigmatism becomes weaker, but the focal shift increases. On the other hand, for the beam self-focusing case, the analytical formula of the self-focusing focal length of focused astigmatic Gaussian beams in the Kerr nonlinear medium is derived. It is found that the number of foci can be controlled by applying beam astigmatism. The results obtained in this paper are of theoretical and practical significance.
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Keywords:
- Kerr effect /
- astigmatism /
- focal shift /
- focus control
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[1] Hanna D C 1969 IEEE J. Quantum Electron. 5 483Google Scholar
[2] Zhao B, Li Z 1998 Appl. Opt. 37 2563Google Scholar
[3] Thaning A, Jaroszewicz Z, Friberg A T 2003 Appl. Opt. 42 9Google Scholar
[4] 江新光, 吴逢铁 2008 物理学报 57 4202Google Scholar
Jiang X G, Wu F T 2008 Acta Phys. Sin. 57 4202Google Scholar
[5] 杨艳飞, 陈婧, 吴逢铁, 胡润, 张惠忠, 胡汉青 2018 物理学报 67 224201Google Scholar
Yang Y F, Chen J, Wu F T, Hu R, Zhang H Z, Hu H Q 2018 Acta Phys. Sin. 67 224201Google Scholar
[6] Lin Q, Cai Y J 2002 Opt. Lett. 27 216Google Scholar
[7] 董一鸣, 徐云飞, 张璋, 林强 2006 物理学报 55 5755Google Scholar
Dong Y M, Xu Y F, Zhang Z, Lin Q 2006 Acta Phys. Sin. 55 5755Google Scholar
[8] Zhao D M, Lin Q, Wang S M 1994 Opt. Quantum Electron. 26 903Google Scholar
[9] Tari T, Richter P 1992 Opt. Quantum Electron. 24 S865Google Scholar
[10] 刘晓丽, 冯国英, 李玮, 唐淳, 周寿桓 2013 物理学报 62 194202Google Scholar
Liu X L, Feng G Y, Li W, Tang C, Zhou S H 2013 Acta Phys. Sin. 62 194202Google Scholar
[11] Cai Y J, He S L 2006 Appl. Phys. Lett. 89 041117Google Scholar
[12] Cai Y J, Lin Q, Ge D 2002 J. Opt. Soc. Am. A 19 2036Google Scholar
[13] 赵贵燕, 张逸新, 王建宇, 贾建军 2010 物理学报 59 1378Google Scholar
Zhao G Y, Zhang Y X, Wang J Y, Jia J J 2010 Acta Phys. Sin. 59 1378Google Scholar
[14] Soljacic M, Segev M, Coskun T, Christodoulides D N, Vishwanath A 2000 Phys. Rev. Lett. 84 467Google Scholar
[15] Mitchell M, Chen Z G, Shih M F, Segev M 1996 Phys. Rev. Lett. 77 490Google Scholar
[16] Sun C, Dylov D V, Fleischer J W 2009 Opt. Lett. 34 3003Google Scholar
[17] Wang H, Ji X L, Zhang H, Li X Q, Deng Y 2019 Opt. Lett. 44 743Google Scholar
[18] Wang H, Ji X L, Deng Y, Li X Q, Yu H 2020 Opt. Lett. 45 710Google Scholar
[19] Hu J, Wang H, Ji X L, Deng Y, Chen L F 2020 J. Opt. Soc. Am. A 37 1282Google Scholar
[20] 王形华, 郭旗 2005 物理学报 54 3183Google Scholar
Wang X H, Guo Q 2005 Acta Phys. Sin. 54 3183Google Scholar
[21] Goncharenko A M, Logvin Y A, Samson A M, Shapovalov P S 1991 Opt. Commun. 81 225Google Scholar
[22] Cornolti F, Lucchesi M, Zambon B 1990 Opt. Commun. 75 129Google Scholar
[23] Singh T, Saini N S, Kaul S S 2000 Pramana-J. Phys. 55 423Google Scholar
[24] 季小玲, 吕百达 2000 强激光与粒子束 4 12
Ji X L, Lü B D 2000 High Power Laser and Particle Beams 4 12
[25] Guo S F, Tian Q 2010 Chin. Phys. B 6 19Google Scholar
[26] Porras M A, Alda J, Bernabeu E 1993 Appl. Opt. 30 32Google Scholar
[27] Yariv A, Yeh P 1978 Opt. Commun. 2 27Google Scholar
[28] Miller R I, Roberts T G 1987 Appl. Opt. 21 26Google Scholar
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