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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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图 1 Kerr非线性介质中聚焦像散高斯光束传输的示意图
Figure 1. Schematic diagram of a focused astigmatic Gaussian beam propagating in Kerr nonlinear media.
图 2 束腰位置s2x随像散系数C6的变化
Figure 2. Beam waist position s2x versus the astigmatic coefficient C6.
图 3 像散参数β随相对传输距离z/f的变化 (a)不同像散系数; (b)不同Kerr效应强度
Figure 3. Astigmatic parameter β versus the relative propagation distance z/f: (a) Different values of the astigmatic coefficient; (b) different strength of the Kerr effect.
图 4 (a)轴上光强I(0, 0, z)和(b)光斑面积S(z)随相对传输距离z/f的变化, C6 = 0.2 m–1
Figure 4. (a) Axial intensity and (b) the area of beam spot versus the relative propagation distance z/f.
图 5 焦移Δ随像散系数C6的变化 (a)自聚焦介质; (b)自散焦介质
Figure 5. Focal shift Δ versus the astigmatic coefficient C6: (a) Self-focusing media; (b) self-defocusing media.
图 6 自聚焦焦距zf随像散系数C6的变化
Figure 6. Self-focusing focal length zf versus the astigmatic coefficient C6.
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[1] Hanna D C 1969 IEEE J. Quantum Electron. 5 483
Google Scholar
[2] Zhao B, Li Z 1998 Appl. Opt. 37 2563
Google Scholar
[3] Thaning A, Jaroszewicz Z, Friberg A T 2003 Appl. Opt. 42 9
Google Scholar
[4] 江新光, 吴逢铁 2008 物理学报 57 4202
Google Scholar
Jiang X G, Wu F T 2008 Acta Phys. Sin. 57 4202
Google Scholar
[5] 杨艳飞, 陈婧, 吴逢铁, 胡润, 张惠忠, 胡汉青 2018 物理学报 67 224201
Google Scholar
Yang Y F, Chen J, Wu F T, Hu R, Zhang H Z, Hu H Q 2018 Acta Phys. Sin. 67 224201
Google Scholar
[6] Lin Q, Cai Y J 2002 Opt. Lett. 27 216
Google Scholar
[7] 董一鸣, 徐云飞, 张璋, 林强 2006 物理学报 55 5755
Google Scholar
Dong Y M, Xu Y F, Zhang Z, Lin Q 2006 Acta Phys. Sin. 55 5755
Google Scholar
[8] Zhao D M, Lin Q, Wang S M 1994 Opt. Quantum Electron. 26 903
Google Scholar
[9] Tari T, Richter P 1992 Opt. Quantum Electron. 24 S865
Google Scholar
[10] 刘晓丽, 冯国英, 李玮, 唐淳, 周寿桓 2013 物理学报 62 194202
Google Scholar
Liu X L, Feng G Y, Li W, Tang C, Zhou S H 2013 Acta Phys. Sin. 62 194202
Google Scholar
[11] Cai Y J, He S L 2006 Appl. Phys. Lett. 89 041117
Google Scholar
[12] Cai Y J, Lin Q, Ge D 2002 J. Opt. Soc. Am. A 19 2036
Google Scholar
[13] 赵贵燕, 张逸新, 王建宇, 贾建军 2010 物理学报 59 1378
Google Scholar
Zhao G Y, Zhang Y X, Wang J Y, Jia J J 2010 Acta Phys. Sin. 59 1378
Google Scholar
[14] Soljacic M, Segev M, Coskun T, Christodoulides D N, Vishwanath A 2000 Phys. Rev. Lett. 84 467
Google Scholar
[15] Mitchell M, Chen Z G, Shih M F, Segev M 1996 Phys. Rev. Lett. 77 490
Google Scholar
[16] Sun C, Dylov D V, Fleischer J W 2009 Opt. Lett. 34 3003
Google Scholar
[17] Wang H, Ji X L, Zhang H, Li X Q, Deng Y 2019 Opt. Lett. 44 743
Google Scholar
[18] Wang H, Ji X L, Deng Y, Li X Q, Yu H 2020 Opt. Lett. 45 710
Google Scholar
[19] Hu J, Wang H, Ji X L, Deng Y, Chen L F 2020 J. Opt. Soc. Am. A 37 1282
Google Scholar
[20] 王形华, 郭旗 2005 物理学报 54 3183
Google Scholar
Wang X H, Guo Q 2005 Acta Phys. Sin. 54 3183
Google Scholar
[21] Goncharenko A M, Logvin Y A, Samson A M, Shapovalov P S 1991 Opt. Commun. 81 225
Google Scholar
[22] Cornolti F, Lucchesi M, Zambon B 1990 Opt. Commun. 75 129
Google Scholar
[23] Singh T, Saini N S, Kaul S S 2000 Pramana-J. Phys. 55 423
Google 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 19
Google Scholar
[26] Porras M A, Alda J, Bernabeu E 1993 Appl. Opt. 30 32
Google Scholar
[27] Yariv A, Yeh P 1978 Opt. Commun. 2 27
Google Scholar
[28] Miller R I, Roberts T G 1987 Appl. Opt. 21 26
Google Scholar
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