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采用光线光学方法对非线性自聚焦现象进行仿真, 能够从宏观上直观地体现强激光的传输过程, 同时避免采用近轴近似、自相似近似等. 本文采用在光传输路径上垂直于光轴切片的方法, 将光的非线性传输转化为切片上的光对折射率的调制作用和切片间的线性传输. 在切片端面上统计光强后对量化误差进行了抑制, 而线性传输过程采用了亚当斯法求解光线方程从而解决了龙格库塔法等不能用于非线性光传输仿真的问题. 仿真结果显示, 强激光自聚焦在轴上有多个焦点, 且第一个焦点的位置随光功率的增大而更靠近入射位置; 由于追迹的是实际光线, 故可以得到近轴区以外区域自聚焦及成丝(环)的情况, 这对于强激光系统安全是有重要意义的. 利用已有的同样基于光线追迹方法的光学设计、仿真软件, 可以把非线性自聚焦介质和线性介质结合起来, 仿真光在实际强激光系统中的传输.The simulation of nonlinear self-focusing phenomenon using ray-tracing method can macroscopically provide an intuitive picture of the propagation of light in a self-focusing material, without adopting paraxial approximation or self-similar hypothesis. In this paper, propagation of light is sampled by discrete slices along a certain direction. Thus nonlinear propagation is turned into the combination of optical modulation of the refractive index on separate slices and linear propagation between each two adjacent slices. On each slice, after calculating the flux, we use a novel algorithm to suppress the quantized errors. For the linear propagating process, Adams method is adopted to solve the ray equations, which solve the problem that the widely used Runge-Kutta method cannot be used in simulation of light in nonlinear materials. The simulation results reveal that there are several foci along the propagating axis and the location of the first focus becomes closer to the incident plane as the power of light goes up. Furthermore, because the program traces real rays, it is possible to reach the non-paraxial region and reveal the phenomenon of ring-structure flux distributions caused by self-focusing. This is significant for the safety of high-power laser systems. Some commercial optical design and simulation software are also based on ray-tracing methods. Thus the systems including both nonlinear and linear materials are possible to simulate, which can guide people to set up the corresponding experimental systems.
[1] Askar’yan G A 1962 Soviet. Phys. JETP 15 1088
[2] Chiao R, Garmire E, Townes C H 1964 Phys. Rev. Lett. 13 479
[3] Kelley P L 1965 Phys. Rev. Lett. 15 1005
[4] Shen Y R (Translated by Gu S J) 1987 The Principles of Nonlinear Optics (1st Ed.) (Beijing: Science Press) p327 (in Chinese) [沈元壤著 (顾世杰译) 1987 非线性光学原理 (上册) (北京: 科学出版社) 第327页]
[5] Hercher M 1964 J. Opt. Soc. Am. 54 563
[6] Braun A, Korn G, Liu X, Du D, Squier J, Mourou G 1995 Opt. Lett. 20 73
[7] Liu W, Kosareva O, Golubtsov I S, Iwasaki A, Becker A, Kandidov V P, Chin S L 2003 Appl. Phys. B 76 215
[8] Agrawal G P (Translated by Jia D F, Yu Z H) 2002 Nonlinear Fiber Optics, Third Edition and Applications of Nonlinear Fiber Optics (1st Ed.) (Beijing: Publishing House of Electronics Industry) p33 (in Chinese) [阿戈沃著 (贾东方, 余震虹译) 2002 非线性光纤光学原理及应用 (第一版) (北京: 电子工业出版社) 第33页]
[9] Hardin R H, Tappen E D 1975 SIAM Rev. Chronicle. 15 423
[10] Sinkin O V, Holzlöner R, Zweck J, Menyuk C R 2003 J. Lightwave Technol. 21 61
[11] Godoy-Rubio R, Romero-García S, Ortega-Moñux A, Wangümert-Pérez J G 2011 J. Opt. Soc. Am. B 28 2142
[12] Feit M, Fleck J 1988 J. Opt. Soc. Am. B 5 633
[13] Chi S, Guo Q 1995 Opt. Lett. 20 1598
[14] Li Z D, Guo Q, Lin W G 1999 Chin. J. Lasers 26 711 (in Chinese) [李忠东, 郭旗, 林为干 1999 中国激光 26 711]
[15] Wen S H 2001 Ph. D. Dissertation (Shanghai: Graduate University of Chinese Academy of Sciences) (in Chinese) [文双春 2001 博士学位论文 (上海: 中国科学院研究生院)]
[16] Wen S C, Fan D Y 2000 Acta Phys. Sin. 49 460 (in Chinese) [文双春, 范滇元 2000 物理学报 49 460]
[17] Wen S C, Fan D Y 2000 Acta Phys. Sin. 49 1282 (in Chinese) [文双春, 范滇元 2000 物理学报 49 1282]
[18] Censor D 1977 Phys. Rev. A 16 1673
[19] Kasparian J, Solle J, Richard M, Wolf J P 2004 Appl. Phys. B 79 947
[20] Dragoman D 1996 Appl. Opt. 35 4142
[21] Zhang Y C, Lü B D 2004 Opt. Lett. 29 2710
[22] Gao H H, Tian L, Zhang B, Barbastathis G 2010 Opt. Lett. 35 4148
[23] Peng Z T, Jing F, Liu L Q, Zhu Q H, Chen B, Zhang K, Liu H, Zhang Q Q, Cheng X F, Jiang D B, Liu H J, Peng H S 2003 Acta Phys. Sin. 52 87 (in Chinese) [彭志涛, 景峰, 刘兰琴, 朱启华, 陈波, 张昆, 刘华, 张清泉, 程晓峰, 蒋东镔, 刘红婕, 彭翰生 2003 物理学报 52 87]
[24] Qiao Y T 1991 Gradient Index Optics (1st Ed.) (Beijing: Science Press) p170 (in Chinese) [乔亚天 1991 梯度折射率光学 (第一版) (北京: 科学出版社) 第170页]
[25] Dyshko A L, Lugovoi V N, Prokhorov A M 1967 ZhETF Pis’ma 6 655
[26] Garmire E, Chiao R Y, Townes C H 1966 Phys. Rev. Lett. 16 347
[27] Wanger W G, Haus H A, Marburger J H 1968 Phys. Rev. 175 256
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[1] Askar’yan G A 1962 Soviet. Phys. JETP 15 1088
[2] Chiao R, Garmire E, Townes C H 1964 Phys. Rev. Lett. 13 479
[3] Kelley P L 1965 Phys. Rev. Lett. 15 1005
[4] Shen Y R (Translated by Gu S J) 1987 The Principles of Nonlinear Optics (1st Ed.) (Beijing: Science Press) p327 (in Chinese) [沈元壤著 (顾世杰译) 1987 非线性光学原理 (上册) (北京: 科学出版社) 第327页]
[5] Hercher M 1964 J. Opt. Soc. Am. 54 563
[6] Braun A, Korn G, Liu X, Du D, Squier J, Mourou G 1995 Opt. Lett. 20 73
[7] Liu W, Kosareva O, Golubtsov I S, Iwasaki A, Becker A, Kandidov V P, Chin S L 2003 Appl. Phys. B 76 215
[8] Agrawal G P (Translated by Jia D F, Yu Z H) 2002 Nonlinear Fiber Optics, Third Edition and Applications of Nonlinear Fiber Optics (1st Ed.) (Beijing: Publishing House of Electronics Industry) p33 (in Chinese) [阿戈沃著 (贾东方, 余震虹译) 2002 非线性光纤光学原理及应用 (第一版) (北京: 电子工业出版社) 第33页]
[9] Hardin R H, Tappen E D 1975 SIAM Rev. Chronicle. 15 423
[10] Sinkin O V, Holzlöner R, Zweck J, Menyuk C R 2003 J. Lightwave Technol. 21 61
[11] Godoy-Rubio R, Romero-García S, Ortega-Moñux A, Wangümert-Pérez J G 2011 J. Opt. Soc. Am. B 28 2142
[12] Feit M, Fleck J 1988 J. Opt. Soc. Am. B 5 633
[13] Chi S, Guo Q 1995 Opt. Lett. 20 1598
[14] Li Z D, Guo Q, Lin W G 1999 Chin. J. Lasers 26 711 (in Chinese) [李忠东, 郭旗, 林为干 1999 中国激光 26 711]
[15] Wen S H 2001 Ph. D. Dissertation (Shanghai: Graduate University of Chinese Academy of Sciences) (in Chinese) [文双春 2001 博士学位论文 (上海: 中国科学院研究生院)]
[16] Wen S C, Fan D Y 2000 Acta Phys. Sin. 49 460 (in Chinese) [文双春, 范滇元 2000 物理学报 49 460]
[17] Wen S C, Fan D Y 2000 Acta Phys. Sin. 49 1282 (in Chinese) [文双春, 范滇元 2000 物理学报 49 1282]
[18] Censor D 1977 Phys. Rev. A 16 1673
[19] Kasparian J, Solle J, Richard M, Wolf J P 2004 Appl. Phys. B 79 947
[20] Dragoman D 1996 Appl. Opt. 35 4142
[21] Zhang Y C, Lü B D 2004 Opt. Lett. 29 2710
[22] Gao H H, Tian L, Zhang B, Barbastathis G 2010 Opt. Lett. 35 4148
[23] Peng Z T, Jing F, Liu L Q, Zhu Q H, Chen B, Zhang K, Liu H, Zhang Q Q, Cheng X F, Jiang D B, Liu H J, Peng H S 2003 Acta Phys. Sin. 52 87 (in Chinese) [彭志涛, 景峰, 刘兰琴, 朱启华, 陈波, 张昆, 刘华, 张清泉, 程晓峰, 蒋东镔, 刘红婕, 彭翰生 2003 物理学报 52 87]
[24] Qiao Y T 1991 Gradient Index Optics (1st Ed.) (Beijing: Science Press) p170 (in Chinese) [乔亚天 1991 梯度折射率光学 (第一版) (北京: 科学出版社) 第170页]
[25] Dyshko A L, Lugovoi V N, Prokhorov A M 1967 ZhETF Pis’ma 6 655
[26] Garmire E, Chiao R Y, Townes C H 1966 Phys. Rev. Lett. 16 347
[27] Wanger W G, Haus H A, Marburger J H 1968 Phys. Rev. 175 256
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