三阶非线性效应对ICF激光驱动器中光束均匀性的影响
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摘要
在惯性约束聚变(ICF)高功率固体激光驱动系统中，三阶非线性效应会使光强分布的不均匀性加剧，甚至导致光学元件的损伤与破坏，随着我国ICF激光驱动系统研制进程的不断推进，该问题已越来越引起人们的关注。因此，在本论文中，我们系统地对与介质三阶非线性有关的两种现象(小尺度自聚焦效应和“热像”现象)进行了研究。
我们首先介绍了三阶非线性引起的光克尔效应，由此引出了描述非线性介质中光传输的近轴波方程以及用于分析小扰动增长的B-T理论，同时叙述了近轴波方程的近似条件及B-T理论的不足。在此基础上我们研究了介质增益及边界条件等对纹波增益的影响，指出了最大增长频率和最快增长频率的区别。在考虑了介质的增益后，截止空间频率、最快增长频率以及最大增长因子不再像原始B-T理论中那样保持不变，它成了和光强、介质增益系数及传播距离有关的一个量。而考虑边界条件以后，出现了这样两个特征：在B-T理论截止频率以外的一些小纹波依然有一定的增益；同时大纹波也有较大的增益。
在理论分析的基础上，我们用数值模拟的方法研究了一个具体的四程放大系统中光束非均匀性和B积分的关系，以此确定出了系统运行的“红线”(安
四川大之户下员d匕论文
全运行警戒线);同时探讨了滤波小孔尺寸与光束质量的关系。
最后，我们研究了“热像”的形成机理及其规律，用数值模拟的方法形象
地说明了非线性介质的成像作用，提出了用非线性介质和高功率激光形成全息
成像系统的概念和思路，丰富了“全息成像”内涵，同时，首次发现了亮像和
暗像同时并存的现象。
In an Inertial Confinement Fusion (ICF) laser driver, the 3rd order nonlinear effect can make beam irregularity grow, even damage the expensive optics. With the development of the research and fabrication of ICF drivers in our country, more and more attention has been paid to this issue. So, the two main effects (small-scale self-focusing and "hot image") relate to the 3rd order nonlinear effect have been studied in this work.
At first, we describe the optical Keer effect induced by the 3rd order nonlinear effect, then we introduce the nonlinear paraxial equation and B-T theory. After describing the approximations adopted to arrive at the paraxial equation, the limitations of B-T theory have been identified. Then the influence of medium's gain and boundary conditions on ripple's gain has been discussed. It is pointed out that "the most quickly growing spatial frequency" and "the maximum growth spatial frequency" are different. The results also indicate that, in a piece of gain medium, the cutoff frequency,
"the most quickly growing frequency" and the integral exponential gain are variables of the beam intensity, medium gain coefficient and propagation distance. Taking into account the boundary conditions, two results were gotten: 1) The nonlinear medium provides gain to small ripples which is beyond the Bespalov-talanov cutoff spatial frequency; 2) Large ripples can also get large gain.
Besides the theoretical analysis, we also numerically studied the relation between the beam irregularity and B integral for a special four-pass amplifying system. Based on these calculations, a "red line" has been set up for the safety of the system. In addition, the variation of beam irregularity with the size of filter's hole has been studied.
At last, we illustrate the imaging process of nonlinear medium by numerical simulation, and the image position and intensity are studied. At the same time, it is pointed out that a piece of nonlinear medium and high power laser beam can form a hologram system. For the first time, we found that a "dark image"(or "cold image") may emerge along with a "hot image".
我们首先介绍了三阶非线性引起的光克尔效应，由此引出了描述非线性介质中光传输的近轴波方程以及用于分析小扰动增长的B-T理论，同时叙述了近轴波方程的近似条件及B-T理论的不足。在此基础上我们研究了介质增益及边界条件等对纹波增益的影响，指出了最大增长频率和最快增长频率的区别。在考虑了介质的增益后，截止空间频率、最快增长频率以及最大增长因子不再像原始B-T理论中那样保持不变，它成了和光强、介质增益系数及传播距离有关的一个量。而考虑边界条件以后，出现了这样两个特征：在B-T理论截止频率以外的一些小纹波依然有一定的增益；同时大纹波也有较大的增益。
在理论分析的基础上，我们用数值模拟的方法研究了一个具体的四程放大系统中光束非均匀性和B积分的关系，以此确定出了系统运行的“红线”(安
四川大之户下员d匕论文
全运行警戒线);同时探讨了滤波小孔尺寸与光束质量的关系。
最后，我们研究了“热像”的形成机理及其规律，用数值模拟的方法形象
地说明了非线性介质的成像作用，提出了用非线性介质和高功率激光形成全息
成像系统的概念和思路，丰富了“全息成像”内涵，同时，首次发现了亮像和
暗像同时并存的现象。
In an Inertial Confinement Fusion (ICF) laser driver, the 3rd order nonlinear effect can make beam irregularity grow, even damage the expensive optics. With the development of the research and fabrication of ICF drivers in our country, more and more attention has been paid to this issue. So, the two main effects (small-scale self-focusing and "hot image") relate to the 3rd order nonlinear effect have been studied in this work.
At first, we describe the optical Keer effect induced by the 3rd order nonlinear effect, then we introduce the nonlinear paraxial equation and B-T theory. After describing the approximations adopted to arrive at the paraxial equation, the limitations of B-T theory have been identified. Then the influence of medium's gain and boundary conditions on ripple's gain has been discussed. It is pointed out that "the most quickly growing spatial frequency" and "the maximum growth spatial frequency" are different. The results also indicate that, in a piece of gain medium, the cutoff frequency,
"the most quickly growing frequency" and the integral exponential gain are variables of the beam intensity, medium gain coefficient and propagation distance. Taking into account the boundary conditions, two results were gotten: 1) The nonlinear medium provides gain to small ripples which is beyond the Bespalov-talanov cutoff spatial frequency; 2) Large ripples can also get large gain.
Besides the theoretical analysis, we also numerically studied the relation between the beam irregularity and B integral for a special four-pass amplifying system. Based on these calculations, a "red line" has been set up for the safety of the system. In addition, the variation of beam irregularity with the size of filter's hole has been studied.
At last, we illustrate the imaging process of nonlinear medium by numerical simulation, and the image position and intensity are studied. At the same time, it is pointed out that a piece of nonlinear medium and high power laser beam can form a hologram system. For the first time, we found that a "dark image"(or "cold image") may emerge along with a "hot image".
引文
[1]王乃彦，《聚变能及其未来》，清华大学出版社，2001
[2]范滇元，贺贤土，“惯性约束聚变能源与激光驱动器”，大自然探索vol．18(Sum NO．67)1999年第1期(总第67期)：31-35
[3]钱士雄，王恭明编著，《非线性光学——原理与进展》，复旦大学出版社2001第一版
[4]G. C. Wang, "Suggestion of Neutron Generation with Powerful lasers", Chinese J of Lasers,1987,14(11):641
[5]H．F．巴索夫等，《稠密等离子体诊断学》，《强激光与粒子束》杂志社，1992年12月第一版
[6]J. H. Nuckolls, L. Wood, A. Thiessen, and G.B. Zimmermam, Laser compression of matter to super-high densities: thermonuclear(CTR) application. Nature 239,129(1972)
[7]彭翰生，张小民，范滇元，朱健强，“高功率固体激光装置的发展与工程科学问题”，中国工程科学，Vol．3，No．3(2001)
[8]国家高技术惯性约束聚变委员会，863-416-5专题专家组，神光-Ⅲ原型装置(TIL)概念设计报告，第三版，2000
[9]粟敬钦，魏晓锋，马驰，激光束低频畸变波前模型的计算模拟，强激光与粒子束，Vol．12(2000)
[10]J. A. Paisner, National Ignition Facility Conceptual Design Report, Lawrence Livermore ROP-117093 (1994).
[11]J. A. Paisner, Utility of the National Ignition Facility , Lawrenc e Livermore National Laboratory, Livermore,CA,NIF-LLNL-94- 240, UCRL-PROP- 117384, 1994.
[12]中物院核化所强激光技术室，惯性约束聚变——驱动源技术译文集(1)，1996
[13]W.H. Lowdermilk, "Status of the National Ignition Facility project", SPIE vol.3047, 16～37
[14] H. S. Peng, X. M. Zhang, X. E Wei, et al., Status of the SG-Ⅲ solid state laser project. SPIE,Vol. 3492, 25～33, 1992
[15] W．克希耐尔，《固体激光工程》，科学出版社，1983
[16] Y. R. SHEN, The Principles of NONLINEAR OPTICS (John Willy & sons, Inc., New York, 1984). Chap.17
[17] V. I. Bespanlov, V, I. Tanalov, Filamentary. structure of light beams in nonlinear liquids, JETP Lett. ,vol. 3, 1966
[18] S.C. Wen, D.Y. Fan, "Small-Scale Self-Focusing of Intense Laser Beams in Nonlinear Media with Loss" ,CHINESE JOURNAL OF LASERS, B9-4 (2000): 356
[19] J. J.Duderstadt and G. A. Moses, Inertial Confinement Fusion, 1982
[20] 宫本健郎[日]．金尚宪译，《热核聚变等离子体物理学》，科学出版社，1981
[21] 景峰，钕玻璃激光多程放大技术研究，博士学位论文，1998
[22] J. A. Paisner, J. D. Boyes, S. A. Kumpan, et al. Conceptual design of the national ignition facility[A]. Solid state lasers for Application to ICF[C], June 1995 2-12
[23] J.A.Paisner, E.M.Campbell, W.J.Hogan, The National Ignition Facility Project, Fusion Technology, Nol.26 1994:755-761
[24] 景峰，张小民，朱启华等，钕玻璃介质中强激光束传输特性的初步研究，《强激光与粒子束》，Vol．12，No．5(2000)：551-555
[25] W. W. Simmons, and S. Guch, F. Rainer, and J. E. Murray, "High-energy Spatial Filter for Removal of Small-scale Beam Instabilities in High-Power Lasers" . IEEE J. Quantum Electron. QE-11,300(1975)
[26] J. A. Fleck, "Temporal aspects of the Self-Focusing of Optical Beams", Appl. Phys. Lett., Vol.15, No.10(1969)
[27] J. A. Fleck, Jr. and R. L. Carman, "Effect of Relaxation on Small-Scale Filament Formation by Ultrashort Light Pulses," Appl. Phys. Lett. 20,290 (1972).
[28] F. Shimizu, "Numerical Calculation of Self-Focusing and Trapping of a Short Light Pulse in Kerr Liquids," IBM J. Res. Develop.,17, 286(1973).
[29] A. L. Dyshko, V. N. Lugovi and A. M. Prokhorov, ZhETF, pis'ma Red. 61, 2305; English translation: "Multifocus Structure of a Beam in a Nonlinear Medium," Soy. Phys. JETP 34, 1235(1972).
[30] E. Yablonovitch and B. Bloembergen, "Avalanche Ionization and the Limiting Diameter of Filaments Induced by Light Pulses in Transparent Media," Phys. Rev. Lett.29 907(1972).
[31] M. D. Feit, and J.A. Fleck, Jr. , "Beam Nonparaxality, Filament Formation, and Beam Breakup in the Self-Focusing of Optical Beams" ,J. Opt. Soc. Am., vol.5 No.3 B5(1988),633.
[32] W. H. Williams, P. A. Renard, K. R. Manes etc., "Modeling of Self-Focusing Experiments by Beam Propagation Codes" , UCRL-LR-105821-96-1
[33] B. Crosignani, P. Di Porto and A. Yariv,"Nonparaxial equation for linear and nonlinear optical propagation",Optics Letters / Vol. 22, No.11 / June 1, 1997 / pp:778-780 B. Crosignani, P, Di Porto, Opt. Lett., 22(1997), 778,errata, 22(1997),18
[34] 林晓东，ICF固体驱动器中的小尺度自聚焦效应研究，硕士学位论文，2002
[35] 师智全，大型固体激光装置光学元件稳定性分析研究，博士学位论文，2003
[36] J. T. Hunt, K. R. Manes, and P. A. Renard 'Hot Images from Obscurations' Appl. Opt. Vol. 32, No.30(1993): 5973-5982
[2]范滇元，贺贤土，“惯性约束聚变能源与激光驱动器”，大自然探索vol．18(Sum NO．67)1999年第1期(总第67期)：31-35
[3]钱士雄，王恭明编著，《非线性光学——原理与进展》，复旦大学出版社2001第一版
[4]G. C. Wang, "Suggestion of Neutron Generation with Powerful lasers", Chinese J of Lasers,1987,14(11):641
[5]H．F．巴索夫等，《稠密等离子体诊断学》，《强激光与粒子束》杂志社，1992年12月第一版
[6]J. H. Nuckolls, L. Wood, A. Thiessen, and G.B. Zimmermam, Laser compression of matter to super-high densities: thermonuclear(CTR) application. Nature 239,129(1972)
[7]彭翰生，张小民，范滇元，朱健强，“高功率固体激光装置的发展与工程科学问题”，中国工程科学，Vol．3，No．3(2001)
[8]国家高技术惯性约束聚变委员会，863-416-5专题专家组，神光-Ⅲ原型装置(TIL)概念设计报告，第三版，2000
[9]粟敬钦，魏晓锋，马驰，激光束低频畸变波前模型的计算模拟，强激光与粒子束，Vol．12(2000)
[10]J. A. Paisner, National Ignition Facility Conceptual Design Report, Lawrence Livermore ROP-117093 (1994).
[11]J. A. Paisner, Utility of the National Ignition Facility , Lawrenc e Livermore National Laboratory, Livermore,CA,NIF-LLNL-94- 240, UCRL-PROP- 117384, 1994.
[12]中物院核化所强激光技术室，惯性约束聚变——驱动源技术译文集(1)，1996
[13]W.H. Lowdermilk, "Status of the National Ignition Facility project", SPIE vol.3047, 16～37
[14] H. S. Peng, X. M. Zhang, X. E Wei, et al., Status of the SG-Ⅲ solid state laser project. SPIE,Vol. 3492, 25～33, 1992
[15] W．克希耐尔，《固体激光工程》，科学出版社，1983
[16] Y. R. SHEN, The Principles of NONLINEAR OPTICS (John Willy & sons, Inc., New York, 1984). Chap.17
[17] V. I. Bespanlov, V, I. Tanalov, Filamentary. structure of light beams in nonlinear liquids, JETP Lett. ,vol. 3, 1966
[18] S.C. Wen, D.Y. Fan, "Small-Scale Self-Focusing of Intense Laser Beams in Nonlinear Media with Loss" ,CHINESE JOURNAL OF LASERS, B9-4 (2000): 356
[19] J. J.Duderstadt and G. A. Moses, Inertial Confinement Fusion, 1982
[20] 宫本健郎[日]．金尚宪译，《热核聚变等离子体物理学》，科学出版社，1981
[21] 景峰，钕玻璃激光多程放大技术研究，博士学位论文，1998
[22] J. A. Paisner, J. D. Boyes, S. A. Kumpan, et al. Conceptual design of the national ignition facility[A]. Solid state lasers for Application to ICF[C], June 1995 2-12
[23] J.A.Paisner, E.M.Campbell, W.J.Hogan, The National Ignition Facility Project, Fusion Technology, Nol.26 1994:755-761
[24] 景峰，张小民，朱启华等，钕玻璃介质中强激光束传输特性的初步研究，《强激光与粒子束》，Vol．12，No．5(2000)：551-555
[25] W. W. Simmons, and S. Guch, F. Rainer, and J. E. Murray, "High-energy Spatial Filter for Removal of Small-scale Beam Instabilities in High-Power Lasers" . IEEE J. Quantum Electron. QE-11,300(1975)
[26] J. A. Fleck, "Temporal aspects of the Self-Focusing of Optical Beams", Appl. Phys. Lett., Vol.15, No.10(1969)
[27] J. A. Fleck, Jr. and R. L. Carman, "Effect of Relaxation on Small-Scale Filament Formation by Ultrashort Light Pulses," Appl. Phys. Lett. 20,290 (1972).
[28] F. Shimizu, "Numerical Calculation of Self-Focusing and Trapping of a Short Light Pulse in Kerr Liquids," IBM J. Res. Develop.,17, 286(1973).
[29] A. L. Dyshko, V. N. Lugovi and A. M. Prokhorov, ZhETF, pis'ma Red. 61, 2305; English translation: "Multifocus Structure of a Beam in a Nonlinear Medium," Soy. Phys. JETP 34, 1235(1972).
[30] E. Yablonovitch and B. Bloembergen, "Avalanche Ionization and the Limiting Diameter of Filaments Induced by Light Pulses in Transparent Media," Phys. Rev. Lett.29 907(1972).
[31] M. D. Feit, and J.A. Fleck, Jr. , "Beam Nonparaxality, Filament Formation, and Beam Breakup in the Self-Focusing of Optical Beams" ,J. Opt. Soc. Am., vol.5 No.3 B5(1988),633.
[32] W. H. Williams, P. A. Renard, K. R. Manes etc., "Modeling of Self-Focusing Experiments by Beam Propagation Codes" , UCRL-LR-105821-96-1
[33] B. Crosignani, P. Di Porto and A. Yariv,"Nonparaxial equation for linear and nonlinear optical propagation",Optics Letters / Vol. 22, No.11 / June 1, 1997 / pp:778-780 B. Crosignani, P, Di Porto, Opt. Lett., 22(1997), 778,errata, 22(1997),18
[34] 林晓东，ICF固体驱动器中的小尺度自聚焦效应研究，硕士学位论文，2002
[35] 师智全，大型固体激光装置光学元件稳定性分析研究，博士学位论文，2003
[36] J. T. Hunt, K. R. Manes, and P. A. Renard 'Hot Images from Obscurations' Appl. Opt. Vol. 32, No.30(1993): 5973-5982