[1] E. S. Bliss, J. T. Hunt, P. A. Renard. Effects of nonlinear propagation on laser focusing properties［J］. IEEE J. Quantum Electron., 1976, QE-12(7): 402～406

[2] B. R. Suydam. Self-focusing of very powerful laser beams II［J］. IEEE J. Quantum Electron., 1974, QE-10(11): 837～843

[3] J. H. Marburger. Self-focusing theory［J］. Prog. Quantum Electron., 1975, 4: 35～110

[4] J. A. Fleck, Jr., C. Layne. Study of self-focusing damage in a high-power Ndglass-rod amplifer［J］. Appl. Phys. Lett., 1973, 22(9): 467～469

[5] A. J. Campillo, S. L. Shapiro, B. R. Suydam. Periodic breakup of optical beams due to self-focusing［J］. Appl. Phys. Lett., 1973, 23(11): 628～630

[6] V. I. Bespalov, V. I. Talanov. Filamentary structure of light beams in nonlinear liquids［J］. JETP Lett., 1966, 3(11): 307～310

[7] J. A. Fleck, Jr., J. R. Morris, E. S. Bliss. Small-scale self-focusing effects in a high power glass laser amplifier［J］. IEEE J. Quantum Electron., 1978, QE-14(5): 353～363

[8] S. R. Jokipii, J. Marbmger. Homogeneity requirements for minimizing self-focusing damage by strong electromagnetic waves［J］. Appl. Phys. Lett., 1973, 23(12): 696～698

[9] S. B. Trenholm. Small-scale instability growth [R]. Lawrence Livermore-Laboratory Laser Program Annual Report-1974, 1975 UCRL50021-74: 179～191

[10] N. B. Baranova, N. E. Bykovskii, B. Yazel′dovich et al.. Diffraction and self-focusing during amplification of high-power light pulses. I. development of diffraction and self-focusing in an amplifier［J］. Sov. J. Quantum Elecron., 1975, 4(11): 1354～1361

[11] 文双春, 范滇元. 非线性自聚焦介质中光束的非傍轴传输［J］. 中国激光, 2001, A28(12): 1066～1070

    Wen Shuangchun, Fan Dianyuan. Non-paraxial propagation of optical beams in nonlinear self-focusing media［J］. Chinese J. Lasers, 2001, A28(12): 1066～1070

[12] 文双春, 范滇元. 增益(损耗)介质中的高功率激光束的小尺度自聚焦理论研究［J］. 物理学报, 2000, 49(7): 1282～1286

    Wen Shuangchun, Fan Dianyuan. Theory of small-scale self-focusing of intense laser beams in media with gain and loss［J］. Acta Physica Sinica, 2000, 49(7): 1282～1286

[13] 文双春, 范滇元. 光束成丝的非线性理论［J］. 光学学报, 2001, 21(12): 1458～1462

    Wen Shuangchun, Fan Dianyuan. Nonlinear theory of filamentation of intense laser beams［J］. Acta Optica Sinica, 2001, 21(12): 1458～1462

[14] W. Williams, J. Trenholme, C. Orth et al.. NIF design optimization [R]. Lawrence Livermore Laboratory Laser Program Quarterly Report, 1996, UCRL-LR-105821-96-4: 181～191

[15] Joshua E. Rothenberg. Pulse splitting during self-focusing in normally dispersive media［J］. Opt. Lett., 1992, 17(8): 583～585

[16] 冯则胡, 傅喜泉, 章礼富 等. 超短脉冲激光空间调制下小尺度自聚焦的实验研究［J］. 物理学报, 2008, 57(4): 2253～2259

    Feng Zehu, Fu Xiquan, Zhang Lifu et al.. Experimental research of small-scale self-focusing of ultrashort pulse with spatial modulation［J］. Acta Optica Sinica, 2008, 57(4): 2253～2259

[17] 张双根, 黄章超, 薛玉明 等. 准相位匹配晶体中超短脉冲传输的自聚焦效应［J］. 中国激光, 2010, 37(10): 2550～2553

    Zhang Shuanggen, Huang Zhangchao, Xue Yuming et al.. Self-focusing effect of ultra-short laser pulse propagation during quasi-phase matched crystal［J］. Chinese J. Lasers, 2010, 37(10): 2550～2553

[18] F. Shimizu. Numerical calculation of self-focusing and trapping of a short light pulse in Kerr liquids［J］. IBM J. Research and Development, 1973, 17(4): 286～289

[19] Kiessling Armin, Rausch Anne, Matusevich Vladislav et al.. Self-focusing in a BaTiO3 crystal without external electric fields［C］. SPIE, 2006, 6027: 60270B

[20] W. G. Wagner, H. A. Haus, J. H. Marburger. Large-scale self-trapping of optical beams in the paraxial ray approximation［J］. Phys. Rev., 1968, 175(1): 256～266

[21] A. L. Dyshko, V. N. Lugovoi, A. M. Prokhorov. Self-focusing of intense light beams［J］. JETP Lett., 1967, 6(5): 146～148

[22] M. D. Feit, J. A. Fleck, Jr. Beam nonparaxiality, filament formation, and beam breakup in the self-focusing of optical beams［J］. J. Opt. Soc. Am. B, 1988, 5: 633～640

[23] M. M. Loy, Y. R. Shen. Small-scale filaments in liquids and tracks of moving foci［J］. Phys. Rev. Lett., 1969, 22(19): 994～997

[24] E. S. Bliss, J. T. Hunt, P. A. Renard et al.. Whole-beam self-focusing, focal zoom [R]. Lawrence Livermore-Laboratory Laser Program Annual Report-1975, 1976, UCRL-50021-75: 225～227

[25] A. Dubik, A. Sarzynski. A study of the problem of propagation and focusing of laser radiation in an apertured super-Gaussian form［J］. J. Techn. Phys. Polish Acad. Sci., 1984, 25(3-4): 441～445

[26] P. L. Kelly. Self-focusing of optical beams［J］. Phys. Rev. Lett., 1965, 15(26): 1005～1008

[27] J. Murray, R. Sacks, J. Auerbach et al.. Laser requirements and performance [R]. Lawrence Livermore-Laboratory Laser Program Quarterly Report, 1996, UCRL-LR-105821-97-3: 99～105

[28] U. Roth, F. Loewenthal, R. Tommasini et al.. Compensation of nonlinear self-focusing in high-power lasers［J］. IEEE J. Quantum Electron., 2000, 36(6): 687～691

[29] G. M. Muslu, H. A. Erbay. High-order split-step Fourier schemes for the generalized nonlinear Schrodinger equation［J］. Math. Comput. Simulat., 2005, 67(6): 581～595

[30] M. D. Feit, J. A. Fleck. Light propagation in graded-index optical fibers［J］. Appl. Opt., 1978, 17(24): 3990～3998

[31] H. M. Ozaktas, B. Barshan, D. Mendlovic. Fractional Fourier transforms as a tool for analyzing beam propagation and spherical mirror resonators［J］. Opt. Lett., 1994, 19(21): 1678～1680

[32] H. Bercegol, L. Lamaignère, B. Le Garrec et al.. Self-focusing and rear surface damage in a fused silica window at 1064 nm and 355 nm［C］. SPIE, 2003, 4392: 276～285

[33] J. T. Hunt, P. A. Renard, W. W. Simmons. Improved performance of fusion lasers using the imaging properties of multiple spatial filters［J］. Appl. Opt., 1977, 16(4): 779～782

[34] 邵敏, 傅海威, 罗小东 等. 高功率激光系统中B积分的研究［J］. 光学与光电技术, 2007, 5(6): 1～4

    Shao Min, Fu Haiwei, Luo Xiaodong et al.. B integral in high power laser system［J］. Optics & Optoelectronic Technology, 2007, 5(6): 1～4

[35] C. Bibeau, D. R. Speck, R. B. Ehrlich et al.. Power, energy, and temporal performance of the Nova laser facility with recent improvements to the amplifier system［J］. Appl. Opt., 1992, 31(27): 5799～5809

[36] Hidetsugu Yoshida, Hisanori Fujita, Masahiro Nakatsuka et al.. Dependences of laser-induced bulk damage threshold and crack patterns in several nonlinear crystals on irradiation direction［J］. Jpn J. Appl. Phys., 2006, 45(2A): 766～769

[37] 李恪宇, 向勇, 冯斌 等. 高强度三倍频近场测量实验与模拟计算的误差分析［J］. 强激光与粒子束, 2002, 14(5): 731～734

    Li Keyu, Xiang Yong, Feng Bin et al.. Analysis of the errors between measurement and simulation of near field for high-intensity THG［J］. High Power Laser and Particle Beams, 2002, 14(5): 731～734

[38] Fang Wang, Jingqin Su, Wenyi Wang et al.. Influence of medium-high frequency phase aberrations on 3ω focal spot in frequency tripling［J］. Chin. Opt. Lett., 2007, 5(s): 190～193

[39] P. Wegner, J. Auerbach, T. Biesiada et al.. NIF final optics system: frequency conversion and beam conditioning［C］. SPIE, 2004, 5341: 180～189

[40] 余文炎, 郑玉霞, 谢梓铭 等. 一种直接测定高功率激光系统“B积分”的方法［J］. 光学学报, 1985, 5(1): 19

    Yu Wenyan, Zheng Yuxia, Xie Zhimin et al.. A method of directly measuring B-integral in a high power laser system［J］. Acta Optica Sinica, 1985, 5(1): 19

[41] A. Adolf, D. Chatrefou, D. Euzenne et al.. Spatial frequencies generation in an optical nonlinear medium［J］. J. Appl. Phys., 1984, 55(11): 4116～4119

[42] J. T. Hunt, J. A. Glaze, W. W. Simmons et al.. Suppression of self-focusing through low-pass spatial filtering and relay imaging［J］. Appl. Opt., 1978, 17(13): 2053～2057

[43] K. Fujioka, S. Matsuo, T. Kanabe et al.. Optical properties of rapidly grown KDP crystal improved by thermal conditioning［J］. J. Crystal. Growth., 1997, 181(3): 265～271

[44] N. B. Baranova, N. E. Bykovskii, B.Ya. Zel′dovich et al.. Diffraction and self-focusing during amplification of high-power light pulses. II. Suppression of harmful influence of diffraction and self-focusing on a laser beam［J］. Sov. J. Quantum Electron., 1975, 4(11): 1362～1366

[45] V. R. Costich, B. C. Johnson. Apertures to shape high-power laser beams［J］. Laser Focus, 1974, 10(9): 43～46

[46] B. G. Gorshkov, V. K. Ivanchenko, V. K. Karpovich et al.. Apodizing induced-absorption apertures with a large optical beam diameter and their application in high-power 1.06 mm laser systems［J］. Sov. J. Quantum Electron., 1985, 15(7): 959～962

[47] S. G. Lukishova. Apodized Apertures for Visible and Near-Infrared Band Powerful Lasers [M]. SPIE Milestone Series, Selected Papers on Apodization: Coherent Optical Systems, J. P. Mills and B.J. Thomson (Eds.), 1996, MS 119: 334～341

[48] 章礼富, 傅喜泉, 冯则胡 等. 脉冲啁啾对空间小尺度自聚焦影响的实验研究［J］. 中国科学(G辑：物理学，力学和天文学), 2008, 38(10): 1372～1379

    Zhang Lifu, Fu Xiquan, Feng Zehu et al.. Experimental research on the influence of chirped pulse on small-scale self-focusing［J］. Science in China (Series G:Physics, Mechanics & Astronomy), 2008, 38(10): 1372～1379

[49] P. W. McKenty, J. H. Kelly, R. W. Short et al.. Self-focusing of broad bandwidth laser light [R]. LLE/LLNL Workshop Laser Science and ICF Target Science Collaborative Research, 1992, Rochester

[50] M. P. Vanyukov, V. I. Kryzhanovskii, V. A. Serebryakov et al.. Laser systems for the generation of picosecond high-irradiance light pulses［J］. Sov. J. Quantum Electron., 1972, 1(5): 483～488

[51] Yu. V. Senatskii. Active elements for high-power neodymium lasers［J］. Sov. J. Quantum Electron., 1972, 1(5): 521～523

[52] Yanli Zhang, Xiaoyan Li, Yan Zhang et al.. Small-scale self-focusing of divergent beam in nonlinear media with loss［J］. Chin. Opt. Lett., 2010, 8(2): 210～212

[53] 张艳丽, 李小燕, 朱健强. 增益介质中发散光束的小尺度自聚焦［J］. 光学学报, 2009, 29(3): 786～793

    Zhang Yanli, Li Xiaoyan, Zhu Jianqiang. Small-scale self-focusing of divergent beams in gain medium［J］. Acta Optica Sinica, 2009, 29(3): 786～793

[54] 顾亚龙, 朱健强. 发散光束小尺度自聚焦特性的研究［J］. 光学学报, 2006, 26(11): 1734～1738

    Gu Yalong, Zhu Jianqiang. Small-scale self-focusing of divergent beams［J］. Acta Optica Sinica, 2006, 26(11): 1734～1738

[55] A. A. Mak, V. A. Serebryakov, V. E. Yashin. Suppression of Self-Focusing in Spatially Incoherent Light Beams [M]. SPIE Milestone Series, Selected Papers on High-Power Lasers, J.M. Soures (Eds.), 1991, MS 43: 460～461

[56] R. H. Lehmberg, S. P. Obenschain. Use of induced spatial incoherence for uniform illumination of laser fusion targets［J］. Opt. Commun., 1983, 46(1): 27～31

[57] S. I. Fedotov, L. P. Feoktistov, M. V. Osipov et al.. Laser for ICF with a controllable function of mutual coherence of radiation［J］. J. Sov. Laser Res., 2004, 25(1): 79～92

[58] P. Donnat, C. Gouedard, D. Veron et al.. Induced spatial incoherence and nonlinear effects in Ndglass amplifiers［J］. Opt. Lett., 1992, 17(5): 331～333

[59] D. Auric, A. Labadens. On the use of a circulary polarized beam to reduce the self-focusing effect in a glass rod amplifier［J］. Opt. Commun., 1977, 21(2): 241～242

[60] S. N. Vlasov, V. I. Kryzhanovski, V. E. Yashin. Use of circularly polarized optical beams to suppress self-focusing instability in a nonlinear cubic medium with repeaters［J］. Sov. J. Quantum Electron., 1982, 12(1): 7～10

[61] G. Fibich, B. Ilan. Self-focusing of circularly polarized beams［J］. Phys. Rev. E, 2003, 67(3): 036622

[62] W. W. Simmons, W. F. Hagen, J. T. Hunt et al.. Performance improvements through image relaying [R]. Lawrence Livermore-Laboratory Laser Program Annual Report-1976, 1977, UCRL-50021-76: 2-19-2-28

[63] W. W. Simmons, J. E. Murray, F. Rainer et al.. Design, theory, and performance of a high-intensity spatial filter [R]. Lawrence Livermore-Laboratory Laser Program Annual Report-1974, 1975, UCRL-50021-74: 169～174

[64] V. N. Alekseev, A. D. Starikov, A. V. Charukhchev et al.. Enhancement of the brightness of radiation from a high-power phosphate-glass Nd3+ laser by spatial filtering of the beam in an amplifying channel［J］. Sov. J. Quantum Electron., 1979, 9(8): 981～984

[65] J. B. Trenholme. Theory of irregularity growth on laser beams [R]. Lawrence Livermore Laboratory Laser Program Annual Report-1975,1976, UCRL-50021-75: 237～242

[66] S. M. Babichenko, N. E. Bykovski, Yu. V. Senatski. Feasibility of reducing nonlinear losses in the case of small-scale self-focusing in a piecewise-continuous medium［J］. Sov. J. Quantum Electron., 1982, 12(1): 105～107

[67] A. A. Mak, L. N. Soms, V. A. Fromzel et al.. Ndglass Lasers [M]. Moscow: Nauka, 1990. 288

[68] J. M. Auerbach, C. Barker, P. J. Wenger et al.. Frequency tripling of beam noise［C］. SPIE, 3047: 381～386

[69] A. N. Zherikhin, Yu. A. Matveets, S. V. Chekalin. Self-focusing limitation of brightness in amplification of ultrashort pulses in neodymium glass and yttrium aluminum garnet［J］. Sov. J. Quantum Electron., 1976, 6(7): 858～860

[70] P. G. Kryukov, Yu. A. Matveets, Yu. V. Senatskii et al.. Mechanisms of radiation energy and power limitation in the amplification of ultrashort pulses in neodymium glass lasers［J］. Sov. J. Quantum Electron., 1973, 3(1): 161～162

[71] A. E. Siegman. Small-scale self-focusing effects in tapered optical beams, 2002, www.stanford.edu/_siegman/self_focusing_memo.pdf

[72] A. Baltuska, Z. Wei, M. S. Pshenichnikov et al.. Optical pulse compression to 5 fs at a 1 MHz repetition rate［J］. Opt. Lett., 1997, 22(2): 102～104

[73] A. A. Zozulya, S. A. Diddams, A. G. van Engen et al.. Propagation dynamics of intense femtosecond pulses: Multiple splittings, coalescence, and continuum generation［J］. Phys. Rev. Lett., 1999, 82(7): 1430～1433

[74] https://www.llnl.gov/news/newsreleases/2010/nnsa/NR-NNSA-10-10-02.html

[75] N. V. Didenko, A. V. Konyashchenko, A. P. Lutsenko et al.. Contrast degradation in a chirped-pulse amplifier due to generation of prepulses by postpulses［J］. Opt. Express, 2008, 16(5): 3178～3190

[76] 李小燕, 张艳丽, 欧阳小平 等. 寄生反射对高功率激光小尺度自聚焦的影响［J］. 中国激光, 2010, 37(11): 2844～2848

    Li Xiaoyan, Zhang Yanli, Ouyang Xiaoping et al.. Effect of reflection on high power small-scale self-focusing［J］. Chinese J. Lasers, 2010, 37(11): 2844～2848