全息空间光孤子的理论研究
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摘要
在光学介质中,横相位调制一度被认为只能伴随着自相位调制出现,不能单独存在,直到一种新型的空间光孤子—全息空间光孤子在光折变介质中提出才给出了一种横相位调制单独存在的方式。对全息光孤子,两束相干光之间由于干涉在介质中形成折射率光栅,两束光在通过该光栅时发生布拉格衍射产生横相位调制,使得两束光同时被捕获形成空间光孤子。每束光都是全息孤子的一个必不可少的分量,因为单独一束光是不可能形成孤子的。
由于全息光孤子的独特性,它吸引了人们越来越多的研究兴趣。在本论文中,我们主要研究了哈密顿系统中全息明孤子所诱导波导的特性,耗散系统中全息孤子的稳定性以及哈密顿系统和耗散系统中的全息孤子解的问题。
根据哈密顿系统中全息孤子的理论模型,我们考察了哈密顿系统中两分量相同的全息明孤子所形成波导的特性,发现波导可能的导模数主要依赖于孤子的峰值强度和背景光之间的强度比,导模数随着比值的增加而单调增加。我们对导模以及正弦波、余弦波在波导中的动态演化做了数值模拟。结果显示,由这种明全息孤子所诱导的波导可以用来实现对某一维上有周期性并具有慢变包络振幅的探测波的导引。
在已有的关于耗散系统全息空间光孤子的理论模型中,一束光输出能量给另一束光,输出能量的光为泵浦光,能量流入的光为信号光,并认为泵浦光的强度为常数并忽略它的演化。对由该模型所得到的耗散全息孤子解,我们通过用数值模拟的方法研究系统参数,如介质的吸收、外电场等,对孤子的稳定传播的影响,考察了这种孤子解的稳定性。同时也用理论分析的方法研究了这种孤子解的稳定性。数值分析和理论分析的结果都显示泵浦光强为常数的耗散全息孤子模型所给出的信号光孤子解对微扰具有稳定性。但是进一步的研究表明当泵浦光强为常数时系统会出现泵浦光清空以及泵浦光调制不稳定性,这两种效应又会极大的影响信号孤子光的稳定传播。因此需要在考虑忽略泵浦光演化的基础上寻找更合适的耗散全息孤子解。
为了得到哈密顿系统中两分量不同的全息孤子解,我们通过两个模式耦合的方法得到了哈密顿系统中两分量显著不同的全息孤子解以及任意振幅的全息孤子解。我们发现两个同阶模式之间的耦合可以得到单峰-单峰、双峰-双峰、多峰-多峰组合的任意振幅的全息孤子解,两个不同阶数模式之间的耦合可以得到单峰-双峰,单峰-多峰,双峰-多峰组合的全息孤子解。同时在每一个组合中又包括了很多可能的孤子解,涵盖了从一般到特殊的很多种的情况,极大的丰富了全息孤子解的形式,也扩大了全息孤子解参数的取值范围。另一方面,模式耦合的方法可以推广到耗散系统中,得到不存在调制不稳定性的耗散全息孤子解。而且,在这样一种模式耦合的过程中可以看到模式以及峰值强度对横相位调制的影响,从而横相位调制有更深的了解。
In optically materials, cross-phase modulation (XPM) has been traditionally believed to be always accompanied by self-phase modulation (SPM). However, a new kind of spatial solitons, holographic solitons, has been suggested theoretically in photorefractive media and can be supported by strong XPM but lack SPM altogether. For holographic solitons, the interference of two mutually coherent beams will induce a grating in refractive index and lead to simultaneous trapping of the two beams in a form of spatial solitons via XPM, arising from Bragg diffraction from the induced grating. The presence of both beams is required and each beam is a necessary component of a holographic soliton, since each beam alone cannot survive as a soliton if the other beam is absent. A considerable research interest has been invested in the study of holographic solitons due to its specialty.
In this dissertation we investigate theoretically the properties of waveguide induced by holographic solitons in Hamiltonian system, and the stability of holographic soliton solutions in dissipative system (DHS), and holographic soliton solutions with two significantly different components in both Hamiltonian system and dissipative system.
Based on the theoretical model of holographic solitons in Hamiltonian system, we analyze the properties of waveguided induced by bright holographic solitons with two identical components. We find that the number of possible guided modes in such waveguide is solely dependent on the intensity ratio of the soliton, which is the ratio between the soliton max intensity and the sum of background illumination. The number of guided modes increases monotonically with increasing intensity ratio. We perform numerical simulation of the wave guiding in such waveguide for guided mode beams and cosine waves and sine waves. The results imply that it is possible to realize the wave guiding in the bright holographic soliton-induced waveguide for a probe beam periodic in one dimension and with slowly varying amplitude.
In a proposed model for DHS, one beam can act as pump beam to supply energy for the other beam, which behaves as the signal beam. And the intensity of pump beam has been considered as constant so that the evolution of pump beam is ignored. Based on such model, a numerical study is performed on the stability property of DHS solutions through analyzing the role of every single system parameter, such as the linear loss of the crystal, the external biased field. For comparison, a theoretic analysis on the stability of DHS solutions is presented. Both numerical result and theoretic result indicate the signal soliton beam is stable against small perturbation under the assumption that the evolution of pump beam is ignored. However, further investigation reveals that the assumption of constant pump beam intensity will bring the depleted effect and the modulational instability (MI) on pump beam, which can greatly influence the stable propagation of signal beam. Proper DHS solutions should be obtained in the model with the evolution of pump beam.
In order to obtain the holographic soliton solutions with two constituents significantly dissimilar, a mode coupling method is applied in Hamiltonian system. The coupling between two modes of the same mode-order will give rise to single hump-single hump, two humps-two humps, and multihumps-multihumps holographic soliton solutions with arbitrary amplitude. And the coupling between two modes of different mode-order can generate single hump-two humps, two humps-multihumps, and single hump-two humps holographic soliton solutions. These results will lead to the enormously various shapes for holographic solitons and greatly enriches the form of holographic solitons, and expand the range of parameters of holographic solitons. On the other hand, the mode coupling method can be extended to dissipative system and find the corresponding DHS solutions without the MI on pump beam. Moreover, a clear vision on XPM can be available through such mode coupling processes, especially the influence induced by mode-order as well as the peak intensity of soliton on XPM.
由于全息光孤子的独特性,它吸引了人们越来越多的研究兴趣。在本论文中,我们主要研究了哈密顿系统中全息明孤子所诱导波导的特性,耗散系统中全息孤子的稳定性以及哈密顿系统和耗散系统中的全息孤子解的问题。
根据哈密顿系统中全息孤子的理论模型,我们考察了哈密顿系统中两分量相同的全息明孤子所形成波导的特性,发现波导可能的导模数主要依赖于孤子的峰值强度和背景光之间的强度比,导模数随着比值的增加而单调增加。我们对导模以及正弦波、余弦波在波导中的动态演化做了数值模拟。结果显示,由这种明全息孤子所诱导的波导可以用来实现对某一维上有周期性并具有慢变包络振幅的探测波的导引。
在已有的关于耗散系统全息空间光孤子的理论模型中,一束光输出能量给另一束光,输出能量的光为泵浦光,能量流入的光为信号光,并认为泵浦光的强度为常数并忽略它的演化。对由该模型所得到的耗散全息孤子解,我们通过用数值模拟的方法研究系统参数,如介质的吸收、外电场等,对孤子的稳定传播的影响,考察了这种孤子解的稳定性。同时也用理论分析的方法研究了这种孤子解的稳定性。数值分析和理论分析的结果都显示泵浦光强为常数的耗散全息孤子模型所给出的信号光孤子解对微扰具有稳定性。但是进一步的研究表明当泵浦光强为常数时系统会出现泵浦光清空以及泵浦光调制不稳定性,这两种效应又会极大的影响信号孤子光的稳定传播。因此需要在考虑忽略泵浦光演化的基础上寻找更合适的耗散全息孤子解。
为了得到哈密顿系统中两分量不同的全息孤子解,我们通过两个模式耦合的方法得到了哈密顿系统中两分量显著不同的全息孤子解以及任意振幅的全息孤子解。我们发现两个同阶模式之间的耦合可以得到单峰-单峰、双峰-双峰、多峰-多峰组合的任意振幅的全息孤子解,两个不同阶数模式之间的耦合可以得到单峰-双峰,单峰-多峰,双峰-多峰组合的全息孤子解。同时在每一个组合中又包括了很多可能的孤子解,涵盖了从一般到特殊的很多种的情况,极大的丰富了全息孤子解的形式,也扩大了全息孤子解参数的取值范围。另一方面,模式耦合的方法可以推广到耗散系统中,得到不存在调制不稳定性的耗散全息孤子解。而且,在这样一种模式耦合的过程中可以看到模式以及峰值强度对横相位调制的影响,从而横相位调制有更深的了解。
In optically materials, cross-phase modulation (XPM) has been traditionally believed to be always accompanied by self-phase modulation (SPM). However, a new kind of spatial solitons, holographic solitons, has been suggested theoretically in photorefractive media and can be supported by strong XPM but lack SPM altogether. For holographic solitons, the interference of two mutually coherent beams will induce a grating in refractive index and lead to simultaneous trapping of the two beams in a form of spatial solitons via XPM, arising from Bragg diffraction from the induced grating. The presence of both beams is required and each beam is a necessary component of a holographic soliton, since each beam alone cannot survive as a soliton if the other beam is absent. A considerable research interest has been invested in the study of holographic solitons due to its specialty.
In this dissertation we investigate theoretically the properties of waveguide induced by holographic solitons in Hamiltonian system, and the stability of holographic soliton solutions in dissipative system (DHS), and holographic soliton solutions with two significantly different components in both Hamiltonian system and dissipative system.
Based on the theoretical model of holographic solitons in Hamiltonian system, we analyze the properties of waveguided induced by bright holographic solitons with two identical components. We find that the number of possible guided modes in such waveguide is solely dependent on the intensity ratio of the soliton, which is the ratio between the soliton max intensity and the sum of background illumination. The number of guided modes increases monotonically with increasing intensity ratio. We perform numerical simulation of the wave guiding in such waveguide for guided mode beams and cosine waves and sine waves. The results imply that it is possible to realize the wave guiding in the bright holographic soliton-induced waveguide for a probe beam periodic in one dimension and with slowly varying amplitude.
In a proposed model for DHS, one beam can act as pump beam to supply energy for the other beam, which behaves as the signal beam. And the intensity of pump beam has been considered as constant so that the evolution of pump beam is ignored. Based on such model, a numerical study is performed on the stability property of DHS solutions through analyzing the role of every single system parameter, such as the linear loss of the crystal, the external biased field. For comparison, a theoretic analysis on the stability of DHS solutions is presented. Both numerical result and theoretic result indicate the signal soliton beam is stable against small perturbation under the assumption that the evolution of pump beam is ignored. However, further investigation reveals that the assumption of constant pump beam intensity will bring the depleted effect and the modulational instability (MI) on pump beam, which can greatly influence the stable propagation of signal beam. Proper DHS solutions should be obtained in the model with the evolution of pump beam.
In order to obtain the holographic soliton solutions with two constituents significantly dissimilar, a mode coupling method is applied in Hamiltonian system. The coupling between two modes of the same mode-order will give rise to single hump-single hump, two humps-two humps, and multihumps-multihumps holographic soliton solutions with arbitrary amplitude. And the coupling between two modes of different mode-order can generate single hump-two humps, two humps-multihumps, and single hump-two humps holographic soliton solutions. These results will lead to the enormously various shapes for holographic solitons and greatly enriches the form of holographic solitons, and expand the range of parameters of holographic solitons. On the other hand, the mode coupling method can be extended to dissipative system and find the corresponding DHS solutions without the MI on pump beam. Moreover, a clear vision on XPM can be available through such mode coupling processes, especially the influence induced by mode-order as well as the peak intensity of soliton on XPM.
引文
[1] D. J. Korteweg, G.de.Vries. On the change of form of long waves advancing in a rectangular channel and on a new type of long stationary wave. Phil. Mag., 1895, 5: 422～443
[2] N. J. Zabusky, M. D. Kruskal. Interaction of "Solitons" in a collisionless plasma and the recurrence of initial states. Phys. Rev. Lett., 1965, 15: 240～243
[3] G. I. Stegeman, M. Segev. Optical spatial solitons and their interactions: universality and diversity. Science, 1999, 286: 1518～1523
[4] K. E. Lonngren. Soliton experiments in plasmas. Plasma Phys., 1983, 25: 943～982
[5] E. Polturak, P. G. N. devegvar, E. K. Zeise, et al. Solitonlike propagation of zero sound in superfluid 3He. Phys. Rev. Lett., 1981, 46: 1588～1591
[6] M. Mohebi, P. F. Aiello, G. Reali et al. Self-focusing in CS2 at 10.6mum. Opt. Lett., 1985, 10(8): 396～398
[7] J. S. Aitchison, A. M. Weiner, Y. Silberberg, et al. Observation of spatial optical solitons in a nonlinear glass waveguide. Opt. Lett., 1990, 15: 471～473
[8] J. S. Aitchison, K. Al-Hemyari, C. N. Ironside, et al. Observation of spatial solitons in AlGaAs waveguides. Electron. Lett., 1992, 28: 1879～880
[9] Xiao-sheng Wang, Wei-long She, Win-Kee Lee. Optical spatial solitons supported by photoisomerization nonlinearity in a polymer. Opt. Lett., 2004, 28(3): 277～279
[10] R. Y. Chiao, E. Garmire, C. H. Townes. Self-trapping of optical beams. Phys. Rev. Lett., 1964, 13: 479～482
[11] M. Hercher. Laser-induced damage in transparent media. J. Opt. Sov. Amer., 1964, 54: 563～569
[12] G. P. Agrawal. Nonlinear Fiber Optics. 1st ed. San Diego CA: Academic Press Inc., 1989. 150～198
[13] L. F. Mollenauer, R. H. Stolen, J. P. Gordon. Experimental observation of picosecond pulse narrowing and solitons in optical Fibers. Phys. Rev. Lett. 1980, 45: 1095～1098
[14] A. Hasegawa. Solitons in Optical Fibers. 1st ed. Berlin: Springer-Verlag, 1989. 121～140
[15] M. Nakazawa, E. Yamada, H. Kubota K. Suzuki. 10 Gbit/s soliton data transmission over one million kilometers. Electron. Lett., 1991, 27(14): 1270～1272
[16] J. E. Bjorkholm, A. Ashkin. Self-focusing and self-trapping of light in sodium vapor. Phys. Rev. Lett., 1974, 32: 129～132
[17] G. I. A. Stegeman, D. N. Christodoulides, M. Segev. Optical spatial solitons: historical perspectives. IEEE on selected Toptics in Quantum Electronics, 2000, 6(6): 1419～1427
[18] Ming-Feng Shih. Photorefractive screening solitons, their induced waveguides and interactions: [doctoral dissertation]. Princeton University: the Department of Electrical Engineering, 1998
[19] G. A. Askar,yan. Effects of the gradient of a strong electromagnetic beam on electrons and atoms. Sov. Phys. JETP, 1962, 15: 1088～1090
[20] A. W. Snyder, D. J. Mitchell, L. Polodian et al. Self-induced optical fibers: spatial solitary waves. Opt. Lett., 1991, 16: 21～23
[21] W. Snyder, A. P. Sheppard. Collisions, steering, and guidance with spatial solitons. Opt. Lett., 1993, 18: 482～484
[22] W. Snyder, S. J. Hewlett, D. J. Mitchell. Dynamic spatial solitons. Phys. Rev. Lett., 1994, 72: 1012～1015
[23] Y. S. Kivshar, B. A. Malomed. Dynamic of solitons in nearly integrable systems. Rev. Mod. Phys., 1989, 61(4): 763～915
[24] Song Lan. Potorefractive spatial solitons, induced waveguides, and their application: [doctoral dissertation]. Princeton University: the Department of Electrical Engineering, 2002
[25] V. I. Talanov. On self-focusing of electromagnetic waves in nonlinear media. Radio Phys., 1964, 7: 254～260
[26] P. L. Kelley. Self-focusing of optical beams. Phys. Rev. Lett., 1965, 15: 1005～1008
[27] V. E. Zakharov, A. M. Rubenchik. Instability of waveguides and solitons in nonlinearmedia. Sov. Phys. JETP, 1974, 38: 494～452
[28] M. Soljacic, S. Sears, M. Segev. Self-trapping of“necklace”beams in self-focusing Kerr media. Phys. Rev. Lett., 1998, 81: 4851～4854
[29] A. Barthelemy, C. Froehly, M. Shalaby. Nonlinear propagation of picosecond tubular beams: self phase modulation and induced refraction. Proceeding of SPIE, 1993, 2041: 104～113
[30] Barthelemy, S. Maneuf, C. Froehly. Propagation soliton et auto-confinement de faisceaux laser par non linearitéoptique de kerr. Opt. Commun., 1985, 55: 201～206
[31] U. Bartuch, U. Peschel, Th. Gabler, et al. Experimental investigations and numerical simulations of spatial solitons in planar polymer waveguides. Opt. Commun., 1997, 134: 49～54
[32] E. L. Dawes, J. H. Marburger. Computer studies in self-focusing. Phys. Rev., 1969, 179: 862～868
[33] M. Segev, B. Crosignani, A. Yariv et al. Spatial solitons in photorefractive media. Phys. Rev. Lett., 1992, 68: 923～926
[34] G. C. Duree, Jr., J. L. Shultz, G. J. Salamo et al. Observation of self-trapping of an optical beam due to the photorefractive effect. Phys. Rev. Lett., 1993, 71: 533～536
[35] A. Ashkin, G. D. Boyd, J. M. Dziedzic, et al. Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3. Appl. Phys. Lett., 1966, 9: 72～74
[36] P. Gunter, J. P. Huignard. Topics in applied physics in: Photorefractive Materials and Their Applications I, II. Berlin: Springer-Verlag, 1989. 61～62
[37] D. L. Steabler, J. J. Awodei. Coupled-wave analysis of holographic storage in LiNbO3. J. Appl. Phys., 1972, 43(3): 1042～1049
[38] F. S. Chen, J. T. LaMacchia, D. B. Fraser. Holographic storage in lithium niobate. Appl. Phys. Lett., 1968, 13: 223～225
[39] F. S. Chen. Optically induced change of refractive indices in LiNbO3 and LiTaO3. J. Appl. Phys., 1969, 40(8): 3389～3396
[40] A. M. Glass, D. von der Linde, T. J. Negran. High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3. Appl. Phys. Lett., 1974, 25: 233～235
[41] P. Yeh. Introduction to photorefractive non-linear optics. 1st ed. New York: John Wiley & Sons, Inc., 1993. 83～122
[42] M. Mitchell, M. Segev. Self-trapping of incoherent white light. Nature, 1997, 387: 880～883
[43] Z. Chen, M. Mitchell, M. Segev et al. Self-trapping of dark incoherent light beams. Science, 1998, 280: 889～892
[44] M.F-shih, Z. Chen, M. Mitchell et al. Waveguides induced by photorefractive screening solitons. J. Opt. Soc. Am. B, 1997, 14: 3091～3101
[45] Anastassiou, M-f Shih, M. Mitchell et al. Optically inducedphotovoltaic self-defocusing-to-self-focusing transition. Opt. Lett, 1998, 23: 924～926
[46] A. Cohen, T. Carmon, M. Segev et al. Holographic solitons. Opt. Lett., 2002, 27: 2031～2033
[47] M. Segev, G. C. Valley, B. Crosignani et al. Steady-state spatial screening solitons in photorefractive materials with external applied field. Phys. Rev. Lett., 1994, 73: 3211～3214
[48] N. Christodoulides, M. I. Carvalho. Bright, dark, and gray spatial soliton states in phtorefractive media. J. Opt. Sov. Am. B, 1995, 12: 1628～1633
[49] M. Segev, M. Shih, G. C. Valley. Photorefractive screening solitons of low and high intensity. J. Opt. Soc. Am. B, 1996, 13: 706～718
[50] M. Segev, A. Agranat. Spatial solitons incentrosymmetric photorefractive media. Opt. Lett., 1997, 22: 1299～1301
[51] M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon et al. Spatial solitons in photorefractive Bi12TiO20 with drift mechanism of nonlinearity. Appl. Phys. Lett, 1994, 64: 408～410
[52] M. Shih, M. Segev, G. C. Valley et al. Observation of two-dimensional steady-state photorefractive screening solitons. Electron. Lett., 1995, 31: 826～827
[53] M. Shih, M. Segev, G. C. Valley et al. Two-dimensional steady-state photorefractive screening solitons. Opt. Lett., 1996, 21: 324～326
[54] K. Kos, H. Ming, G. Salamo et al. One-dimensional steady-state photorefractivescreening solitons. Phys. Rev. E, 1996, 53: R4330～R4333
[55]刘思敏,郭儒,许京军.光折变非线性光学及其应用. (第一版).北京:科学出版社, 2004. 17～28
[56] G. C. Valley, M. Segev, B. Crosignani et al. Dark and bright photovoltaic spatial solitons. Phys. Rev. A, 1994, 50: R4457～R4460
[57] M. Taya, M. Bashaw, M. M. Fejer et al. Observation of dark photovoltaic spatial solitons. Phys. Rev. A, 1995, 52: 3095～3100
[58] M. Taya, M. Bashaw, M. M. Fejer et al. Y junctions arising from dark-soliton propagation in photovoltaic media. Opt. Lett., 1996, 21: 943～945
[59] Jinsong Liu, Keqing Lu. Screening-photovoltaic spatial solitons in biased photovoltaic-photorefractive crystals and their self-deflection. J. Opt. Soc. Am. B, 1999, 16: 550～555
[60] Fazio, F. Renzi, R. Rinaldi et al. Screening-photovoltaic bright solitons in lithium niobate and associatedsingle-mode waveguides. Appl. Phys. Lett, 2004, 85(12): 2193～2195
[61] A. A. Zozulya, D. Z. Anderson. Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field. Phys. Rev. A, 1995, 51: 1520～1531
[62] N. Fressengeas, J. Maufoy, G. Kugel. Temporal behavior of bidimensional photorefractive bright spatial solitons. Phys. Rev. E, 1996, 54: 6866～6875
[63] J. Maufoy, N. Fressengeas, D. Wolfersberger et al. Simulation of the temporal behavior of soliton propagation in photorefractive media. Phys. Rev. E, 1999, 59: 6116～6121
[64] Wolfersberger, N. Fressengeas, J. Maufoy et al. Self-focusing of a single laser pulse in a photorefractive medium. Phys. Rev. E, 2000, 62: 8700～8704
[65] M. D. Iturbe Castillo, J. J. Sanchez-Mondragon, S. I. Stepanov et al. (1 + 1)-Dimension dark spatial solitons in photorefractive Bi12TiO20 crystal. Opt. Commun., 1995, 118: 515～519
[66] Duree, M. Morin, G. Salamo et al. Dark photorefractive spatial solitons andphotorefractive vortex solitons. Phys. Rev. Lett., 1995, 74: 1978～1981
[67] M. I. Carvalho, S. R. Singh, D. N. Christodoulides. State bright spatial solitons in biased photorefractive crystals. Opt. Commun., 1995, 120: 311～315
[68] W. Królikowski, N. Akhmediev, B. Luther-Davies. Self-bending photorefractive solitons. Phys. Rev. E, 1996, 54: 5761～5765
[69] M. Morin, G. Duree, G. Salamo et al. Waveguides formed by quasi-steady-state photorefractive spatial solitons. Opt. Lett., 1995, 20: 2066～2068
[70] M. Shih, M. Segev, G. Salamo. Circular waveguides induced by two-dimensonal bright steady-state photorefractive screening solitons. Opt. Lett., 1996, 21: 931～933
[71] M. D. Iturbe-Castillo, M. Torres-Cisneros, J. J. Sanchez-Mondragon et al. Experimental evidence of modulational instability in a photorefractive Bi TiO crystal. Opt. Lett., 1995, 20: 1853～1855
[72] A. V. Mamaev, M. Saffman, D. Z. Anderson et al. Propagation of light beams in anisotropic nonlinear media: from symmetry breaking to spatial turbulence. Phys. Rev. A, 1996, 54: 870～879
[73] N. Fressengeas, D. Wolfersberger, J. Maufoy et al. Experimental study of the self-focusing process temporal behavior in photorefractive Bi TiO. J. Appl. Phys., 1999, 85: 2062～2067
[74] J. Tsai, A. Chiou, T. C. Hseih et al. One-dimensional self-focusing in photorefractive Bi SiO crystal: Theoretical modeling and experimental demonstration. Opt. Commun., 1999, 162: 237～240
[75] E. Fazio, F. Mariani, A. Funto et al. Experimental demonstration of (1+1) D self-confinement and breathing soliton-like propagation in photorefractive crystals with strong optical activity. Journal of Optics A: Pure and Applied Optics, 2001, 3: 466～469
[76] E. Fazio, V. Babin, M. Bertolotti et al. Solitonlike propagation in photorefractive crystals with large optical activity and absorption. Phys. Rev. E, 2002, 66: 016605～016616
[77] R. Ryf, M. Wiki, G. Montemezzani et al. Launching one-transverse-dimensionalphotorefractive solitons in KnbO crystals Opt. Commun., 1999, 159: 339～348
[78] R. Uzdin, M. Segev, G. J. Salamo. Theory of self-focusing in photorefractive InP. Opt. Lett., 2001, 26: 1547～1549
[79] R. Ryf, G. Montemezzani, P. Gunter et al. High-frame-rate joint Fourier-transform correlator based on Sn2P2S6 crystal. Opt. Lett., 2001, 26: 1666～1668
[80] S. Lan, M.-f. Shih, M. Segev. Self-trapping of one-dimensional and two-dimensional optical beams and induced waveguides in photorefractive KnBO. Opt. Lett., 1997, 22: 1467～1469
[81] M. Chauvet, S. Hawkins, G. Salamo et al. Self-trapping of planar optical beams by use of the photorefractive effect in InP:Fe. Opt. Lett., 1996, 21: 1333～1335
[82] T. Schwartz, Y. Ganor, T. Carmon et al. Photorefractive solitons and light-induced resonance control in semiconductor CdZnTe. Opt. Lett., 2002, 27: 1229～1231
[83] E. DelRe, B. Crossignani, M. Tamburrini et al. One-dimensional steady-state photorefractive spatial solitons in centrosymmetric paraelectric KLTN. Opt. Lett., 1998, 23: 421～423
[84] P. Agrawal. Nonlinear fiber optics. 2nd ed. San Diego, CA: Academic Press Inc., 1995. 253～262
[85] Y. N. Karamzin, A. P. Sukhorukov. Mutual focusing of high-power light beams in media with quadratic nonlinearity. Sov. Phys. JETP, 1976, 41: 414～416
[86] W. E. Torruellas, Z. Wang, D. J. Hagan et al. Observation of two-dimensional spatial solitary waves in a quadratic medium. Phys. Rev. Lett., 1995, 74: 5036～5039
[87] M. Vaupel, C. Seror, R. Dykstra. Self-focusing in photo refractive two-wave mixing. Opt. Lett., 1997, 22: 1470～1472
[88] M. Vaupel, O. Mandel, N.R. Heckenberg. Two-wave-mixing induced self-focusing in an active photorefractive oscillator. Journal of Optics B: Quantum and Semiclassical Optics, 1999, 1: 96～100
[89] Shvets, A. Pukhov. Electromagnetically induced guiding of counterpropagating lasers in plasmas. Phys. Rev. E., 1999, 59: 1033～1037
[90] Jinsong Liu. Holographic solitons in photorefractive dissipative systems. Opt. Lett.,2003, 28: 2237～2239
[91] R. Salgueiro, A. A. Sukhorukov, Yu. S. Kivshar. Spatial optical solitons supported by mutual focusing. Opt. Lett., 2003, 28: 1457～1459
[92] O. Cohen, B. Freedman, J. W. Fleischer et al. Grating-Mediated Waveguiding. Phys. Rev. Lett., 2004, 93: 103902_1～103902_4
[93] B. Freedman, O. Cohen, O. Manela et al. Grating-mediated wave guiding and holographic solitons. J. Opt. Soc. Am. B, 2005, 22: 1349～1355
[94] O. Cohen, M. M. Murnane, H. C. Kapteyn. Cross-phase-modulation nonlinearities and holographic solitons in periodically poled photovoltaic photorefracives. Opt. Lett., 2006, 31: 954～956
[95] Z. Chen, M. Segev, T. H. Coskun et al. Coupled photorefractive spatial-soliton pairs. J. Opt. Soc. Am. B, 1997, 14: 3066～3077
[96] Jinsong. Liu. Existence and property of spatial solitons in a photorefractive dissipative system. J. Opt. Soc. Am. B, 2003, 20: 1732～1738
[97] Jinsong. Liu. Existence and stability of rigid photovoltaic solitons in an open-circuit amplifying or absorbing photovoltaic medium. Phys. Rev. E, 2003, 68: 026607_1～026607_7
[98] Jinsong Liu, H. J. Eichler. Holographic screening-photovoltaic solitons in biased photovoltaic-photorefractive crystals with two-wave mixing. Europhys. Lett., 2004, 65: 658～664
[99] Z. Chen, M. Segev, T. Coskun et al. Observation of incoherently coupled photorefractive spatial soliton pairs. Opt. Lett., 1996, 21: 1436～1438
[100] Z. Chen, M. Segev, T. Coskun et al. Incoherently coupled dark-bright photorefractive solitons. Opt. Lett., 1996, 21: 1821～1823
[101] M. Shalaby, A. J. Barthelemy. Observation of the self-guided propagation of a dark and bright spatial soliton pair in a focusing nonlinear medium. IEEE J. Quantum Electron., 1992, 28: 2736～2741
[102] S. Trillo, S. Wabnitz, E. M. Wright et al. Optical solitary waves induced by cross-phase modulation. Opt. Lett., 1988, 13: 871～873
[103] N. Christodoulides, S. R. Singh, M. I. Carvalho et al. Incoherently coupled soliton pairs in biased photorefractive crystals. Appl.Phys. Lett., 1996, 68: 1763～1765
[104] S. V. Manakov. On the theory of two-dimensional stationary self-focusing of electronmagnetic wave. Sov. Phys. JETP, 1974, 38: 248～253
[105] U. Kang, G. I. Stegeman, J. S. Aitchison et al. Observation of Manakov Spatial Solitons in AlGaAs Planar Waveguides. Phys.Rev. Lett., 1996, 76: 3699～3702
[106] M. Dianov, P. V. Mamyshev, A. M. Prokhorov et al. Generation of a train of fundamental solitons at a high repetition rate in optical fibers. Opt. Lett., 1989, 14: 1008～1010
[107] P. V. Mamyshev, C. Bosshard, G. I. Stegeman. Generation of a periodic array of dark spatial solitons in the regime of effective amplification. J. Opt. Sov. Am. B, 1994, 11: 1254～1260
[108] M. I. Carvalho, S. R. Singh, D. N. Christodoulides. Modulational instability of quasi-plane-wave optical beams biased in photorefractive crystals. Opt. Comm., 1996, 126: 167～174
[109] A. Hasegawa. Generation of a train of soliton pulses by induced modulational instability in optical fibers. Opt. Lett., 1984, 9: 288～230
[110] M. Artiglia, E. Ciaramella, P. Gallina. Demonstration of CW soliton trains at 10, 40 and 160 Ghz by means of induced modulation instability in: OSA Trends in Optics and Photonics. USA: OSA, 1997, 12: 305～308
[111] M. Soljacic, M. Segev, T. Coskun et al. Modulation instability of incoherent beams in noninstantaneous nonlinear media. Phys.Rev. Lett., 2000, 84: 467～470
[112] Kip, M. Soljacic, M. Segev et al. Modulation instability and pattern formation in spatially incoherent light beams. Science, 2000, 290: 495～498
[113] B. Whitham. A general approach to linear and nonlinear water waves using a Lagrangian. J. Fluid Mech., 1965, 22: 273～283
[114] Jinsong Liu, Huilan Zhang, Guangyong Zhang et al. Evolution and stability of spatial solitons in a photorefractive two-wave mixing system. Chinese Phys., 2006, 15(2): 394～402
[115] Jinsong Liu, D.Y.Zhang, C.H.Liang. Stability of bright screening-photovoltaic spatial solitons. Chin. Phys., 2000, 9: 667～671
[116] Z. G. Chen, M. Mitchell, M. Segev. Steady-state photorefractive soliton-induced Y-junction waveguides and high-order dark spatial solitons. Opt. Lett., 1996, 21: 716～718
[117] Luther-Davies, Y. P. Xiao. Waveguides and Y junctions formed in bulk media by using dark spatial solitons. Opt. Lett., 1992, 17: 496～498
[118] R. De La Fuente, A. Barthelemy, C. Froehly. Spatial-soliton-induced guided waves in a homogeneousnonlinear Kerr medium. Opt. Lett., 1991, 11: 793～795
[119] A. W. Snyder, D. J. Mitchell, B. Luther-Davies. Dark spatial solitons constructed from modes of linear waveguides. J. Opt. Soc. Am. B, 1993, 10: 2345～2356
[120] W. Snyder, D. J. Mitchell, L. Polodian et al. Observation of spatial optical solitons in a nonlinear glass waveguide. Opt. Lett., 1990, 15: 471～473
[121] E. A. Ostrovskaya, Yu. S. Kivshar. Nonlinear theory ofsoliton-induced waveguides. Opt. Lett., 1998, 23: 1268～1270
[122] P. Yeh. Two-wave mixing in nonlinear media. IEEE J. Quantum Electron. 1989, 25: 484～519
[123] Oda, Y. Otani, L. Liu et al. Polarization effect for vibration detection using photorefractive two-wave mixing in KNSBN: Cu crystals. Opt. Commun., 1998, 148: 95～100
[124] P. Huignard, A. Marrakchi. Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20 crystals. Opt. Commun., 1981, 38: 249～254
[125] Jinsong Liu, Yinyuan Zhang, Hans J. Eichler. Dynamical evolution of dissipative holographic solitons in photorefractive media via two-wave mixing with a moving grating. Journal of Modern Optic, 2005, 52(4): 563～572
[126] N. N. Akhmediev, V. V. Afanasjev. Novel arbitrary-amplitude soliton solutions of the cubic-quintic complex Ginzburg-Landau equation. Phys. Rev. Lett., 1995, 75: 2320～2323
[127]刘劲松.非对称光折变全息空间光孤子的存在曲线.物理学报, 2004, 53(9): 3014～3019
[128] N. N. Akhmediev, V. V. Afanasjev, J. M. Soto-Crespo. Singularities and special soliton solutions of the cubic-quintic complex Ginzburg-Landau equation. Phys. Rev. E, 1996, 53: 1190～1201
[129] N. N. Akhmediev, V. V. Afanasjev. Spatial solitons. 1st ed. Berlin: Springer, 2001. 20～66
[130] J. M. Soto-Crespo, N. N. Akhmediev, V. V. Afanasjev. Stability of the pulselike solutions of the quintic complex Ginzburg-Landau equation. J. Opt. Soc. Am. B, 1996, 13: 1439～1449
[131] Y. Silberberg, G. I. Stegeman. Spatial Solitons. 1st ed. Berlin: Springer-Verlag, 2001. 37～60
[2] N. J. Zabusky, M. D. Kruskal. Interaction of "Solitons" in a collisionless plasma and the recurrence of initial states. Phys. Rev. Lett., 1965, 15: 240～243
[3] G. I. Stegeman, M. Segev. Optical spatial solitons and their interactions: universality and diversity. Science, 1999, 286: 1518～1523
[4] K. E. Lonngren. Soliton experiments in plasmas. Plasma Phys., 1983, 25: 943～982
[5] E. Polturak, P. G. N. devegvar, E. K. Zeise, et al. Solitonlike propagation of zero sound in superfluid 3He. Phys. Rev. Lett., 1981, 46: 1588～1591
[6] M. Mohebi, P. F. Aiello, G. Reali et al. Self-focusing in CS2 at 10.6mum. Opt. Lett., 1985, 10(8): 396～398
[7] J. S. Aitchison, A. M. Weiner, Y. Silberberg, et al. Observation of spatial optical solitons in a nonlinear glass waveguide. Opt. Lett., 1990, 15: 471～473
[8] J. S. Aitchison, K. Al-Hemyari, C. N. Ironside, et al. Observation of spatial solitons in AlGaAs waveguides. Electron. Lett., 1992, 28: 1879～880
[9] Xiao-sheng Wang, Wei-long She, Win-Kee Lee. Optical spatial solitons supported by photoisomerization nonlinearity in a polymer. Opt. Lett., 2004, 28(3): 277～279
[10] R. Y. Chiao, E. Garmire, C. H. Townes. Self-trapping of optical beams. Phys. Rev. Lett., 1964, 13: 479～482
[11] M. Hercher. Laser-induced damage in transparent media. J. Opt. Sov. Amer., 1964, 54: 563～569
[12] G. P. Agrawal. Nonlinear Fiber Optics. 1st ed. San Diego CA: Academic Press Inc., 1989. 150～198
[13] L. F. Mollenauer, R. H. Stolen, J. P. Gordon. Experimental observation of picosecond pulse narrowing and solitons in optical Fibers. Phys. Rev. Lett. 1980, 45: 1095～1098
[14] A. Hasegawa. Solitons in Optical Fibers. 1st ed. Berlin: Springer-Verlag, 1989. 121～140
[15] M. Nakazawa, E. Yamada, H. Kubota K. Suzuki. 10 Gbit/s soliton data transmission over one million kilometers. Electron. Lett., 1991, 27(14): 1270～1272
[16] J. E. Bjorkholm, A. Ashkin. Self-focusing and self-trapping of light in sodium vapor. Phys. Rev. Lett., 1974, 32: 129～132
[17] G. I. A. Stegeman, D. N. Christodoulides, M. Segev. Optical spatial solitons: historical perspectives. IEEE on selected Toptics in Quantum Electronics, 2000, 6(6): 1419～1427
[18] Ming-Feng Shih. Photorefractive screening solitons, their induced waveguides and interactions: [doctoral dissertation]. Princeton University: the Department of Electrical Engineering, 1998
[19] G. A. Askar,yan. Effects of the gradient of a strong electromagnetic beam on electrons and atoms. Sov. Phys. JETP, 1962, 15: 1088～1090
[20] A. W. Snyder, D. J. Mitchell, L. Polodian et al. Self-induced optical fibers: spatial solitary waves. Opt. Lett., 1991, 16: 21～23
[21] W. Snyder, A. P. Sheppard. Collisions, steering, and guidance with spatial solitons. Opt. Lett., 1993, 18: 482～484
[22] W. Snyder, S. J. Hewlett, D. J. Mitchell. Dynamic spatial solitons. Phys. Rev. Lett., 1994, 72: 1012～1015
[23] Y. S. Kivshar, B. A. Malomed. Dynamic of solitons in nearly integrable systems. Rev. Mod. Phys., 1989, 61(4): 763～915
[24] Song Lan. Potorefractive spatial solitons, induced waveguides, and their application: [doctoral dissertation]. Princeton University: the Department of Electrical Engineering, 2002
[25] V. I. Talanov. On self-focusing of electromagnetic waves in nonlinear media. Radio Phys., 1964, 7: 254～260
[26] P. L. Kelley. Self-focusing of optical beams. Phys. Rev. Lett., 1965, 15: 1005～1008
[27] V. E. Zakharov, A. M. Rubenchik. Instability of waveguides and solitons in nonlinearmedia. Sov. Phys. JETP, 1974, 38: 494～452
[28] M. Soljacic, S. Sears, M. Segev. Self-trapping of“necklace”beams in self-focusing Kerr media. Phys. Rev. Lett., 1998, 81: 4851～4854
[29] A. Barthelemy, C. Froehly, M. Shalaby. Nonlinear propagation of picosecond tubular beams: self phase modulation and induced refraction. Proceeding of SPIE, 1993, 2041: 104～113
[30] Barthelemy, S. Maneuf, C. Froehly. Propagation soliton et auto-confinement de faisceaux laser par non linearitéoptique de kerr. Opt. Commun., 1985, 55: 201～206
[31] U. Bartuch, U. Peschel, Th. Gabler, et al. Experimental investigations and numerical simulations of spatial solitons in planar polymer waveguides. Opt. Commun., 1997, 134: 49～54
[32] E. L. Dawes, J. H. Marburger. Computer studies in self-focusing. Phys. Rev., 1969, 179: 862～868
[33] M. Segev, B. Crosignani, A. Yariv et al. Spatial solitons in photorefractive media. Phys. Rev. Lett., 1992, 68: 923～926
[34] G. C. Duree, Jr., J. L. Shultz, G. J. Salamo et al. Observation of self-trapping of an optical beam due to the photorefractive effect. Phys. Rev. Lett., 1993, 71: 533～536
[35] A. Ashkin, G. D. Boyd, J. M. Dziedzic, et al. Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3. Appl. Phys. Lett., 1966, 9: 72～74
[36] P. Gunter, J. P. Huignard. Topics in applied physics in: Photorefractive Materials and Their Applications I, II. Berlin: Springer-Verlag, 1989. 61～62
[37] D. L. Steabler, J. J. Awodei. Coupled-wave analysis of holographic storage in LiNbO3. J. Appl. Phys., 1972, 43(3): 1042～1049
[38] F. S. Chen, J. T. LaMacchia, D. B. Fraser. Holographic storage in lithium niobate. Appl. Phys. Lett., 1968, 13: 223～225
[39] F. S. Chen. Optically induced change of refractive indices in LiNbO3 and LiTaO3. J. Appl. Phys., 1969, 40(8): 3389～3396
[40] A. M. Glass, D. von der Linde, T. J. Negran. High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3. Appl. Phys. Lett., 1974, 25: 233～235
[41] P. Yeh. Introduction to photorefractive non-linear optics. 1st ed. New York: John Wiley & Sons, Inc., 1993. 83～122
[42] M. Mitchell, M. Segev. Self-trapping of incoherent white light. Nature, 1997, 387: 880～883
[43] Z. Chen, M. Mitchell, M. Segev et al. Self-trapping of dark incoherent light beams. Science, 1998, 280: 889～892
[44] M.F-shih, Z. Chen, M. Mitchell et al. Waveguides induced by photorefractive screening solitons. J. Opt. Soc. Am. B, 1997, 14: 3091～3101
[45] Anastassiou, M-f Shih, M. Mitchell et al. Optically inducedphotovoltaic self-defocusing-to-self-focusing transition. Opt. Lett, 1998, 23: 924～926
[46] A. Cohen, T. Carmon, M. Segev et al. Holographic solitons. Opt. Lett., 2002, 27: 2031～2033
[47] M. Segev, G. C. Valley, B. Crosignani et al. Steady-state spatial screening solitons in photorefractive materials with external applied field. Phys. Rev. Lett., 1994, 73: 3211～3214
[48] N. Christodoulides, M. I. Carvalho. Bright, dark, and gray spatial soliton states in phtorefractive media. J. Opt. Sov. Am. B, 1995, 12: 1628～1633
[49] M. Segev, M. Shih, G. C. Valley. Photorefractive screening solitons of low and high intensity. J. Opt. Soc. Am. B, 1996, 13: 706～718
[50] M. Segev, A. Agranat. Spatial solitons incentrosymmetric photorefractive media. Opt. Lett., 1997, 22: 1299～1301
[51] M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon et al. Spatial solitons in photorefractive Bi12TiO20 with drift mechanism of nonlinearity. Appl. Phys. Lett, 1994, 64: 408～410
[52] M. Shih, M. Segev, G. C. Valley et al. Observation of two-dimensional steady-state photorefractive screening solitons. Electron. Lett., 1995, 31: 826～827
[53] M. Shih, M. Segev, G. C. Valley et al. Two-dimensional steady-state photorefractive screening solitons. Opt. Lett., 1996, 21: 324～326
[54] K. Kos, H. Ming, G. Salamo et al. One-dimensional steady-state photorefractivescreening solitons. Phys. Rev. E, 1996, 53: R4330～R4333
[55]刘思敏,郭儒,许京军.光折变非线性光学及其应用. (第一版).北京:科学出版社, 2004. 17～28
[56] G. C. Valley, M. Segev, B. Crosignani et al. Dark and bright photovoltaic spatial solitons. Phys. Rev. A, 1994, 50: R4457～R4460
[57] M. Taya, M. Bashaw, M. M. Fejer et al. Observation of dark photovoltaic spatial solitons. Phys. Rev. A, 1995, 52: 3095～3100
[58] M. Taya, M. Bashaw, M. M. Fejer et al. Y junctions arising from dark-soliton propagation in photovoltaic media. Opt. Lett., 1996, 21: 943～945
[59] Jinsong Liu, Keqing Lu. Screening-photovoltaic spatial solitons in biased photovoltaic-photorefractive crystals and their self-deflection. J. Opt. Soc. Am. B, 1999, 16: 550～555
[60] Fazio, F. Renzi, R. Rinaldi et al. Screening-photovoltaic bright solitons in lithium niobate and associatedsingle-mode waveguides. Appl. Phys. Lett, 2004, 85(12): 2193～2195
[61] A. A. Zozulya, D. Z. Anderson. Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field. Phys. Rev. A, 1995, 51: 1520～1531
[62] N. Fressengeas, J. Maufoy, G. Kugel. Temporal behavior of bidimensional photorefractive bright spatial solitons. Phys. Rev. E, 1996, 54: 6866～6875
[63] J. Maufoy, N. Fressengeas, D. Wolfersberger et al. Simulation of the temporal behavior of soliton propagation in photorefractive media. Phys. Rev. E, 1999, 59: 6116～6121
[64] Wolfersberger, N. Fressengeas, J. Maufoy et al. Self-focusing of a single laser pulse in a photorefractive medium. Phys. Rev. E, 2000, 62: 8700～8704
[65] M. D. Iturbe Castillo, J. J. Sanchez-Mondragon, S. I. Stepanov et al. (1 + 1)-Dimension dark spatial solitons in photorefractive Bi12TiO20 crystal. Opt. Commun., 1995, 118: 515～519
[66] Duree, M. Morin, G. Salamo et al. Dark photorefractive spatial solitons andphotorefractive vortex solitons. Phys. Rev. Lett., 1995, 74: 1978～1981
[67] M. I. Carvalho, S. R. Singh, D. N. Christodoulides. State bright spatial solitons in biased photorefractive crystals. Opt. Commun., 1995, 120: 311～315
[68] W. Królikowski, N. Akhmediev, B. Luther-Davies. Self-bending photorefractive solitons. Phys. Rev. E, 1996, 54: 5761～5765
[69] M. Morin, G. Duree, G. Salamo et al. Waveguides formed by quasi-steady-state photorefractive spatial solitons. Opt. Lett., 1995, 20: 2066～2068
[70] M. Shih, M. Segev, G. Salamo. Circular waveguides induced by two-dimensonal bright steady-state photorefractive screening solitons. Opt. Lett., 1996, 21: 931～933
[71] M. D. Iturbe-Castillo, M. Torres-Cisneros, J. J. Sanchez-Mondragon et al. Experimental evidence of modulational instability in a photorefractive Bi TiO crystal. Opt. Lett., 1995, 20: 1853～1855
[72] A. V. Mamaev, M. Saffman, D. Z. Anderson et al. Propagation of light beams in anisotropic nonlinear media: from symmetry breaking to spatial turbulence. Phys. Rev. A, 1996, 54: 870～879
[73] N. Fressengeas, D. Wolfersberger, J. Maufoy et al. Experimental study of the self-focusing process temporal behavior in photorefractive Bi TiO. J. Appl. Phys., 1999, 85: 2062～2067
[74] J. Tsai, A. Chiou, T. C. Hseih et al. One-dimensional self-focusing in photorefractive Bi SiO crystal: Theoretical modeling and experimental demonstration. Opt. Commun., 1999, 162: 237～240
[75] E. Fazio, F. Mariani, A. Funto et al. Experimental demonstration of (1+1) D self-confinement and breathing soliton-like propagation in photorefractive crystals with strong optical activity. Journal of Optics A: Pure and Applied Optics, 2001, 3: 466～469
[76] E. Fazio, V. Babin, M. Bertolotti et al. Solitonlike propagation in photorefractive crystals with large optical activity and absorption. Phys. Rev. E, 2002, 66: 016605～016616
[77] R. Ryf, M. Wiki, G. Montemezzani et al. Launching one-transverse-dimensionalphotorefractive solitons in KnbO crystals Opt. Commun., 1999, 159: 339～348
[78] R. Uzdin, M. Segev, G. J. Salamo. Theory of self-focusing in photorefractive InP. Opt. Lett., 2001, 26: 1547～1549
[79] R. Ryf, G. Montemezzani, P. Gunter et al. High-frame-rate joint Fourier-transform correlator based on Sn2P2S6 crystal. Opt. Lett., 2001, 26: 1666～1668
[80] S. Lan, M.-f. Shih, M. Segev. Self-trapping of one-dimensional and two-dimensional optical beams and induced waveguides in photorefractive KnBO. Opt. Lett., 1997, 22: 1467～1469
[81] M. Chauvet, S. Hawkins, G. Salamo et al. Self-trapping of planar optical beams by use of the photorefractive effect in InP:Fe. Opt. Lett., 1996, 21: 1333～1335
[82] T. Schwartz, Y. Ganor, T. Carmon et al. Photorefractive solitons and light-induced resonance control in semiconductor CdZnTe. Opt. Lett., 2002, 27: 1229～1231
[83] E. DelRe, B. Crossignani, M. Tamburrini et al. One-dimensional steady-state photorefractive spatial solitons in centrosymmetric paraelectric KLTN. Opt. Lett., 1998, 23: 421～423
[84] P. Agrawal. Nonlinear fiber optics. 2nd ed. San Diego, CA: Academic Press Inc., 1995. 253～262
[85] Y. N. Karamzin, A. P. Sukhorukov. Mutual focusing of high-power light beams in media with quadratic nonlinearity. Sov. Phys. JETP, 1976, 41: 414～416
[86] W. E. Torruellas, Z. Wang, D. J. Hagan et al. Observation of two-dimensional spatial solitary waves in a quadratic medium. Phys. Rev. Lett., 1995, 74: 5036～5039
[87] M. Vaupel, C. Seror, R. Dykstra. Self-focusing in photo refractive two-wave mixing. Opt. Lett., 1997, 22: 1470～1472
[88] M. Vaupel, O. Mandel, N.R. Heckenberg. Two-wave-mixing induced self-focusing in an active photorefractive oscillator. Journal of Optics B: Quantum and Semiclassical Optics, 1999, 1: 96～100
[89] Shvets, A. Pukhov. Electromagnetically induced guiding of counterpropagating lasers in plasmas. Phys. Rev. E., 1999, 59: 1033～1037
[90] Jinsong Liu. Holographic solitons in photorefractive dissipative systems. Opt. Lett.,2003, 28: 2237～2239
[91] R. Salgueiro, A. A. Sukhorukov, Yu. S. Kivshar. Spatial optical solitons supported by mutual focusing. Opt. Lett., 2003, 28: 1457～1459
[92] O. Cohen, B. Freedman, J. W. Fleischer et al. Grating-Mediated Waveguiding. Phys. Rev. Lett., 2004, 93: 103902_1～103902_4
[93] B. Freedman, O. Cohen, O. Manela et al. Grating-mediated wave guiding and holographic solitons. J. Opt. Soc. Am. B, 2005, 22: 1349～1355
[94] O. Cohen, M. M. Murnane, H. C. Kapteyn. Cross-phase-modulation nonlinearities and holographic solitons in periodically poled photovoltaic photorefracives. Opt. Lett., 2006, 31: 954～956
[95] Z. Chen, M. Segev, T. H. Coskun et al. Coupled photorefractive spatial-soliton pairs. J. Opt. Soc. Am. B, 1997, 14: 3066～3077
[96] Jinsong. Liu. Existence and property of spatial solitons in a photorefractive dissipative system. J. Opt. Soc. Am. B, 2003, 20: 1732～1738
[97] Jinsong. Liu. Existence and stability of rigid photovoltaic solitons in an open-circuit amplifying or absorbing photovoltaic medium. Phys. Rev. E, 2003, 68: 026607_1～026607_7
[98] Jinsong Liu, H. J. Eichler. Holographic screening-photovoltaic solitons in biased photovoltaic-photorefractive crystals with two-wave mixing. Europhys. Lett., 2004, 65: 658～664
[99] Z. Chen, M. Segev, T. Coskun et al. Observation of incoherently coupled photorefractive spatial soliton pairs. Opt. Lett., 1996, 21: 1436～1438
[100] Z. Chen, M. Segev, T. Coskun et al. Incoherently coupled dark-bright photorefractive solitons. Opt. Lett., 1996, 21: 1821～1823
[101] M. Shalaby, A. J. Barthelemy. Observation of the self-guided propagation of a dark and bright spatial soliton pair in a focusing nonlinear medium. IEEE J. Quantum Electron., 1992, 28: 2736～2741
[102] S. Trillo, S. Wabnitz, E. M. Wright et al. Optical solitary waves induced by cross-phase modulation. Opt. Lett., 1988, 13: 871～873
[103] N. Christodoulides, S. R. Singh, M. I. Carvalho et al. Incoherently coupled soliton pairs in biased photorefractive crystals. Appl.Phys. Lett., 1996, 68: 1763～1765
[104] S. V. Manakov. On the theory of two-dimensional stationary self-focusing of electronmagnetic wave. Sov. Phys. JETP, 1974, 38: 248～253
[105] U. Kang, G. I. Stegeman, J. S. Aitchison et al. Observation of Manakov Spatial Solitons in AlGaAs Planar Waveguides. Phys.Rev. Lett., 1996, 76: 3699～3702
[106] M. Dianov, P. V. Mamyshev, A. M. Prokhorov et al. Generation of a train of fundamental solitons at a high repetition rate in optical fibers. Opt. Lett., 1989, 14: 1008～1010
[107] P. V. Mamyshev, C. Bosshard, G. I. Stegeman. Generation of a periodic array of dark spatial solitons in the regime of effective amplification. J. Opt. Sov. Am. B, 1994, 11: 1254～1260
[108] M. I. Carvalho, S. R. Singh, D. N. Christodoulides. Modulational instability of quasi-plane-wave optical beams biased in photorefractive crystals. Opt. Comm., 1996, 126: 167～174
[109] A. Hasegawa. Generation of a train of soliton pulses by induced modulational instability in optical fibers. Opt. Lett., 1984, 9: 288～230
[110] M. Artiglia, E. Ciaramella, P. Gallina. Demonstration of CW soliton trains at 10, 40 and 160 Ghz by means of induced modulation instability in: OSA Trends in Optics and Photonics. USA: OSA, 1997, 12: 305～308
[111] M. Soljacic, M. Segev, T. Coskun et al. Modulation instability of incoherent beams in noninstantaneous nonlinear media. Phys.Rev. Lett., 2000, 84: 467～470
[112] Kip, M. Soljacic, M. Segev et al. Modulation instability and pattern formation in spatially incoherent light beams. Science, 2000, 290: 495～498
[113] B. Whitham. A general approach to linear and nonlinear water waves using a Lagrangian. J. Fluid Mech., 1965, 22: 273～283
[114] Jinsong Liu, Huilan Zhang, Guangyong Zhang et al. Evolution and stability of spatial solitons in a photorefractive two-wave mixing system. Chinese Phys., 2006, 15(2): 394～402
[115] Jinsong Liu, D.Y.Zhang, C.H.Liang. Stability of bright screening-photovoltaic spatial solitons. Chin. Phys., 2000, 9: 667～671
[116] Z. G. Chen, M. Mitchell, M. Segev. Steady-state photorefractive soliton-induced Y-junction waveguides and high-order dark spatial solitons. Opt. Lett., 1996, 21: 716～718
[117] Luther-Davies, Y. P. Xiao. Waveguides and Y junctions formed in bulk media by using dark spatial solitons. Opt. Lett., 1992, 17: 496～498
[118] R. De La Fuente, A. Barthelemy, C. Froehly. Spatial-soliton-induced guided waves in a homogeneousnonlinear Kerr medium. Opt. Lett., 1991, 11: 793～795
[119] A. W. Snyder, D. J. Mitchell, B. Luther-Davies. Dark spatial solitons constructed from modes of linear waveguides. J. Opt. Soc. Am. B, 1993, 10: 2345～2356
[120] W. Snyder, D. J. Mitchell, L. Polodian et al. Observation of spatial optical solitons in a nonlinear glass waveguide. Opt. Lett., 1990, 15: 471～473
[121] E. A. Ostrovskaya, Yu. S. Kivshar. Nonlinear theory ofsoliton-induced waveguides. Opt. Lett., 1998, 23: 1268～1270
[122] P. Yeh. Two-wave mixing in nonlinear media. IEEE J. Quantum Electron. 1989, 25: 484～519
[123] Oda, Y. Otani, L. Liu et al. Polarization effect for vibration detection using photorefractive two-wave mixing in KNSBN: Cu crystals. Opt. Commun., 1998, 148: 95～100
[124] P. Huignard, A. Marrakchi. Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20 crystals. Opt. Commun., 1981, 38: 249～254
[125] Jinsong Liu, Yinyuan Zhang, Hans J. Eichler. Dynamical evolution of dissipative holographic solitons in photorefractive media via two-wave mixing with a moving grating. Journal of Modern Optic, 2005, 52(4): 563～572
[126] N. N. Akhmediev, V. V. Afanasjev. Novel arbitrary-amplitude soliton solutions of the cubic-quintic complex Ginzburg-Landau equation. Phys. Rev. Lett., 1995, 75: 2320～2323
[127]刘劲松.非对称光折变全息空间光孤子的存在曲线.物理学报, 2004, 53(9): 3014～3019
[128] N. N. Akhmediev, V. V. Afanasjev, J. M. Soto-Crespo. Singularities and special soliton solutions of the cubic-quintic complex Ginzburg-Landau equation. Phys. Rev. E, 1996, 53: 1190～1201
[129] N. N. Akhmediev, V. V. Afanasjev. Spatial solitons. 1st ed. Berlin: Springer, 2001. 20～66
[130] J. M. Soto-Crespo, N. N. Akhmediev, V. V. Afanasjev. Stability of the pulselike solutions of the quintic complex Ginzburg-Landau equation. J. Opt. Soc. Am. B, 1996, 13: 1439～1449
[131] Y. Silberberg, G. I. Stegeman. Spatial Solitons. 1st ed. Berlin: Springer-Verlag, 2001. 37～60