光生伏打空间孤子理论及实验研究
|
摘要
本文对光折变空间孤子,特别是光生伏打空间孤子进行了理论和实验研究。首先基于光折变效应的物理过程并根据光折变空间孤子的行成机理,从光折变效应的动力学方程出发,得出了无背景光作用的光伏孤子空间电荷场及其演化方程。同时,在适当的约束条件下,得出了相应的亮、暗孤子解。
在已有理论基础上详细分析了背景光在光伏孤子形成过程中的作用,得出了△n＜0和△n＞0两种类型光折变晶体中分别形成亮、暗光伏孤子的条件;并从实验上首次观察到折射率改变为负的LiNbO_3晶体中实现自散焦向自聚焦特性的转化,并进而形成亮光伏孤子的实验事实;依据Glass常数的光伏效应表征意义,提出了光伏孤子形成过程中背景光的引入所导致的光伏载流子的竞争效应模型。基于此,分析了背景光在此两种类型光折变晶体中实现自散焦和自聚焦特性相互转化过程中的作用,得出了与前述理论分析相一致的结论,最终阐明了此光折变特性相互转化的内在物理机制。
同时,也对部分非相干暗光伏孤子进行了实验研究。在LiNbO_3∶Fe晶体中观察到了部分空间非相干光形成的一维暗光伏孤子,并由此暗光伏孤子在该晶体中诱导出一维波导。这一实验证明了用低能量非相干光束控制转换高能量相干光束的可能性。
Theoretical analysis and experimental research were done in this thesis about photorefractive spatial solitons, especially photovoltaic solitons. Firstly, based on the physical process of photorefractive effect and self-trapping mechanism of photorefractive spatial solitons, the related space charge field and the evolution equation of photovoltaic spatial solitons without background illumination from Kukhtarev-Vinestskii model are derived directly from the dynamics equations of the photorefrctive effect. Meanwhile, the solutions for both bright and dark spatial solitons were achieved under appropriate constraint conditions.
Based on the previously obtained theory, the influence of specifically added background illumination on the forming process of photovoltaic solitons was analyzed deliberately, which brought in the concrete conditions for the formation of both bright photovoltaic spatial solitons and dark one in photorefractive crystal with An < 0 orΔn > 0. And what's more, for what is to our knowledge the first time, the transition from self-defocusing to self-focusing characteristics and thereby the ultimate formation of bright photovoltaic solitons were experimentally observed in lithium niobate crystal with negative refractivity change(Δn < 0 ). And what is worth specifically noting is that, on the basis of the physical meaning of Glass constant upon photovoltaic effect, a theoretical model that demonstrates clearly the existence of the carriers competition effect in photovoltaic solitons forming process was established. As a result, the profound effect of background illumination on mutual transition between self-defocusing characteristics and self-focusing one was discussed, which brought out the same result as ever obtained. So, the intrinsic physical mechanism of the referenced characteristics transition was illustrated explicitly.
What makes my thesis rounded is as follows: one-dimensional dark photovoltaic solitons was formed in LiNO3: Fe photorefractive crystal by light beams with partially spatial noncoherence, and consequently the one-dimensional waveguides in the crystal was available. The experimental phenomenon proves the possibility of controlling and switching high-power laser beams with low-power incoherent lightsources.
在已有理论基础上详细分析了背景光在光伏孤子形成过程中的作用,得出了△n＜0和△n＞0两种类型光折变晶体中分别形成亮、暗光伏孤子的条件;并从实验上首次观察到折射率改变为负的LiNbO_3晶体中实现自散焦向自聚焦特性的转化,并进而形成亮光伏孤子的实验事实;依据Glass常数的光伏效应表征意义,提出了光伏孤子形成过程中背景光的引入所导致的光伏载流子的竞争效应模型。基于此,分析了背景光在此两种类型光折变晶体中实现自散焦和自聚焦特性相互转化过程中的作用,得出了与前述理论分析相一致的结论,最终阐明了此光折变特性相互转化的内在物理机制。
同时,也对部分非相干暗光伏孤子进行了实验研究。在LiNbO_3∶Fe晶体中观察到了部分空间非相干光形成的一维暗光伏孤子,并由此暗光伏孤子在该晶体中诱导出一维波导。这一实验证明了用低能量非相干光束控制转换高能量相干光束的可能性。
Theoretical analysis and experimental research were done in this thesis about photorefractive spatial solitons, especially photovoltaic solitons. Firstly, based on the physical process of photorefractive effect and self-trapping mechanism of photorefractive spatial solitons, the related space charge field and the evolution equation of photovoltaic spatial solitons without background illumination from Kukhtarev-Vinestskii model are derived directly from the dynamics equations of the photorefrctive effect. Meanwhile, the solutions for both bright and dark spatial solitons were achieved under appropriate constraint conditions.
Based on the previously obtained theory, the influence of specifically added background illumination on the forming process of photovoltaic solitons was analyzed deliberately, which brought in the concrete conditions for the formation of both bright photovoltaic spatial solitons and dark one in photorefractive crystal with An < 0 orΔn > 0. And what's more, for what is to our knowledge the first time, the transition from self-defocusing to self-focusing characteristics and thereby the ultimate formation of bright photovoltaic solitons were experimentally observed in lithium niobate crystal with negative refractivity change(Δn < 0 ). And what is worth specifically noting is that, on the basis of the physical meaning of Glass constant upon photovoltaic effect, a theoretical model that demonstrates clearly the existence of the carriers competition effect in photovoltaic solitons forming process was established. As a result, the profound effect of background illumination on mutual transition between self-defocusing characteristics and self-focusing one was discussed, which brought out the same result as ever obtained. So, the intrinsic physical mechanism of the referenced characteristics transition was illustrated explicitly.
What makes my thesis rounded is as follows: one-dimensional dark photovoltaic solitons was formed in LiNO3: Fe photorefractive crystal by light beams with partially spatial noncoherence, and consequently the one-dimensional waveguides in the crystal was available. The experimental phenomenon proves the possibility of controlling and switching high-power laser beams with low-power incoherent lightsources.
引文
[1]郭柏灵,庞小峰.孤立子.北京:科学出版社,1986,1-3.
[2]谷超豪,郭柏灵,李神等.孤立子理论与应用.杭州:浙江科学技术出版社,1990,1-5.
[3]陈陆君,梁昌洪.孤立子理论及应用.西安:西安电子科技大学出版社,1997,3-5.
[4]N.J.Zabusky,M.D.Kruskal Phys.Rev.Lett.1965,15(6):240-243.
[5]A.Hasegawa,F.Tappert.Appl.Phys.Lett.1973,23(3):142-144.
[6]L.F.Mollenauer,R.H.Stolen,J.P.Gordon.Phys.Rev.Lett.1980,45(13):1095-1098.
[7]L.F.Mollenauer,R.H.Stolen.Opt.Lett.1984,9(1):13-15.
[8]L.F.Mollenauer,B.M.Nyman,M.J.Neubelt,et al.Electron.Lett.1991,27(2):178-179.
[9]K.Smith,J.E.Greer,R.Wyatt,et al.Electron.Lett.1991,27(3):244-246.
[10]M.Segev,G.Stegeman.Physics Today,1998,51(8):42-48.
[11]M.Segev,B.Crosignani,A.Yariv,et al.Phy.Rev.Lett.1992,68(7):923-926.
[12]B.Crosignani,M.Segev,D.Engin,et al.J.Opt.Soc.Am.B.1993,10(3):446-453.
[13]G.C.Duree,J.L.Shultz,G.J.Salamo,et al.Phy.Rev.Lett.1993,71(4):533-536.
[14]M.Segev,B.Crosignani,P.Diporto,et al.Opt.Lett.1994,19(17):1296-1298.
[15]G.C.Duree,M.Morin,G.Salamo,et al.Dark Photorefractive Spatial Solitons and Photorefractive Vortex Solitons.Phys.Rev.Lett.1995,74(11):1978-1981.
[16]M.Morin,G.Duree,G.Salamo,et al.Waveguides Formed by Qusi-Steady Photorefractive Spatial Solition.Opt.Lett.1995,20(20):2066-2068.
[17]N.Fressengeas,J.Maufoy and G.Kugel.Temporal Behavior of Bidimensional Photorefractive Bright Spatial Solitons.Phys.Rev.E.1996,54(6):6866-6875.
[18]N.Fressengeas,D.Wolferberger,J.Maufoy,et al.Build up Mechanisms of (1+1)-Dimensional Photorefractive Bright Spatial Quasi-Steady-State and Screening Solitons.Opt.Comm.1998,(145):393-400.
[19]J.Maufoy,N.Fressengeas,D.Wolferberger,et al.Simulation of the Temporal Behavior of Soliton Propagation in Photorefractive Media.Phys.Rev.E.1999,59(5):6116-6121.
[20]W.L.She,K.K.Lee and W.K.Lee.All Optical Quasi-Steady-State Photorefractive Spatial Solitons.Phys.Rev.Lett.2000,85(12):2498-2501.
[21]佘卫龙,李荣基.全光双准稳态空间孤子.物理学报.2001,50(5):886-891.
[22]M.Segev,G.C.Valley,B.Crosignani P.Di Porto.et al.Steady-State Spatial Screening Solitons in Photoretractive Materials with External Applied Field.Phys.Rev.Lett.1994,73(24):3211-3214.
[23]D.N.Christodoulides,M.I.Carvalho.J.Opt.Soc.Am.B.1995,12(9):1628-1633.
[24]K.V.Kukhtarev,V.B.Markov,S.G.Odulov,et al.Ferroelectrics,1993,22:949-960.
[25]M.Shih,M.Segev,G.C.Valley,et al.Observation of Two-Dimensional Steady-State Photorefractive Screening Solitons.Electron.Lett.1995,31(30):826-827.
[26]S.R.Singly,D.N.Christodoulides.Evolution of Spatial Solitons in Biased Photorefractive Media.Opt.Commun.1995,118(5/6):569-576.
[27]M.I.Carvalho,S.D.Singh,D.N.Christodoulides.Self-Deflection of Steady-State Bright Spatial Solitons in Biased Photorefractive Crystals.Optical Commun.1995,120(5/6):311-315.
[28]M.Shih,P.Leach,M.Segev,et al.Two-Dimensional Steady-State Photorefractive Screening Solitons.Opt.Lett.1996,21(5):324-326.
[29]Z.Chen,M.Mitchell,M.Shih,et al.Steay-State Dark Photorefractive Screening Solitons.Opt.Lett.1996,21(9):629-631.
[30]K.Kos,H.Meng,G.Salamo,et al.One-dimensional Steady-State Photorefractive Screening Solitons.Phys.Rev.E.1996,53(5):R4330-R4333.
[31]Z.Cheng,M.Segev,S.R.Singh,et al.Sequential Formation of Dark Potorefractive Spatial Solitons:Experiments and Theory.J.Opt.Soc.Am.B.1997,14(6):1407-1417.
[32]G C.Valley,M.Segev,B.Crosignani,et al.Dark and Bright Photovoltaic Spatial Solitons.Phys.Rev.A.1994,50(6):R4457-R4460.
[33]M.Taya,M.C.Bashaw,M.M.Fejer,et al.Observation of Dark Photovoltaic Spatial Solitons.Phys.Rev.A.1995,52(4):3095-3100.
[34]M.Segev,G C.Valley,M.C.Bashaw,et al.Photovoltaic Spatial Solitons.J.Opt.Soc.Am.B.1997,14(7):1772-1781.
[35]W.L.She,K.K.Lee and W.K.Lee.Observation of Two-Dimensional Bright Photovoltaic Spatial Solitons.Phys.Rev.Lett.1999,83(16):3182-3185.
[36]凌振芳,郭儒,刘思敏等.光生伏打一光折变介质中光学涡旋孤子.物理学报.2000,49(3):455-458.
[37]A.Charalambos,S.hih.M.F,et al.Optically induced Photovoltaic Self-defocsing-to-self-focsing transition.Opt.Lett.1998,23(12):924-926.
[38]佘卫龙,王晓声,何国岗等.折射率改变为正的光折变晶体中形成一维光伏暗孤子.物理学报.2001,50(11):2166-2171.
[39]D.N.Christodoulides,S.R.Singh,M.I.Carvalho.Incoherently Coupled Solitons Paris in Biased Photorefractive Crystals.Appl.Phys.Lett.1996,68(13):1763-1765.
[40]Z.Chen,M.Segev,H.Coskun,et al.Observation of Incoherently Coupled Photorefractive Spatial Soliton Pairs.Opt.Lett.1996,21(18):1436-1438.
[41]Z.Chen,M.Segev,H.Coskun,et al.Incoherently Coupled Dark-Bright Photorefractive Solitons.Opt.Lett.21(22):1821-1823.
[42]M.Shih,M.Segev.Incoherent Collisions between Two-Dimensional Bright Steady-State Photorefractive Spatial Screening Solitons.Opt.Lett.1996,21(19):1538-1540.
[43]W.Krolikowski,B.Luther-Davies,C.Denz,et al.Annihilation of Photorefractive Solitons.Opt.Lett.1998,23(2):97-99.
[44]S.Garcia Quirino,M.D.Iturbe_Castillo,V A.Vysloukh,et al.Observation of Interaction Forces between One-Dimensional Spatial Solitons in Photorefractive Crystals.Opt.Lett.1997,22(3):154-156.
[45]M.Shih,M.Segev,G.Salamo.Three-Dimensional Sprialing of Interacting Spatial Solitons. Phys. Rev. Lett. 1997, 78(13):2551-2554.
[46] D. Kip, M. Wesner, C. Herden, et al. Interaction of Spatial Photorefractive Soliton in Planar Waveguide. Appl. Phys. B. 1999, 68 :971-974.
[47] G. I. Stegeman, M. Segev. Optical Spatial Solitons and Their Interactions:Universality and Diversity. Science. 1999, 286:1518-1523.
[48] Y S. Kivshar, A. Nepomnyashchy, V. Tikhonenko, et al. Vortex-Stripe Soliton Interactions. Opt. Lett. 2000,25(2): 123-125.
[49] E. Delre, S. Trillo, A. J. Agranat, et al. Collisions and Inhomogeneous Forces between Solitons of Different Dimensionality. Opt. Lett. 2000,25(8):560-562.
[50] T. H. Coskum, A. G. Grandpierre, D. N. Christodoulides, et al. Coherent Enhancement of Spatially Incoherent Light Beams through Soliton Interactions. Opt. Lett. 2000, 25(11): 826-828.
[1] A.Ashkin et al. Appl. Phys. Lett. 1966, 9:72.
[2] P. Yeh. Introduction to Photorefractive nonlinear Optics, Wiley and Sons, New York, 1993.
[3] N. V. Kukhtarev et al. Ferroelective, 1979,22:949,961; K. Buse, Appl. Phys. B. 1997,64:273;1994, 64:391.
[4] G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, Dark and bright photovoltaic spatial solitons. Phys. Rev. A. 1994, 50(6):R4457～R4460.
[5] G. C. Valley, J. Lam, in Photorefractive Materials and their Applications I, P. Gunter, J. P. Huignard, eds.(Springer-Verlag, New York, 1988), Chap.3.
[6] M. F. Shih, Z. Chen, M. Segev, T. Coskun and D. N. Christodoulides. Incoherent Collisions Between One-Dimensional Steady-State Photorefractive Screening Solitons, Appl. Phys. Lett. 1996,69(27): 4151-4153.
[7] M. Segev, M. Shih, and G. C. Valley, Photorefractive screening solitons of high and low intensity. J. Opt. Soc. Am. B. 1996,13(4):706-718.
[8] M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev, and G C. Valley, Observation of dark photovoltaic spatial solitons. Phys. Rev. A 1995, 52(4):3095-3100.
[9] S. Orlov, A. Yariv, and M. Segev, Appl. Phys. Lett. 1996, 68:1610.
[10]G. C. Valley, J.Lam, in Photorefractive Material and their Applications I. P. Gunter and J. P. Huignard, eds. (Springer-Verlag, New York, 1988), Chap. 3.
[11]B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, J. Opt. Soc. Am B. 1995,12:1642.
[12]M. Segev, G. C. Valley, M. C. Bashaw, M. Taya and M. M. Fejer, Photovoltaic spatial solitons. J. Opt. Soc. Am B. 1997,14(7):1772-1781.
[13]M. Segev, G. C. Valley, B. Crosignani, P. Diporto, and A. Yariv, Steady-State Spatial Screening Solitons in Photorefractive Materials with External Applied Field. Phys. Rev. Lett. 1994, 73(24):3211-3214.
[14]S. Bian, J. Frejlich, and K. Ringhofer, Phys. Rev. Lett. 1997, 78:4035.
[1] M. Segev, B. Crosignani, A. Yariv and B. Fischer, Phys. Rev. Lett. 68, 923(1992);G. C. Duree, J. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Diporto, E. J. Sharp, Observation of Self-Trapping of an Optical Beam Due to the Photorefractive Effect. Phys.Rev. Lett. 1993, 71(4):553-536.
[2] M. Segev, G. C. Valley, B. Crosignani, P. Diporto, A. Yariv, Steady-State Spatial Screening in Photorefractive Materials with External Applied Field. Phys.Rev. Lett. 1994, 73(24):3211-3215; M. Segev, M. Shih , G. C. Valley, Photorefractive screening solitons of high and low intensity. J. Opt. Soc. Am B. 1996, 13(4):706-718.
[3] D. N. Christodoulides, M. I. Carvalho, Bright, dark, and gray spatial soliton states in photorefractive medial. J. Opt. Soc. Am B. 1995,12(4):1628-1633.
[4] M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. Stepanov and V. Vysloukh, Appl. Phys. Lett. 1994, 64:408.
[5] M. Shih, M. Segev, G C. Valley, et al. Observation of Two-Dimensional Steady-State Photorefractive Screening Solitons. Electron. Lett. 1995, 31(30):826-827.
[6] G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer and M. C. Bashaw, Dark and bright photovoltaic spatial solitons. Phys. Rev. A. 1994, 50(6):R4457-R4460.
[7] M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev and G. C. Valley, Observation of dark photovoltaic spatial solitons. Phys. Rev. A 1995, 52(4):3095-3103.
[8] M. Segev, G. C. Valley, M. C. Bashaw, M. Taya and M. M. Fejer, Photovoltaic spatial solitons. J. Opt. Soc. Am B. 1997,14(7): 1772-1781.
[9] S. Bian, J. Frejlich and Ringhofer, Phys. Rev. Lett. 1997, 78,:4035.
[10]Z. Chen, M. Segev, D. W. Wilson, R. E. Muller and P. D. Maker, Self-Trapping of Optical Vortex by Use of the Bulk Photovoltaic Effect. Phys. Rev. Lett. 1997, 78(15):2948-2951.
[11] Note that Photorefractive solitons that rely on the dc kerr effect in centrosymmetric media,for which Δn ∞ E~2 also exist;see M.Segev,A.Agranat,Opt.Lett.1997,22:1299.
[12]The term "focused" is used to distinguish the narrow beam which is focused to the input face of the crystal from the broad uniform background beam.It should not be confused with the self-focused or self-defocused terms which describe the output beam at steady state.
[13]For a review of the photovoltaic effect,see P.Gunter and J.P.Huignard,"Photorefractive materials and their applications Ⅰ",Springer-Verlag,Berlin 1988;B.I.Sturman and V.M.Fridkin in The Photovoltaic and Photorefractive Effect in Non-Centrosymmetric Materials(Gordon and Breach,Philadelphia,1992).
[14]S.Orlov,A.Yariv,M.Segev,Appl.Phys.Lett.1996,68:1610.
[15]C.Anastassiou,M.F.Shih,M.Mitchell,Z.Chen,and M.Segev,Optically induced photovoltaic self-defocusing-to-self-focusing transition.Opt.Lett.1998,23(12):924-926.
[16]G.C.Valley,M.Segev,B.Crosignani,et al.Dark and bright photovoltaic spatial solitons[J].Phys Rev A,1994,50(6):R4457-R4460;
刘劲松,张都应.损耗对屏蔽光伏空间孤子演化特性的影响.2001,50(5):880-885.
[17]李金萍,卢克清,赵卫,等.暗光伏孤子的实验研究.光子学报,2006,35(8):1225-1228.
[18]佘卫龙,王晓生,何国岗,陶孟仙,林励平,李荣基.折射率改变为正的光折变晶体中形成一维光伏暗孤子.物理学报,2001,50(11):2166-2171.
[1] M. Mitchell, Z. Chen, and M. F. Shih et al., "Self-trapping of partially spatially incoherent light," Phys. Rev. Lett. 1996, 77 (3): 490-493.
[2] M. Mitchell and M. Segev, "Self-trapping of incoherent white light," Nature. 1997, 387: 880-883.
[3] Z. Chen, M. Mitchell, and M. Segev et al., "Self-trapping of dark incoherent light beams," Science. 1998, 280 (5365): 889-892.
[4] T. H. Coskun, D. N. Christodoulides, M. Mitchell, Z.G.Chen and M. Segev. Dynamics of Incoherent Bright and Dark Self-Trapped Beams and Their Coherence Properties in Photorefractive Crystal, Opt.Lett. 1998,23(6): 418-420
[5] M. I. Carvalho, T. H. Coskun, D. N. Christodoulides, M. Mitchell and M. Segev. Coherence Properties of Multimode Incoherent Spatial Solitons in Noninstantaneous Kerr Media, Phy. Rev E. 1999, 59(1): 1193-1197
[6] T. H. Coskun, A. G. Grandpierre, D. N. Christodoulides and M. Segev. Coherence Enhancement of Spatially Incoherent Light Beams Through Soliton Interactions, Opt. Lett. 2000,25(11): 826-829
[7] T. H. Coskun, D. N. Christodoulides, Y. R. Kim, Z. G. Chen, M. Soljacic and M. Segev. Bright Spatial Solitons on a Partially Incoherent Background, Phys. Rev Lett. 2000, 84(11): 2374-2377
[8] A. Picozzi and M. Haelterman. Parametric Three-Wave Soliton Generated from Incoherent Light, Phys. Rev Lett. 2001, 86(10):2010-2013
[9] J. Serna and J. M. Movilla. Orbital Angular Momentum of Partially Coherent Beams, Opt. Lett. 2001, 26(7): 405-407
[10]J.C.Bronski, M. Segev and M. I. Weinstein, Mathematical Frontiers in Optical Solitons, Proc. Natl. Acad. Sci. 2001, 98(23):2872-2873
[11]H. Buljan, M. Segev, M. Soljacic, N. K. Efremidis and D. N. Christodoulides. White-Light Solitons, Opt. Lett. 2003, 28(14): 1239-1241
[12]H. Buljan, A. Siber, M. Soljacic, T.Schwartx, M. Segev and D. N. Christodoulides. Incoherent White Light Solitons in Logarithmically Saturable Noninstantaneous Nonlinear Media, Phys. Rev E. 2003, 68: 036607-036612
[13]V. Kutuzov, V. M. Petnikova, V. V. Shuvalov, and V. A. Vysloukh. Cross-Modulation Coupling of Incoherent Soliton Modes in Photorefractive Crystals, Phys. Rev. E. 1998, 57(7): 6056-6065.
[14]Z. Chen, M. Segev, T. H. Coskun and D. N. Christodoulides. Observation of Incoherently Coupled Photorefractive Spatial Soliton Pairs, Opt.Lett. 1996, 21(18):1436-1439.
[15]D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides. Modulation Instability and Pattern Formation in Spatially Incoherent Light Beams, Science. 2000, 290(10): 495-498.
[16] J. Klinger, H. Martin and Z.Chen, Experiments on Induced Modulational Instability of An Incoherent Optical Beam, Opt. Lett. 2001, 26(5): 271-273.
[17]Y. S. Kivshar and D. E. Pelinovsky. Self-focusing and transverse instabilities of solitary waves, Phys. Rep. 2000, 331(4): 117-195.
[18]M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath. Modulation Instability of Incoherent Beams in Noninstantaneous Nonlinear Media, Phys. Rev. Lett. 2000, 84(3): 467-470.
[19]O. Bang, D. Edmundson and W. Kr o likowski. Collapse of Incoherent Light Beams in Inertial Bulk Kerr Media, Phys. Rev. Lett. 1999, 83(26): 5479-5482
[20] G. I. Stegeman and M. Segev. Optical Spatial Solitons and Their Interactions: Universality and Diversity, Science. 1999, 286: 1518-1523.
[21] A. Stepken, M. R. Belie, F. Kaiser, W. Krolikowski and B. Luther-Davies. Three Dimensional Trajectories of Interacting Incoherent Photorefractive Solitons, Phys. Rev. Lett. 1999, 82(3): 540-543.
[22] M. F. Shih and M. Segev. Incoherent Collisions Between Two-Dimensional Bright Steady-state Photorefractive Spatial Screening Solitons, Opt. Lett. 1996, 21(19):538-542.
[23] M. F. Shih, Z. Chen, M. Segev, T. Coskun and D. N. Christodoulides. Incoherent Collisions Between One-Dimensional Steady-State Photorefractive Screening Solitons, Appl. Phys. Lett. 1996, 69(27): 4151-4153.
[24] T. H. Coskun, A. G Grandpierre, N. Christodoulides and M. Segev. Coherence Enhancement of Spatially Incoherent Light Beams Through Soliton Interactions. Opt. Lett. 2000, 25(11): 826-828.
[25] D. Kip, C. Anastassiou, E. Eugenieva, D. Christodoulides and M. Segev. Transmission of Images Through Highly Nonlinear Media by Gradient-Index Lenses Formed by Incoherent Solitons, Opt. Lett. 2001, 26(8): 524-526.
[26] Z. Chen, M. Segev, D. N. Christodoulides and R. S. Feigelson. Waveguides Formed by Incoherent Dark Solitons, Opt. Lett. 2001,24(16): 1160-1162.
[27] M. J. Abliwitz, G. Biondini L. A. Ostrovsky. Optical Solitons: Perspectives and Applications, Chaos. 2000,10(3): 471-474
[28]D. N. Christodoulides, T. H. Coskun, M. Mitchell, Z. G. Chen and M. Segev.Theory of Incoherent Dark Solitons, Phys. Rev. Lett. 1998, 80(23): 5113-5116.
[29] V. V. Shkunov and D. L. Anderson, "Radiation transfer model of self-trapping spatially incoherent radiation by nonlinear media," Phys. Rev. Lett. 1998, 81(13): 2683-2686.
[30]D. N. Christodoulides, T. H. Coskun, and R. I. Joseph, "Incoherent spatial solitons in saturable nonlinear media," Opt. Lett. 1997, 22 (14): 1080-1082.
[31]H. Buljan, M. Segev, and M. Soljacic et al., "White-light solitons," Opt. Lett. 2003, 28 (14): 1239-1241.
[32] Z. Chen and K. McCarthy, "Spatial soliton pixels from partially incoherent light," Opt. Lett. 2002, 27 (22): 2019-2021.
[33] O. Katz, T. Cannon, and T. Schwartz et al.,"Observation of elliptic incoherent spatial solitons," Opt. Lett. 2004,29 (11): 1248-1250.
[34]T. H. Coskun, D. N. Christodoulides, and Z. Chen et al., "Dark incoherent soliton splitting and "phase-memory" effects: Theory and experiment," Phys. Rev. E. 1999, 59 (5): 4777-4780.
[35] D. N. Christodoulides, T. H. Coskun, M. Mitchell and M. Segev. Theory of Incoherent Self-Trapping in Biased Photorefractive Media, Phys. Rev. Lett., 1997; 78(4): 646-650
[36] W. Kr 6 likowski, D. Edmundson and O. Bang. Unified Model for Partially Coherent Solitons in Logarithmically Nonlinear Media, Phy:s. Rev. E, 2000; 61(3): 3122-3126.
[37] C. Anastaeeiou, M. Soljacic and M. Segev et al. Eliminating the Transverse Instabilities of Kerr Solitons, Phy. Rev. Lett., 2000; 85(23): 4888-4891.
[38] M. Mitchell, M. Segev, T. H. Coskun and D. N. Christodoulides. Theory of Self-Trapped Spatially Incoherent Light Beams, Phys. Rev. Lett., 1997; 79(25): 4990-4994.
[39] D. N. Christodoulides, T. H. Coskun, M. Mitchell and M. Segev. Multimode Incoherent Spatial Solitons in Logarithmically Saturable Nonlinear Media, Phys. Rev. Lett., 1998; 80(11): 2310-2315.
[40] A. W. Snyder and D. J. Mitchell. Big Incoherent Solitons, Phy. Rev. Lett. 1998; 80(7): 1422-1424.
[41]D. N. Christodoulides, E. Eugenieva, T. H. Coskun, M. Segev and M. Mitchell. Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media, Phys. Rev E, 2001;63(2): 35601-35605.
[2]谷超豪,郭柏灵,李神等.孤立子理论与应用.杭州:浙江科学技术出版社,1990,1-5.
[3]陈陆君,梁昌洪.孤立子理论及应用.西安:西安电子科技大学出版社,1997,3-5.
[4]N.J.Zabusky,M.D.Kruskal Phys.Rev.Lett.1965,15(6):240-243.
[5]A.Hasegawa,F.Tappert.Appl.Phys.Lett.1973,23(3):142-144.
[6]L.F.Mollenauer,R.H.Stolen,J.P.Gordon.Phys.Rev.Lett.1980,45(13):1095-1098.
[7]L.F.Mollenauer,R.H.Stolen.Opt.Lett.1984,9(1):13-15.
[8]L.F.Mollenauer,B.M.Nyman,M.J.Neubelt,et al.Electron.Lett.1991,27(2):178-179.
[9]K.Smith,J.E.Greer,R.Wyatt,et al.Electron.Lett.1991,27(3):244-246.
[10]M.Segev,G.Stegeman.Physics Today,1998,51(8):42-48.
[11]M.Segev,B.Crosignani,A.Yariv,et al.Phy.Rev.Lett.1992,68(7):923-926.
[12]B.Crosignani,M.Segev,D.Engin,et al.J.Opt.Soc.Am.B.1993,10(3):446-453.
[13]G.C.Duree,J.L.Shultz,G.J.Salamo,et al.Phy.Rev.Lett.1993,71(4):533-536.
[14]M.Segev,B.Crosignani,P.Diporto,et al.Opt.Lett.1994,19(17):1296-1298.
[15]G.C.Duree,M.Morin,G.Salamo,et al.Dark Photorefractive Spatial Solitons and Photorefractive Vortex Solitons.Phys.Rev.Lett.1995,74(11):1978-1981.
[16]M.Morin,G.Duree,G.Salamo,et al.Waveguides Formed by Qusi-Steady Photorefractive Spatial Solition.Opt.Lett.1995,20(20):2066-2068.
[17]N.Fressengeas,J.Maufoy and G.Kugel.Temporal Behavior of Bidimensional Photorefractive Bright Spatial Solitons.Phys.Rev.E.1996,54(6):6866-6875.
[18]N.Fressengeas,D.Wolferberger,J.Maufoy,et al.Build up Mechanisms of (1+1)-Dimensional Photorefractive Bright Spatial Quasi-Steady-State and Screening Solitons.Opt.Comm.1998,(145):393-400.
[19]J.Maufoy,N.Fressengeas,D.Wolferberger,et al.Simulation of the Temporal Behavior of Soliton Propagation in Photorefractive Media.Phys.Rev.E.1999,59(5):6116-6121.
[20]W.L.She,K.K.Lee and W.K.Lee.All Optical Quasi-Steady-State Photorefractive Spatial Solitons.Phys.Rev.Lett.2000,85(12):2498-2501.
[21]佘卫龙,李荣基.全光双准稳态空间孤子.物理学报.2001,50(5):886-891.
[22]M.Segev,G.C.Valley,B.Crosignani P.Di Porto.et al.Steady-State Spatial Screening Solitons in Photoretractive Materials with External Applied Field.Phys.Rev.Lett.1994,73(24):3211-3214.
[23]D.N.Christodoulides,M.I.Carvalho.J.Opt.Soc.Am.B.1995,12(9):1628-1633.
[24]K.V.Kukhtarev,V.B.Markov,S.G.Odulov,et al.Ferroelectrics,1993,22:949-960.
[25]M.Shih,M.Segev,G.C.Valley,et al.Observation of Two-Dimensional Steady-State Photorefractive Screening Solitons.Electron.Lett.1995,31(30):826-827.
[26]S.R.Singly,D.N.Christodoulides.Evolution of Spatial Solitons in Biased Photorefractive Media.Opt.Commun.1995,118(5/6):569-576.
[27]M.I.Carvalho,S.D.Singh,D.N.Christodoulides.Self-Deflection of Steady-State Bright Spatial Solitons in Biased Photorefractive Crystals.Optical Commun.1995,120(5/6):311-315.
[28]M.Shih,P.Leach,M.Segev,et al.Two-Dimensional Steady-State Photorefractive Screening Solitons.Opt.Lett.1996,21(5):324-326.
[29]Z.Chen,M.Mitchell,M.Shih,et al.Steay-State Dark Photorefractive Screening Solitons.Opt.Lett.1996,21(9):629-631.
[30]K.Kos,H.Meng,G.Salamo,et al.One-dimensional Steady-State Photorefractive Screening Solitons.Phys.Rev.E.1996,53(5):R4330-R4333.
[31]Z.Cheng,M.Segev,S.R.Singh,et al.Sequential Formation of Dark Potorefractive Spatial Solitons:Experiments and Theory.J.Opt.Soc.Am.B.1997,14(6):1407-1417.
[32]G C.Valley,M.Segev,B.Crosignani,et al.Dark and Bright Photovoltaic Spatial Solitons.Phys.Rev.A.1994,50(6):R4457-R4460.
[33]M.Taya,M.C.Bashaw,M.M.Fejer,et al.Observation of Dark Photovoltaic Spatial Solitons.Phys.Rev.A.1995,52(4):3095-3100.
[34]M.Segev,G C.Valley,M.C.Bashaw,et al.Photovoltaic Spatial Solitons.J.Opt.Soc.Am.B.1997,14(7):1772-1781.
[35]W.L.She,K.K.Lee and W.K.Lee.Observation of Two-Dimensional Bright Photovoltaic Spatial Solitons.Phys.Rev.Lett.1999,83(16):3182-3185.
[36]凌振芳,郭儒,刘思敏等.光生伏打一光折变介质中光学涡旋孤子.物理学报.2000,49(3):455-458.
[37]A.Charalambos,S.hih.M.F,et al.Optically induced Photovoltaic Self-defocsing-to-self-focsing transition.Opt.Lett.1998,23(12):924-926.
[38]佘卫龙,王晓声,何国岗等.折射率改变为正的光折变晶体中形成一维光伏暗孤子.物理学报.2001,50(11):2166-2171.
[39]D.N.Christodoulides,S.R.Singh,M.I.Carvalho.Incoherently Coupled Solitons Paris in Biased Photorefractive Crystals.Appl.Phys.Lett.1996,68(13):1763-1765.
[40]Z.Chen,M.Segev,H.Coskun,et al.Observation of Incoherently Coupled Photorefractive Spatial Soliton Pairs.Opt.Lett.1996,21(18):1436-1438.
[41]Z.Chen,M.Segev,H.Coskun,et al.Incoherently Coupled Dark-Bright Photorefractive Solitons.Opt.Lett.21(22):1821-1823.
[42]M.Shih,M.Segev.Incoherent Collisions between Two-Dimensional Bright Steady-State Photorefractive Spatial Screening Solitons.Opt.Lett.1996,21(19):1538-1540.
[43]W.Krolikowski,B.Luther-Davies,C.Denz,et al.Annihilation of Photorefractive Solitons.Opt.Lett.1998,23(2):97-99.
[44]S.Garcia Quirino,M.D.Iturbe_Castillo,V A.Vysloukh,et al.Observation of Interaction Forces between One-Dimensional Spatial Solitons in Photorefractive Crystals.Opt.Lett.1997,22(3):154-156.
[45]M.Shih,M.Segev,G.Salamo.Three-Dimensional Sprialing of Interacting Spatial Solitons. Phys. Rev. Lett. 1997, 78(13):2551-2554.
[46] D. Kip, M. Wesner, C. Herden, et al. Interaction of Spatial Photorefractive Soliton in Planar Waveguide. Appl. Phys. B. 1999, 68 :971-974.
[47] G. I. Stegeman, M. Segev. Optical Spatial Solitons and Their Interactions:Universality and Diversity. Science. 1999, 286:1518-1523.
[48] Y S. Kivshar, A. Nepomnyashchy, V. Tikhonenko, et al. Vortex-Stripe Soliton Interactions. Opt. Lett. 2000,25(2): 123-125.
[49] E. Delre, S. Trillo, A. J. Agranat, et al. Collisions and Inhomogeneous Forces between Solitons of Different Dimensionality. Opt. Lett. 2000,25(8):560-562.
[50] T. H. Coskum, A. G. Grandpierre, D. N. Christodoulides, et al. Coherent Enhancement of Spatially Incoherent Light Beams through Soliton Interactions. Opt. Lett. 2000, 25(11): 826-828.
[1] A.Ashkin et al. Appl. Phys. Lett. 1966, 9:72.
[2] P. Yeh. Introduction to Photorefractive nonlinear Optics, Wiley and Sons, New York, 1993.
[3] N. V. Kukhtarev et al. Ferroelective, 1979,22:949,961; K. Buse, Appl. Phys. B. 1997,64:273;1994, 64:391.
[4] G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, Dark and bright photovoltaic spatial solitons. Phys. Rev. A. 1994, 50(6):R4457～R4460.
[5] G. C. Valley, J. Lam, in Photorefractive Materials and their Applications I, P. Gunter, J. P. Huignard, eds.(Springer-Verlag, New York, 1988), Chap.3.
[6] M. F. Shih, Z. Chen, M. Segev, T. Coskun and D. N. Christodoulides. Incoherent Collisions Between One-Dimensional Steady-State Photorefractive Screening Solitons, Appl. Phys. Lett. 1996,69(27): 4151-4153.
[7] M. Segev, M. Shih, and G. C. Valley, Photorefractive screening solitons of high and low intensity. J. Opt. Soc. Am. B. 1996,13(4):706-718.
[8] M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev, and G C. Valley, Observation of dark photovoltaic spatial solitons. Phys. Rev. A 1995, 52(4):3095-3100.
[9] S. Orlov, A. Yariv, and M. Segev, Appl. Phys. Lett. 1996, 68:1610.
[10]G. C. Valley, J.Lam, in Photorefractive Material and their Applications I. P. Gunter and J. P. Huignard, eds. (Springer-Verlag, New York, 1988), Chap. 3.
[11]B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, J. Opt. Soc. Am B. 1995,12:1642.
[12]M. Segev, G. C. Valley, M. C. Bashaw, M. Taya and M. M. Fejer, Photovoltaic spatial solitons. J. Opt. Soc. Am B. 1997,14(7):1772-1781.
[13]M. Segev, G. C. Valley, B. Crosignani, P. Diporto, and A. Yariv, Steady-State Spatial Screening Solitons in Photorefractive Materials with External Applied Field. Phys. Rev. Lett. 1994, 73(24):3211-3214.
[14]S. Bian, J. Frejlich, and K. Ringhofer, Phys. Rev. Lett. 1997, 78:4035.
[1] M. Segev, B. Crosignani, A. Yariv and B. Fischer, Phys. Rev. Lett. 68, 923(1992);G. C. Duree, J. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Diporto, E. J. Sharp, Observation of Self-Trapping of an Optical Beam Due to the Photorefractive Effect. Phys.Rev. Lett. 1993, 71(4):553-536.
[2] M. Segev, G. C. Valley, B. Crosignani, P. Diporto, A. Yariv, Steady-State Spatial Screening in Photorefractive Materials with External Applied Field. Phys.Rev. Lett. 1994, 73(24):3211-3215; M. Segev, M. Shih , G. C. Valley, Photorefractive screening solitons of high and low intensity. J. Opt. Soc. Am B. 1996, 13(4):706-718.
[3] D. N. Christodoulides, M. I. Carvalho, Bright, dark, and gray spatial soliton states in photorefractive medial. J. Opt. Soc. Am B. 1995,12(4):1628-1633.
[4] M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. Stepanov and V. Vysloukh, Appl. Phys. Lett. 1994, 64:408.
[5] M. Shih, M. Segev, G C. Valley, et al. Observation of Two-Dimensional Steady-State Photorefractive Screening Solitons. Electron. Lett. 1995, 31(30):826-827.
[6] G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer and M. C. Bashaw, Dark and bright photovoltaic spatial solitons. Phys. Rev. A. 1994, 50(6):R4457-R4460.
[7] M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev and G. C. Valley, Observation of dark photovoltaic spatial solitons. Phys. Rev. A 1995, 52(4):3095-3103.
[8] M. Segev, G. C. Valley, M. C. Bashaw, M. Taya and M. M. Fejer, Photovoltaic spatial solitons. J. Opt. Soc. Am B. 1997,14(7): 1772-1781.
[9] S. Bian, J. Frejlich and Ringhofer, Phys. Rev. Lett. 1997, 78,:4035.
[10]Z. Chen, M. Segev, D. W. Wilson, R. E. Muller and P. D. Maker, Self-Trapping of Optical Vortex by Use of the Bulk Photovoltaic Effect. Phys. Rev. Lett. 1997, 78(15):2948-2951.
[11] Note that Photorefractive solitons that rely on the dc kerr effect in centrosymmetric media,for which Δn ∞ E~2 also exist;see M.Segev,A.Agranat,Opt.Lett.1997,22:1299.
[12]The term "focused" is used to distinguish the narrow beam which is focused to the input face of the crystal from the broad uniform background beam.It should not be confused with the self-focused or self-defocused terms which describe the output beam at steady state.
[13]For a review of the photovoltaic effect,see P.Gunter and J.P.Huignard,"Photorefractive materials and their applications Ⅰ",Springer-Verlag,Berlin 1988;B.I.Sturman and V.M.Fridkin in The Photovoltaic and Photorefractive Effect in Non-Centrosymmetric Materials(Gordon and Breach,Philadelphia,1992).
[14]S.Orlov,A.Yariv,M.Segev,Appl.Phys.Lett.1996,68:1610.
[15]C.Anastassiou,M.F.Shih,M.Mitchell,Z.Chen,and M.Segev,Optically induced photovoltaic self-defocusing-to-self-focusing transition.Opt.Lett.1998,23(12):924-926.
[16]G.C.Valley,M.Segev,B.Crosignani,et al.Dark and bright photovoltaic spatial solitons[J].Phys Rev A,1994,50(6):R4457-R4460;
刘劲松,张都应.损耗对屏蔽光伏空间孤子演化特性的影响.2001,50(5):880-885.
[17]李金萍,卢克清,赵卫,等.暗光伏孤子的实验研究.光子学报,2006,35(8):1225-1228.
[18]佘卫龙,王晓生,何国岗,陶孟仙,林励平,李荣基.折射率改变为正的光折变晶体中形成一维光伏暗孤子.物理学报,2001,50(11):2166-2171.
[1] M. Mitchell, Z. Chen, and M. F. Shih et al., "Self-trapping of partially spatially incoherent light," Phys. Rev. Lett. 1996, 77 (3): 490-493.
[2] M. Mitchell and M. Segev, "Self-trapping of incoherent white light," Nature. 1997, 387: 880-883.
[3] Z. Chen, M. Mitchell, and M. Segev et al., "Self-trapping of dark incoherent light beams," Science. 1998, 280 (5365): 889-892.
[4] T. H. Coskun, D. N. Christodoulides, M. Mitchell, Z.G.Chen and M. Segev. Dynamics of Incoherent Bright and Dark Self-Trapped Beams and Their Coherence Properties in Photorefractive Crystal, Opt.Lett. 1998,23(6): 418-420
[5] M. I. Carvalho, T. H. Coskun, D. N. Christodoulides, M. Mitchell and M. Segev. Coherence Properties of Multimode Incoherent Spatial Solitons in Noninstantaneous Kerr Media, Phy. Rev E. 1999, 59(1): 1193-1197
[6] T. H. Coskun, A. G. Grandpierre, D. N. Christodoulides and M. Segev. Coherence Enhancement of Spatially Incoherent Light Beams Through Soliton Interactions, Opt. Lett. 2000,25(11): 826-829
[7] T. H. Coskun, D. N. Christodoulides, Y. R. Kim, Z. G. Chen, M. Soljacic and M. Segev. Bright Spatial Solitons on a Partially Incoherent Background, Phys. Rev Lett. 2000, 84(11): 2374-2377
[8] A. Picozzi and M. Haelterman. Parametric Three-Wave Soliton Generated from Incoherent Light, Phys. Rev Lett. 2001, 86(10):2010-2013
[9] J. Serna and J. M. Movilla. Orbital Angular Momentum of Partially Coherent Beams, Opt. Lett. 2001, 26(7): 405-407
[10]J.C.Bronski, M. Segev and M. I. Weinstein, Mathematical Frontiers in Optical Solitons, Proc. Natl. Acad. Sci. 2001, 98(23):2872-2873
[11]H. Buljan, M. Segev, M. Soljacic, N. K. Efremidis and D. N. Christodoulides. White-Light Solitons, Opt. Lett. 2003, 28(14): 1239-1241
[12]H. Buljan, A. Siber, M. Soljacic, T.Schwartx, M. Segev and D. N. Christodoulides. Incoherent White Light Solitons in Logarithmically Saturable Noninstantaneous Nonlinear Media, Phys. Rev E. 2003, 68: 036607-036612
[13]V. Kutuzov, V. M. Petnikova, V. V. Shuvalov, and V. A. Vysloukh. Cross-Modulation Coupling of Incoherent Soliton Modes in Photorefractive Crystals, Phys. Rev. E. 1998, 57(7): 6056-6065.
[14]Z. Chen, M. Segev, T. H. Coskun and D. N. Christodoulides. Observation of Incoherently Coupled Photorefractive Spatial Soliton Pairs, Opt.Lett. 1996, 21(18):1436-1439.
[15]D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides. Modulation Instability and Pattern Formation in Spatially Incoherent Light Beams, Science. 2000, 290(10): 495-498.
[16] J. Klinger, H. Martin and Z.Chen, Experiments on Induced Modulational Instability of An Incoherent Optical Beam, Opt. Lett. 2001, 26(5): 271-273.
[17]Y. S. Kivshar and D. E. Pelinovsky. Self-focusing and transverse instabilities of solitary waves, Phys. Rep. 2000, 331(4): 117-195.
[18]M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath. Modulation Instability of Incoherent Beams in Noninstantaneous Nonlinear Media, Phys. Rev. Lett. 2000, 84(3): 467-470.
[19]O. Bang, D. Edmundson and W. Kr o likowski. Collapse of Incoherent Light Beams in Inertial Bulk Kerr Media, Phys. Rev. Lett. 1999, 83(26): 5479-5482
[20] G. I. Stegeman and M. Segev. Optical Spatial Solitons and Their Interactions: Universality and Diversity, Science. 1999, 286: 1518-1523.
[21] A. Stepken, M. R. Belie, F. Kaiser, W. Krolikowski and B. Luther-Davies. Three Dimensional Trajectories of Interacting Incoherent Photorefractive Solitons, Phys. Rev. Lett. 1999, 82(3): 540-543.
[22] M. F. Shih and M. Segev. Incoherent Collisions Between Two-Dimensional Bright Steady-state Photorefractive Spatial Screening Solitons, Opt. Lett. 1996, 21(19):538-542.
[23] M. F. Shih, Z. Chen, M. Segev, T. Coskun and D. N. Christodoulides. Incoherent Collisions Between One-Dimensional Steady-State Photorefractive Screening Solitons, Appl. Phys. Lett. 1996, 69(27): 4151-4153.
[24] T. H. Coskun, A. G Grandpierre, N. Christodoulides and M. Segev. Coherence Enhancement of Spatially Incoherent Light Beams Through Soliton Interactions. Opt. Lett. 2000, 25(11): 826-828.
[25] D. Kip, C. Anastassiou, E. Eugenieva, D. Christodoulides and M. Segev. Transmission of Images Through Highly Nonlinear Media by Gradient-Index Lenses Formed by Incoherent Solitons, Opt. Lett. 2001, 26(8): 524-526.
[26] Z. Chen, M. Segev, D. N. Christodoulides and R. S. Feigelson. Waveguides Formed by Incoherent Dark Solitons, Opt. Lett. 2001,24(16): 1160-1162.
[27] M. J. Abliwitz, G. Biondini L. A. Ostrovsky. Optical Solitons: Perspectives and Applications, Chaos. 2000,10(3): 471-474
[28]D. N. Christodoulides, T. H. Coskun, M. Mitchell, Z. G. Chen and M. Segev.Theory of Incoherent Dark Solitons, Phys. Rev. Lett. 1998, 80(23): 5113-5116.
[29] V. V. Shkunov and D. L. Anderson, "Radiation transfer model of self-trapping spatially incoherent radiation by nonlinear media," Phys. Rev. Lett. 1998, 81(13): 2683-2686.
[30]D. N. Christodoulides, T. H. Coskun, and R. I. Joseph, "Incoherent spatial solitons in saturable nonlinear media," Opt. Lett. 1997, 22 (14): 1080-1082.
[31]H. Buljan, M. Segev, and M. Soljacic et al., "White-light solitons," Opt. Lett. 2003, 28 (14): 1239-1241.
[32] Z. Chen and K. McCarthy, "Spatial soliton pixels from partially incoherent light," Opt. Lett. 2002, 27 (22): 2019-2021.
[33] O. Katz, T. Cannon, and T. Schwartz et al.,"Observation of elliptic incoherent spatial solitons," Opt. Lett. 2004,29 (11): 1248-1250.
[34]T. H. Coskun, D. N. Christodoulides, and Z. Chen et al., "Dark incoherent soliton splitting and "phase-memory" effects: Theory and experiment," Phys. Rev. E. 1999, 59 (5): 4777-4780.
[35] D. N. Christodoulides, T. H. Coskun, M. Mitchell and M. Segev. Theory of Incoherent Self-Trapping in Biased Photorefractive Media, Phys. Rev. Lett., 1997; 78(4): 646-650
[36] W. Kr 6 likowski, D. Edmundson and O. Bang. Unified Model for Partially Coherent Solitons in Logarithmically Nonlinear Media, Phy:s. Rev. E, 2000; 61(3): 3122-3126.
[37] C. Anastaeeiou, M. Soljacic and M. Segev et al. Eliminating the Transverse Instabilities of Kerr Solitons, Phy. Rev. Lett., 2000; 85(23): 4888-4891.
[38] M. Mitchell, M. Segev, T. H. Coskun and D. N. Christodoulides. Theory of Self-Trapped Spatially Incoherent Light Beams, Phys. Rev. Lett., 1997; 79(25): 4990-4994.
[39] D. N. Christodoulides, T. H. Coskun, M. Mitchell and M. Segev. Multimode Incoherent Spatial Solitons in Logarithmically Saturable Nonlinear Media, Phys. Rev. Lett., 1998; 80(11): 2310-2315.
[40] A. W. Snyder and D. J. Mitchell. Big Incoherent Solitons, Phy. Rev. Lett. 1998; 80(7): 1422-1424.
[41]D. N. Christodoulides, E. Eugenieva, T. H. Coskun, M. Segev and M. Mitchell. Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media, Phys. Rev E, 2001;63(2): 35601-35605.