有限波束传输特性的若干问题的研究
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摘要
随着集成光学的发展,有限波束在介质中的传播特性受到了广泛关注,特别是非线性介质中空间光孤子的传输以及微结构中有限光束的Goo-H(?)nchen(GH)位移。这些现象极大地简化了目前光通讯中各类器件的结构,对于集成光学中光互连技术及光导向器件的研制具有重要的现实意义。
空间光孤子是非线性光学领域中的一个重要研究分支,是有限光束在光与物质相互作用中非线性效应和衍射效应互相制衡的结果。经过近40年的研究,人们已取得了丰硕的研究成果,但一直以来,人们对于光孤子理论和实验上的研究绝大多数都采用相干光源,即得到相干光孤子。近年来,随着实验水平和材料研究的发展,人们已开始利用非相干光源来产生非相干光孤子。非相干空间光孤子的发现改变了人们对孤子的传统观念,为孤子科学、非线性光学以及其他非线性领域开辟了新的研究领域,在实用上也将大大推动基于光孤子的全光通讯器件的发展。
另一方面,有限波束在单界面上发生全反射时,反射光束相对于几何光学的结果存在GH位移。目前,微结构中的GH位移已成为了实验和理论的研究热点之一。事实上,GH位移的深入讨论将进一步加深人们对于有限波束传播特性的理解。
本文将围绕着有限光束的传播动力学,主要研究在界面反射时有限光束的GH位移和非相干光束在非线性介质中的自陷行为,其中包括局域和非相干光孤子的传播特性和非相干耦合孤子对的传播演化特性。主要取得以下四个方面的研究成果:
一.研究了一种新型的非相干耦合孤子对在光折变介质中的传播特性,这种孤子对中的两束孤子分量光束波长相同,偏振方向相同,彼此不相干,且孤子分量光束本身也是空间非相干的。(1)得到了亮—亮、暗—暗和亮—暗型耦合孤子对中非相干孤子分量光束的强度分布,发现耦合孤子对的形成与光束的非相干性无关,但耦合孤子对的存在形式与外加电场的偏置方向有关;(2)在亮—暗型耦合孤子对的研究中,在亮、暗孤子分量强度峰值近似相等的条件下,可以得到了孤子对的解析表达式;(3)分析了构成孤子对非相干孤子分量光束的彼此无关的各相干组份光束的传播演化特性,结果表明光束的非相干性仅影响到各相干组份的强度分布,而与孤子对的强度分布无关。
二.用互谱密度法研究了白光光束在饱和对数型非线性介质中的自陷行为,得到了孤子的形成条件,光束半径和光束相干半径的精确表达式,发现光束的相干特性不但会随传播距离产生周期性的变化,且随组份频率的增大而减弱。三.首次从理论上研究了非相干白光孤子在强非局域非瞬时Kerr介质中的传输特性。发现孤子有着椭圆高斯形式的光强分布和各向异性的时空相干特性,孤子的相干半径随着频率的增大而减小。当光束的入射功率不满足孤子稳定传输的临界值时,非相干光束将会产生线性的谐振,相关特性做了详细的讨论。
四.明确提出了GH位移的概念只有在反射光束的波形与入射光束的波形基本不变时才有物理意义。数值计算表明:当光束入射角和发散度满足一定条件时,构成反射光束的每一平面波的反射相移与波矢平行与界面的分量k_y成正比关系,反射光束的波形与入射光束的波形基本不变;当光束入射角接近临界角或90度时,反射相移与波矢平行与界面的分量k_y之间的线性关系不在成立,反射光束的波形与入射光束的波形有变形,实际光束反射峰的位置已与GH位移不一致了。
With the development of integrated optics, the propagations of bounded beams in media have attracted much attention, specially the propagation of spatial optical soliton and Goos-H(a|¨)nchen (GH) displacement of finite-sized beams. These phenomena can greatly predigest the structure of the current optical communication apparatus, and have very important meaning for the optical interconnects, beam steering, and other applications.
The spatial soliton is one of major research fields in nonlinear optics, and its existence is correlated with the dynamic balance between diffraction and nonlinear effects for finite-sized beams in the interactions between optical fields and media. Much progress has been achieved in the last 40 years. But all along, attentions were mainly paid to coherent solitons in both theoretical and experimental investigations. With the recent developments in material science and experimental technology, incoherent solitons excited with incoherent light sources were experimentally observed. The findings of incoherent solitons have changed our traditional understanding of soliton phenomena and led to many new research topics. It's hopeful that the application of incoherent solitons shall improve the development of soliton-based all optical communication systems.
On the other hand, the GH displacement is the lateral displacement of the totally reflected bounded light beam off dielectric interface from the position predicted by geometrical optics. In recent years, the GH displacements in various microstructures have already become one of the hottest research topics. As a matter of fact, the further investigations of GH displacement will improve our understanding the propagation characteristics of finite-sized beams.
In this Ph.D dissertation, we will investigate the GH displacements for finite-sized beams totally reflected from a single interface, and the self-trapping behaviors of incoherent light beams in nonlinear media, including the propagation characteristics of local and nonlocal incoherent solitons, incoherently coupled screening soliton pairs. The main results given by the author include the following four parts:
(1) Incoherently coupled screening soliton pairs can be established in biased photorefractive media under steady-state conditions, each constituent of which is not only spatially incoherent with the other, but also with itself. (a) The properties of incoherently coupled soliton pairs in bright-bright, dark-dark and bright-dark configurations are studied with the coherent density approach, and the intensity expressions for these soliton pairs are given. The results show that the existence of coupled soliton pairs has nothing to do with the incoherence property of beams. However, the types of soliton pairs depend on the direction of external bias voltage. (b) The analytical solution of bright-dark soliton pair can be found when the intensity peaks of the two soliton constituents are approximately equal. (c) The propagation characteristics of coherent components that compose each constituent of coupled soliton pairs are discussed in detail. And their intensity distributions depend closely upon the incoherence property of beams.
(2) The propagation of incoherent white light beam in logarithmically saturable noninstantaneous nonlinear media is studied by using the mutual spectral density theory. The existing condition and the analytical expression of the beam radii and the coherence radii of white light solitons are obtained. The initial condition of the beam and the nonlinearity of the media decide the propagation of the beam. It is find that the coherence properties of beam evolve periodically with the distance and the spatial correlation distance is smaller for higher frequency constituents of the incoherent light.
(3) We present a theoretical investigation of incoherent accessible white-light solitons in strongly nonlocal medium with noninstantaneous Kerr nonlinearity. This soliton has elliptic Gaussian intensity profile and anisotropic spatiotemporal coherence properties. For this soliton to exist, the spatial coherence distance should be larger for lower frequencies and shorter for higher frequencies. When the incident power differs from the critical value, we demonstrate the periodic harmonic oscillations of the accessible white-light solitons.
(4) The concept of GH displacement is applicable only when the reflected beam retains the shape of the geometrically reflected or incident beam. The necessary and sufficient condition has been advanced for the totally reflected beam to retain the shape of the incident beam. Numerical simulations have shown that when the angular divergency and the incidence angle of the beam satisfies some condition, the reflection phase shift of the constituting plane wave within the divergency is linearlydependent on k_y, the parallel component of the wave vector to the interface, so that the totally reflected beam retains the shape of the incident beam well. When the incidence angle of the beam is very close to critical angle for total reflection or 90°, the requirement of linear dependence of the reflection phase shift upon k_y cannotbe fulfilled, so that the totally reflected beam is distorted from the shape of the incident beam. The actually displacement of the reflected beam cannot be regarded as a GH displacement.
空间光孤子是非线性光学领域中的一个重要研究分支,是有限光束在光与物质相互作用中非线性效应和衍射效应互相制衡的结果。经过近40年的研究,人们已取得了丰硕的研究成果,但一直以来,人们对于光孤子理论和实验上的研究绝大多数都采用相干光源,即得到相干光孤子。近年来,随着实验水平和材料研究的发展,人们已开始利用非相干光源来产生非相干光孤子。非相干空间光孤子的发现改变了人们对孤子的传统观念,为孤子科学、非线性光学以及其他非线性领域开辟了新的研究领域,在实用上也将大大推动基于光孤子的全光通讯器件的发展。
另一方面,有限波束在单界面上发生全反射时,反射光束相对于几何光学的结果存在GH位移。目前,微结构中的GH位移已成为了实验和理论的研究热点之一。事实上,GH位移的深入讨论将进一步加深人们对于有限波束传播特性的理解。
本文将围绕着有限光束的传播动力学,主要研究在界面反射时有限光束的GH位移和非相干光束在非线性介质中的自陷行为,其中包括局域和非相干光孤子的传播特性和非相干耦合孤子对的传播演化特性。主要取得以下四个方面的研究成果:
一.研究了一种新型的非相干耦合孤子对在光折变介质中的传播特性,这种孤子对中的两束孤子分量光束波长相同,偏振方向相同,彼此不相干,且孤子分量光束本身也是空间非相干的。(1)得到了亮—亮、暗—暗和亮—暗型耦合孤子对中非相干孤子分量光束的强度分布,发现耦合孤子对的形成与光束的非相干性无关,但耦合孤子对的存在形式与外加电场的偏置方向有关;(2)在亮—暗型耦合孤子对的研究中,在亮、暗孤子分量强度峰值近似相等的条件下,可以得到了孤子对的解析表达式;(3)分析了构成孤子对非相干孤子分量光束的彼此无关的各相干组份光束的传播演化特性,结果表明光束的非相干性仅影响到各相干组份的强度分布,而与孤子对的强度分布无关。
二.用互谱密度法研究了白光光束在饱和对数型非线性介质中的自陷行为,得到了孤子的形成条件,光束半径和光束相干半径的精确表达式,发现光束的相干特性不但会随传播距离产生周期性的变化,且随组份频率的增大而减弱。三.首次从理论上研究了非相干白光孤子在强非局域非瞬时Kerr介质中的传输特性。发现孤子有着椭圆高斯形式的光强分布和各向异性的时空相干特性,孤子的相干半径随着频率的增大而减小。当光束的入射功率不满足孤子稳定传输的临界值时,非相干光束将会产生线性的谐振,相关特性做了详细的讨论。
四.明确提出了GH位移的概念只有在反射光束的波形与入射光束的波形基本不变时才有物理意义。数值计算表明:当光束入射角和发散度满足一定条件时,构成反射光束的每一平面波的反射相移与波矢平行与界面的分量k_y成正比关系,反射光束的波形与入射光束的波形基本不变;当光束入射角接近临界角或90度时,反射相移与波矢平行与界面的分量k_y之间的线性关系不在成立,反射光束的波形与入射光束的波形有变形,实际光束反射峰的位置已与GH位移不一致了。
With the development of integrated optics, the propagations of bounded beams in media have attracted much attention, specially the propagation of spatial optical soliton and Goos-H(a|¨)nchen (GH) displacement of finite-sized beams. These phenomena can greatly predigest the structure of the current optical communication apparatus, and have very important meaning for the optical interconnects, beam steering, and other applications.
The spatial soliton is one of major research fields in nonlinear optics, and its existence is correlated with the dynamic balance between diffraction and nonlinear effects for finite-sized beams in the interactions between optical fields and media. Much progress has been achieved in the last 40 years. But all along, attentions were mainly paid to coherent solitons in both theoretical and experimental investigations. With the recent developments in material science and experimental technology, incoherent solitons excited with incoherent light sources were experimentally observed. The findings of incoherent solitons have changed our traditional understanding of soliton phenomena and led to many new research topics. It's hopeful that the application of incoherent solitons shall improve the development of soliton-based all optical communication systems.
On the other hand, the GH displacement is the lateral displacement of the totally reflected bounded light beam off dielectric interface from the position predicted by geometrical optics. In recent years, the GH displacements in various microstructures have already become one of the hottest research topics. As a matter of fact, the further investigations of GH displacement will improve our understanding the propagation characteristics of finite-sized beams.
In this Ph.D dissertation, we will investigate the GH displacements for finite-sized beams totally reflected from a single interface, and the self-trapping behaviors of incoherent light beams in nonlinear media, including the propagation characteristics of local and nonlocal incoherent solitons, incoherently coupled screening soliton pairs. The main results given by the author include the following four parts:
(1) Incoherently coupled screening soliton pairs can be established in biased photorefractive media under steady-state conditions, each constituent of which is not only spatially incoherent with the other, but also with itself. (a) The properties of incoherently coupled soliton pairs in bright-bright, dark-dark and bright-dark configurations are studied with the coherent density approach, and the intensity expressions for these soliton pairs are given. The results show that the existence of coupled soliton pairs has nothing to do with the incoherence property of beams. However, the types of soliton pairs depend on the direction of external bias voltage. (b) The analytical solution of bright-dark soliton pair can be found when the intensity peaks of the two soliton constituents are approximately equal. (c) The propagation characteristics of coherent components that compose each constituent of coupled soliton pairs are discussed in detail. And their intensity distributions depend closely upon the incoherence property of beams.
(2) The propagation of incoherent white light beam in logarithmically saturable noninstantaneous nonlinear media is studied by using the mutual spectral density theory. The existing condition and the analytical expression of the beam radii and the coherence radii of white light solitons are obtained. The initial condition of the beam and the nonlinearity of the media decide the propagation of the beam. It is find that the coherence properties of beam evolve periodically with the distance and the spatial correlation distance is smaller for higher frequency constituents of the incoherent light.
(3) We present a theoretical investigation of incoherent accessible white-light solitons in strongly nonlocal medium with noninstantaneous Kerr nonlinearity. This soliton has elliptic Gaussian intensity profile and anisotropic spatiotemporal coherence properties. For this soliton to exist, the spatial coherence distance should be larger for lower frequencies and shorter for higher frequencies. When the incident power differs from the critical value, we demonstrate the periodic harmonic oscillations of the accessible white-light solitons.
(4) The concept of GH displacement is applicable only when the reflected beam retains the shape of the geometrically reflected or incident beam. The necessary and sufficient condition has been advanced for the totally reflected beam to retain the shape of the incident beam. Numerical simulations have shown that when the angular divergency and the incidence angle of the beam satisfies some condition, the reflection phase shift of the constituting plane wave within the divergency is linearlydependent on k_y, the parallel component of the wave vector to the interface, so that the totally reflected beam retains the shape of the incident beam well. When the incidence angle of the beam is very close to critical angle for total reflection or 90°, the requirement of linear dependence of the reflection phase shift upon k_y cannotbe fulfilled, so that the totally reflected beam is distorted from the shape of the incident beam. The actually displacement of the reflected beam cannot be regarded as a GH displacement.
引文
[1] R.Y.Chiao, E.Garmire, and C.H.Townes, "Self-Trapping of Optical Beams", Phys. Rev. Lett., 13(15), 479-482 (1964)
[2] M. Segev and G. Stegeman, "Self-Trapping of Optical Beams: Spatial Solitons", Phys. Today, 51(8): 42-48 (1998).
[3] G. I. A. Stegeman, D. N. Christodoulides and M. Segev, "Optical Spatical Solitons: Historical Perspectives", IEEE J. Quan. Elec, 6(6), 1419-1422 (2000)
[4] Duree G. et al. 1993, "Observation of an optical beam due to the photorefractive effect". Phys. Rev. Lett., 71, 533-536(1993)
[5] M. Mitchell, Z. Chen, M. Shih, and M. Segev, "Self trappingof partially spatially incoherent light", Phys. Rev. Lett., 77(3), 490-493(1996).
[6] M. Mitchell, and M. Segev, "Self-trapping of incoherent white light", Nature (London) 387(26), 880-883(1997).
[7] Z.Chen, M. Mitchell, M. Megev, T. H.Coskun, and D. N. Christodoulides, "Self-trapping of dark incoherent light beams", Science 280, 889 (1998)
[8] O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segevand D. N. Christodoulides, "Observation of random-phase lattice solitons", Nature(London) 433, 500(2005)
[9] M. Peccianti and G. Assanto, "Incoherent spatial solitary waves in nematic liquid crystals", Opt. Lett., 26, 1791 (2001)
[10] M. Peccianti and G. Assanto, "Nematic liquid crystals: A suitable medium for self-confinement of coherent and incoherent light", Phys. Rev. E 65, 035603(R)(2002)
[11] W. Krolikowski, O. Bang, and J. Wyller, "Nonlocal incoherent solitons", Phys. Rev. E 70, 036617 (2004)
[12] K. G. Makris, H. Sarkissian, D. N. Christodoulides, and G. Assanto, "Nonlocal incoherent spatial solitons in liquid crystals", J. Opt. Soc. Am. B22, 1371 (2005)
[13]F.Goos and H.Hanchen,"Ein neuer und funamentaler Versuch zur Totalreflexion",Ann.Phys.,(Leipzig) 1,333-346(1947)
[14]F.Goos and H.Hanchen,"Neumessung des Strahlversetzungs effektes bei Totalreflexion",Ann.Phys.(Leipzig) 5,251-252(1949)
[15]K.V.Artmann,"Berechung der seitenversetzung des reflektieren strahles".Ann.Phys.(Leipzig) 2,87-102(1948)
[16]R.H.Renard,"Total reflection:a new evaluation of the Goos- Hanchen shift",J.Opt.Soc.Am.54(10),1190-1197(1964)
[17]J.J.Cowan and B.Anicin,"Longitudinal and transsver displacements of a bounded microwave beam at total internal reflection",J.Opt.Soc.Am.67(10),1307-1314(1977)
[18]F.Bretenaker,A.L.Floch and L.Dutriaux,"Direct measurement of the optical Goos- Hanchen effect in lasers",Phys.Rev.Lett.,68(7),931-933(1992)
[19]H.Gills,S.Girard,and J.Hamel,"Simple technique for measuring the Goos-Hanchen effect with polarization modulation and a position-sensitive detector",Opt.lett.,27(16) 1421-1423(2002)
[20]W.J.Wild and C.L.Giles,"Goos-Hanchen shift from absorbing media",phys.Rev.A 25(4) 2099-2101(1982)
[21]E.Pfleghaar,A.Mareseille and A.Weis,"Quantitative investigation of the effect of resonant absorbers on the Goos-Hanchen stift",phys.Rev.lett.,70 2281-2284(1993)
[22]O.Emile,T.Galstyan,A.LeFloch,and F.Bretenaker,"Measurement of the nonlinear Goos-Hanchen effect for Gaussian optical beams",Phys.Rev.Lett.75,1511-1513(1995)
[23]B.M.Jost,A.A.R.Al-Rashed,and B.E.A.Salch,"Observation of the Goos-Hanchen effect in a phase-conjugate mirror",Phys.Rev.Lett.,81,2233-2235(1998)
[24]P.R.Berman,"Goos-Hanchen shift in negatively refractive media",phys.Rev.E 66(6) 067603(2002)
[25]R.Kaiser,Y.Levy,J.Fleming atal,"Resonances in a single thin dielectric layer:enhanement of the Goos-Hanchen shift",Pure Appl.Opt.,5(6) 891-898(1996)
[26] C.F.Li and X. Y. Yang, "Thin-film enhanced Goos-Hanchen shift in total internal reflection", Chin. Phys. Lett. 21(3) 485-488 (2004)
[27] F.Pillon, H.Gilles, S. Girard , "Goos-Hanchen and Imbert-Fedorov shift for leaky guided modes", J.Opt. Soc. Am. B. 22(6) 1290-1299 (2005)
[28] X. Yin, L. Hesselink, Z. Liu etal, "Large positive and negative lateral optical beam displacements due to surface plasmon resonance", Appl. Phys. Lett., 85(3) 372-373 (2004)
[29] H. M. Lai, F. C. Chang and W. K. Tang, "Goos-Hanchen effect around and off the critical angle", J. Opt. Soc. Am. A, 3(4) 550-557 (1986)
[30] C.K.Carniglia and K.R.Brownstein, "Focal shift and mode for total internal reflection", J. Opt. Soc. Am., 67 121-122 (1977)
[31] C. W. Huse and T. Tamir, "Lateral displacement and distortion of beams incident upon a transmitting layer configuration", J. Opt. Soc. Am. A, 2 978-987(1985)
[32] A. W. Snyder and D. J. Mitchell, "Accessible solitons", Science 276, 1538 (1997)
[33] D. J. Mitchell and A. W. Snyder, "Soliton dynamics in a nonlocal medium", J. Opt. Soc. Am. B 16, 236 (1999).
[34] Y. R. Shen, "Solitons made simple", Science 276, 1520 (1997).
[35] W. Krolikowski and O. Bang, "Solitons in nonlocal nonlinear media: Exact solutions", Phys. Rev. E 63, 016610 (2001).
[36] Zhiyong Xu, Y. V. Kartashov and L. Torner, "Upper threshold for stability of multipole-mode solitons in nonlocal nonlinear media", Opt. Lett. 30, 3171(2005)
[37] C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, L. Torner, and O. Cohen, "Two-dimensional multipole solitons in nonlocal nonlinear media", Opt. Lett. 31, 3312(2006)
[38] Y. V. Kartashov, L. Torner, V. A. Vysloukh, and D. Mihalache, "Multipole vector solitons in nonlocal nonlinear media", Opt. Lett. 31, 1483 (2006)
[39] Zhiyong Xu, Y. V. Kartashov, and L. Torner, "Stabilization of vector soliton complexes in nonlocal nonlinear media", Phys. Rev. E 73, 055601(R)(2006)
[40] A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz and M. A. Karpierz, "Discrete propagation and spatial solitons in nematic liquid crystals", Opt. Lett. 29, 1530(2004)
[41] A. Fratalocchi and G. Assanto, "Discrete light localization in one-dimensional nonlinear lattices with arbitrary nonlocality", Phys. Rev. E 72,066608 (2005)
[42] Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Tunable Soliton Self-Bending in Optical Lattices with Nonlocal Nonlinearity", Phys. Rev. Lett., 93, 153903(2004)
[43] Zhiyong Xu, Y. V. Kartashov, and L. Torner, "Soliton Mobility in Nonlocal Optical Lattices", Phys. Rev. Lett., 95, 113901 (2005)
[44] N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, "Attraction of nonlocal dark optical solitons", Opt. Lett., 29, 286 (2004)
[45] W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, "Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media", J. Opt. B: Quantum Semiclassical Opt. 6, S288 (2004)
[46] W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, "Modulational instability in nonlocal nonlinear Kerr media", Phys. Rev. E 64, 016612 (2001)
[47] J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, "Generic features of modulational instability in nonlocal Kerr media", Phys. Rev. E 66, 066615(2002)
[48] C. Conti, Marco Peccianti, and G. Assanto, "Spatial solitons and modulational instability in the presence of large birefringence: The case of highly nonlocal liquid crystals", Phys. Rev. E 72, 066614 (2005)
[49] M. Peccianti, C. Conti, and G. Assanto, "Optical modulational instability in a nonlocal medium", Phys. Rev., E 68, 025602(R) (2003)
[50] M. Peccianti, C. Conti, G. Assanto, A. D. Luca and C. Umeton, "Routing of anisotropic spatial solitons and modulational instability in liquid crystals", Nature (London) 432, 733 (2004)
[51] M. Peccianti, C. Conti, E. Alberici and G. Assanto, "Spatially incoherent modulation instability in a nonlocal medium", Laser Physics Letters 2, 25 (2005)
[52] X. Hutsebaut, C. Cambournac, M. Haelterman, A. Admski, and K. Neyts, "Single-component higher-order mode solitons in nematic liquid crystals", Opt. Commun., 233, 211 (2004)
[53] C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, "Solitons in Nonlinear Media with an Infinite Range of Nonlocality: First Observation of Coherent Elliptic Solitons and of Vortex-Ring Solitons", Phys. Rev. lett., 95, 213904 (2005)
[54] M. Peccianti, K. A. Brzdakiewicz, and G. Assanto, "Nonlocal spatial soliton interactions in nematic liquid crystals", Opt. Lett., 27, 1460 (2002)
[55] P. D. Rasmussen, O. Bang, and W. Krolikowski, "Theory of nonlocal soliton interaction in nematic liquid crystals", Phys. Rev. E 72, 066611 (2005)
[56] C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, "Long-range interactions between optical solitons", Nature Physics 2, 769 (2006)
[57] D. Briedis, D. E. Petersen, D. Edmundson et. al., "Ring vortex solitons in nonlocal nonlinear media", Opt. Exp. 13, 435 (2005)
[58] A. I. Yakimenko, Y. A. Zaliznyak, and Yu. S. Kivshar, "Stable vortex solitons in nonlocal self-focusing nonlinear media", Phys. Rev. E 71, 065603(R)(2005)
[59] S. Lopez-Aguayo, A. S. Desyatnikov, Yu. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, "Stable rotating dipole solitons in nonlocal optical media", Opt. Lett., 31, 1100 (2006)
[60] D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L. C. Crasovan, and L. Torner, "Three-dimensional spatiotemporal optical solitons in nonlocal nonlinear media", Phys. Rev. E 73, 025602(R) (2006)
[61] S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, "Stability of two-dimensional spatial solitons in nonlocal nonlinear media", Phys. Rev. E 73, 066603 (2006)
[62]Y.V.Kartashov,L.Torner,and V.A.Vysloukh,"Lattice-supported surface solitons in nonlocal nonlinear media",Opt.Lett.31,2595(2006)
[63]陈园园,王奇,施解龙,卫青,“部分相干光束的振荡自陷特性”,物理学报,51(03),559(2002)
[64]陈园园,王奇,施解龙,“非相干多分量空间双稳态孤子”,物理学报,53(4),1070(2004)
[65]陈园园,王奇,施解龙,“空间非相干多分量光束构成的非相干耦合屏蔽孤子对”,物理学报,53(9),2980(2004)
[66]M.Shen,Q.Wang,J.L.Shi,Y.Y.Chen,and X.L.Wang,"Nonlocal incoherent white-light solitons in logarithmically nonlinear media",Phys.Rev.E 72,026604(2005)
[67]M.Shen,Q.Wang,J.L.Shi,P.Hou,and Q.Kong,"Partially coherent accessible solitons in strongly nonlocal media",Phys.Rev.E 73,056602(2006)
[68]M.Shen,J.L.Shi,and Q.Wang,"Incoherent accessible white-light solitons in strongly nonlocal Kerr media",Phys.Rev.E 74,027601(2006)
[69]M.Shen,Q.Wang,and J.L.Shi,"Elliptic incoherent accessible solitons in strongly nonlocal media",Opt.Commun.,270,384(2007)
[70]王晓生,何国岗,佘卫龙.复色光光伏空间孤子,物理学报,50(3)496-500(2001)
[71]王晓生,余卫龙.部分空间非相干光光伏空间孤子,物理学报,51(3)573-578(2002)
[72]Q.Guo,B.Luo,F.Yi,S.Chi,and Yiqun Xie,"Large phase shift of nonlocal optical spatial solitons",Phys.Rev.E 69,016602(2004)
[73]Y.Q.Xie and Q.Guo,"Phase modulations due to collisions of beam pairs in nonlocal nonlinear media",Optical and Quantum Electronics 6,1335(2004)
[74]Q.Guo,B.Luo,and S.Chi,"Optical beams in sub-strongly non-local nonlinear media:A variational solution",Opt.Commun.,259,336(2005)
[75]Y.Huang,Q.Guo,and J.Cao,"Optical beams in lossy non-local Kerr media", Opt. Commun., 261, 175 (2006)
[76] D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, "Theory of incoherent self-focusing in biased photorefractive media", Phys. Rev. Lett., 78,646(1997)
[77] D. N. Christodoulides, T. H. Coskun, and R. I. Joseph, "Incoherent spatial solitons in saturable nonlinear media", Opt. Lett., 22, 1080 (1997)
[78] T. H. Coskun, D. N. Christodoulides, M. Mitchell, Z. Chen, and M. Segev, "Dynamics of incoherent bright and dark self-trapped beams and their coherence properties in photorefracrive crystals", Opt. Lett., 23(6), 418-420(1998)
[79] T. H. Coskun, A. G. Drandpierre, D. N. Christodoulides, and M. Segev, "Coherence enhancement of spatially incoherent light beams through soliton interactions", Opt. Lett., 25, 826 (2000)
[80] M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, "Theory of self-trapped spatially incoherent light beams", Phys. Rev. Lett., 79, 4990(1997)
[81] D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, "Multimode incoherent spatial solitons in logarithmically saturable nonlinear media", Phys. Rev. Lett., 80, 2310-2313 (1998)
[82] 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", Phys. Rev. E 59, 1193 (1999)
[83] W. Krolikowski, D. Edmundson, and O. Bang, "Unified model for partially coherent solitons in logarithmically nonlinear media", Phys. Rev. E 61(3), 3122-3126(2000)
[84] S. A. Ponomarenko, "Linear superposition principle for partially coherent solitons", Phys. Rev. E 65, 055601(R) (2002)
[85] H. Buljan, A. Siber, M. Soljacic, and M. Segev, "Propagation of incoherent white light and modulation instability in noninstantaneous nonlinear media", Phys. Rev. E 66, 035601(R) (2002)
[86] H. Buljan, M. Segev, M. Soljacic, N. K. Efremidis, and D. N. Christodoulides, "White-light solitons", Opt. Lett., 28, 1239(2003)
[87] H. Buljan, A. Siber, M. Soljacic, T. Schwartz, M. Segev, and D. N. Christodoulides, "Incoherent white light solitons in logarithmically saturable noninstantaneous nonlinear media", Phys. Rev. E 68, 036607(2003)
[88] H. Buljan, T. Schwartz, M. Segev, M. Soljacic, and D. N. Christodoulides, "Polychromatic partially spatially incoherent solitons in a noninstantaneous Kerr nonlinear medium" , J. Opt. Soc. Am. B 21, 397 (2004)
[89] K.Yasumoto and Y. Oishi, "A new evaluation of the Goos-Hanchen shift and associated time delay", J. Appl. Phys., 54(5) 2170-2176 (1983)
[90] Y. S. Kivshar and G. I. Stegeman, "Spatial Optical Solitons: Guiding Light for Future Technologies", Optics and Photonics News, 2, 59-63 (2002)
[91] Y. Kivshar. Dark solitons in nonlinear optics, IEEE J.Quantum Electron., 29(1),250-264(1993)
[92] A. W. Snyder, D. J. Mitchell and Y. S. Kivshar, "Unification of Linear and Nonlinear Wave Optics", Mod. Phys. Lett. B, 9 1479-1506 (1995)
[93] D. N. Christodoulides, S. R. Singh, M. I.Carvalho and M. Segev. "Incoherently Coupled Soliton Pairs in Biased Photorefractive Crystals", Appl. Phys. Lett., 68(13): 1763-1965 (1996)
[94] Z. G. Chen, M. Segev and T. H. Coskun, et al. "Coupled Photorefractive Spatial Soliton Pairs", J. Opt. Soc. Am. B, 14(11), 3066-3069 (1997)
[95]H. Meng, G. Salamo and M. Segev. "Coherent Collisions of Photorefractive Solitons", Opt. Lett., 22(7), 448-453 (1997)
[96] W. Krolikowski, N. Akhmediev, B. L. Davies and M. C. Golomb "Self-Bending Photorefractive Solitons", Phys. Rev. E, 54(5): 5761-5763 (1996)
[97] A.W. Snyder and A. P. Sheppard. "Collisions, Steering, and Guidance with Spatial Solitons", Opt. Lett., 18(7). 482-485 (1993)
[98] D. M. Baboiu, G. I. Stegeman and L. Torner. "Interaction of One-Dimensional Bright Solitary Waves in Quadratic Media", Opt. Lett., 20(22): 2282-2283 (1995)
[99] S. Trillo, S. Wabnitz, E. M. Wright and G. I. Stegeman. "Optical Solitary Waves Induced by Cross-Phase Modulation", Opt. Lett., 13(10): 871-874 (1988)
[100] V. V. Afanasjev, Y. Kivshar, V.V.Konotop and V.N.Serkin. "Dynamics of Coupled Dark and Bright Optical Solitons", Opt. Lett., 14(15) 805-809 (1989)
[101] R. De La Fuente and A. Barthelemy. "Spatial Solitons Pairing by Cross Phase Modulation", Opt. Commun., 88(5): 419-423 (1992)
[102] M. Shalaby and 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., 28(12) 2736-2741(1992)
[103] T. P. Valkering, J. V. Honschoten and H. J. W. M. Hoekstra, Ultra-Sharp Soliton Switching in a Directional Coupler, Opt. Comm., 159(1): 215-218(1999)
[104]M. Segev, B .Crosignani, A. Yuriv and A. Fischer. "Spatial Solitons in Photorefractive Media", Phys. Rev. Lett., 68(7) 923-926 (1992)
[105] Z.Chen, M.Segev and T.H.Coskun, et al. "Incoherently Coupled Dark-Bright Photorefractive Solitons", Opt. Lett., 21(22) 1821-1823 (1996)
[106] H. C. Feng and J. Y. Yuan et al. "Incoherently Coupled Soliton Pairs in Photorefractive Polymer", Opt. Mat., 19(3) 377-381 (2002)
[107] L. Mandel and E. Wolf. "Optical Coherence and Quantum Optics". New York : Cambridge University Press, (1995)
[108] A. W. Snyder and D. J. Mitchell. "Big Incoherent Solitons", Phy. Rev. Lett., 80(7) 1422-1424(1998)
[109] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical Functions", New York: Dover, (1970)
[110] C. Conti, M. Peccianti, and G. Assanto, "Route to nonlocality and observation of accessible solitons", Phys. Rev. lett. 91, 073901 (2003)
[111] C. Conti, M. Peccianti, and G. Assanto, "Observation of optical spatial solitons in a highly nonlocal medium", Phys. Rev. lett., 92, 113902 (2004)
[112] O. Cohen, H. Buljan, T. Schwartz, J. W. Fleischer, and M. Segev, "Incoherent solitons in instantaneous nonlocal nonlinear media", Phys. Rev. E73, 015601(R)(2006)
[113]E. D. Eugenieva, D.N. Christodoulides and M. Segev, "Elliptic incoherent solitons in saturable nonlinear media", Opt. Lett., 25, 972 (2000)
[114]O. Katz, T. Carmon, T. Schwartz, M. Segev, and D. N. Christodoulides, "Observation of elliptic incoherent spatial solitons", Opt. Lett. 29, 1248 (2004)
[115] O. Bang, W. Krolikowski, J. Wyller and J. J. Rasmussen, "Collapse arrest and soliton stabilization in nonlocal nonlinear media", Phys. Rev. E 66, 046619(2002)
[116] L. Brillouin, "Wave propagation and Group Velocity", New York: Academic Press (1960)
[117] O. C. de Beauregard and C. Imbert, "Quantized Longitudinal and Transverse Shifts Associated with Total Internal Reflection" Phys. Rev. Lett., 28 1211 (1972)
[118] R. Fischer, D. N. Neshev, W. Krolikowski, Y. S. Kivshar, D. Iturbe-Castillo, S.Chavez-Cerda, M. R. Meneghetti, D. P. Caetano and J. M. Hickman " Oblique interaction of spatial dark-soliton stripes in nonlocal media," Opt. Lett., 31, 3010 (2006)
[119] M. Peccianti, A. Dyadyusha, M. Kaczmarek and G. Assanto, "Tunable refraction andreflection of self-confined light beams," Nature Physics 2, 737 (2006).
[ 120] Y. S. Kivshar, " Bending light at will," Nature Physics 2, 729 (2006).
[121] S. Ouyang, Q. Guo, and Wei Hu, " Perturbative analysis of generally nonlocal spatial optical solitons," Phys. Rev. E (in press).
[2] M. Segev and G. Stegeman, "Self-Trapping of Optical Beams: Spatial Solitons", Phys. Today, 51(8): 42-48 (1998).
[3] G. I. A. Stegeman, D. N. Christodoulides and M. Segev, "Optical Spatical Solitons: Historical Perspectives", IEEE J. Quan. Elec, 6(6), 1419-1422 (2000)
[4] Duree G. et al. 1993, "Observation of an optical beam due to the photorefractive effect". Phys. Rev. Lett., 71, 533-536(1993)
[5] M. Mitchell, Z. Chen, M. Shih, and M. Segev, "Self trappingof partially spatially incoherent light", Phys. Rev. Lett., 77(3), 490-493(1996).
[6] M. Mitchell, and M. Segev, "Self-trapping of incoherent white light", Nature (London) 387(26), 880-883(1997).
[7] Z.Chen, M. Mitchell, M. Megev, T. H.Coskun, and D. N. Christodoulides, "Self-trapping of dark incoherent light beams", Science 280, 889 (1998)
[8] O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segevand D. N. Christodoulides, "Observation of random-phase lattice solitons", Nature(London) 433, 500(2005)
[9] M. Peccianti and G. Assanto, "Incoherent spatial solitary waves in nematic liquid crystals", Opt. Lett., 26, 1791 (2001)
[10] M. Peccianti and G. Assanto, "Nematic liquid crystals: A suitable medium for self-confinement of coherent and incoherent light", Phys. Rev. E 65, 035603(R)(2002)
[11] W. Krolikowski, O. Bang, and J. Wyller, "Nonlocal incoherent solitons", Phys. Rev. E 70, 036617 (2004)
[12] K. G. Makris, H. Sarkissian, D. N. Christodoulides, and G. Assanto, "Nonlocal incoherent spatial solitons in liquid crystals", J. Opt. Soc. Am. B22, 1371 (2005)
[13]F.Goos and H.Hanchen,"Ein neuer und funamentaler Versuch zur Totalreflexion",Ann.Phys.,(Leipzig) 1,333-346(1947)
[14]F.Goos and H.Hanchen,"Neumessung des Strahlversetzungs effektes bei Totalreflexion",Ann.Phys.(Leipzig) 5,251-252(1949)
[15]K.V.Artmann,"Berechung der seitenversetzung des reflektieren strahles".Ann.Phys.(Leipzig) 2,87-102(1948)
[16]R.H.Renard,"Total reflection:a new evaluation of the Goos- Hanchen shift",J.Opt.Soc.Am.54(10),1190-1197(1964)
[17]J.J.Cowan and B.Anicin,"Longitudinal and transsver displacements of a bounded microwave beam at total internal reflection",J.Opt.Soc.Am.67(10),1307-1314(1977)
[18]F.Bretenaker,A.L.Floch and L.Dutriaux,"Direct measurement of the optical Goos- Hanchen effect in lasers",Phys.Rev.Lett.,68(7),931-933(1992)
[19]H.Gills,S.Girard,and J.Hamel,"Simple technique for measuring the Goos-Hanchen effect with polarization modulation and a position-sensitive detector",Opt.lett.,27(16) 1421-1423(2002)
[20]W.J.Wild and C.L.Giles,"Goos-Hanchen shift from absorbing media",phys.Rev.A 25(4) 2099-2101(1982)
[21]E.Pfleghaar,A.Mareseille and A.Weis,"Quantitative investigation of the effect of resonant absorbers on the Goos-Hanchen stift",phys.Rev.lett.,70 2281-2284(1993)
[22]O.Emile,T.Galstyan,A.LeFloch,and F.Bretenaker,"Measurement of the nonlinear Goos-Hanchen effect for Gaussian optical beams",Phys.Rev.Lett.75,1511-1513(1995)
[23]B.M.Jost,A.A.R.Al-Rashed,and B.E.A.Salch,"Observation of the Goos-Hanchen effect in a phase-conjugate mirror",Phys.Rev.Lett.,81,2233-2235(1998)
[24]P.R.Berman,"Goos-Hanchen shift in negatively refractive media",phys.Rev.E 66(6) 067603(2002)
[25]R.Kaiser,Y.Levy,J.Fleming atal,"Resonances in a single thin dielectric layer:enhanement of the Goos-Hanchen shift",Pure Appl.Opt.,5(6) 891-898(1996)
[26] C.F.Li and X. Y. Yang, "Thin-film enhanced Goos-Hanchen shift in total internal reflection", Chin. Phys. Lett. 21(3) 485-488 (2004)
[27] F.Pillon, H.Gilles, S. Girard , "Goos-Hanchen and Imbert-Fedorov shift for leaky guided modes", J.Opt. Soc. Am. B. 22(6) 1290-1299 (2005)
[28] X. Yin, L. Hesselink, Z. Liu etal, "Large positive and negative lateral optical beam displacements due to surface plasmon resonance", Appl. Phys. Lett., 85(3) 372-373 (2004)
[29] H. M. Lai, F. C. Chang and W. K. Tang, "Goos-Hanchen effect around and off the critical angle", J. Opt. Soc. Am. A, 3(4) 550-557 (1986)
[30] C.K.Carniglia and K.R.Brownstein, "Focal shift and mode for total internal reflection", J. Opt. Soc. Am., 67 121-122 (1977)
[31] C. W. Huse and T. Tamir, "Lateral displacement and distortion of beams incident upon a transmitting layer configuration", J. Opt. Soc. Am. A, 2 978-987(1985)
[32] A. W. Snyder and D. J. Mitchell, "Accessible solitons", Science 276, 1538 (1997)
[33] D. J. Mitchell and A. W. Snyder, "Soliton dynamics in a nonlocal medium", J. Opt. Soc. Am. B 16, 236 (1999).
[34] Y. R. Shen, "Solitons made simple", Science 276, 1520 (1997).
[35] W. Krolikowski and O. Bang, "Solitons in nonlocal nonlinear media: Exact solutions", Phys. Rev. E 63, 016610 (2001).
[36] Zhiyong Xu, Y. V. Kartashov and L. Torner, "Upper threshold for stability of multipole-mode solitons in nonlocal nonlinear media", Opt. Lett. 30, 3171(2005)
[37] C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, L. Torner, and O. Cohen, "Two-dimensional multipole solitons in nonlocal nonlinear media", Opt. Lett. 31, 3312(2006)
[38] Y. V. Kartashov, L. Torner, V. A. Vysloukh, and D. Mihalache, "Multipole vector solitons in nonlocal nonlinear media", Opt. Lett. 31, 1483 (2006)
[39] Zhiyong Xu, Y. V. Kartashov, and L. Torner, "Stabilization of vector soliton complexes in nonlocal nonlinear media", Phys. Rev. E 73, 055601(R)(2006)
[40] A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz and M. A. Karpierz, "Discrete propagation and spatial solitons in nematic liquid crystals", Opt. Lett. 29, 1530(2004)
[41] A. Fratalocchi and G. Assanto, "Discrete light localization in one-dimensional nonlinear lattices with arbitrary nonlocality", Phys. Rev. E 72,066608 (2005)
[42] Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Tunable Soliton Self-Bending in Optical Lattices with Nonlocal Nonlinearity", Phys. Rev. Lett., 93, 153903(2004)
[43] Zhiyong Xu, Y. V. Kartashov, and L. Torner, "Soliton Mobility in Nonlocal Optical Lattices", Phys. Rev. Lett., 95, 113901 (2005)
[44] N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, "Attraction of nonlocal dark optical solitons", Opt. Lett., 29, 286 (2004)
[45] W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, "Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media", J. Opt. B: Quantum Semiclassical Opt. 6, S288 (2004)
[46] W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, "Modulational instability in nonlocal nonlinear Kerr media", Phys. Rev. E 64, 016612 (2001)
[47] J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, "Generic features of modulational instability in nonlocal Kerr media", Phys. Rev. E 66, 066615(2002)
[48] C. Conti, Marco Peccianti, and G. Assanto, "Spatial solitons and modulational instability in the presence of large birefringence: The case of highly nonlocal liquid crystals", Phys. Rev. E 72, 066614 (2005)
[49] M. Peccianti, C. Conti, and G. Assanto, "Optical modulational instability in a nonlocal medium", Phys. Rev., E 68, 025602(R) (2003)
[50] M. Peccianti, C. Conti, G. Assanto, A. D. Luca and C. Umeton, "Routing of anisotropic spatial solitons and modulational instability in liquid crystals", Nature (London) 432, 733 (2004)
[51] M. Peccianti, C. Conti, E. Alberici and G. Assanto, "Spatially incoherent modulation instability in a nonlocal medium", Laser Physics Letters 2, 25 (2005)
[52] X. Hutsebaut, C. Cambournac, M. Haelterman, A. Admski, and K. Neyts, "Single-component higher-order mode solitons in nematic liquid crystals", Opt. Commun., 233, 211 (2004)
[53] C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, "Solitons in Nonlinear Media with an Infinite Range of Nonlocality: First Observation of Coherent Elliptic Solitons and of Vortex-Ring Solitons", Phys. Rev. lett., 95, 213904 (2005)
[54] M. Peccianti, K. A. Brzdakiewicz, and G. Assanto, "Nonlocal spatial soliton interactions in nematic liquid crystals", Opt. Lett., 27, 1460 (2002)
[55] P. D. Rasmussen, O. Bang, and W. Krolikowski, "Theory of nonlocal soliton interaction in nematic liquid crystals", Phys. Rev. E 72, 066611 (2005)
[56] C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, "Long-range interactions between optical solitons", Nature Physics 2, 769 (2006)
[57] D. Briedis, D. E. Petersen, D. Edmundson et. al., "Ring vortex solitons in nonlocal nonlinear media", Opt. Exp. 13, 435 (2005)
[58] A. I. Yakimenko, Y. A. Zaliznyak, and Yu. S. Kivshar, "Stable vortex solitons in nonlocal self-focusing nonlinear media", Phys. Rev. E 71, 065603(R)(2005)
[59] S. Lopez-Aguayo, A. S. Desyatnikov, Yu. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, "Stable rotating dipole solitons in nonlocal optical media", Opt. Lett., 31, 1100 (2006)
[60] D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L. C. Crasovan, and L. Torner, "Three-dimensional spatiotemporal optical solitons in nonlocal nonlinear media", Phys. Rev. E 73, 025602(R) (2006)
[61] S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, "Stability of two-dimensional spatial solitons in nonlocal nonlinear media", Phys. Rev. E 73, 066603 (2006)
[62]Y.V.Kartashov,L.Torner,and V.A.Vysloukh,"Lattice-supported surface solitons in nonlocal nonlinear media",Opt.Lett.31,2595(2006)
[63]陈园园,王奇,施解龙,卫青,“部分相干光束的振荡自陷特性”,物理学报,51(03),559(2002)
[64]陈园园,王奇,施解龙,“非相干多分量空间双稳态孤子”,物理学报,53(4),1070(2004)
[65]陈园园,王奇,施解龙,“空间非相干多分量光束构成的非相干耦合屏蔽孤子对”,物理学报,53(9),2980(2004)
[66]M.Shen,Q.Wang,J.L.Shi,Y.Y.Chen,and X.L.Wang,"Nonlocal incoherent white-light solitons in logarithmically nonlinear media",Phys.Rev.E 72,026604(2005)
[67]M.Shen,Q.Wang,J.L.Shi,P.Hou,and Q.Kong,"Partially coherent accessible solitons in strongly nonlocal media",Phys.Rev.E 73,056602(2006)
[68]M.Shen,J.L.Shi,and Q.Wang,"Incoherent accessible white-light solitons in strongly nonlocal Kerr media",Phys.Rev.E 74,027601(2006)
[69]M.Shen,Q.Wang,and J.L.Shi,"Elliptic incoherent accessible solitons in strongly nonlocal media",Opt.Commun.,270,384(2007)
[70]王晓生,何国岗,佘卫龙.复色光光伏空间孤子,物理学报,50(3)496-500(2001)
[71]王晓生,余卫龙.部分空间非相干光光伏空间孤子,物理学报,51(3)573-578(2002)
[72]Q.Guo,B.Luo,F.Yi,S.Chi,and Yiqun Xie,"Large phase shift of nonlocal optical spatial solitons",Phys.Rev.E 69,016602(2004)
[73]Y.Q.Xie and Q.Guo,"Phase modulations due to collisions of beam pairs in nonlocal nonlinear media",Optical and Quantum Electronics 6,1335(2004)
[74]Q.Guo,B.Luo,and S.Chi,"Optical beams in sub-strongly non-local nonlinear media:A variational solution",Opt.Commun.,259,336(2005)
[75]Y.Huang,Q.Guo,and J.Cao,"Optical beams in lossy non-local Kerr media", Opt. Commun., 261, 175 (2006)
[76] D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, "Theory of incoherent self-focusing in biased photorefractive media", Phys. Rev. Lett., 78,646(1997)
[77] D. N. Christodoulides, T. H. Coskun, and R. I. Joseph, "Incoherent spatial solitons in saturable nonlinear media", Opt. Lett., 22, 1080 (1997)
[78] T. H. Coskun, D. N. Christodoulides, M. Mitchell, Z. Chen, and M. Segev, "Dynamics of incoherent bright and dark self-trapped beams and their coherence properties in photorefracrive crystals", Opt. Lett., 23(6), 418-420(1998)
[79] T. H. Coskun, A. G. Drandpierre, D. N. Christodoulides, and M. Segev, "Coherence enhancement of spatially incoherent light beams through soliton interactions", Opt. Lett., 25, 826 (2000)
[80] M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, "Theory of self-trapped spatially incoherent light beams", Phys. Rev. Lett., 79, 4990(1997)
[81] D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, "Multimode incoherent spatial solitons in logarithmically saturable nonlinear media", Phys. Rev. Lett., 80, 2310-2313 (1998)
[82] 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", Phys. Rev. E 59, 1193 (1999)
[83] W. Krolikowski, D. Edmundson, and O. Bang, "Unified model for partially coherent solitons in logarithmically nonlinear media", Phys. Rev. E 61(3), 3122-3126(2000)
[84] S. A. Ponomarenko, "Linear superposition principle for partially coherent solitons", Phys. Rev. E 65, 055601(R) (2002)
[85] H. Buljan, A. Siber, M. Soljacic, and M. Segev, "Propagation of incoherent white light and modulation instability in noninstantaneous nonlinear media", Phys. Rev. E 66, 035601(R) (2002)
[86] H. Buljan, M. Segev, M. Soljacic, N. K. Efremidis, and D. N. Christodoulides, "White-light solitons", Opt. Lett., 28, 1239(2003)
[87] H. Buljan, A. Siber, M. Soljacic, T. Schwartz, M. Segev, and D. N. Christodoulides, "Incoherent white light solitons in logarithmically saturable noninstantaneous nonlinear media", Phys. Rev. E 68, 036607(2003)
[88] H. Buljan, T. Schwartz, M. Segev, M. Soljacic, and D. N. Christodoulides, "Polychromatic partially spatially incoherent solitons in a noninstantaneous Kerr nonlinear medium" , J. Opt. Soc. Am. B 21, 397 (2004)
[89] K.Yasumoto and Y. Oishi, "A new evaluation of the Goos-Hanchen shift and associated time delay", J. Appl. Phys., 54(5) 2170-2176 (1983)
[90] Y. S. Kivshar and G. I. Stegeman, "Spatial Optical Solitons: Guiding Light for Future Technologies", Optics and Photonics News, 2, 59-63 (2002)
[91] Y. Kivshar. Dark solitons in nonlinear optics, IEEE J.Quantum Electron., 29(1),250-264(1993)
[92] A. W. Snyder, D. J. Mitchell and Y. S. Kivshar, "Unification of Linear and Nonlinear Wave Optics", Mod. Phys. Lett. B, 9 1479-1506 (1995)
[93] D. N. Christodoulides, S. R. Singh, M. I.Carvalho and M. Segev. "Incoherently Coupled Soliton Pairs in Biased Photorefractive Crystals", Appl. Phys. Lett., 68(13): 1763-1965 (1996)
[94] Z. G. Chen, M. Segev and T. H. Coskun, et al. "Coupled Photorefractive Spatial Soliton Pairs", J. Opt. Soc. Am. B, 14(11), 3066-3069 (1997)
[95]H. Meng, G. Salamo and M. Segev. "Coherent Collisions of Photorefractive Solitons", Opt. Lett., 22(7), 448-453 (1997)
[96] W. Krolikowski, N. Akhmediev, B. L. Davies and M. C. Golomb "Self-Bending Photorefractive Solitons", Phys. Rev. E, 54(5): 5761-5763 (1996)
[97] A.W. Snyder and A. P. Sheppard. "Collisions, Steering, and Guidance with Spatial Solitons", Opt. Lett., 18(7). 482-485 (1993)
[98] D. M. Baboiu, G. I. Stegeman and L. Torner. "Interaction of One-Dimensional Bright Solitary Waves in Quadratic Media", Opt. Lett., 20(22): 2282-2283 (1995)
[99] S. Trillo, S. Wabnitz, E. M. Wright and G. I. Stegeman. "Optical Solitary Waves Induced by Cross-Phase Modulation", Opt. Lett., 13(10): 871-874 (1988)
[100] V. V. Afanasjev, Y. Kivshar, V.V.Konotop and V.N.Serkin. "Dynamics of Coupled Dark and Bright Optical Solitons", Opt. Lett., 14(15) 805-809 (1989)
[101] R. De La Fuente and A. Barthelemy. "Spatial Solitons Pairing by Cross Phase Modulation", Opt. Commun., 88(5): 419-423 (1992)
[102] M. Shalaby and 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., 28(12) 2736-2741(1992)
[103] T. P. Valkering, J. V. Honschoten and H. J. W. M. Hoekstra, Ultra-Sharp Soliton Switching in a Directional Coupler, Opt. Comm., 159(1): 215-218(1999)
[104]M. Segev, B .Crosignani, A. Yuriv and A. Fischer. "Spatial Solitons in Photorefractive Media", Phys. Rev. Lett., 68(7) 923-926 (1992)
[105] Z.Chen, M.Segev and T.H.Coskun, et al. "Incoherently Coupled Dark-Bright Photorefractive Solitons", Opt. Lett., 21(22) 1821-1823 (1996)
[106] H. C. Feng and J. Y. Yuan et al. "Incoherently Coupled Soliton Pairs in Photorefractive Polymer", Opt. Mat., 19(3) 377-381 (2002)
[107] L. Mandel and E. Wolf. "Optical Coherence and Quantum Optics". New York : Cambridge University Press, (1995)
[108] A. W. Snyder and D. J. Mitchell. "Big Incoherent Solitons", Phy. Rev. Lett., 80(7) 1422-1424(1998)
[109] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical Functions", New York: Dover, (1970)
[110] C. Conti, M. Peccianti, and G. Assanto, "Route to nonlocality and observation of accessible solitons", Phys. Rev. lett. 91, 073901 (2003)
[111] C. Conti, M. Peccianti, and G. Assanto, "Observation of optical spatial solitons in a highly nonlocal medium", Phys. Rev. lett., 92, 113902 (2004)
[112] O. Cohen, H. Buljan, T. Schwartz, J. W. Fleischer, and M. Segev, "Incoherent solitons in instantaneous nonlocal nonlinear media", Phys. Rev. E73, 015601(R)(2006)
[113]E. D. Eugenieva, D.N. Christodoulides and M. Segev, "Elliptic incoherent solitons in saturable nonlinear media", Opt. Lett., 25, 972 (2000)
[114]O. Katz, T. Carmon, T. Schwartz, M. Segev, and D. N. Christodoulides, "Observation of elliptic incoherent spatial solitons", Opt. Lett. 29, 1248 (2004)
[115] O. Bang, W. Krolikowski, J. Wyller and J. J. Rasmussen, "Collapse arrest and soliton stabilization in nonlocal nonlinear media", Phys. Rev. E 66, 046619(2002)
[116] L. Brillouin, "Wave propagation and Group Velocity", New York: Academic Press (1960)
[117] O. C. de Beauregard and C. Imbert, "Quantized Longitudinal and Transverse Shifts Associated with Total Internal Reflection" Phys. Rev. Lett., 28 1211 (1972)
[118] R. Fischer, D. N. Neshev, W. Krolikowski, Y. S. Kivshar, D. Iturbe-Castillo, S.Chavez-Cerda, M. R. Meneghetti, D. P. Caetano and J. M. Hickman " Oblique interaction of spatial dark-soliton stripes in nonlocal media," Opt. Lett., 31, 3010 (2006)
[119] M. Peccianti, A. Dyadyusha, M. Kaczmarek and G. Assanto, "Tunable refraction andreflection of self-confined light beams," Nature Physics 2, 737 (2006).
[ 120] Y. S. Kivshar, " Bending light at will," Nature Physics 2, 729 (2006).
[121] S. Ouyang, Q. Guo, and Wei Hu, " Perturbative analysis of generally nonlocal spatial optical solitons," Phys. Rev. E (in press).