中心对称光折变晶体中空间光孤子的理论研究
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摘要
由于光折变空间孤子在很低的入射光强下即可产生,以及潜在的应用价值,从最初理论预言和实验报道以来一直是非线性光学领域的一个研究热点。目前,对光折变空间光孤子的研究主要集中在非中心对称光折变晶体中,人们已经在该种晶体中相继理论预测和实验报道了多种不同类型的空间孤子。本文将对中心对称光折变晶体中空间孤子现象进行全面系统的研究。
分别用数值模拟方法和微扰法研究了单光子中心对称光折变晶体中扩散场对亮空间孤子传播的影响。在扩散效应的作用下,亮空间孤子沿着外加电场的反方向发生了自偏转效应,孤子的中心轨迹是一条抛物线,偏转量与外加电场的三次方成正比。讨论了晶体的温度对中心对称光折变晶体中亮孤子的形状及由扩散效应引起的自偏转效应的影响。温度影响因素有三个,分别是扩散效应、暗辐射强度和相对介电常数,其中相对介电常数的影响处于主导地位。
理论研究了中心对称光折变晶体中空间光孤子的时间行为,给出了中心对称光折变晶体中随时间变化的空间光孤子演化方程,讨论了亮暗空间孤子的时间行为。对于高入射能量饱和值,亮孤子的演化过程存在准稳态孤子和稳态孤子两种状态,当入射光强较低时,不存在准稳态。对于任意的入射光强,暗空间孤子的宽度均随时间单调的减小至最小值,直至稳态暗孤子的形成。
对在中心对称光折变晶体中两束偏振方向和波长都相同的非相干高斯光束的传播行为进行了研究。理论证明了二次电光系数为正值的中心对称光折变晶体可以支持稳定的高斯型亮-亮非相干孤子对,讨论了这些孤子对的性质。
研究了中心对称光折变哈密顿系统和耗散系统中全息孤子形成的条件及其特征。在中心对称光折变哈密顿系统中,两束光可以同时演化为暗或亮空间孤子。理论预言了,信号光可以在同一种中心对称光折变耗散系统中,形成暗或亮全息孤子。
由Castro–Camus双光子模型出发,推导出了基于双光子光折变效应的外加电场作用下的中心对称光折变晶体中一维稳态屏蔽空间光孤子的演化方程,理论预言了亮暗屏蔽孤子态,用微扰法研究了扩散场引起的亮孤子的自偏转效应。此外,理论预言了双光子中心对称光折变晶体中可以形成非相干亮、暗孤子族以及亮暗混合孤子族;对于只含有两束非相干光束耦合的情况,当两束光的总能量远低于暗辐射强度时,双光子中心对称光折变晶体中可以形成暗–暗,亮–亮和亮–暗Manakov孤子对。
理论研究了中心对称光折变晶体中宽光束的调制不稳定性。给出单光子中心对称光折变晶体中宽光束的全局调制不稳定增长率和局域调制不稳定增长率,以及双光子中心对称光折变晶体中宽光束的局域调制不稳定增长率。
Since their existence was first predicted and observed, photorefractive optical spatial solitons have been the subject of very intense experimental and theoretical studies for their feature of formation at low laser power and potential important applications. Thus far, several different kinds of photorefractive spatial solitons have been investigated in non-centrosymmetric photorefractive crystals. In this dissertation, the spatial optical solitons in centrosymmetric photorefractive crystals are investigate systematically.
The effects of diffusion on self-deflection of steady-state bright spatial optical soliton are studied systematically by both numerical and perturbation methods. The center of the soliton moves on a parabolic trajectory, and the deflection effects vary cubically with applied external field. Moreover, a theoretical investigation of temperature effects on bright solitons in centrosymmetric photorefractive crystals is provided. Three physical factors related to the temperature, i.e., the dielectric constant, diffusion process and dark irradiance, are considered. It is shown that the dielectric constant temperature dependence dominates the process.
A one-dimensional time-dependent wave propagation equation wihich in centrosymmetric photorefractive crystals is derived. The equation exhibits the bright and dark soliton solutions whose evolutions against time are investigated. It is shown that the screening bright soliton exists in both quasi-steady-state and steady-state regimes for high intensity saturation values. When the intensity ratio is smaller than unity, only steady-state regime is shown. Moreover, the wave equation exhibits only steady-state screening dark spatial optical solitons.
The coupling between two mutually incoherent Gaussian beams that propagate collinearly in centrosymmetric photorefractive crystals is investigated. The centrosymmetric photorefractive crystals with a positive effective quadratic electro-optic coefficient can support bright-bright Gaussian spatial soliton pairs. The physical properties of these soliton pairs are also discussed in detail.
A comprehensive theoretical study on holographic solitons is provided in centrosymmetric photorefractive crystals. It is predicted that both dark and bright spatial soliton states can exist in centrosymmetric photorefractive Hamiltonian systems and that the signal beam alone can evolve into steady-state bright and dark holographic solitons in a centrosymmetric photorefractive dissipative system.
Based on Castro-Camus model, the evolution equation of one-dimensional steady-state spatial solitons is presented in two-photon centrosymmetric photorefractive crystals, which predicts not only bright but also dark solitons. By using a perturbation method, the effect of diffusion on the self-deflection of bright solitons is also investigated. Furthermore, it is shown that incoherently coupled dark, bright and bright-dark soliton families are possible in two-photon centrosymmetric photorefractive crystals and that Manakov soliton pairs can be established provided that the total intensity of two mutually incoherent optical beams is much lower than the dark irradiance.
By global and locally treating the space-charge field, one-dimensional modulation instability of broad optical beams in biased centrosymmetric photorefractive crystals is studied under steady-state conditions. The expressions of global and locally modulation instability gains in single-photon centrosymmetric photorefractive crystals and locally modulation instability gain in two-photon centrosymmetric photorefractive crystals are provided.
分别用数值模拟方法和微扰法研究了单光子中心对称光折变晶体中扩散场对亮空间孤子传播的影响。在扩散效应的作用下,亮空间孤子沿着外加电场的反方向发生了自偏转效应,孤子的中心轨迹是一条抛物线,偏转量与外加电场的三次方成正比。讨论了晶体的温度对中心对称光折变晶体中亮孤子的形状及由扩散效应引起的自偏转效应的影响。温度影响因素有三个,分别是扩散效应、暗辐射强度和相对介电常数,其中相对介电常数的影响处于主导地位。
理论研究了中心对称光折变晶体中空间光孤子的时间行为,给出了中心对称光折变晶体中随时间变化的空间光孤子演化方程,讨论了亮暗空间孤子的时间行为。对于高入射能量饱和值,亮孤子的演化过程存在准稳态孤子和稳态孤子两种状态,当入射光强较低时,不存在准稳态。对于任意的入射光强,暗空间孤子的宽度均随时间单调的减小至最小值,直至稳态暗孤子的形成。
对在中心对称光折变晶体中两束偏振方向和波长都相同的非相干高斯光束的传播行为进行了研究。理论证明了二次电光系数为正值的中心对称光折变晶体可以支持稳定的高斯型亮-亮非相干孤子对,讨论了这些孤子对的性质。
研究了中心对称光折变哈密顿系统和耗散系统中全息孤子形成的条件及其特征。在中心对称光折变哈密顿系统中,两束光可以同时演化为暗或亮空间孤子。理论预言了,信号光可以在同一种中心对称光折变耗散系统中,形成暗或亮全息孤子。
由Castro–Camus双光子模型出发,推导出了基于双光子光折变效应的外加电场作用下的中心对称光折变晶体中一维稳态屏蔽空间光孤子的演化方程,理论预言了亮暗屏蔽孤子态,用微扰法研究了扩散场引起的亮孤子的自偏转效应。此外,理论预言了双光子中心对称光折变晶体中可以形成非相干亮、暗孤子族以及亮暗混合孤子族;对于只含有两束非相干光束耦合的情况,当两束光的总能量远低于暗辐射强度时,双光子中心对称光折变晶体中可以形成暗–暗,亮–亮和亮–暗Manakov孤子对。
理论研究了中心对称光折变晶体中宽光束的调制不稳定性。给出单光子中心对称光折变晶体中宽光束的全局调制不稳定增长率和局域调制不稳定增长率,以及双光子中心对称光折变晶体中宽光束的局域调制不稳定增长率。
Since their existence was first predicted and observed, photorefractive optical spatial solitons have been the subject of very intense experimental and theoretical studies for their feature of formation at low laser power and potential important applications. Thus far, several different kinds of photorefractive spatial solitons have been investigated in non-centrosymmetric photorefractive crystals. In this dissertation, the spatial optical solitons in centrosymmetric photorefractive crystals are investigate systematically.
The effects of diffusion on self-deflection of steady-state bright spatial optical soliton are studied systematically by both numerical and perturbation methods. The center of the soliton moves on a parabolic trajectory, and the deflection effects vary cubically with applied external field. Moreover, a theoretical investigation of temperature effects on bright solitons in centrosymmetric photorefractive crystals is provided. Three physical factors related to the temperature, i.e., the dielectric constant, diffusion process and dark irradiance, are considered. It is shown that the dielectric constant temperature dependence dominates the process.
A one-dimensional time-dependent wave propagation equation wihich in centrosymmetric photorefractive crystals is derived. The equation exhibits the bright and dark soliton solutions whose evolutions against time are investigated. It is shown that the screening bright soliton exists in both quasi-steady-state and steady-state regimes for high intensity saturation values. When the intensity ratio is smaller than unity, only steady-state regime is shown. Moreover, the wave equation exhibits only steady-state screening dark spatial optical solitons.
The coupling between two mutually incoherent Gaussian beams that propagate collinearly in centrosymmetric photorefractive crystals is investigated. The centrosymmetric photorefractive crystals with a positive effective quadratic electro-optic coefficient can support bright-bright Gaussian spatial soliton pairs. The physical properties of these soliton pairs are also discussed in detail.
A comprehensive theoretical study on holographic solitons is provided in centrosymmetric photorefractive crystals. It is predicted that both dark and bright spatial soliton states can exist in centrosymmetric photorefractive Hamiltonian systems and that the signal beam alone can evolve into steady-state bright and dark holographic solitons in a centrosymmetric photorefractive dissipative system.
Based on Castro-Camus model, the evolution equation of one-dimensional steady-state spatial solitons is presented in two-photon centrosymmetric photorefractive crystals, which predicts not only bright but also dark solitons. By using a perturbation method, the effect of diffusion on the self-deflection of bright solitons is also investigated. Furthermore, it is shown that incoherently coupled dark, bright and bright-dark soliton families are possible in two-photon centrosymmetric photorefractive crystals and that Manakov soliton pairs can be established provided that the total intensity of two mutually incoherent optical beams is much lower than the dark irradiance.
By global and locally treating the space-charge field, one-dimensional modulation instability of broad optical beams in biased centrosymmetric photorefractive crystals is studied under steady-state conditions. The expressions of global and locally modulation instability gains in single-photon centrosymmetric photorefractive crystals and locally modulation instability gain in two-photon centrosymmetric photorefractive crystals are provided.
引文
[1] Segev M, Stegeman G. Self-Trapping of Optical Beams: Spatial Solitons[J]. Phys. Today, 1998,51(8):42-46.
[2] Kortteweg D J, de. Vries G. On the Change of Form of Long Wave Advancing in a Rectangular Channel and on a New Type of Long Stationary Wave[J]. Philos. Mag.,1895,39(5):422-443.
[3] Skyrme T H R. A Non-Linear Theory of Strong Interactions[J]. P. Roy. Soc. A,1958,247(1249):260-278.
[4] Hasegawa A, Tappert F. Transmission of Stationary Nonlinear Optical Pulses in Dispersive Dielectric Fibers I. Anomalous Dispersion[J]. Appl. Phys. Lett.,1973,23(4):142-144.
[5] Hasegawa A, Tappert F. Transmission of Stationary Nonlinear Optical Pulses in Dispersive Dielectric Fibers II. Normal Dispersion[J]. Appl. Phys. Lett.,1973,23(4):171-172.
[6] Mollenauer L F, Stolen R H, Gordon J P. Experimental Observation of Picosecond Pulse Narrowing and Solitons in Optical Fibers[J]. Phys. Rev. Lett.,1980,45(13):1095-1098.
[7] Segev M, Crosignani B, Yariv A, et al. Spatial Solitons in Photorefractive Media[J]. Phys. Rev. Lett.,1992,68(7):923-926.
[8] Duree G C, Shultz J L, Salamo G J, et al. Observation of Self-Trapping of an Optical Beam Due to the Photorefractive Effect[J]. Phys. Rev. Lett.,1993,71(4):533-536.
[9] Segev M, Crosignani B, Di Porto P, et al. Stability of Photorefractive Spatial Solitons[J]. Opt. Lett.,1994,19(17):1296-1298.
[10] Fressengeas N, Maufoy J, Kugel G. Temporal Behavior of Bidimensional Photorefractive Bright Spatial Solitons[J]. Phys. Rev. E,1996,54(6):6866-6875.
[11] Shen W L, Lee K K, Lee W K. All Optical Quasi-Steady-State Photorefractive Spatial Solitons[J]. Phys. Rev. Lett.,2000,85(12):2498-2501.
[12] DelRe E, Palange E. Optical Nonlinearity and Existence Conditions for Quasi-Steady-State Photorefractive Solitons[J]. J. Opt. Soc. Am. B,2006,23(11):2323-2327.
[13] Segev M, Valley G C, Crosignani B, et al. Steady-State Spatial ScreeningSolitons in Photorefractive Materials with External Applied Field[J]. Phys. Rev. Lett.,1994,73(24):3211-3214.
[14] Christodoulides D N, Carvalho M I. Bright, Dark and Gray Spatial Soliton States in Photorefractive Media[J]. J. Opt. Soc. Am. B,1995,12(9):1628-1633.
[15] Shih M, Segev M. Valley G C, et al. Observation of Two-Dimensional Steady-State Photorefractive Screening Solitons[J]. Electron. Lett.,1995,31(10):826-827.
[16] Carvalho M I, Singh S R, Christodoulides D N. Self-Deflection of Steady-State Bright Spatial Solitons in Biased Photorefractive Crystals[J]. Opt. Commun.,1995,120:311-315.
[17] Singh S R, Carvalho M I, Christodoulides D N. Higher-Order Space Charge Field Effects on the Evolution of Spatial Solitons in Biased Photorefractive Crystals[J]. Opt. Commun.,1996,130:288-294.
[18] Christodoulides D N, Singh S R, Carvalho M I. Incoherently Coupled Solitons Pairs in Biased Photorefractive Crystals[J]. Appl. Phys. Lett.,1996,68(13):1763-1765.
[19] Chen Z G, Segev M. Coskun T. H, et al. Observation of Incoherently Coupled Photorefractive Solitons Pairs[J]. Opt. Lett.,1996,21(18):1436-1438.
[20] Chen Z G, Segev M. Coskun T H, et al. Incoherently Coupled Dark-Bright Photorefractive Solitons[J]. Opt. Lett.,1996,21(22):1821-1823.
[21] Imbrock J, Heese C, Denz C. Spatial Photorefractive Solitons with Picosecond Laser Pulse[J]. Appl. Phys. B,2009,95(2):261-268.
[22] Valley G C, Segev M, Crosignani B, et al. Dark and Bright Photovoltaic Spatial Solitons[J]. Phys. Rev. A,1994,50(6):R4457-R4460.
[23] Taya M, Bashaw M C, Fejer M M, et al. Observation of Dark Photovoltaic Spatial Solitons[J]. Phys. Rev. A,1995,52(4):3095-3100.
[24] Segev M, Valley G C, Bashaw M C, et al. Photovoltaic Spatial Solitons[J], J. Opt. Soc. Am. B,1997,14(7):1772-1781.
[25] Chen Z G, Segev M, Wilson D W, et al. Self-Trapping of an Optical Vortex by Use of the Bulk Photovoltaic Effect[J]. Phys. Rev. Lett.,1997,78(15):2948-2951.
[26] She W L, Lee K K, Lee W K. Observation of Two-Dimensional Bright Photovoltaic Spatial Solitons[J]. Phys. Rev. Lett.,1999,83(16):3182-3185.
[27] She W L, Lee W K. Dark and Bright Photovoltaic Spatial Solitons inPhotorefractive Crystals with Positive Refractive-Index Perturbation[J]. Opt. Lett.,2001,26(14):1093-1095.
[28]颜利芬,王红成,佘卫龙.扩散效应对光伏孤子相互作用的影响[J].物理学报,2006,55(10):5257-5262.
[29]江德生,佘卫龙.光伏孤子对向传播相互作用研究[J].物理学报,2007,56(1):245-251.
[30]颜利芬,王红成,张冰志,等.光伏暗孤子和灰孤子自偏转[J].物理学报,2007,56(8):4627-4634.
[31] Zhang L, Lu K Q, Zhang M Z, et al. Temporal Development of Open-Circuit Bright Photovoltaic Solitons[J]. Chin. Phys. B,2008,17(7):2539-2543.
[32] Lu K Q, Zhao W, Zhang L, et al. Temporal Behavior of Dark Spatial Solitons in Closed-Circuit Photovoltaic Media[J]. Opt. Commun.,2008,281(10):2913-2917.
[33] Zhang Y Q, Lu K Q, Zhang M Z, et al. Dynamics of Incoherent Photovoltaic Spatial Solitons[J]. Chin. Phys. Lett.,2009,26(3):034212.
[34] Wang H, Lin J. Solitons in Photovoltaic Photorefractive Media with an External Electric Field[J]. Opt. Commun.,2011,284(6):1485-1490.
[35]崔虎,张冰志,佘卫龙.非相干耦合的亮和暗光伏孤子对的偏转特性[J].物理学报,2010,59(3):1823-1830.
[36] Zhang B Z, Wang H C, She W L. Internal Mode of Incoherent Photovoltaic Vector Solitons[J]. Chin. Phys.,2007,16(4):1052-1056.
[37] Yan L F, Jin Q L, Zhang D, et al. Interaction of Dark Solitons in Photovoltaic Photorefractive Crystals with Diffusion Nonlinearity[J]. Opt. Commun.,2011,284(6):1682-1685.
[38] Liu J S, Lu K Q. Screening-Photovoltaic Spatial Solitons in Biased Photovoltaic-Photorefractive Crystals and Their Self-Deflection[J], J. Opt. Soc. Am. B,1999,16(4):550-555.
[39] Lu K Q, Tang T T, Zhang Y P. One-Dimensional Steady-State Spatial Solitons in Photovoltaic Photorefractive Materials with an External Applied Field[J]. Phys. Rev. A,2000,61(5):053822.
[40] Hou C F, Li Y, Yuan B H, et al. Low-Amplitude Screening-Phtovoltaic Spatial Solitons in Biased Photovoltaic Photorefractive Crystals[J]. Chin. J. Laser B,2000,9(6):551-557.
[41] Hou C F, Li Y, Zhang X F, et al. Grey Screening-Photovoltaic Spatial Soliton in Biased Photovoltaic Photorefractive Crystals[J]. Opt. Commun.,2000,181:141-144.
[42]侯春风,袁保红,孙秀冬,等.非相干耦合屏蔽光伏孤子对[J].物理学报,2000,49(10):1969-1972.
[43] Hou C, Zhou Z, Yuan B, et al. Incoherently Coupled Bright-Dark Hybrid Soliton Families in Biased Photovoltaic-Photorefractive Crystals[J]. Appl. Phys. B,2001,72(2):191-194.
[44] Hou C F, Li B, Sun X D, et al. Incoherently Coupled Screening-Photovoltaic Soliton Families in Biased Photovoltaic Photorefractive Crystals[J]. Chin. Phys.,2001,10(4):310-313.
[45] Fazio E, Renzi F, Rinaldi R, et al. Screening-Photovoltaic Bright Solitons in Lithium Niobate and Associated Single-Mode Waveguides[J]. Appl. Phys. Lett.,2004,85(12):2193-2195.
[46] Keshavarz A, kamranfard M. One-Dimensional Optical Dark Screening Photovoltaic-Photorefractive Solitons, Soliton Pairs and Incoherent Interaction between Them in BaTiO3 Crystal[J]. Optik,2011,122(3):235-240.
[47] Lu K Q, Zhang M Z, Zhao W, et al. Waveguides Induced by Screening-Photovoltaic Solitons in Biased Photorefractive-Photovoltaic Crystals[J]. Chin. Phys. Lett.,2006,23(10):2770-2773.
[48] Lu K Q, Zhao W, Yang Y L, et al. Soliton-Induced Waveguides in Photorefractive Photovoltaic Materials[J]. J. Mod. Opt.,2006,53(15):2137-2151.
[49] Lu K Q, Zhao W, Chen Y Z, et al. Temporal Development of Spatial Solitons in Biased Photorefractive-Photovoltaic Materials[J]. J. Mod. Opt.,2008,55(10):1571-1585.
[50] Lu K Q, Miao C Y, Lu P Y, et al. Dark Incoherent Soliton Splitting in Biased Photorefractive-Photovoltaic Crystals[J]. Opt. Commun.,2009,282(16):3335-3338.
[51] Mitchell M, Chen Z G, Shih M, et al. Self-Trapping of Partially Spatially Incoherent Light[J]. Phys. Rev. Lett.,1996,77(3):490-493.
[52] Christodoulides D N, Coskum T H, Mitchell M, et al. Theory of Incoherent Self-Focusing in Biased Photorefractive Media[J]. Phys. Rev. Lett.,1997,78(4):646-649.
[53] Chen Z G, Mitchell M, Segev M, et al. Self-Trapping of Dark Incoherent Light Beams[J]. Science,1998,280(5365):889-892.
[54]王晓生,佘卫龙.部分空间非相干光光伏空间孤子[J].物理学报,2002,51(3):573-575.
[55] Yan L F, Wang H C, Jin Q L, et al. Self-Deflection of Partially Spatial Incoherent Beams and Solitons in Photovoltaic Photorefractive Crystals[J]. Opt. Commun.,2008,281(22):5610-5613.
[56] Ruelas A, Lopez-Aguayo S, Gutierrez-Vega J C. Stable Solitons in Elliptical Photonic Lattices[J]. Opt. Lett.,2008,33(23):2785-2787.
[57] Zhu X, Wang H, Wu T W, et al. Defect Solitons in Triangular Optical Lattices[J]. J. Opt. Soc. Am. B,2011,28(3):521-527.
[58] Kartashov Y V, Vysloukh V A, Torner L. Surface Lattice Solitons in Diffusive Nonlinear Media[J]. Opt. Lett.,2008,33(8):773-775.
[59] Koke S, Trager D, Jander P, et al. Stabilization of Counterpropagating Solitons by Photonic Lattices[J]. Opt. Express,2007,15(10):6279-6292.
[60] Dong L W, Li H J. Surface Solitons in Nonlinear Lattices[J]. J. Opt. Soc. Am. B,2010,27(6):1179-1183.
[61] Cohen O, Carmon T, Segev M, et al. Holographic Solitons[J]. Opt. Lett.,2002,27(22):2013-2015.
[62] Liu J S. Holographic Solitons in Photorefractive Dissipative Systems[J]. Opt. Lett.,2003,28(22):2237-2239.
[63] Liu J S. Existence and Stability of Rigid Photovoltaic Solitons in an Open-Circuit Amplifying or Absorbing Photovoltaic Medium[J]. Phys. Rev. E,2003,68(2):026607
[64] Liu J S, Eichler H J. Holographic Screening-Photovoltaic Solitons in Biased Photovoltaic-Photorefractive Crystals with Two-Wave Mixing[J]. Europhys. Lett.,2004,65(5):658-664.
[65] Liu J S, Liu S X, Zhang G Y, et al. Observation of Two-Dimensional Holographic Photovoltaic Bright Solitons in a Photorefractive-Photovoltaic Crystal[J]. Appl. Phys. Lett.,2007,91(11):111113.
[66]张绘蓝,张光勇,王程,等.全息明孤子的波导特性[J].物理学报,2007,56(1):236-239.
[67] Cai X, Liu J S, Wang S L. Separate Spatial Holographic-Hamiltonian Soliton Pairs and Solitons Interaction in an Unbiased Series Photorefractive Crystal Circuit[J]. Opt. Express,2009,17(4):2287-2297.
[68] Castro-Camus E, Magana L F. Prediction of the Physical Response for the Two-Photon Photorefractive Effect[J]. Opt. Lett.,2003,28(13):1129-1131.
[69] Hou C F, Pei Y B, Zhou Z X, et al. Spatial Solitons in Two-PhotonPhotorefractive Media[J]. Phys. Rev. A,2005,71(5):053817.
[70] Hou C F, Zhang Y, Jiang Y Y, et al. Photovoltaic Solitons in Two-Photon Photorefractive Materials under Open-Circuit Conditions[J]. Opt. Commun.,2007,273(2):544-548.
[71] Zhang Y, Hou C F, Sun X D. Grey Spatial Solitons Due to Two-Photon Photorefractive Effect[J]. Chin. Phys.,2007,16(1):159-164.
[72]张宇,侯春风,孙秀冬.双光子光折变介质中的非相干耦合空间孤子对[J].物理学报,2007,56(6):3261-3265.
[73] Lu K, Zhao W, Yang Y, et al. One-Dimensional Incoherently Coupled Grey Soliton in Two-Photon Photorefractive Media[J]. Appl. Phys. B,2007,87(3):468-473.
[74] Zhang Y, Hou C F, Sun X D. Grey Photovoltaic Solitons in Two-Photon Photorefractive Materials under the Open-Circuit Case[J]. J. Opt. A: Pure Appl. Opt.,2008,10(2):025101.
[75] Zhang Y, Hou C Y, Wang F, et al. Incoherently Coupled Grey-Grey Spatial Soliton Pairs Due to Two-Photon Photorefractive Media[J]. Optik,2008,119(14):700-704.
[76] Asif N, Shwetanshumala S, Konar S. Photovoltaic Spatial Soliton Pairs in Two-Photon Photorefractive Materials[J]. Phys. Lett. A,2008,372(5):735-740.
[77] Srivastava S, Konar S. Two-Component Coupled Photovoltaic Soliton Pair in Two-Photon Photorefractive Materials under Open Circuit Conditions[J]. Opt. Laser Technol.,2009,41(4):419-423.
[78]姜其畅,苏艳丽,吉选芒.双光子光折变介质中光伏孤子[J].量子光学学报,2007,15(4):364-367.
[79] Zhang Y, Hou C F, Zhan K Y, et al. Incoherently Coupled Bright-Dark Photovoltaic Soliton Pair Based on Two-Photon Photorefractive Effect[J]. Optik,2011,122(3):263-265.
[80] Zhang G Y, Liu J S. Screening-Photovoltaic Spatial Solitons in Biased Two-Photon Photovoltaic Photorefractive Crystals[J]. J. Opt. Soc. Am. B,2009,26(1):113-120.
[81] Zhang G Y, Cheng Y J, Luo Z J, et al. Gray Spatial Solitons in Biased Two-Photon Photovoltaic Photorefractive Crystals[J]. Opt. Commun.,2010,283(2):335-339.
[82] Segev M, Agranat A J. Spatial Solitons in Centrosymmetric PhotorefractiveMedia[J]. Opt. Lett.,1997,22(17):1299-1231.
[83] DelRe E, Crosignani B, Tambruuini M, et al. One-Dimensional Steady-State Photorefractive Spatial Solitons in Centrosymmetric Paraelectric Potassium Lithium Tantalite Niobate[J]. Opt. Lett.,1998,23(6):421-423.
[84] DelRe E, Tambruuini M, Segev M, et al. Two-Dimensional Photorefractive Spatial Solitons in Centrosymmetric Paraelectric Potassium-Lithium-Tantalite-Niobate[J]. Appl. Phys. Lett.,1998,73(1):16-18.
[85] Crosignani B, DelRe E, Di Porto P, et al. Self-Focusing and Self-Trapping in Unbiased Centrosymmetric Photorefractive Media[J]. Opt. Lett.,1998,23(12):912-914.
[86] Crosignani B, Degasperis A, DelRe E, et al. Nonlinear Optical Diffraction Effects and Solitons Due to Anisotropic Charge-Diffusion-Based Self-Interaction[J]. Phys. Rev. Lett.,1999,82(8):1664-1667.
[87] DelRe E, Tamburrini M, Segev M, et al. Spontaneous Self-Trapping of Optical Beams in Metastable Paraelectric Crystals[J]. Phys. Rev. Lett.,1999,83(10):1954-1957.
[88] DelRe E, Trillo S, Agranat A J. Collisions and Inhomogeneous Forces Between Solitons of Different Dimensionality[J]. Opt. Lett.,2000,25(8):560-562.
[89] DelRe E, Tamburrini M, Agranat A J. Soliton Electro-Optic Effects in Paraelectrics[J]. Opt. Lett.,2000,25(13):963-965.
[90] Hou C F, Du C G, Abdurusul, et al. Incoherently Coupled Bright-Dark Soliton Pairs in Biased Centrosymmtric Photorefractive Media[J]. Chin. Phys. Lett.,2001, 18(12):1607-1609.
[91] DelRe E, Agranat A J. Dielectric Nonlinearity in Photorefractive Spatial Soliton Formation[J]. Phys. Rev. A,1999,65(5):053814.
[92] DelRe E, De Masi G, Ciattoni A, et al. Pairing Space-Charge Field Conditions with Self-Guiding for the Attainment of Circular Symmetry in Photorefractive Solitons[J]. Appl. Phys. Lett.,2004,85(23):5499-5501.
[93]侯春风,孟庆鑫,宫德维,等.中心对称光折变材料中的小光强空间孤子[J].物理学报,2004,53(6):1836-1839.
[94] Hou C F, Zhou Z X, Sun X D. Manakov Solitons in Centrosymmetric Photorefractive Materials[J]. Opt. Mater.,2004,27(1):63-66.
[95] Chauvet M, Guo A, Fu G, et al. Electrically Switched Photoinduced Waveguide in Unpoled Strontium Barium Niobate[J]. J. Appl. Phys.,2006,99(11):113107.
[96] Ciattoni A, DelRe E, Rizza C, et al. Miniaturized Bending-Free Solitons by Restoring Symmetry in Periodically Biased Photorefractives[J]. Opt. Lett.,2008,33(18):2110-2112.
[97] Ciattoni A, Marini A, Rizza C , et al. Collision and Fusion of Counterpropagating Micrometer-sized Optical Beams in Periodically Biased Photorefractives[J]. Opt. Lett.,2009,34(7):911-913.
[98] Kukhtarev N, Markov V B, Odulov S G , et al. Holographic Storage in Electrooptic Crystals. I. Steady State[J]. Ferroelectrics,1979,22:949-960.
[99] Krolikowski W, Akhmediev N, Luther-Davies B, et al. Self-Bending Photorefractive Solitons[J]. Phys. Rev. E,1996,54(5):5761-5765.
[100]Carvalho M I, Facao M, Christodoulides D N. Self-Bending of Dark and Gray Photorefractive Solitons[J]. Phys. Rev. E,2007,76(1):016602.
[101]Liu J S, Hao Z H. Higher-Order Space-Charge Field Effects on the Self-Deflection of Bright Screening Photovoltaic Spatial Solitons[J]. J. Opt. Soc. Am. B,2002,19(3):513-521.
[102]Blow K J, Doran N J, Wood D. Suppression of the Soliton Self-Frequency Shift by Bandwidth-Limited Amplification[J]. J. Opt. Soc. Am. B,1988,5(6):1301-1304.
[103]Cheng L J, Partovi A. Temperature and Intensity Dependence of Photorefractive Effect in GaAs[J]. Appl. Phys. Lett.,1986,49(21):1456-1458.
[104]Liu J S, Hao Z H. Temperature Effects on the Self-Deflection of Screening-Photovoltaic Spatial Bright Solitons in Biased Photovoltaic-Photorefractive Crystals[J]. Phys. Lett. A,2001,285:377-382.
[105]Agranat A J, Razvag M, Balberg M. Photorefractive Hologram Fixing a 4K Cooldown to the Phase Transition in K1-xLixTa1-yNbyO3[J]. Appl. Phys. Lett.,1996,68(18):2469-2471.
[106]Zhou Z X, Li Y, Tian H, et al. Photocarrier Transport in Iron-Doped Potassium Lithium Tantalite Niobate Studies by Time-of-Flight Measurement[J]. Opt. Commun.,2009,282(13):2624-2627.
[107]Chauvet M. Temporal Analysis of Open-Circuit Dark Photovoltaic Spatial Solitons[J]. J. Opt. Soc. Am. B,2003,20(12):2515-2522.
[108] Zozulya A A, Anderson D Z. Nonstationary Self-Focusing in Photorefractive Media[J]. Opt. Lett.,1995,20(8):837-839.
[109]Jiang Q C, Su Y L, Ji X M. Temporal Analysis of Low-Amplitude Screening Spatial Solitons Due to Two-Photon Photorefractive Effect[J]. Opt. LaserTechnol.,2011,43(1):91-94.
[110]Fressengeas N, Wolfersberger D, Maufoy J, et al. Build up Mechanisms of (1+1)-Dimensional Photorefractive Bright Spatial Qasi-Steady-State and Screening Soliton[J]. Opt. Commun.,1998,145:393-400.
[111]Konar S, Jana S, Shwetanshumala S. Incoherently Coupled Screening Photovoltaic Spatial Solitons in Biased Photovoltaic Photorefractive Crystals[J]. Opt. Commun.,2007,273(2):324-333.
[112]Agranat A, Hofmeister R, Yariv A. Characterization of a New Photorefractive Material: K1-yLyT1-xNx[J]. Opt. Lett.,1992,17(10):713-715.
[113]Yeh P. Two-Wave Mixing in Nonlinear Media[J]. IEEE J. Quantum Elect.,1989,25(3):484-519.
[114]Tian H, Zhou Z Y, Gong D W, et al. Photorefractive Properties of Paraelectric Potassium Lithium Tantalite Niobate Crystal Doped with Iron[J]. Opt. Commun.,2008,281:1720-1724.
[115]Akhmediev N N, Afanasjev V V, SitiCrespo J M. Singularities and Special Soliton Solutions of the Cubic-Quintic Complex Ginzburg-Landau Equation[J]. Phys. Rev. E,1996,53(1):1190-1201.
[116]Cohen O, Murnane M M, Kapteyn H C. Cross-Phase-Modulation Nonlinearities and Holographic Solitons in Periodically Poled Photovoltaic Photorefractive[J]. Opt. Lett.,2006,31(7):954-956.
[117]Von der Linde D, Glass A M, Rodgers K F. High-Sensitivity Optical Recording in KTN by Two-Photon Absorption[J]. Appl. Phys. Lett.,1975,26(1):22-24.
[118]Geusic J E, Kurtz S K, Van Uitert L G, et al. Electro-Optic Properties of Some ABO3 Preovskites in the Paraelectric Phase[J]. Appl. Phys. Lett.,1964,4(8):141-143.
[119]Manakov S V. On the Theory of Two-Dimensional Stationary Self-Focusing of Electromagnetic Waves[J]. Sov. Phys. JETP,1974,38(2):248-253.
[120]Kip D, Soljacic M, Segev M, et al. Modulation Instability and Pattern Formation in Spatially Incoherent Light Beams[J]. Science,2000,290(5491):495-498.
[121]Joseph A, Senthilnathan K, Porsezian K, et al. Gap Solitons and Modulation Instability in a Dynamic Bragg Grating with Nonlinearity Management[J]. J. Opt. A: Pure Appl. Opt.,2009,11(1):015203.
[122]Jablan M, Buljan H, Manela O, et al. Incoherent Modulation Instability in a Nonlinear Photonic Lattice[J]. Opt. Express,2007,15(8):4623-4633.
[123]Iturbe-Castillo M D, Torres-Cisneros M, Sanchez-Mondragon J J, et al. Experimental Evidence of Modulation Instability in a Photorefractive Bi12TiO20 crystal[J]. Opt. Lett.,1995,20(18):1853-1855.
[124]Carvalho M I, Singh S R, Christodoulides D N. Modulational Instability of Quasi-Plane-Wave Optical Beams Biased in Photorefractive Crystals[J]. Opt. Commun.,1996,126:167-174.
[125]Lu K Q, Zhao W, Yang Y L, et al. Modulation Instability of Quasi-Plane-Wave Optical Beams in Biased Photorefractive-Photovoltaic Crystals[J]. Chin. Phys.,2004,13(12):2077-2081.
[126]Lu K Q, Zhao W, Yang Y L, et al. One-Dimensional Modulation Instability of Broad Optical Beams in Biased Photorefractive-Photovoltaic Crystals under Steady-State Conditions[J]. Opt. Commun.,2005,247:437-445.
[2] Kortteweg D J, de. Vries G. On the Change of Form of Long Wave Advancing in a Rectangular Channel and on a New Type of Long Stationary Wave[J]. Philos. Mag.,1895,39(5):422-443.
[3] Skyrme T H R. A Non-Linear Theory of Strong Interactions[J]. P. Roy. Soc. A,1958,247(1249):260-278.
[4] Hasegawa A, Tappert F. Transmission of Stationary Nonlinear Optical Pulses in Dispersive Dielectric Fibers I. Anomalous Dispersion[J]. Appl. Phys. Lett.,1973,23(4):142-144.
[5] Hasegawa A, Tappert F. Transmission of Stationary Nonlinear Optical Pulses in Dispersive Dielectric Fibers II. Normal Dispersion[J]. Appl. Phys. Lett.,1973,23(4):171-172.
[6] Mollenauer L F, Stolen R H, Gordon J P. Experimental Observation of Picosecond Pulse Narrowing and Solitons in Optical Fibers[J]. Phys. Rev. Lett.,1980,45(13):1095-1098.
[7] Segev M, Crosignani B, Yariv A, et al. Spatial Solitons in Photorefractive Media[J]. Phys. Rev. Lett.,1992,68(7):923-926.
[8] Duree G C, Shultz J L, Salamo G J, et al. Observation of Self-Trapping of an Optical Beam Due to the Photorefractive Effect[J]. Phys. Rev. Lett.,1993,71(4):533-536.
[9] Segev M, Crosignani B, Di Porto P, et al. Stability of Photorefractive Spatial Solitons[J]. Opt. Lett.,1994,19(17):1296-1298.
[10] Fressengeas N, Maufoy J, Kugel G. Temporal Behavior of Bidimensional Photorefractive Bright Spatial Solitons[J]. Phys. Rev. E,1996,54(6):6866-6875.
[11] Shen W L, Lee K K, Lee W K. All Optical Quasi-Steady-State Photorefractive Spatial Solitons[J]. Phys. Rev. Lett.,2000,85(12):2498-2501.
[12] DelRe E, Palange E. Optical Nonlinearity and Existence Conditions for Quasi-Steady-State Photorefractive Solitons[J]. J. Opt. Soc. Am. B,2006,23(11):2323-2327.
[13] Segev M, Valley G C, Crosignani B, et al. Steady-State Spatial ScreeningSolitons in Photorefractive Materials with External Applied Field[J]. Phys. Rev. Lett.,1994,73(24):3211-3214.
[14] Christodoulides D N, Carvalho M I. Bright, Dark and Gray Spatial Soliton States in Photorefractive Media[J]. J. Opt. Soc. Am. B,1995,12(9):1628-1633.
[15] Shih M, Segev M. Valley G C, et al. Observation of Two-Dimensional Steady-State Photorefractive Screening Solitons[J]. Electron. Lett.,1995,31(10):826-827.
[16] Carvalho M I, Singh S R, Christodoulides D N. Self-Deflection of Steady-State Bright Spatial Solitons in Biased Photorefractive Crystals[J]. Opt. Commun.,1995,120:311-315.
[17] Singh S R, Carvalho M I, Christodoulides D N. Higher-Order Space Charge Field Effects on the Evolution of Spatial Solitons in Biased Photorefractive Crystals[J]. Opt. Commun.,1996,130:288-294.
[18] Christodoulides D N, Singh S R, Carvalho M I. Incoherently Coupled Solitons Pairs in Biased Photorefractive Crystals[J]. Appl. Phys. Lett.,1996,68(13):1763-1765.
[19] Chen Z G, Segev M. Coskun T. H, et al. Observation of Incoherently Coupled Photorefractive Solitons Pairs[J]. Opt. Lett.,1996,21(18):1436-1438.
[20] Chen Z G, Segev M. Coskun T H, et al. Incoherently Coupled Dark-Bright Photorefractive Solitons[J]. Opt. Lett.,1996,21(22):1821-1823.
[21] Imbrock J, Heese C, Denz C. Spatial Photorefractive Solitons with Picosecond Laser Pulse[J]. Appl. Phys. B,2009,95(2):261-268.
[22] Valley G C, Segev M, Crosignani B, et al. Dark and Bright Photovoltaic Spatial Solitons[J]. Phys. Rev. A,1994,50(6):R4457-R4460.
[23] Taya M, Bashaw M C, Fejer M M, et al. Observation of Dark Photovoltaic Spatial Solitons[J]. Phys. Rev. A,1995,52(4):3095-3100.
[24] Segev M, Valley G C, Bashaw M C, et al. Photovoltaic Spatial Solitons[J], J. Opt. Soc. Am. B,1997,14(7):1772-1781.
[25] Chen Z G, Segev M, Wilson D W, et al. Self-Trapping of an Optical Vortex by Use of the Bulk Photovoltaic Effect[J]. Phys. Rev. Lett.,1997,78(15):2948-2951.
[26] She W L, Lee K K, Lee W K. Observation of Two-Dimensional Bright Photovoltaic Spatial Solitons[J]. Phys. Rev. Lett.,1999,83(16):3182-3185.
[27] She W L, Lee W K. Dark and Bright Photovoltaic Spatial Solitons inPhotorefractive Crystals with Positive Refractive-Index Perturbation[J]. Opt. Lett.,2001,26(14):1093-1095.
[28]颜利芬,王红成,佘卫龙.扩散效应对光伏孤子相互作用的影响[J].物理学报,2006,55(10):5257-5262.
[29]江德生,佘卫龙.光伏孤子对向传播相互作用研究[J].物理学报,2007,56(1):245-251.
[30]颜利芬,王红成,张冰志,等.光伏暗孤子和灰孤子自偏转[J].物理学报,2007,56(8):4627-4634.
[31] Zhang L, Lu K Q, Zhang M Z, et al. Temporal Development of Open-Circuit Bright Photovoltaic Solitons[J]. Chin. Phys. B,2008,17(7):2539-2543.
[32] Lu K Q, Zhao W, Zhang L, et al. Temporal Behavior of Dark Spatial Solitons in Closed-Circuit Photovoltaic Media[J]. Opt. Commun.,2008,281(10):2913-2917.
[33] Zhang Y Q, Lu K Q, Zhang M Z, et al. Dynamics of Incoherent Photovoltaic Spatial Solitons[J]. Chin. Phys. Lett.,2009,26(3):034212.
[34] Wang H, Lin J. Solitons in Photovoltaic Photorefractive Media with an External Electric Field[J]. Opt. Commun.,2011,284(6):1485-1490.
[35]崔虎,张冰志,佘卫龙.非相干耦合的亮和暗光伏孤子对的偏转特性[J].物理学报,2010,59(3):1823-1830.
[36] Zhang B Z, Wang H C, She W L. Internal Mode of Incoherent Photovoltaic Vector Solitons[J]. Chin. Phys.,2007,16(4):1052-1056.
[37] Yan L F, Jin Q L, Zhang D, et al. Interaction of Dark Solitons in Photovoltaic Photorefractive Crystals with Diffusion Nonlinearity[J]. Opt. Commun.,2011,284(6):1682-1685.
[38] Liu J S, Lu K Q. Screening-Photovoltaic Spatial Solitons in Biased Photovoltaic-Photorefractive Crystals and Their Self-Deflection[J], J. Opt. Soc. Am. B,1999,16(4):550-555.
[39] Lu K Q, Tang T T, Zhang Y P. One-Dimensional Steady-State Spatial Solitons in Photovoltaic Photorefractive Materials with an External Applied Field[J]. Phys. Rev. A,2000,61(5):053822.
[40] Hou C F, Li Y, Yuan B H, et al. Low-Amplitude Screening-Phtovoltaic Spatial Solitons in Biased Photovoltaic Photorefractive Crystals[J]. Chin. J. Laser B,2000,9(6):551-557.
[41] Hou C F, Li Y, Zhang X F, et al. Grey Screening-Photovoltaic Spatial Soliton in Biased Photovoltaic Photorefractive Crystals[J]. Opt. Commun.,2000,181:141-144.
[42]侯春风,袁保红,孙秀冬,等.非相干耦合屏蔽光伏孤子对[J].物理学报,2000,49(10):1969-1972.
[43] Hou C, Zhou Z, Yuan B, et al. Incoherently Coupled Bright-Dark Hybrid Soliton Families in Biased Photovoltaic-Photorefractive Crystals[J]. Appl. Phys. B,2001,72(2):191-194.
[44] Hou C F, Li B, Sun X D, et al. Incoherently Coupled Screening-Photovoltaic Soliton Families in Biased Photovoltaic Photorefractive Crystals[J]. Chin. Phys.,2001,10(4):310-313.
[45] Fazio E, Renzi F, Rinaldi R, et al. Screening-Photovoltaic Bright Solitons in Lithium Niobate and Associated Single-Mode Waveguides[J]. Appl. Phys. Lett.,2004,85(12):2193-2195.
[46] Keshavarz A, kamranfard M. One-Dimensional Optical Dark Screening Photovoltaic-Photorefractive Solitons, Soliton Pairs and Incoherent Interaction between Them in BaTiO3 Crystal[J]. Optik,2011,122(3):235-240.
[47] Lu K Q, Zhang M Z, Zhao W, et al. Waveguides Induced by Screening-Photovoltaic Solitons in Biased Photorefractive-Photovoltaic Crystals[J]. Chin. Phys. Lett.,2006,23(10):2770-2773.
[48] Lu K Q, Zhao W, Yang Y L, et al. Soliton-Induced Waveguides in Photorefractive Photovoltaic Materials[J]. J. Mod. Opt.,2006,53(15):2137-2151.
[49] Lu K Q, Zhao W, Chen Y Z, et al. Temporal Development of Spatial Solitons in Biased Photorefractive-Photovoltaic Materials[J]. J. Mod. Opt.,2008,55(10):1571-1585.
[50] Lu K Q, Miao C Y, Lu P Y, et al. Dark Incoherent Soliton Splitting in Biased Photorefractive-Photovoltaic Crystals[J]. Opt. Commun.,2009,282(16):3335-3338.
[51] Mitchell M, Chen Z G, Shih M, et al. Self-Trapping of Partially Spatially Incoherent Light[J]. Phys. Rev. Lett.,1996,77(3):490-493.
[52] Christodoulides D N, Coskum T H, Mitchell M, et al. Theory of Incoherent Self-Focusing in Biased Photorefractive Media[J]. Phys. Rev. Lett.,1997,78(4):646-649.
[53] Chen Z G, Mitchell M, Segev M, et al. Self-Trapping of Dark Incoherent Light Beams[J]. Science,1998,280(5365):889-892.
[54]王晓生,佘卫龙.部分空间非相干光光伏空间孤子[J].物理学报,2002,51(3):573-575.
[55] Yan L F, Wang H C, Jin Q L, et al. Self-Deflection of Partially Spatial Incoherent Beams and Solitons in Photovoltaic Photorefractive Crystals[J]. Opt. Commun.,2008,281(22):5610-5613.
[56] Ruelas A, Lopez-Aguayo S, Gutierrez-Vega J C. Stable Solitons in Elliptical Photonic Lattices[J]. Opt. Lett.,2008,33(23):2785-2787.
[57] Zhu X, Wang H, Wu T W, et al. Defect Solitons in Triangular Optical Lattices[J]. J. Opt. Soc. Am. B,2011,28(3):521-527.
[58] Kartashov Y V, Vysloukh V A, Torner L. Surface Lattice Solitons in Diffusive Nonlinear Media[J]. Opt. Lett.,2008,33(8):773-775.
[59] Koke S, Trager D, Jander P, et al. Stabilization of Counterpropagating Solitons by Photonic Lattices[J]. Opt. Express,2007,15(10):6279-6292.
[60] Dong L W, Li H J. Surface Solitons in Nonlinear Lattices[J]. J. Opt. Soc. Am. B,2010,27(6):1179-1183.
[61] Cohen O, Carmon T, Segev M, et al. Holographic Solitons[J]. Opt. Lett.,2002,27(22):2013-2015.
[62] Liu J S. Holographic Solitons in Photorefractive Dissipative Systems[J]. Opt. Lett.,2003,28(22):2237-2239.
[63] Liu J S. Existence and Stability of Rigid Photovoltaic Solitons in an Open-Circuit Amplifying or Absorbing Photovoltaic Medium[J]. Phys. Rev. E,2003,68(2):026607
[64] Liu J S, Eichler H J. Holographic Screening-Photovoltaic Solitons in Biased Photovoltaic-Photorefractive Crystals with Two-Wave Mixing[J]. Europhys. Lett.,2004,65(5):658-664.
[65] Liu J S, Liu S X, Zhang G Y, et al. Observation of Two-Dimensional Holographic Photovoltaic Bright Solitons in a Photorefractive-Photovoltaic Crystal[J]. Appl. Phys. Lett.,2007,91(11):111113.
[66]张绘蓝,张光勇,王程,等.全息明孤子的波导特性[J].物理学报,2007,56(1):236-239.
[67] Cai X, Liu J S, Wang S L. Separate Spatial Holographic-Hamiltonian Soliton Pairs and Solitons Interaction in an Unbiased Series Photorefractive Crystal Circuit[J]. Opt. Express,2009,17(4):2287-2297.
[68] Castro-Camus E, Magana L F. Prediction of the Physical Response for the Two-Photon Photorefractive Effect[J]. Opt. Lett.,2003,28(13):1129-1131.
[69] Hou C F, Pei Y B, Zhou Z X, et al. Spatial Solitons in Two-PhotonPhotorefractive Media[J]. Phys. Rev. A,2005,71(5):053817.
[70] Hou C F, Zhang Y, Jiang Y Y, et al. Photovoltaic Solitons in Two-Photon Photorefractive Materials under Open-Circuit Conditions[J]. Opt. Commun.,2007,273(2):544-548.
[71] Zhang Y, Hou C F, Sun X D. Grey Spatial Solitons Due to Two-Photon Photorefractive Effect[J]. Chin. Phys.,2007,16(1):159-164.
[72]张宇,侯春风,孙秀冬.双光子光折变介质中的非相干耦合空间孤子对[J].物理学报,2007,56(6):3261-3265.
[73] Lu K, Zhao W, Yang Y, et al. One-Dimensional Incoherently Coupled Grey Soliton in Two-Photon Photorefractive Media[J]. Appl. Phys. B,2007,87(3):468-473.
[74] Zhang Y, Hou C F, Sun X D. Grey Photovoltaic Solitons in Two-Photon Photorefractive Materials under the Open-Circuit Case[J]. J. Opt. A: Pure Appl. Opt.,2008,10(2):025101.
[75] Zhang Y, Hou C Y, Wang F, et al. Incoherently Coupled Grey-Grey Spatial Soliton Pairs Due to Two-Photon Photorefractive Media[J]. Optik,2008,119(14):700-704.
[76] Asif N, Shwetanshumala S, Konar S. Photovoltaic Spatial Soliton Pairs in Two-Photon Photorefractive Materials[J]. Phys. Lett. A,2008,372(5):735-740.
[77] Srivastava S, Konar S. Two-Component Coupled Photovoltaic Soliton Pair in Two-Photon Photorefractive Materials under Open Circuit Conditions[J]. Opt. Laser Technol.,2009,41(4):419-423.
[78]姜其畅,苏艳丽,吉选芒.双光子光折变介质中光伏孤子[J].量子光学学报,2007,15(4):364-367.
[79] Zhang Y, Hou C F, Zhan K Y, et al. Incoherently Coupled Bright-Dark Photovoltaic Soliton Pair Based on Two-Photon Photorefractive Effect[J]. Optik,2011,122(3):263-265.
[80] Zhang G Y, Liu J S. Screening-Photovoltaic Spatial Solitons in Biased Two-Photon Photovoltaic Photorefractive Crystals[J]. J. Opt. Soc. Am. B,2009,26(1):113-120.
[81] Zhang G Y, Cheng Y J, Luo Z J, et al. Gray Spatial Solitons in Biased Two-Photon Photovoltaic Photorefractive Crystals[J]. Opt. Commun.,2010,283(2):335-339.
[82] Segev M, Agranat A J. Spatial Solitons in Centrosymmetric PhotorefractiveMedia[J]. Opt. Lett.,1997,22(17):1299-1231.
[83] DelRe E, Crosignani B, Tambruuini M, et al. One-Dimensional Steady-State Photorefractive Spatial Solitons in Centrosymmetric Paraelectric Potassium Lithium Tantalite Niobate[J]. Opt. Lett.,1998,23(6):421-423.
[84] DelRe E, Tambruuini M, Segev M, et al. Two-Dimensional Photorefractive Spatial Solitons in Centrosymmetric Paraelectric Potassium-Lithium-Tantalite-Niobate[J]. Appl. Phys. Lett.,1998,73(1):16-18.
[85] Crosignani B, DelRe E, Di Porto P, et al. Self-Focusing and Self-Trapping in Unbiased Centrosymmetric Photorefractive Media[J]. Opt. Lett.,1998,23(12):912-914.
[86] Crosignani B, Degasperis A, DelRe E, et al. Nonlinear Optical Diffraction Effects and Solitons Due to Anisotropic Charge-Diffusion-Based Self-Interaction[J]. Phys. Rev. Lett.,1999,82(8):1664-1667.
[87] DelRe E, Tamburrini M, Segev M, et al. Spontaneous Self-Trapping of Optical Beams in Metastable Paraelectric Crystals[J]. Phys. Rev. Lett.,1999,83(10):1954-1957.
[88] DelRe E, Trillo S, Agranat A J. Collisions and Inhomogeneous Forces Between Solitons of Different Dimensionality[J]. Opt. Lett.,2000,25(8):560-562.
[89] DelRe E, Tamburrini M, Agranat A J. Soliton Electro-Optic Effects in Paraelectrics[J]. Opt. Lett.,2000,25(13):963-965.
[90] Hou C F, Du C G, Abdurusul, et al. Incoherently Coupled Bright-Dark Soliton Pairs in Biased Centrosymmtric Photorefractive Media[J]. Chin. Phys. Lett.,2001, 18(12):1607-1609.
[91] DelRe E, Agranat A J. Dielectric Nonlinearity in Photorefractive Spatial Soliton Formation[J]. Phys. Rev. A,1999,65(5):053814.
[92] DelRe E, De Masi G, Ciattoni A, et al. Pairing Space-Charge Field Conditions with Self-Guiding for the Attainment of Circular Symmetry in Photorefractive Solitons[J]. Appl. Phys. Lett.,2004,85(23):5499-5501.
[93]侯春风,孟庆鑫,宫德维,等.中心对称光折变材料中的小光强空间孤子[J].物理学报,2004,53(6):1836-1839.
[94] Hou C F, Zhou Z X, Sun X D. Manakov Solitons in Centrosymmetric Photorefractive Materials[J]. Opt. Mater.,2004,27(1):63-66.
[95] Chauvet M, Guo A, Fu G, et al. Electrically Switched Photoinduced Waveguide in Unpoled Strontium Barium Niobate[J]. J. Appl. Phys.,2006,99(11):113107.
[96] Ciattoni A, DelRe E, Rizza C, et al. Miniaturized Bending-Free Solitons by Restoring Symmetry in Periodically Biased Photorefractives[J]. Opt. Lett.,2008,33(18):2110-2112.
[97] Ciattoni A, Marini A, Rizza C , et al. Collision and Fusion of Counterpropagating Micrometer-sized Optical Beams in Periodically Biased Photorefractives[J]. Opt. Lett.,2009,34(7):911-913.
[98] Kukhtarev N, Markov V B, Odulov S G , et al. Holographic Storage in Electrooptic Crystals. I. Steady State[J]. Ferroelectrics,1979,22:949-960.
[99] Krolikowski W, Akhmediev N, Luther-Davies B, et al. Self-Bending Photorefractive Solitons[J]. Phys. Rev. E,1996,54(5):5761-5765.
[100]Carvalho M I, Facao M, Christodoulides D N. Self-Bending of Dark and Gray Photorefractive Solitons[J]. Phys. Rev. E,2007,76(1):016602.
[101]Liu J S, Hao Z H. Higher-Order Space-Charge Field Effects on the Self-Deflection of Bright Screening Photovoltaic Spatial Solitons[J]. J. Opt. Soc. Am. B,2002,19(3):513-521.
[102]Blow K J, Doran N J, Wood D. Suppression of the Soliton Self-Frequency Shift by Bandwidth-Limited Amplification[J]. J. Opt. Soc. Am. B,1988,5(6):1301-1304.
[103]Cheng L J, Partovi A. Temperature and Intensity Dependence of Photorefractive Effect in GaAs[J]. Appl. Phys. Lett.,1986,49(21):1456-1458.
[104]Liu J S, Hao Z H. Temperature Effects on the Self-Deflection of Screening-Photovoltaic Spatial Bright Solitons in Biased Photovoltaic-Photorefractive Crystals[J]. Phys. Lett. A,2001,285:377-382.
[105]Agranat A J, Razvag M, Balberg M. Photorefractive Hologram Fixing a 4K Cooldown to the Phase Transition in K1-xLixTa1-yNbyO3[J]. Appl. Phys. Lett.,1996,68(18):2469-2471.
[106]Zhou Z X, Li Y, Tian H, et al. Photocarrier Transport in Iron-Doped Potassium Lithium Tantalite Niobate Studies by Time-of-Flight Measurement[J]. Opt. Commun.,2009,282(13):2624-2627.
[107]Chauvet M. Temporal Analysis of Open-Circuit Dark Photovoltaic Spatial Solitons[J]. J. Opt. Soc. Am. B,2003,20(12):2515-2522.
[108] Zozulya A A, Anderson D Z. Nonstationary Self-Focusing in Photorefractive Media[J]. Opt. Lett.,1995,20(8):837-839.
[109]Jiang Q C, Su Y L, Ji X M. Temporal Analysis of Low-Amplitude Screening Spatial Solitons Due to Two-Photon Photorefractive Effect[J]. Opt. LaserTechnol.,2011,43(1):91-94.
[110]Fressengeas N, Wolfersberger D, Maufoy J, et al. Build up Mechanisms of (1+1)-Dimensional Photorefractive Bright Spatial Qasi-Steady-State and Screening Soliton[J]. Opt. Commun.,1998,145:393-400.
[111]Konar S, Jana S, Shwetanshumala S. Incoherently Coupled Screening Photovoltaic Spatial Solitons in Biased Photovoltaic Photorefractive Crystals[J]. Opt. Commun.,2007,273(2):324-333.
[112]Agranat A, Hofmeister R, Yariv A. Characterization of a New Photorefractive Material: K1-yLyT1-xNx[J]. Opt. Lett.,1992,17(10):713-715.
[113]Yeh P. Two-Wave Mixing in Nonlinear Media[J]. IEEE J. Quantum Elect.,1989,25(3):484-519.
[114]Tian H, Zhou Z Y, Gong D W, et al. Photorefractive Properties of Paraelectric Potassium Lithium Tantalite Niobate Crystal Doped with Iron[J]. Opt. Commun.,2008,281:1720-1724.
[115]Akhmediev N N, Afanasjev V V, SitiCrespo J M. Singularities and Special Soliton Solutions of the Cubic-Quintic Complex Ginzburg-Landau Equation[J]. Phys. Rev. E,1996,53(1):1190-1201.
[116]Cohen O, Murnane M M, Kapteyn H C. Cross-Phase-Modulation Nonlinearities and Holographic Solitons in Periodically Poled Photovoltaic Photorefractive[J]. Opt. Lett.,2006,31(7):954-956.
[117]Von der Linde D, Glass A M, Rodgers K F. High-Sensitivity Optical Recording in KTN by Two-Photon Absorption[J]. Appl. Phys. Lett.,1975,26(1):22-24.
[118]Geusic J E, Kurtz S K, Van Uitert L G, et al. Electro-Optic Properties of Some ABO3 Preovskites in the Paraelectric Phase[J]. Appl. Phys. Lett.,1964,4(8):141-143.
[119]Manakov S V. On the Theory of Two-Dimensional Stationary Self-Focusing of Electromagnetic Waves[J]. Sov. Phys. JETP,1974,38(2):248-253.
[120]Kip D, Soljacic M, Segev M, et al. Modulation Instability and Pattern Formation in Spatially Incoherent Light Beams[J]. Science,2000,290(5491):495-498.
[121]Joseph A, Senthilnathan K, Porsezian K, et al. Gap Solitons and Modulation Instability in a Dynamic Bragg Grating with Nonlinearity Management[J]. J. Opt. A: Pure Appl. Opt.,2009,11(1):015203.
[122]Jablan M, Buljan H, Manela O, et al. Incoherent Modulation Instability in a Nonlinear Photonic Lattice[J]. Opt. Express,2007,15(8):4623-4633.
[123]Iturbe-Castillo M D, Torres-Cisneros M, Sanchez-Mondragon J J, et al. Experimental Evidence of Modulation Instability in a Photorefractive Bi12TiO20 crystal[J]. Opt. Lett.,1995,20(18):1853-1855.
[124]Carvalho M I, Singh S R, Christodoulides D N. Modulational Instability of Quasi-Plane-Wave Optical Beams Biased in Photorefractive Crystals[J]. Opt. Commun.,1996,126:167-174.
[125]Lu K Q, Zhao W, Yang Y L, et al. Modulation Instability of Quasi-Plane-Wave Optical Beams in Biased Photorefractive-Photovoltaic Crystals[J]. Chin. Phys.,2004,13(12):2077-2081.
[126]Lu K Q, Zhao W, Yang Y L, et al. One-Dimensional Modulation Instability of Broad Optical Beams in Biased Photorefractive-Photovoltaic Crystals under Steady-State Conditions[J]. Opt. Commun.,2005,247:437-445.