Dark incoherent soliton splitting in biased photorefractive-photovoltaic crystals

Using the coherent density approach, we study the dark incoherent soliton splitting in biased photorefractive-photovoltaic crystals. We show that when the full width half maximum (FWHM) of the optical beam’s intensity is increased, the odd incoherent dark beam splits into an odd-number sequence of multiple dark stripes, whereas the even incoherent dark beam splits into an even-number sequence of multiple dark stripes. We find that when more incoherent solitons are generated, the separations between adjacent dark stripes become smaller and the stripes far away from the center become less visible and that for a given physical system and for a given splitting, the separations between adjacent dark stripes decrease with an increase in the intensity FWHM of the optical beam. On the other hand, the dark incoherent soliton splitting in biased photorefractive-photovoltaic crystals is the dark incoherent screening soliton splitting when the bulk photovoltaic effect is neglectable and the dark incoherent closed- and open-circuit photovoltaic soliton splitting when the external bias field is absent.     

完全非相干白光一维光生伏打暗空间孤子

使用白炽灯作光源在LiNbO₃∶Fe晶体内实验观察到一维白光光生伏打暗空间孤 子. 由奇数 和偶数初始条件分别产生了灰孤子和灰孤子对，它们所感应的波导能导向白光和相干光. 用 相干光清楚地探测到它们内部的多模结构. 该实验证明了白光光生伏打暗空间孤子的存在， 并指出了用完全非相干的白光暗孤子控制和导向相干光的可能性. 关键词： 光生伏打效应 自陷 完全非相干孤子 波导     

Waveguides Induced by Screening-Photovoltaic Solitons in Biased Photorefractive-Photovoltaic Crystals

We investigate theoretically waveguides induced by screening-photovoltaic solitons in biased photorefractive-photovoltaic crystals. We show that the number of guided modes in a waveguide induced by a bright screening photovoltaic soliton increases monotonically with the increasing intensity ratio of the soliton, which is the ratio between the peak intensity of the soliton and the dark irradiance. On the other hand, waveguides induced by dark screening-photovoltaic solitons are always single mode for all intensity ratios and the confined energy near the centre of a dark screening-photovoltaic soliton increases monotonically with the increasing intensity ratio. When the bulk photovoltaic effect is neglectable, these waveguides are those induced by screening solitons. When the external field is absent, these waveguides predict those induced by photovoltaic solitons.     

在LiNbO3:Fe晶体中写入Y结孤子的实验研究

采用振幅掩模穿过部分空间非相干光的方法产生一暗迹,将暗迹成像在晶体前表面,得到入射暗迹半高宽为16.75 μm,入射光功率为400 μW.基于LiNbO3:Fe晶体的强光伏效应,在无背景光辐照时,在晶体内写入一对部分空间非相干Y结暗光伏孤子.实验结果表明：在无背景光辐射时可以在LiNbO3:Fe晶体内写入部分空间非相干Y结孤子.     

开路低振幅空间光伏孤子的时间分析

理论分析了一维光折变空间孤子在低振幅开路条件下的传输特性和强度宽度的演化特性.研究表明,开始阶段所形成的强度宽度较宽的孤子, 其宽度随着时间演化单调递减到一个最小值,直到稳态形成;对于不同的孤子峰值强度与暗辐射比值,整个过程所需要的时间接近于无照明场时介质的介电驰豫时间.在时间趋于无穷的情况下,系统趋于稳定,得到了暗孤子和亮孤子的解析解.     

开路光伏空间孤子的动态行为

从理论上研究了开路情况下一维光伏空间孤子的时间演化过程.采用数值方法,通过研究有无背景光辐照下光伏空间亮(暗)孤子的含时空间电荷场,分别得到了光伏空间亮(暗)孤子的孤子波形强度微分方程.在此基础上研究了开路情况下通过增加均匀背景光辐照强度对光伏空间孤子及其半峰全宽的影响.结果显示,通过增加均匀背景光辐照强度,光伏空间孤子随时间的演化过程比没有均匀背景光时加快的倍数为均匀背景光强与暗辐照光强之比.光伏空间孤子的半峰全宽达到稳态所需的时间随孤子峰值强度和暗辐照与均匀背景光强度之和的比值的增大而变短.     

Dark incoherent spatial solitons in logarithmically saturable nonlinear media

This paper studies numerically the dark incoherent spatial solitons propagating in logarithmically saturable nonlinear media by using a coherent density approach and a split-step Fourier approach for the first time. Under odd and even initial conditions, a soliton triplet and a doublet are obtained respectively for given parameters. Simultaneously, coherence properties associated with the soliton triplet and doublet are discussed. In addition, if the values of the parameters are properly chosen, five and four splittings from the input dark incoherent spatial solitons can also form. Lastly, the grayness of the soliton triplet and that of the doublet are studied, in detail.     

Multiple incoherent gray photorefractive spatial solitons

We show that an even-number sequence of multiple incoherent gray photorefractive spatial screening solitons is possible. When the external voltage is small, only an incoherent Y-junction photorefractive spatial screening soliton is generated, corresponding to the lowest order in the even-number incoherent soliton sequence. When the external voltage is increased, the incoherent gray soliton beam splits into an even-number sequence of multiple incoherent gray photorefractive spatial screening solitons. For a given physical system such an even-number sequence of multiple incoherent gray photorefractive spatial screening solitons is obtained by either increasing the external voltage and decreasing the full width half maximum (FWHM) of the beam’s intensity or increasing the external voltage and decreasing the beam’s grayness.     

Propagation characteristics of parallel dark solitons in silicon-on-insulator waveguide

The propagation characteristic of two identical and parallel dark solitons in a silicon-on-insulator(SOI) waveguide is simulated numerically using the split-step Fourier method. The parallel dark solitons imposed by the initial chirp are investigated mainly by changing their power, their relative time delay. The simulation shows that the time delay deforms the parallel dark soliton pulse, forming a bright-like soliton in the transmission process and making the transmission quality down. By increasing the power of one dark soliton, the energy of the other dark soliton can be increased, and larger increase in a soliton's power leads to larger increase in the energy of the other. When the initial chirp is introduced into one of the dark solitons, higher energy consumption is observed. In particular, positive chirps resulting in pulse broadening width while negative chirps narrowing, with an obvious compression effect on the other dark soliton. Finally, large negative chirps are found to have a profound impact on parallel and nonparallel dark solitons.     

Waveguides induced by steady-state gray solitons in biased photorefractive-photovoltaic crystals

We carry out a theoretical investigation of the properties of waveguides induced by photorefractive one-dimensional steady-state gray spatial solitons (i.e., screening solitons, photovoltaic solitons, and screening-photovoltaic solitons). We demonstrate that waveguides induced by photorefractive steady-state gray spatial solitons are only a single guided mode for both all soliton graynesses and all values of ρ, where ρ is the ratio between the soliton peak intensity and the dark irradiance, and moreover, waveguides induced by gray photovoltaic solitons for closed-circuit condition are also only a single guided mode for all electric current densities. We find that the confined energy near the center of a photorefractive steady-state gray spatial soliton increases with ρ and decreases with an increase in the soliton grayness. We also find that the confined energy near the center of a gray photovoltaic soliton for closed-circuit condition increases with the electric current density. On the other hand, waveguides induced by gray screening-photovoltaic solitons are gray screening soliton-induced waveguides when the bulk photovoltaic effect is neglectable and are gray photovoltaic soliton-induced waveguides when the external bias field is absent.     

Temporal development of open-circuit bright photovoltaic solitons

This paper investigates the temporal behaviour of open-circuit bright photovoltaic spatial solitons by using numerical techniques. It shows that when the intensity ratio of the soliton, the ratio between the soliton peak intensity and the dark irradiance, is small, the quasi-steady-state soliton width decreases monotonically with the increase of τ-, where τ- is the parameter correlated with the time, that when the intensity ratio of the soliton is big, the quasi-steady-state soliton width decreases with the increase of τ- and then increases with τ, and that the formation time of the steady-state solitons is not correlated with the intensity ratio of the soliton. It finds that the local nonlinear effect increases with the photovoltaic field, which behaves as that the width of soliton beams is small and the self-focusing quasi-period is short. On the other hand, we also discuss that both the time and the temperature have an effect on the beam bending.     

Grey screening-photovoltaic soliton-induced waveguides

This paper shows that waveguides induced by grey screening-photovoltaic solitons are always single mode for all intensity ratios, which are the ratio between the peak intensity of the soliton and the dark irradiance. It finds that the confined energy near the centre of the grey soliton and the propagation constant of the guided mode increase monotonically with increasing intensity ratio. On the other hand, when the soliton greyness increases, the confined energy near the centre of the grey soliton and the propagation constant of the guided mode reduce monotonically. When the bulk photovoltaic effect is neglected for short circuits, these waveguides become waveguides induced by grey screening solitons. When the external bias field is absent, these waveguides become waveguides induced by grey photovoltaic solitons.[第一段]     

Separate spatial soliton pairs in an unbiased series two-photon photorefractive crystal circuit

Dark (bright) steady-state spatial solitons are predicted in one dimension for a series circuit consisting of two two-photon photorefractive crystals of which at least one must be photovoltaic. Each crystal can support a spatial soliton. The two solitons are known collectively as separate spatial soliton pairs with three types: dark-dark, bright-dark and bright-bright. In the limit in which the optical wave has a spatial extent much less than the width of the crystal, the dark soliton can affect the other soliton by light-induced current, but the bright soliton cannot affect the other soliton in the soliton pair.     

闭路光伏灰孤子诱导的波导

理论分析了闭路光伏晶体中灰孤子诱导的波导.研究发现,闭路光伏灰孤子诱导的波导在不同孤子灰度值,电流密度和光强比率下均为单模,文中光强比率指孤子峰值强度与暗辐射之比.研究结果解释了闭路光伏灰孤子限制在中心的能量随着电流密度的增加而增加,随着孤子灰度值和光强比率的增加而减小.文章还提供了光伏晶体的相关例子.     

Odd and even two-dimensional dark spatial solitons

The formation of two-Dimensional (2D) odd dark spatial solutions is analyzed numerically at an initial helical dark-beam phase distribution. Experimental results are presented for the first time confirming the existence of two-dimensional optical even dark solitons (ring dark solitons). Several aspects of the evolution of input 1D and 2D odd/even dark beams are compared qualitatively.     

Interactions of dark solitons in photovoltaic photorefractive crystals with diffusion nonlinearity

We investigate the interaction of spatial dark optical soliton pair in open-circuit photovoltaic photorefractive crystals by considering the effect of background light and diffusion nonlinearity. We show that the spatial dark solitons repel each other and travel along different trajectories for the coherent interactions that one undergoes reflection and the other one deflects significantly when they are closely overlapped, and the dark solitons attract and deflect simultaneously along a parabolic trajectory for the case of incoherent interactions. The deflection distance depends on the intensities and the initial separation between the dark solitons.     

Temporal behavior of dark spatial solitons in closed-circuit photovoltaic media

We show that the time-dependent nonlinear wave equation in closed-circuit photovoltaic media can exhibit quasi-steady-state and steady-state spatial solitons. We demonstrate that the formation time of open-circuit quasi-steady-state and open-circuit steady-state dark solitons decreases with an increase in the intensity ratio of the soliton, which is the ratio between the soliton peak intensity and the dark irradiance. We find that for the time-dependent nonlinear wave equation that exhibits only an open-circuit steady-state dark soliton, changing the electric current density J₀ does not generate quasi-steady-state dark solitons and affects the formation time of steady-state dark solitons and that for the time-dependent nonlinear wave equation that exhibits an open-circuit quasi-steady-state dark soliton, changing J₀ gives rise to three different time evolution regimes of the full width half maximum of the soliton’s intensity. The first regime shows that the formation time of steady-state dark solitons increases with J₀ whereas the formation time of quasi-steady-state dark solitons is independent of J₀. The second regime shows that the formation time of steady-state dark solitons decreases with an increases in J₀ and the formation time of quasi-steady-state dark solitons increases with J₀. The third regime shows that changing J₀ enables only steady-state dark solitons in the time-dependent nonlinear wave equation, of which the formation time increases with J₀.     

Surface dark screening solitons

We report on the existence of surface dark screening solitons at the interface between a dielectric medium (air) and a self-defocusing nonlinear material, taking advantage of photorefractive diffusion and drift nonlinearities. It is very interesting that a surface dark soliton is just like half of a dark soliton in bulk, but not a whole dark soliton propagating along surface. The excitation, propagation, and stability of this type of soliton are studied by using the beam-propagation method. Another interesting thing is that this type of dark soliton can be excited by a planar light beam without a necessary dark notch.     

Solitons in photovoltaic photorefractive media with an external electric field

We use the classical Lie-group method for studying the evolution equation in photovoltaic photorefractive media with an external electric field, reducing it to some similarity equations firstly, and then obtain some exact analytical solutions including the soliton solution, the period solution and the oscillatory solution. We also obtain the bright soliton, dark soliton, gray soliton from these similarity equations with the numerical method. Furthermore, we investigate what factors contribute to the beamwidth of these solitons with the numerical method and know the beamwidth of these solitons are associated with the external electric field, the photovoltaic field and the intensity ratio of the incident soliton.     

Modulation instability of bright photovoltaic solitons on a partially incoherent background

We present the observation of incoherent anti-dark photovoltaic solitons in LiNbO₃:Fe crystal. This new class of soliton states involves bright photovoltaic solitons on a background beam meeting ?? > 1, where ?? is the ratio of background illumination photovoltaic constant to that of soliton beam. For ?? < 1, dark photovoltaic solitons are generated. Furthermore, this novel type solitons are investigated experimentally by injecting coherent light and partially coherent background of infinite extent. In case of spatial coherence of the background lower than the threshold of incoherent modulation instability, these results indicate that bright photovoltaic solitons can propagate in a stable fashion.