Temporal behaviour of open-circuit photovoltaic solitons

Based on the time-dependent band-transport model in a photorefractive medium, dark open-circuit photovoltaic (PV) solitons are investigated both theoretically and experimentally. Compared with those of the time-independent models, our theoretical results revealed that quasi-steady-state and steady-state PV solitons can both be obtained. Our results also revealed that when r < 1 (r is the normalized intensity at infinity), the full width at half maximum (FWHM) of solitons decreases monotonically to a constant value; when r > 1, however, the FWHM of solitons first decreases to a minimum before it increases to a constant value. Moreover, the FWHM of steady solitons decreases with increasing intensity ratio for r < 1, and increases with increasing intensity ratio for r > 1. We further observed dark PV solitons in experiments, and recorded their evolution. These results indicated that steady solitons can be observed at low optical power, while quasi-steady-state solitons can only be generated at higher optical power. Good agreement is found between theory and experiment.     

温度对双光子亮光伏空间孤子演化特性的影响

基于扩散效应及暗辐射强度对温度的依赖关系,研究了温度对双光子光伏光折变介质中亮光伏空间孤子动态演化及自偏转特性的影响。将亮孤子作为入射孤子波,采用数值方法求解孤波演化方程,结果表明:在给定温度下,双光子光折变介质中可以形成稳定的亮光伏空间孤子,当介质的温度变化不大时,孤子将克服较小的扰动而保持稳定的孤子传播,当温度变化足够大时,孤子将变得不稳定甚至崩溃;在一定温度范围内,孤子中心的自偏转距离随着温度的升高而增加,在特定温度下达到最大值,之后随着温度的升高而减小。     

Higher-order space-charge field effects on the self-deflection of two-photon bright photovoltaic spatial solitons

We investigate numerically the effects of higher-order space-charge field on the self-deflection of bright photovoltaic spatial solitons in two-photon photovoltaic photorefractive crystals under steady-state conditions. The expression for an induced space-charge electric field, including higher-order space-charge field terms is obtained. The dynamical evolution equation is built in which the effects that arise from these higher-order terms are considered. Numerical results indicate that bright photovoltaic solitons can bend towards both the same direction as the crystal's c-axis and the opposite direction, respectively. Specifically, self-deflection cannot occur for bright photovoltaic solitons if the strength of the photovoltaic field and the intensity of the input beam are appropriately selected. Relevant examples are provided.     

低振幅双光子屏蔽光伏孤子的时间特性

为了得到低振幅双光子屏蔽光伏孤子时间特性的结果,采用数值模拟的方法对低振幅双光子屏蔽光伏孤子的时间特性进行了理论分析,得到了明和暗孤子时间特性的演化方程。结果表明:孤子的宽度随时间的演化单调递减到一个最小值直至稳态孤子的形成,在相同的演化时间内,孤子的半峰全宽随着孤子峰值强度和暗辐射比值的增大而变窄。     

One-dimensional steady-state bright photovoltaic solitons in LiNbO3:Fe crystal with background illumination

We investigate theoretically and experimentally one-dimensional bright photovoltaic solitons in LiNbO₃:Fe crystal by use of the background illumination. We find that, in LiNbO₃:Fe crystal, bright photovoltaic solitons can be obtained with background illumination for κ>1, where κ is the ratio of the background illumination photovoltaic constant to the soliton optical beam's photovoltaic constant. For κ<1, dark photovoltaic solitons are generated. On the other hand, our experiments show good agreement with theoretical prediction for the soliton existence curve in a special intensity ratio.     

Quasistable bright dissipative holographic solitons in photorefractive two-wave mixing system

The dynamical evolution of both signal and pump beams are traced by numerically solving the coupled-wave equation for a photorefractive two-wave mixing system. The direct simulations show that, when the intensity ratio of the pump beam to the signal beam is large enough, the pump beam presents a common decaying behaviour without modulational instability (MI), while the signal beam can evolve into a quasistable spatial soliton within a regime in which the pump beam is depleted slightly. The larger the ratio is, the longer the regime is. Such quasistable solitons can overcome the initial perturbations and numerical noises in the course of propagation, perform several cycles of slow oscillation in intensity and width, and persist over tens of diffraction lengths. From physical viewpoints, these solitons actually exist as completely rigorous physical objects. If the ratio is quite small, the pump beam is apt to show MI, during which the signal beam experiences strong expansion and shrinking in width and a drastic oscillation in intensity, or completely breaks up. The simulations using actual experimental parameters demonstrate that the observation of an effectively stable soliton is quite possible in the proposed system.     

Pyroelectric photovoltaic spatial solitons in unbiased photorefractive crystals

A new type of spatial solitons i.e. pyroelectric photovoltaic spatial solitons based on the combination of pyroelectric and photovoltaic effect is predicted theoretically. It shows that bright, dark and grey spatial solitons can exist in unbiased photovoltaic photorefractive crystals with appreciable pyroelectric effect. Especially, the bright soliton can form in self-defocusing photovoltaic crystals if it gives larger self-focusing pyroelectric effect.     

Effect of temperature on the evolution of bright and dark screening—photovoltaic spatial solitons

We investigate theoretically the temperature effects on the evolution of both bright and dark screening-photovoltaic optical spatial solitons in biased photovoltaic-photocefractive crystals in the case of neglecting the diffusion process.For a stable bright or dark screening-photovoltaic soliton originally formed in a crystal at a given temperature,when the crystal temperature changes,it will evolve into another stable screening-photovoltaic soliton if the change is quite small,whereas it will become unstable or break down if the temperature change is large enough.The spatial shape of a stable screening-photovoltaic soliton can be reshaped by appropriately adjusting the crystal temperature.     

Waveguides induced by grey screening solitons

We investigate the properties of waveguides induced by one-dimensional grey screening solitons in biased photorefractive crystals. The results show that waveguides induced by grey screening solitons are always of single mode for all intensity ratios, i.e. the ratios between the peak intensity of the soliton and the dark irradiance. Our analysis indicates that the energy confined near the centre of the grey soliton and the propagation constant of the guided mode of the waveguide induced by the grey screening soliton increase monotonically with intensity ratio increasing. On the other hand, when the soliton greyness increases, the energy confined near the centre of the grey soliton and the propagation constant of the guided mode of the waveguide induced by the grey screening soliton decrease monotonically. Relevant examples are provided where photorefractive crystal is of the strontium barium niobate type.     

Temporal Behavior of Low-Amplitude Grey Spatial Solitons in Biased Two-Photon Photorefractive Crystals

The temporal property of grey screening spatial solitons due to two-photon photorefractive effect in lowamplitude regime is analyzed. The results indicate that a broad solitons is generated at the beginning, and as time evolves, the intensity width of grey solitons decreases monotonically to a minimum value toward steady state. In the same propagation time, the FWHM of solitons decreases with p increasing or m decreasing. Moreover, the formation time of solitons is independent of p and m. The time is close to a constant determined by the dielectric relaxation time.     

Bright-dark self-coupled vector spatial solitons in biased two-photon photovoltaic photorefractive crystals

This paper predicts that bright-dark self-coupled vector solitons are possible in biased two-photon photovoltaic photorefractive crystals under steady-state conditions. The solutions of these vector solitons can be determined by use of simple numerical integration procedures. When the photovoltaic effect is neglectable, these vector solitons are bright-dark vector screening solitons. When the external bias field is absent, these vector solitons degenerate the bright-dark vector photovoltaic solitons.     

高斯光束在有外电场的双光子光伏光折变材料中的演化

为了得到一束高斯光束和两束高斯光束的相互作用在有外电场的双光子光伏光折变材料中的演化结果,将高斯光束作为入射波,采用数值方法求解波传播方程。研究结果表明:在外加电场、光强峰值分别与晶体参量匹配的情况下,一束高斯光束能演化为稳定的屏蔽光伏明孤子,而在不匹配时,一束高斯光束在传播过程中则呈现周期性压缩或膨胀现象。同时也发现:在作用距离范围内,同相位的两高斯光束相互吸引,并伴随有融合现象;而相位相反的两高斯光束相互排斥,且其排斥作用随着光束初始间距的减小而增加,当两高斯光束的相位差位于区间(0,π)和(-π,0)时,其相互作用过程中伴有能量的转移,两区间中能量转移方向相反。     

LiNbO3晶体中光伏亮孤子实验研究

从理论上分析了具有不同Class常数的背景光在晶体折射率空间分布相对变化中的作用,得到了折射率改变为负的晶体中形成亮、暗光伏孤子的条件.以此为基础,用532nm的e光作信号光、488nm的o光作背景光并不断变化背景光和信号光的功率,首次在实验上观察到了LiNbO3:Fe晶体中亮光伏孤子的形成.     

Dynamics of bright discrete staggered solitons in photovoltaic photorefractive media

Theoretical results on spatial optical bright solitons excited in arrays of nonlinear defocusing waveguides, that result from the photovoltaic effect in a photorefractive material, are presented. The existence of four types of stationary discrete bright staggered solitons, on-site, inter-site, twisted inter-site, and twisted on-site solitons, is shown both analytically and numerically, and their stability properties are investigated. The maximum Hamiltonian of staggered solitons with the same total power corresponds to stable modes. It is shown that for low total power the on-site mode is stable while in the high power regime the inter-site mode is stable. These results are confirmed numerically. In addition, steering properties of localized modes are investigated by introducing a transversal translational shift. Because of the translational symmetry between on-site and inter-site localized modes they are considered as two dynamical realizations of the same moving mode, and the formalism of the Peierls-Nabarro effective potential is applied to interpret the exchange between trapping and steering of these modes. This critically depends on the mode’s total power and the introduced phase difference. On the other hand, steering of twisted inter-site and on-site localized modes is not numerically observed. Instead, transversal perturbation leads to a transformation of twisted modes either into a trapped on-site mode of smaller power and radiation, or into two trapped on-site modes.     

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.     

Temporal behavior of low-amplitude dark spatial solitons in two-photon centrosymmetric photorefractive media

We investigate the temporal behavior of low-amplitude dark spatial solitons in biased centrosymmetric crystals with two-photon photorefractive effects. The expressions of time-dependent space-charge field and dynamical evolution equation are derived. The temporal behaviors of the intensity profiles and the intensity full width at half maximum (FWHM) of dark solitons are investigated by numerical method. The results indicate that a broad soliton is generated at the beginning, and as time evolves, the intensity width of solitons decrease monotonously to a minimum value toward steady state. Within the same propagation time, the higher the ratio of soliton peak intensity to the dark irradiation intensity is, the shorter the FWHM of dark solitons is.     

光折变空间光孤子的顶侧面观测法

基于CCD图像采集技术与计算机软件处理技术,提出了空间光孤子的顶侧面观测法.此方法能够非常直观地显示出光孤子在晶体内部传输时,在水平及垂直方向上不同位置的轮廓图.用这种方法观测到了KNSBN晶体中的二维光伏明孤子,观测结果与理论模拟结果相一致.     

亮暗屏蔽光伏孤子在LiNbO3晶体中的大自偏转

用数值方法证实了亮、暗屏蔽光伏孤子在有外加电场的LiNbO3晶体中都可以发生大自偏转,并验证了这种自偏转现象不但与晶体中受主浓度NA有关而且还与外加电场E0有关.在E0相同的条件下,NA越小这种自偏转现象越明显,在NA相同的条件下,风越大自偏转现象越明显.还发现亮、暗屏蔽光伏孤子的自偏转现象不同:亮屏蔽光伏孤子整体都发生明显偏转,暗屏蔽光伏孤子的偏转只是发生在一侧,其极值位置和另一侧几乎不发生偏转.     

Coherent interactions of multi bright spatial solitons in biased photorefractive crystals

The coherent interaction scenarios of two solitons, three solitons, and four solitons are presented. For two-soliton interactions, energy transfer and fusion between solitons are dependent on the relative phase of the interaction solitons, and for multi-soliton interactions, energy transfer will occur in all three relative phase conditions. The magnitude and direction of energy transfer can be controlled respectively by adjusting the interval and the relative phase of 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.