Interactions of Localized Wave Structures on Periodic Backgrounds for the Coupled Lakshmanan–Porsezian–Daniel Equations in Birefringent Optical Fibers

Nonlinear waves on periodic backgrounds play an important role in physical systems. In this study, nonlinear waves that include solitons, breathers, rogue waves, and semi-rational solutions on periodic backgrounds for the coupled Lakshmanan-Porsezian-Daniel equations are investigated. Moreover, the interactions between different types of nonlinear waves are examined and their dynamic behaviors are studied. In particular, it is observed that bright-dark rogue waves interact with bright-dark breathers or solitons on periodic backgrounds, four-petaled breathers interact with two eye-shaped breathers on periodic backgrounds, and a four-petal rogue wave interplays with a rogue wave on periodic backgrounds. Furthermore, it is found that the value of the parameter γ₃ affects the weak and strong interactions of these nonlinear waves. These results may be useful in the study of nonlinear wave dynamics in coupled nonlinear wave models.     

Spatial rectification of fields of photorefractive waves

A theory of rectifying electric fields associated with photorefractive waves is presented. The rectification effect is caused by scattering of photorefractive waves from the static grating of a space charge, which is formed as a result of excitation of photorefractive waves due to an interference pattern oscillating about its equilibrium position. The theory predicts high values of rectified fields (of the order of 100 V cm^?1) and agrees well with the available experimental data.     

用体全息术对皮秒光脉冲进行二维测量

本文提供一种测量两束相干的ps光脉冲的空间二维时间振幅相关函数的新方法.在此方法中,光脉冲是被记录在一种光致折变的体积全息介质中,而所记录的信息可以通过直接量度在介质中所形成的光栅的空间分布而读出.这种方法可的可行性已为实验证实,它是通过3.5ps倍频锁模Nd:YAG激光测量光致折变晶体LiNbO₃来实现的。     

光折变振荡器中的模式锁定及阵发混沌

用数值模拟的方法研究了光折变振荡器的一些时空行为，结果表明在简并或准简并条件下的横模空间耦合将使得光折变振荡器表现出与普通激光器相似的时空现象，例如不同横向模式间的合作频率锁定，时空周期行为及多模振荡时的阵发混沌现象等等。     

时空调制对可激发介质螺旋波波头动力学行为影响及控制研究

本文首先研究了时空调制对可激发介质中周期螺旋波波头动力学行为的影响. 随着时空调制的增大, 螺旋波经历了周期螺旋波、外滚螺旋波、旅行螺旋波和内滚螺旋波的显著变化. 通过定义序参量来定量的描述由时空调制引起的螺旋波在不同态之间非平衡跃迁的临界条件, 及漫游螺旋波波头圆滚圆半径随调制参数的变化情况. 当时空调制增大到某个临界值时, 螺旋波发生了破碎; 再增加时空调制, 螺旋波则发生了衰减, 系统最终演化为空间均匀静息态. 在文中给出了螺旋波发生破碎和衰减的机理和原因. 最后将时空调制方法运用于漫游螺旋波, 实现了将漫游螺旋波控制成周期螺旋波, 或将其控制为空间均匀静息态.     

Beam splitting, combining, and cross coupling through multiple superimposed volume-index gratings

We investigate the diffraction properties of multiple-superimposed index gratings from a vector synthetic viewpoint using coupled wave analysis with Bragg and non-Bragg readout. The vector synthetic gratings consist of two volume-index gratings with different grating wave vectors, which can be obtained in photorefractive materials, in optical fibers or in Bragg cells with two driving acoustic waves. This structure can realize beam splitting, beam combining, and beam cross coupling, etc. Analytic expressions for the diffraction efficiency as well as the amplitude of the waves involved are obtained. The results are presented and discussed.     

Dynamics of photorefractive response in sillenite crystals with double-ionized donor centers and shallow traps

The dynamics of the photorefractive response in the Bi₁₂TiO₂₀ crystal with double-ionized donor centers and shallow traps is analyzed. Consideration is given to the time dependences of the recording of a photorefractive grating in the absence of an external electric field, its storage in the dark, and its development upon the application of an external field and turning on of a reading light beam.     

Feedback controlled periodic states for different kinds of photorefractive nonlinear response

We investigate analytically and numerically the influence of the type of the photorefractive nonlinear response on the periodic states (attractors) which occur during feedback controlled 2W-coupling and correspond to almost 100% diffraction efficiency of the dynamic index grating. In addition to the case of the local response typical, for example, for LiNbO₃ crystals we consider the cases of nonlocal (diffusive) response (BaTiO₃, SBN) and resonant response (DC-biased BSO, BTO, and BGO crystals). It is shown that the conditions for the transition to the periodic states and their apparent characteristics are strongly different for the two limiting cases above. Received 16 July 2002 / Received in final form 29 October 2002 Published online 4 March 2003     

Effect of Grating Spacing on Response Time and Sensitivity in Photorefractive Materials at Large Modulation Depth

Photorefractive response time and photorefractive sensitivity are two important parameters characterizing photorefractive materials. We study theoretically the effect of the grating spacing on these parameters at large modulation depth in the absence and presence of an applied electric field for some of the most promising photorefractive materials, namely, LiNbO₃, KNSBN, SPS, BGO, and GaAs. We find that the response time increases with increasing grating spacing for LiNbO₃ and KNSBN, whereas the response time decreases with increasing grating spacing for SPS, BGO, and GaAs. The photorefractive sensitivity is mainly affected by the mobility–lifetime product in the presence of an applied electric field.     

Fe：LiNbO3晶体光折变全息热固定动力学特性分析

以Fe:uNbO3晶体为例,考虑了电子载流子热激发(强烈地依靠于温度),通过对以扩散和光伏特效应为主导输运机制的带输运方程和耦合波方程进行数值求解,分析了热固定过程初始光强入射比和固定温度对光栅空间电荷场的影响,指出记录固定过程中内电场极值的出现来源于质子电场对施主光栅电场的部分补偿,质子光栅电荷场可以导致晶体中记录光束之间能量耦合方向的变化,得出了理论上的加热固定时间。     

Orientational photorefractive effects observed in polymer-dispersed liquid crystals

We present a novel type of photorefractive polymer-dispersed liquid crystal (PDLC) that contains a polymer, low-molecular liquid crystals (LC's), and a photoconductive sensitizer. Photorefractivity is demonstrated by two-beam-coupling experiments with an external dc field. This material shows highly sensitive photorefractivity, and a purely refractive-index grating (Dn >/= 3.0 x 10(-3)) is generated by irradiation of interference light (lambda=632.8 nm) . The grating in the photorefractive PDLC's shows strong anisotropy, and the dynamics depends strongly on the composition. In the case of a 40:60 weight ratio of polymer:LC's, the photorefractive PDLC's present a stable memory effect.     

耦合不连续系统同步转换过程中的多吸引子共存

本文研究了耦合不连续系统的同步转换过程中的动力学行为, 发现由混沌非同步到混沌同步的转换过程中特殊的多吸引子共存现象. 通过计算耦合不连续系统的同步序参量和最大李雅普诺夫指数随耦合强度的变化, 发现了较复杂的同步转换过程: 临界耦合强度之后出现周期非同步态(周期性窗口); 分析了系统周期态的迭代轨道,发现其具有两类不同的迭代轨道: 对称周期轨道和非对称周期轨道, 这两类周期吸引子和同步吸引子同时存在, 系统表现出对初值敏感的多吸引子共存现象. 分析表明, 耦合不连续系统中的周期轨道是由于局部动力学的不连续特性和耦合动力学相互作用的结果. 最后, 对耦合不连续系统的同步转换过程进行了详细的分析, 结果表明其同步呈现出较复杂的转换过程.     

“Running” holograms in photorefractive Bi12SiO20 crystals

It is shown that under uniform illumination and application of an external electric field, a phase volume hologram in a photorefractive crystal exists in the form of relaxing running wave. Effective recording of such a running hologram is possible only by an interference pattern moving synchronously with the recorded grating. The physical nature of this phenomenon, the possible enhancement of the hologram diffraction efficiency upon recording of a running pattern and the main factors limiting its value are discussed for the case of photorefractive Bi₁₂SiO₂₀ crystals.     

Perturbative analysis of cross-talk of two pieces of photorefractive phase gratings stored in one point by angle multiplexing

In this paper, we have applied a perturbative expanding method to the hopping model, and studied the cross-talk between two pieces of phase gratings stored in one point of photorefractive material by angle multiplexing. The coupling equations and their steady solution have been derived. It has been found that the fundamental harmonic of the first grating is coupled with the second-order harmonic of the second grating and the second-order harmonic of the first gating is coupled with the fundamental harmonic of the second grating. The positions of maximums of the plots about the normalised fundamental and second-order harmonics of the space-charge field vs. the normalised grating vector (k/k₀) are at k/k₀=1.414 and k/k₀=1.01 for Δk/k₀=0, respectively, which are at k/k₀=1 and for the case of storing single grating in one point. This kind of deviation has been confirmed by our two-wave coupling experiment with Ce:KNSBN crystal. At the same time, we have found the degree of deviation of the second-order harmonic of the space-charge field strongly depends on the difference of normalised grating vector (k/k₀)between the two pieces of gratings, but that of fundamental harmonic weakly depends on it. In addition, it has been found that the degrees of deviation of both harmonics do not depend on the modulation depth.     

Anomalous behaviour of long-time increase in diffraction efficiency of photorefractive grating in Ce：BaTiO3 in dark

Anomalous long-time increase of the diffraction efficiency is observed in dark-decay experiments of photorefractive gratings in Ce：BaTiO3. It is deduced that a phase-conjugate beam is induced by the writing beam at acute angle to the ＋c axis of the crystal and it interferes with the other writing beam to form a second grating which is perpendicular to the first grating formed by the interference between two writing beams. The rising behaviour of the diffraction efficiency results from the different decay rates of these two photorefractive gratings. Furthermore, a simplified model of two gratings, both induced by two deep traps, is proposed to account for this phenomenon and the fitting results agree well with the experimental results.     

Positive and negative feedback effects of four-wave mixing in photorefractive crystals with two active centres

Based on a two-level model of optical transitions, the problem of positive and negative feedback effects during simultaneous reading and writing of dynamic holograms in photorefractive crystals has been solved analytically. The diffraction efficiency and the gain coefficient are shown to be nonlinear functions of the readout beam intensity and are nonreciprocal with respect to the readout from the two input ports. The readout beam intensity value that affects a previously recorded grating is shown to depend on microscopic parameters such as the cross-section of photoionization, the recombination coefficient and the concentration of photorefractive centres. An analysis of the amplitude of the overall shared grating has shown that with increasing readout beam intensity the holographic grating thickness decreases. In this case, under negative feedback the grating amplitude decreases, while with positive feedback it increases. The possibility is shown of achieving (under positive feedback) a maximum value of diffraction efficiency and complete energy transfer in a finite thickness of the photorefractive crystal, in contrast to the infinite thickness required in the standard two-beam coupling case.     

Dynamic effects in photorefractive crystals at simultaneous read–write of holographic gratings

A two-level model of a simultaneous read–write of holographic gratings in photorefractive crystals has been developed for the nonstationary case at the applied electric field and unequality of recording beam intensities. The recurrent relationships both for the internal field amplitudes and for the amplitudes of the optical waves involved in interactions have been obtained. The use of a truncated power series expansion has allowed to obtain the expressions for diffraction efficiency and intensities of optical waves in nonstationary case. The obtained results were used for the analysis of simultaneous read–write dynamics in Bi₁₂SiO₂₀ crystals.     

Surface electromagnetic waves at the interface between a homogeneous medium and a system of coupled waveguides

An analysis is made of the experimental investigations of the surface waves existing at the interface between a homogeneous medium and a periodically stratified medium that represents a bounded system of coupled waveguides. It is shown that, in all cases of the observation of surface waves, the bounded system of coupled waveguides has its own spectrum of guided modes and a spectrum of leaky modes that become surface waves of the system. It is also demonstrated that a biosensor can successfully operate when two surface waves serve as leaky modes of a Bragg waveguide in which the periodic system of waveguides is used as a distributed Bragg mirror of this waveguide. A structure supporting surface waves is designed on the basis of ten pairs of Nb₂O₅-SiO₂ layers and implemented experimentally. The surface waves are detected with a K8 glass prism according to the Kretschmann scheme.     

Frequency detuning dependence of oscillation condition for a semilinear photorefractive optical resonator in a photorefractive material with reflection gratings

Frequency detuning dependence of four-beam coupling in a photorefractive crystal pumped with two counter-propagating waves for a semilinear coherent optical resonator on the oscillation conditions has been analyzed in the case of non-degenerate-wave mixing under the slowly varying amplitude approximation method. Self oscillation can be achieved when the gain arising from the four-beam coupling is large enough to overcome the cavity loss. The effects of frequency detuning (i.e., non-degeneracy), dielectric constant and photoconductivity of the photorefractive materials on the performance of the semilinear photorefractive coherent resonator with the reflection grating configuration have also been studied in detail. The phase-conjugate reflectivity of the pumped crystal and oscillation intensity has been calculated for different input pump beam intensity ratio, intensity reflectivity of the conventional mirrors, degenerate energy coupling strength of the interacting beams. It has been found that for the higher value of the photoconductivity σ_p(>2.0 pS/cm) of photorefractive crystal, the semilinear resonator can oscillate at almost any frequency detuning (Ω) of the oscillation beam with respect to the fixed frequency of the pump waves whereas for the lower value of photoconductivity σ_p(<0.1 pS/cm) oscillation occurs only when the frequency detuning is limited to small region around Ω = 0. But reverse of the case is found for dielectric constant (?), pump intensity ratio (p) and conventional mirror reflectivity (R).