Self-focusing in photorefractive two-wave mixing

Self-focusing and self-defocusing of light in two-wave mixing are investigated experimentally. Amplification and self-focusing are measured as functions of the frequency shift between signal and pump beams. A frequency dependence is found in Kramers-Kronig form, as is plausible by the analogy of photorefractive amplification and laser amplification. Reversal of the external dc field on the material or a change in the frequency shift between the signal and pump beams is found to change self-focusing to self-defocusing.     

Transverse effects in photorefractive two-wave mixing

In a biased photorefractive crystal, the process of two one-dimensional waves mixing, i.e., the dynamical evolution of both pump beam and signal beam, is traced by numerically solving the coupled-wave equation. Direct simulations show that the propagation and stability of the two beams are completely determined by the system parameters, such as the external bias field, the intensity and the beam waist of the pump beam. By adjusting these parameters, one can control the state of two Gaussian waves mixing. The numerical results are helpful for performing a two-wave mixing experiment.     

Transverse instabilities in photorefractive counterpropagating two-wave mixing

Threshold analysis for transverse instabilities in photorefractive counterpropagating two-wave mixing through reflection gratings is performed. A numerical algorithm for the treatment of wave equations in this geometry is developed, displaying the emergence of running transverse waves. They appear above a threshold in the applied electric field, and their transverse wave number and oscillation frequency agree well with the values predicted by stability analysis.     

Spatiotemporal self-organization upon two-wave mixing in a photorefractive medium

Nonlinear dynamics of recording volume holographic gratings upon two-wave mixing in an inertial photorefractive media were studied. It is found that the space-time dependence of the grating diffraction efficiency can be quasi-regular, allowing the understanding of the experimentally observed irregular behavior of the diffracted light intensity.     

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.     

Degenerate two-wave mixing in photorefractive crystals with multiple internal reflections

The effect of multiple internal reflections on the stationary energy transfer in degenerate two-wave mixing, in a reflection geometry, with photorefractive crystals is studied. Numerical results obtained by using the shooting method are presented graphically. Generally it is found that the presence of multiple internal reflections reduces the amount of energy transferred between the two interacting beams. However, under some special conditions the energy transfer can be enhanced.     

Detection of small phase modulation using two-wave mixing in photorefractive crystals

Two-wave mixing of phase-modulated beams in photorefractive crystals under a dc electric field is studied both theoretically and experimentally. Based on the vectorial theory of light diffraction in crystals of cubic symmetry, we derived an analytical expression that describes the phase demodulation in crystals with an arbitrarily oriented electric field. The phase-demodulation technique was used for estimation of the space-charge field created in photorefractive crystals. It is shown that the space-charge-field grating created in GaP and Bi₁₂TiO₂₀ crystals is much smaller than that predicted from the one-level band-transport model of the photorefractive effect. Received: 12 December 2000 / Revised version: 8 February 2001 / Published online: 27 April 2001     

Voltage reduction for photorefractive two-wave mixing in InP:Fe by optical gap control

We report a method to increase the photorefractive two-wave mixing gain coefficient in semiconductors by using additional incident laser radiation. Two auxiliary beams are used to optimize the spatial distribution of an applied electrical field via modulation of the photoconductivity of the sample. By applying a voltage of 3.5 kV on a 4.3 mm thick InP:Fe crystal we obtain a two-wave mixing gain of 9 cm^–1. This is about 50% larger than that obtained without auxiliary beams.     

Control of the energy exchange upon double two-wave mixing in photorefractive crystals

The problem of double two-wave mixing in photorefractive crystals is analytically solved in the framework of the two-level model of optical transitions. Relationships are derived for calculating the intensities of all four interacting waves and the amplitude of the holographic grating. It is demonstrated that the magnitude and direction of energy exchange between the interacting beams can be controlled by a purely optical method, namely, by varying the intensity ratio and the initial phase shift between the interference patterns.     

Evolution and stability of spatial solitons in a photorefractive two-wave mixing system

The dynamical evolution and stability of bright dissipative holographic solitons in biased photorefractive materials in which the self-trapping beam obtains a gain from the pump beam via two-wave mixing has been investigated numerically. Results show that these solitons are stable relative to small perturbations. Adjusting some system parameters, such as the bias field and the angle between beams, can easily control the generation of such solitons. Potential applications in optical switches or repeaters are discussed.     

Oscillation dependence of two-wave mixing gain for unidirectional ring resonator in photorefractive materials

Dependence of the coupling strength of two-wave mixing gain in photorefractive materials for the single unidirectional ring resonator on oscillation conditions has been analyzed in the strong nonlinear regime. In this regime, difference between the frequency of the pump beam and oscillating beam is proportional to the cavity-length detuning, which can be explained in terms of the photorefractive phase-shift. This phase-shift results due to slightly non-degenerate two-wave mixing that compensates for cavity detuning and satisfies the round-trip phase condition for the steady-state oscillation. The presence of such a phase-shift allows the possibility of the nonreciprocal steady-state energy transfer between the pump and oscillating beams. If the gain due to the beam coupling is large enough to overcome the cavity losses then the signal beam is amplified in the presence of material absorption. Such amplification is responsible for the oscillations. For the single unidirectional ring resonator, the effects of cavity-length detuning, energy coupling coefficient, crystal thickness of the material, reflectivity of the cavity mirrors and material's absorption coefficient on the frequency and intensity of oscillations have also been studied in detail. It has been found that for the smaller value of absorption coefficient (α) of the photorefractive crystal, the unidirectional ring resonator can oscillate at almost any cavity-length detuning (ΔΓ) whereas for the larger value of α oscillation occurs only when the cavity-length detuning is limited to small region (around ΔΓ=0). But reverse of the case is found for energy coupling coefficient (γ₀).     

光折变晶体LiNbO3：Fe简并两波混频在干涉测量中的应用

本文从理论上深入地分析光折变晶体中简并两波混频的动态特性。通过有关公式的推导,阐明动态两波混频在实时干涉测量中应用的原理。文中还提出利用LiNbO_3:Fe晶体的测量光路,给出其实测结果。并对测量精度作出分析。     

Giant momentary readout produced by switching electric fields during two-wave mixing in sillenites

We show theoretically and experimentally that switching an applied square-wave field produces strong and short pulses of the outgoing signal during two-wave mixing in sillenite crystals. These pulses originate from the strong effect of the field on the optical eigenmodes and can be used in new optical schemes based on time-separated recording and readout processes.     

基于光折变双光束耦合的刚性全息明孤子的温度依赖特性研究

研究了基于双光束耦合的光折变耗散系统中全息明孤子的温度演化特性.数值计算结果表明，晶体温度与刚性全息孤子的稳定性密切相关.在一定温度下，全息孤子能在晶体中传播足够远的距离；当晶体温度漂移不大时，入射孤子能演化成稳定的全息孤子继续传播；而当晶体温度变化足够大时，孤子波强度随传播距离增加或减小，入射孤子不能以稳定的全息孤子态传播.讨论了将刚性全息孤子的温度特性应用于光学衰减、中继器件的可能性. 关键词： 空间光孤子 光折变非线性光学 耗散系统 全息聚焦     

Resonant two-wave mixing in photorefractive materials with the aid of dc and ac fields

A recently predicted resonant effect for the enhancement of two-wave mixing in photorefractive materials is investigated. The resonance occurs when the frequency of the applied ac field agrees with the eigenfrequency of the excited space-charge wave. Experimentally a clear resonance is found, as predicted by the theory, for high dc electric fields, but the resonance is smeared out for lower fields. A modified theory, taking into account the second temporal harmonic of the space-charge wave, shows good agreement with the experimental results.     

Shaping of photorefractive two-wave coupling by fast phase modulation

Using the distinctive features of the photorefractive nonlinearity, we derive a general self-consistent set of equations to describe two-wave coupling in the presence of fast and arbitrary strong-phase modulation. By considering a number of important particular cases, we show that phase modulation is a powerful and useful tool for shaping the characteristics of two-wave coupling such as the value of the energy exchange, the diffraction efficiency of the recorded grating, and the structure of the grating fringes. Finally, we analyze the role of the phase modulation in the active stabilization of wave coupling by means of an electronically introduced phase feedback.     

基于运动光栅光折变双光束耦合的刚性全息明孤子的动态演化

研究基于运动光栅双光束耦合的耗散光折变系统中的空间光孤子的动态演化问题.数值计算 表明，系统参数同这种孤子的稳定性密切相关.在某组系统参数下，孤子可以在晶体内稳定 传播足够远的距离.双光束耦合的相位与强度耦合系数之比越大，孤子的稳定性越好.讨论了 将这种系统应用于光学开关、中继及分路器件的可能性. 关键词： 空间光孤子 光折变非线性光学 耗散系统 全息光栅     

Numerical simulations and experimental investigations on transverse effects of two-wave mixing in a photovoltaic photorefractive crystal

The transverse effects of two Gauss waves mixing in a photovoltaic photorefractive crystal,i.e.,the dynamical evolutions of signal beam with different parameters,are traced numerically and experimentally.Both the one-dimensional numerical simulations and two-dimensional experimental investigations show that the self-focusing effect of signal beam becomes more obvious as the intensity of pump beam and the angle between the signal and pump beams increase.In accordance with these results,the state of two Gauss...     

Calculation of the gain in optically active photorefractive crystals considering the self-diffraction in a two-wave mixing process

We present a physical and computational procedure to calculate the gain in a two-wave mixing process in a thick optically active photorefractive BSO crystal under diffusion regime. The procedure is based on the integration of the amplitude of the signal beam through the sample. In the model, the effects of self-diffraction are taken into account by using the more general expression of the diffraction efficiency for the case of dynamic gratings. It allows also including the effects of the optical activity on the coupling factors and not only on the rotation of the optical field vectors when the waves are propagated along the crystal. The <001> crystallographic configuration is used. The model is used to predict the behavior of the gain as a function of the beam polarization angle. Numerical and experimental results using crystals with thickness of 5 mm and 10 mm are presented. A good agreement between the proposed model and the experimental measurements is observed.