Beam coupling and decoupling in degenerate two-wave mixing in a reflection geometry with photorefractive Bi2GeO20 crystals

The dependence of the effective gain on the incident angle of the beams and on the initial beam intensity ratio is studied in the experiment of degenerate two-wave mixing (TWM) in a reflection geometry with photorefractive Bi₁₂GeO₂₀ (BGO) crystals. A saturation value of the effective coupling constant ¦g¦-0.4 cm^–1 is obtained. In contrast to TWM operated in the drift mode (i.e. with a nonzero electric field applied to the crystal), for TWM operated in the diffusion mode (zero external electric field) as is our case, beam coupling is reduced by moving the crystal or the interference fringes at a constant speed. At high moving speeds, complete beam decoupling can be reached. A comparison between the theoretical and measured dependence of the effective gain on the moving speed is also made. Using this technique, complete isolation of two intersecting coherent beams inside a nonlinear medium can be achieved.     

Steady holographic gratings in semiconductor multiple quantum wells

A theoretical model based on the Dember mechanism is proposed to describe the steady state photorefractive gratings generated in semiconductor multiple quantum wells (MQW). It has been applied to an GaAs/AlGaAs MQW in parallel configuration (external electric field applied parallel to the MQW layers) for which recent experimental data are available. The model predicts a dependence of the first-order diffraction efficiency on the applied field in qualitative accordance with experiments, including the occurrence of saturation at high field values. Absolute values of the efficiencies are in good agreement with the experimental ones. Finally, high second-order diffraction efficiencies, associated with the development of a perpendicular space charge field, are also predicted by the model.     

Self-pumped phase conjugation in Bi12TiO20 crystal without external cavity

We present an experimental study of the self-pumped phase-conjugate-mirror (SPPCM) recording in a Bi₁₂TiO₂₀ sample due to the partial internal reflection of the pump beam from the rear face. SPPCM has been recorded under an external alternating electric field of a square-wave form with response time equal to 170 s at the pump beam intensity of 520 mW/cm². The mechanism of the SPPCM formation is similar to that of photorefractive double-phase-conjugate mirrors. The most effective SPPCM is recorded at the much larger pump-beam-incident angle than it could be supposed from the typical angular dependence of the two-wave-mixing gain factor. Strong dependence of the gain distribution on the pump-beam-propagation angle is observed. It is found that the response time strongly depends on the preliminary history of the sample. Received: 11 August 1998 / Revised version: 14 January 1999 / Published online: 28 April 1999     

温度对闭路光伏明空间孤子演化和自偏转的影响 (英文)

通过考虑扩散效应的影响，采用数值方法研究了温度对光伏光折变介质中的明空间孤子演化和自偏转的影响。结果表明，当晶体温度变化时，明孤子可以呈现为稳定态、较大周期的压缩和膨胀态，或塌陷态。同时，明空间孤子中心偏转距离随温度增加而增加，在一个特定温度处达到最大值，之后随温度增加而减小，在高温和低温区域此偏转距离趋于零。孤子的最大偏转距离和对应的特定温度随入射孤子波强度的增加而增加。进一步采用微扰方法研究了明孤子自偏转过程，其结果与数值方法获得的结果一致。     

Enhancement of the diffraction efficiency of the hologram recorded in photorefractive media under the action of external electric field

Diffraction efficiency as a function of the applied electric field for the non-linear regime has been calculated by solving numerically the beam coupling equations. The refractive index variation used in the beam coupling equations was calculated directly from the material rate equations via the total space charge field. The diffraction efficiency of the holograms recorded in photorefractive media is not only a function of the applied external electric field but also a function of crystal thickness, diffusion field, reduced fringe contrast modulation ratio and absorption coefficient of the materials. The effects of these parameters on the efficiency of the holograms have been studied in details. In the absence of the external applied field, it is found that the diffraction efficiency of the holograms could be maximized for a thinner photorefractive crystal having lower absorption coefficient and higher value of diffusion field, which could exist at a much lower value of reduced fringe contrast modulation ratio of the index grating. More efficient holograms can be recorded in the presence of the externally applied electric field as compared to the case of no external field.     

Diffraction efficiency and energy transfer during hologram formation in reduced KNbO3

Volume phase-hologram formation by the photorefractive effect in KNbO₃ is accompanied by a stationary energy transfer between writing beams. The change in energy transfer by applying an electric field on the reduced crystals is shown to be due to an efficient increase in migration length which can reach values comparable or larger than the fringe spacing. It is demonstrated that photovoltaic contribution to the diffraction efficiency and energy transfer is rather small in reduced KNbO₃ and that diffusion of photogenerated free holes is the dominant charge transport for the photorefractive effect in unbiased crystals. The experimental results for diffraction efficiency and energy transfer as a function of grating spacing, electric field, light intensity and temperature is well described by a recent theory of Kukhtarev and Vinetskii.     

Dependence of space charge field and gain coefficient on the applied electric field in photorefractive materials

Intensity dependent space charge field and gain coefficient in the photorefractive medium due to the two interfering beams have been calculated by solving the material rate equations in presence of externally applied dc electric field. The gain coefficient has been studied with respect to variations in the input intensity, modulation depth, concentration ratio and normalized diffusion field in the absence and presence of the externally applied dc electric field. Space charge field has also been computed by varying the intensity ratio in the presence and absence of the externally applied dc electric field. It has been found that the rate of change of the space charge field with the normalized dc field decreases with the increasing intensity ratio for different values of the normalized diffusion field. It has also been found that the externally applied dc electric field has appreciable effect only when it is larger than the diffusion field.     

High-sensitivity read-write volume holographic storage in reduced KNbO3 crystals

Reduced KNbO₃ is a photoconductive ferroelectric in which holograms can be recorded by the photorefractive effect. Read-write volume hologram storage and erase sensitivities ofS ⁻¹=100 J/cm² andS ⁻¹=84 J/cm² (S=d(Δn)/d(I₀t)‖_t=0) have been measured at zero applied electric field, where the charge transport is shown to be due to diffusion of photoexcited electrons. By applying an electric field along thec-axis, the migration length of the photoexcited electrons becomes comparable to the holographic grating spacing. This leads to storage sensitivities comparable to high-resolution photographic plates. Experimental data on storage and erase sensitivity as a function of the grating spacing, applied electric field, writing light intensity and temperature are reported and interpreted on the basis of the theoretical results of Young et al. and Amodei. Changes of the intensity ratio of the writing beams by self diffraction (beam coupling), reflections from surfaces and the residual dark conductivity are assumed to cause experimental results which deviate from the theoretical models. It is shown, that in reduced KNbO₃ and other ferroelectric photoconductors having photocarrier transport lengths much larger than the unit cell dimension, photovoltaic currents do not contribute significantly to the build-up of space-charges leading to the photorefractive effect.     

Self-Bending of the Light Beam Trajectory in Photorefractive Crystals in an External Alternating-Sign Electric Field

The self-action effects of a light beam propagating in a cubic photorefractive crystal in a square-wave electric field are studied. It is demonstrated that the dark conductivity of the crystal or its illumination by noncoherent radiation distorts the beam profile with the initial Gaussian intensity distribution. The results of investigations into the influence of the nonlinearity of the space-charge field formation on self-bending of the beam trajectory are presented. It is demonstrated that the evolution of modulation instability in the light field distribution over the beam cross section depends on the initial beam profile, its asymmetry, and the direction of bending caused by the inhomogeneity of induced refractive-index changes.     

Solitonlike beam propagation along light-induced singularity of space charge in fast photorefractive media

We investigate light beam propagation in a fast photorefractive medium placed in an alternating electric ac field to enhance the nonlinear response. It is shown that the joint action of the optical and material nonlinearities leads to formation of a narrow singularity of the light-induced space charge at the intensity maximum and to self-trapping of the light energy near the corresponding discontinuity of the index profile. Owing to the strong saturation of the material nonlinearity, the trapped beam propagates over long distances with only a weak loss of its power.     

Polymeric photorefractive surface waves

We theoretically studied photorefractive surface waves supported by polymers with orientationally enhanced photorefractive effect. We find that the orientational enhancement and the dependency of the quantum efficiency of generating mobile holes on the electric field make the diffusion nonlinearity in photorefractive polymers dependent not on only the variation of light intensity but also on external electric field, which is very different from the external electric field independent diffusion nonlinearity in inorganic photorefractive crystals. Consequently the profile, frequency and especially the penetration depth of polymeric photorefractive surface waves strongly depend on external electric field, which makes it more controllable than that in photorefractive inorganic crystals. The stability of polymeric photorefractive surface waves, the effects of birefringence component and electro-optic component of orientationally enhanced photorefractive nonlinearity on the formation of x or y-polarized polymeric photorefractive surface waves are also discussed.     

有偏压光折变晶体中的高斯孤子

利用变分方法求解了小光强光折变非线性薛定谔方程，得到了高斯光束在外加正偏压光折变晶体中的演化特性，以及高斯光束宽度压缩与展宽的动态振荡规律，给出了高斯光束的宽度、振幅和波前曲率的表达式，研究了势函数与光束宽度的关系.结果表明，小光强高斯光束在正偏压光折变晶体中传播时，其宽度和振幅将经历周期地变化或者展宽发散，在一定条件下高斯光束在晶体中可以形状不变地传播，形成“高斯孤子”，这些特性在工程实践中具有很高的实用价值. 关键词： 高斯孤子 高斯光束 变分方法 光折变非线性方程     

All-Optical Photorefractive Effect in Carbazole-Based Azo-Side Group Polymer

We observe the photorefractivity without bias voltage or prepoling in a bifunctional photorefractive polymer. The maximum two-beam coupling gain is measured to be 126cm^-1 at zero bias voltage. The sample is considered to be poled by the photoinduced longitudinal electric field, which is formed due to the light intensity gradient along the light path. The expression of the electric field was deduced. The energy transfer direction between two writing beams and light intensity dependence of the two-beam coupling gain coefficient is predicted to be consistent with the experimental results. Furthermore, the dependence of the two-beam coupling gain coefficient on external applied electrical field is measured and this experiment verifies the existence of the photoinduced longitudinal electric field.     

Modification of Photorefractive Waveguides in Lithium Niobate by Guided Beam for Optical Dynamic Interconnection

We investigate experimentally and numerically a novel method of modifying photorefractive waveguides in a lithium niobate crystal by a guided beam. The guided beam with a strong optical power can change the refractive index of the photorefractive waveguide because of the photorefractive effect. The modification of waveguide structure can be utilized for optical dynamic interconnection. Changes of optical characteristics of a probe beam caused by a modification beam are investigated. Experimental results show that the transmitted power or the peak intensity of the probe beam decreases exponentially as a function of total exposure energy of the modification beam. We also numerically analyze the refractive index change caused by the modification beam in the photorefractive waveguide. The numerical results show good agreement with the experimental results.     

畴腐蚀掺镁铌酸锂可调阵列光分束器的研究

研究了不同畴腐蚀深度的掺镁铌酸锂二维六角可调阵列光分束器的分数Talbot效应.对不同Talbot分数β和不同畴腐蚀深度的阵列光分束器Talbot衍射像进行了数值模拟理论研究.模拟结果表明,Talbot分数β可以改变Talbot衍射像的周期及结构分布,而畴腐蚀深度可有效调制衍射像的光强分布.在理论研究的基础上,设计并制备了具有不同畴腐蚀深度的掺镁铌酸锂二维六角阵列光分束器,对其在不同Talbot分数β条件下的分数Talbot效应进行了通光实验研究,实现了畴腐蚀阵列光分束器对近场Talbot衍射光强分布的调制,实验结果与理论研究结果一致.     

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...     

Effect of photoconductivity and dielectric constant of the photorefractive materials on two-beam coupling gain and phase-shifts for a single unidirectional photorefractive ring resonator

Photoconductive dependence of two-beam coupling between the pump beam and the signal beam in photorefractive materials have been analyzed in case of non-degenerate wave mixing under the undepleted pump approximation method. During the two-wave mixing in photorefractive materials, steady state amplification of the signal beam and oscillation characteristics of a single unidirectional ring resonator has been studied. The domination of the two-beam coupling gain over the combined absorption and resonator losses such as Fresnel reflections from the crystal and imperfect mirrors builds up unidirectional oscillation. The buildup of such an oscillation leads to a saturation of the gain, which can be explained in terms of the photorefractive phase-shift. The existence of this phase-shift between the photorefractive index grating and the illumination intensity pattern, which is of characteristic of the photorefractive effect, leads to an energy transfer between the two beams. For a single unidirectional ring resonators, the effects of photoconductivity of the materials, two-beam energy coupling coefficient, dielectric constant, crystal thickness, and material's absorption coefficient on amplification of the two-beam coupling gain and photorefractive phase-shifts of the signal beam have also been studied in detail. It has been found that amplification of the signal beam and phase-shift can be enhanced by taking the photorefractive crystal having higher photoconductivity and lower dielectric constant, which improves performance of the resonators.     

Self-trapping of weak optical beams in photorefractive materials

Intensity-independent self-trapping of optical beams in photorefractive crystals was found recently. But we show that due to the existence of dark conductivity in some photorefractive materials or coherent and non-coherent background irradiance, the self-trapping of weak optical beams in photorefractive materials, such as SBN, becomes intensity dependent. The threshold condition of the applied external de electric field for self-trapping is determined as function of the material parameters as well as the initial transverse sizes and relative intensities of the beams.     

Transmission behavior in a photorefractive polymer film

When a p-polarized beam propagates through a high-performance photorefractive polymer composite, poly dimethyl-4-(4^′-nitrophenylazo)benzene, its transmission behavior is influenced by three effects: the electroabsorption, the photorefractive coupling with the reflected beam from the rear surface, and the amplified scattering. From the measurements on the incidence angle dependence as well as the applied-electric-field dependence of the three effects, some conclusions are obtained. At a small incidence angle with a low applied electric field, both the amplified scattering and the electroabsorption are small whereas the coupling between the incident beam and the reflected beam plays a principal role. At a large incidence angle or with a high poling electric field, the transmission is influenced mainly by the amplified scattering and the electroabsorption. A poling electric field asymmetric loss to the amplification scattering is also observed. Received: 18 November 1998 / Revised version: 10 February 1999 / Published online: 12 April 1999     

Phase-conjugate wavefront generation via four wave mixing in Bi12GeO20 crystals - reflection hologram type

Phase-conjugate wavefront generation via real-time holography in degenerate four-wave mixing experiments in photorefractive crystals Bi₁₂GeO₂₀ is presented. The phase volume hologram responsible for the phase-conjugate wavefront generation is a reflection hologram. No external electric field is applied and electron diffusion is the main mechanism responsible for the formation of the hologram. The theoretical and experimental results for wavefront reflectivity as a function of the intensity ratio of the writing beams are given.