Effect of partial coherence on four-wave mixing in photorefractive materials via reflection grating approximation

We investigate the effect of beam coherence on four-wave mixing via reflection gratings in photorefractive media. For the case of phase conjugation, the results of our theoretical analysis indicate that partial coherence always leads to a drop of signal gain and phase conjugate reflectivity in non-depleted cases. In general, the mutual coherence of the signal beam and the pump beam can be enhanced due to the process of wave mixing. The mutual coherence of the phase conjugate beam and one of the pump beams depends on the beam intensity ratio as well as the optical path difference. This is distinctly different from the four-wave mixing case with a transmission grating. Received: 15 October 1999 / Revised version: 26 June 2000 / Published online: 7 February 2001     

Photorefractive power transfer from parallel laser diode amplifiers into a single output beam

Photorefractive BaTiO(3):Ce was used to combine coherently a signal beam and two amplified pump beams at lambda=678 nm. The master laser beam was split and then amplified in two semiconductor laser amplifiers with gain of as much as 6. The amplifiers were made from quantum-well laser chips by use of antireflection coating. 40% of the power could be transferred to the signal beam without transferring the phase distortions of the pump beams.     

Ce:KNSBN光折变类光纤简并四波混频特性研究

研究了Ce:KNSBN光折变类光纤在泵浦光和信号光夹角分别为小角度和大角度两种情况下简并四波混频的基本特性.当夹角较大时,在光折变类光纤内部形成了两个四波混频作用区域,获得了比小角度情况提高4倍的大相位共轭反射率.给出了Ce:KNSBN光折变类光纤中,在入射夹角分别为小角度和大角度两种情况下,相位共轭光反射率分别随信号光光强、两束泵浦光光强比变化的实验结果,并用理论公式进行了拟合,理论分析和实验结果相符.还研究了Ce:KNSBN光折变类光纤四波混频光栅模式和相位共轭光时间响应特性.光折变类光纤的相位共轭响应时间较快,可为秒量级.     

Comparative Study of the Signal-to-Noise Ratio and Gain in Photorefractive Materials

We calculate the dependence of the signal-to-noise ratio and gain on the angle α between the pump and signal beams and the beam ratio β in Cu-doped potassium-sodium-strontium-barium niobate (Cu:KNSBN) crystal and compare them with the experimental results available in the literature. We find good qualitative agreement between the calculated and experimental results. Also we study variations of SNR and gain with α and β in BaTiO₃ crystal. Experimental data for this crystal are not available.     

Large-signal results for degenerate four-wave mixing and phase conjugate resonators

A numerical calculation procedure and various large-signal numerical solutions are presented for degenerate four-wave mixing in optical Kerr media, and for phase conjugate resonators using degenerate four-wave mixing. The solutions presented take full account of nonlinear refractive index changes, pump depletion, signal saturation, distributed losses, and possible external mirrors with laser gain. We find that including the nonlinear index change generally causes little change in the reflectivity or power output of degenerate four-wave mixing devices, at least with symmetric pumping. The optimum power output from a phase conjugate resonator with and without a laser gain medium is calculated. The results provide some theoretical guidance for designing phase conjugate resonators.     

Coexistence of Self-pumped Phase Conjugation and Mutual-pumped Phase Conjugation in Ce∶BaTiO3

Self-pumped phase conjugation(SPPC) and mutual-pumped phase conjugation (MPPC) have been found to coexist in Ce∶BaTiO3 by using two coherent beams of 514.5nm wavelength from an argon ion laser. Both phase conjugations are of the stimulated backscattering and four-wave mixing type. For 7/6 incident power ratio and 26 mW total incident power,he shortest phase conjugate mirror formation time is 10s . Phase conjugate reflectivity of one the beams can reach 70%,hich is ～20% higher than the SPPC reflectivity using only one beam. When the total incident power is increased to 40 mW and the incident power ratio remains constant,a maximum phase conjugatate reflectivity of as much as 88% is obtained.     

Coexistence of Self-pumped Phase Conjugation and Mutual-pumped Phase Conjugation in Ce:BaTiO3

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Dynamically reconfigurable characteristics of a double phase conjugate mirror using Sn2P2S6 crystals and their application to optical inter-satellite communication

A double phase conjugate mirror (DPCM), created by two mutually incoherent beams entering photorefractive nonlinear materials, can generate a phase conjugate beam whose reflectivity may be greater than 100%. Even though the conditions of the incident beams are changed, the DPCM can be dynamically reconfigured by using a Sn₂P₂S₆ crystal with a high response speed. These features of the DPCM are advantageous, particularly in an optical inter-satellite communication system. In particular, use of the phase conjugate beam from the DPCM offers wavefront compensation and amplification in satellite communication. In addition, the dynamically reconfigurable DPCM using a Sn₂P₂S₆ crystal relaxes the acquisition accuracy of the signal beam in the system. In this study, the temporal and spatial operating characteristics of the DPCM using a Sn2P2S6 crystal were first clarified. Next, an inter-satellite system based on the DPCM was proposed, and it was demonstrated that our system significantly improves the tolerance of the acquisition accuracy and tracking time.     

Study on Optimum Incident Angles of Cross Polarized Four-Wave Mixing with a Photorefractive Crystal

We consider the optimum incident angles of cross polarized four-wave mixing with a photorefractive crystal. First, the phase matching angles are obtained for two operation modes: one in which the writing beams are ordinary rays and the reading beam is an extraordinary ray, we call this Mode 1. The other in which the writing beams are extraordinary rays and the reading beam is an ordinary ray, Mode 2. Next, practicable ranges of the incident angles are calculated considering of the total internal reflection of the phase conjugate beam in cases where the two writing beams illuminate the same surface of the BaTiO₃ crystal and where they illuminate the neighboring right-angled surfaces, respectively. Then, the coupling coefficient is determined as a function of the incident angle, and the optimum incident angles for effective beam interaction in Mode 1 and Mode 2 are estimated.     

SBN:Cr晶体的光折变四波混频相位共轭特性实验研究

从实验上研究了同成分SBN:Cr晶体在He-Ne激光照射下的四波混频相位共轭特性.首先测量了在不同泵浦光与信号光光强比m及不同光束夹角2θ的情况下,晶体的四波混频相位共轭反射率R随泵浦光强比p的变化关系.其次测量了泵浦光束与信号光束耦合方向对SBN:Cr晶体的四波混频相位共轭特性的影响,并就两种不同掺杂浓度的晶体样品进行了对比,所得实验结果与理论分析基本一致.最后,利用SBN:Cr晶体四波混频相位共轭特性进行了图象畸变消除实验.     

Polarization-Dependent Light-Gated Phase Conjugation in Methyl-Orange Doped Polymer Film

We have investigated the polarization state of a gated phase conjugate beam using a methyl-orange doped poly-vinyl alcohol (MO/PVA) film in 16 different combinations of linear and circular polarization states of a probe beam and pump beams. The experimental results agree with the theoretical prediction based on the Jones matrix method. Of the third-order nonlinear susceptibility tensors X_ijkl of the MO/PVA film, the X₁₂₂₁ at the 647 nm wavelength in degenerate four-wave mixing under exposure of a gating 515 nm light takes a very small value compared with X₁₁₁₁ and X₁₁₂₂. On the other hand, in the configuration of a probe beam and pump beams having linearly crossed polarizations and without gating light, the MO/PVA film generates a strong linearly polarized PC beam, so that X₁₂₂₁ takes a large value at 515 nm.     

Photorefractive Multi-Beam Induced Phase Conjugation

We demonstrate the simultaneous phase conjugation of multiple beams incident on the a face of a photorefractive barium titanate crystal. The input beam power, angle and position were set so that no phase conjugation occurs unless a switchable incoherent inducing beam is present on the — c face of the crystal. The use of the inducing technique with two mutually pumped phase conjugations for four input beams, or one self-pumped and one mutually pumped phase conjugation for three input beams can be performed in a crystal. Unlike the setup of conventional phase conjugation, which requires more precise arrangements, the novel setup of the multi-beam induced phase conjugation is relatively relaxed. The mechanism responsible for our discovery is qualitatively explained, and possible applications are mentioned.     

Polarization properties in two wave mixing with moving grating in photorefractive BSO crystals. Application to dynamic interferometry

The polarization properties of the volume gratings in photorefractive B₁₂SiO₂₀ crystals permit to increase the contrast and signal to noise ratio in the image plane of a large size vibrating object structure. The experiment is based on the nearly degenerate two wave mixing of a pump beam with a low intensity signal beam due to the object structure (moving grating recording with an externally applied field in the 110 crystallographic direction). For a correct orientation of the incident recording beam polarizations, the pump beam emerging from the crystal is linearly polarized, while the signal, after two beam coupling is elliptically polarized. The selective attenuation of the direct pump and scattered beams is obtained with a polarizer. Improved contrasts in the interferogram plane of the vibrating object are demonstrated.     

Feedback method of the noise suppression in wave-mixing amplifiers based on non-linear materials with photorefractive response in a reflection grating configuration

In the photorefractive wave-mixing system, fluctuation in the signal beam intensity of the photorefractive output with a reflection grating has been analyzed by employing pump feedback method. In this method, fluctuations of the photorefractive wave-mixing process not only induce the intensity fluctuation of the mixing waves but also induce phase fluctuation of the mixing waves. Thus, the phase of the pump and signal beams at the output surface fluctuates in time around a mean value. Using such a positive feedback method of a pump beams, the relative fluctuation in the photorefractive output signal beam intensity with respect to its mean intensity can be minimized significantly without reducing its mean intensity. The factors that control the fluctuation in the signal beam intensity, such as the phase fluctuation of the output pump beam, absorption strength of the material and the feedback reflectivity of the cavity mirrors, on the relative fluctuation of the output signal intensity in the photorefractive wave-mixing systems have been studied in detail. It has been found that the fluctuation of the output signal intensity relative to its mean intensity in the photorefractive wave-mixing system can be suppressed to larger extent by taking lower value of feedback reflectivity of the cavity mirrors which could exist at a higher value of absorption strength of the photorefractive materials.     

Mutually pumped phase conjugate mirror using cross polarized photorefractive coupling

This paper presents a new proposal for a mutually pumped phase conjugate mirror (MPPCM) using cross polarization. In the cross polarized MPPCM, two light beams, whose polarizations are orthogonal to each other, incident on a photorefractive crystal, causing photorefractive interaction to generate phase conjugate waves with an orthogonal polarization to an incident beam. The use of Ar⁺ laser and BaTiO₃ crystal in an experiment for the cross polarized MPPCM found that diffraction efficiency for an extraordinary beam is about 20%. As opposed to a conventional parallel polarized MPPCM in which the use of a beam splitter is required to separate a diffraction beam, the cross polarized MPPCM can efficiently extract phase conjugate waves by means of a polarized beam splitter, demonstrating the advantage of substantially improved efficiency.     

自散焦介质中光束聚焦的最佳参数选择

对自散焦介质中由交叉相位调制效应引发的光束聚焦过程进行了细致的系统研究,讨论了抽运光初始振幅、抽运光信号光初始间距和抽运光信号光波长比三个参量对信号光聚焦过程的影响.数值模拟结果表明:抽运光越强,信号光聚焦程度越大;抽运光信号光初始间距和抽运光信号光波长比均存在一个最佳值,使得光束聚焦达到最佳效果.通过参数最佳值的选择,可提高光束聚焦的效率 关键词： 非线性折射率系数 交叉相位调制效应 自散焦介质 光束聚焦     

Phase conjugation with gaussian beams

We investigate the saturation effects in phase conjugation in the case of gaussian beams. We derive analytical expressions for the phase conjugate reflectivity R_PC for arbitrary values of the pump beams. We show that the results can be drastically different from what is expected from a plane-wave analysis. At last, we show the influence of the overlapping of the three beams.     

三维自散焦介质中光束聚焦的最佳参量选择

对三维自散焦介质中由交叉相位调制效应诱导的光束聚焦过程进行了系统研究,讨论了抽运光振幅、抽运光-信号光初始偏移和抽运光-信号光波长比三个参量对信号光聚焦过程的影响。根据自散焦介质中强抽运光诱导弱信号光聚焦满足抽运光与探测光模型,对传输方程进行了优化,大大减少了数值模拟运算时间。数值方法采用分布傅里叶方法。数值模拟结果表明：抽运光越强、抽运光-信号光波长比越大,信号光聚焦程度越大;抽运光-信号光初始偏移存在一个最佳值,使得光束聚焦达到最佳效果。通过参量最佳值的选择,可提高光束聚焦的效率。     

Influence of the volume speckle on fiber specklegram sensors based on four-wave mixing in photorefractive materials

In this work, the dependence on the speckle size in the performance of a micro displacement sensor based on fiber specklegrams stored in a photorefractive BSO (Bi₁₂SiO₂₀) crystal is experimentally demonstrated. In our experimental setup, a plastic optical fiber (POF) was used to generate a subjective speckle pattern which was recorded in the crystal by using a four-wave mixing arrangement in transmission geometry. The speckle size was controlled by modifying the diameter of a pupil aperture adjacent to a lens producing the image of the speckle. The signal speckle beam was mixed into the crystal with two counter propagating pump beams to generate a fourth beam which is proportional to the conjugate of the original speckle beam. Real time fringe patterns were obtained at the output of the system by producing micro displacements of the fiber output end. Increases of the phase conjugation reflectivity and the visibility of the fringe patterns were appreciated when the speckle length was increased by decreasing the pupil aperture diameter. This behavior allowed recovering the autocorrelation functions of fringe patterns associated to micro displacements that initially led to decorrelation, and therefore, to improve the dynamic range of the metrological system. Until the best of our knowledge this is the first report about the influence of the speckle size on fiber specklegrams sensors recorded on photorefractive materials by four-wave mixing.     

Gain induced stability of active plane-parallel resonators

It has been observed for a plane-parallel resonator with a saturated medium that under certain conditions confined beams mainly concentrated near the axis are present. The experiments have been done with a sealed-off plane-parallel CO₂ laser of one meter length and with an internal diameter of 20 mm. Without gain variations such a system is unstable because of thermal defocussing by the heated gas. But due to sufficiently high gain variations the beam converges nevertheless. Since the gain variation increases with decreasing reflectivity confined beams near the optical axis are only observed at sufficiently low reflectivity. The experiments were done with a totally reflecting mirror and an outcoupling mirror having a reflectivity of, respectively, 90%, 80%, 50%, and 36%. For the high reflectivities the outcoupled beam is mainly concentrated near the edge with irregular density distributions. For the low reflectivity the beam is more or less radially symmetric, concentrated near the axis having decreasing intensity with the distance from the axis. The behaviour can be understood by an analysis in which the constant and quadratic term of the complex propagation constant near the optical axis due to gain variations, dispersion and heat effects are taken into account.