Positive feedback effect in four-wave mixing in photorefractive crystals with absorption

Using a two-level model of optical transitions, the positive feedback effect observed in the presence of absorption in four-wave mixing in photorefractive crystals has been determined analytically. It is shown that with positive feedback, as the intensity of readout beam increases, the values of diffraction efficiency and intensity of amplified beam also increase. An analysis of the holographic grating amplitude shows that the effective thickness of the grating decreases in this case, but its amplitude increases. The dependences obtained, very important from the practical point of view, show that the optimal thickness of the crystal is different for diffraction efficiency and intensity of the amplified beam, and decreases with increasing readout beam intensity.     

Degenerate four-wave mixing via shifted phase holograms in cubic photorefractive crystals

It is shown that it is possible to increase dramatically the efficiency of stationary four-wave mixing in cubic photorefractive crystals of the sillenite family. In order to do this one has to use a holographic arrangement of the cubic crystal where the same volume phase hologram has opposite contrasts for orthogonally polarized light waves traversing the sample in opposite directions. In combination with a new efficient nonstationary mechanism of shifted hologram formation, this arrangement can enable phase conjugation of amplified waves and stationary selfoscillation without an external resonator cavity.     

Real-time non-destructive testing of phase objects using four-wave mixing with photorefractive BGO crystals

Real-time non-destructive testing of phase and transparent objects using degenerate four-wave mixing with photorefractive BGO crystals is described. Some quantitative results of thickness variations of phase objects such as a thin optical wedge and a thin BGO crystal are also given.     

A simple analytic solution for transient simultaneous four-wave mixing in photorefractive crystals

Very simple solution of the coupled partial differential equations that leads to analytic formula for diffraction efficiency which describes the time dependence of four-wave mixing in photorefractive crystals is presented. The obtained results were used for analysis of simultaneous read–write dynamics in Bi₁₂SiO₂₀ crystal.     

Exact solution of stationary holographic four-wave mixing in photorefractive crystals: two-level model

Based on the two-level model of recording and read-out of dynamic holographic gratings, precise expressions for wave amplitudes, diffraction efficiency and the gain coefficient representing the generalization of the corresponding formula by Kukhtarevet al. have been obtained. This model allows one to take into account the effect of the read-out beam on the holographic grating and to solve a problem of four-wave mixing in transmission geometry with wave depletion and arbitrary value of the spatial phase shift between the holographic grating and the interference pattern.     

Transient effects in four-wave mixing in photorefractive Passive Phase Conjugate Mirrors

Partial differential equations are set up and solved partly analytically, partly numerically for the spatial and temporal variation of the amplitudes and phases of the four beams participating in four-wave mixing in a linear Passive Phase Conjugate Mirror. The instantaneous frequency of the resonating beam is also determined. It is shown that the duration and main features of the transient regime are determined not only by the properties of the photorefractive crystal but also by the external optical circuit, in particular by the quality factor and detuning of the resonator.Moscow Power Engineering Institute SU-105835, Moscow, Krasnokazarmennaia, 14 USSR     

Degenerate four-wave mixing in photorefractive Bi12GeO20 crystals involving internal reflections

Degenerate four-wave mixing in photorefractive Bi₁₂GeO₂₀ crystals involving internal reflections is studied theoretically and experimentally. Two sets of four-wave mixing exist simultaneously. One set is at the Bragg angle while the other is off the Bragg angle. Theoretical and experimental relations between the wavefront reflectivity and the external incident angle of the reading beam, as well as the reference-to-object beam ratio, are investigated.     

四波混频实时光学检测

分析了利用掺铁铌酸锂晶体作介质的简并四波混频及其在干涉计量术中应用的原理,描述了被测透明样品的表面各光波及其干涉形成的透射条纹及反射条纹,利用光折变晶体的介电驰豫特性,求得透射条纹和反射条纹的对比度随时间变化的公式及各参数的相互关系。对由透射条纹及反射条纹计算被测透明物体样品折射率和厚度不均匀性的方法作了数学分析,提出一种新型四波混频实时测量透明物体的光学不均匀性的方法和实验光路,对相关参数对测量过程及测量结果的影响作了探讨,得到了平板玻璃样品的干涉条纹图像,计算出实验结果。     

Three-wave and four-wave forward mixing in photorefractive materials

An amplification mechanism relying mainly on the real part of the arising space charge field in the presence of two strong pump beams is described. The dependence of amplification on frequency detuning, applied electric field and pump beam ratio are investigated in the undepleted beam approximation.     

The two photorefractive centres in iron doped nearly stoichiometric lithium niobate crystals

This paper investigates the photorefractive properties of iron doped lithium niobate with different [Li]/[Nb] ratios The experimental results show two photorefractive centres for iron doped near-stoichiometric lithium niobate crystal Besides Fe^2＋ and Fe^3＋ ions, small polarons and bipolarons are considered as another photoactive centre.     

Real-time image subtraction in four-wave mixing with photorefractive Bi12GeO20 crystals

Based on a classical two-exposure holographic technique, real-time image subtraction is obtained in four-wave mixing of a reflection hologram type with highly sensitive photorefractive Bi₁₂GeO₂₀ crystals. This method takes advantage of the relatively slow response and erasure times of holographic recording in Bi₁₂GeO₂₀ crystals.     

Real-time image division in four-wave mixing with photorefractive Bi12GeO20 crystals

Real-time image division is obtained by using four-wave mixing of a reflection hologram type with photorefractive Bi₁₂GeO₂₀ crystals. This method utilizes the nonlinear characteristic of four-wave mixing which reverses the phase of the incident wave.     

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.     

Anisotropic scattering generated by photorefractive four-wave mixing in BaTiO3 crystal

A new type of anisotropic scattering with ring-and-line structure is observed for the first time from a BaTiO₃ crystal illuminated by a linearly polarized laser beam. The analysis presented herein is based on the photorefractive four-wave interaction of the incident, reflected, and scattered beams. The experimental results agree well with the theoretical analysis.     

Level-splitting effects in resonant four-wave mixing

Resonant spectral structures of four-wave mixing (FWM) in molecular sodium are investigated. For a double- ? configuration with strong-weak-strong-weak fields, split components in FWM spectra induced by the strong pump fields are observed. It is shown that the split components merge into a single peak for a certain ratio of the strong field intensities. A correlation between the level-splitting effects and the saturation behavior of the FWM signal is experimentally demonstrated.     

Hexagonal optical structures in photorefractive crystals with a feedback mirror

A nonlinear theory is presented for the formation of hexagonal optical structures in a photorefractive medium equipped with a feedback mirror. Oppositely directed beams in photorefractive crystals are unstable against the excitation of sideband waves. It is shown here that as this instability evolves to its nonlinear stage, the three-wave interaction between weak sideband beams does not stabilize it, but rather leads to explosive growth of the amplitudes of beams whose transverse wave vectors form angles that are multiples of π/3. As a result, sideband beams at these angles are found to be correlated. A range of parameters is found in which four-wave interactions saturate the explosive instability, which explains the appearance of stable hexagons in the experiment. Outside this region, nonlinearities of higher order saturate the explosive instability, and the process of hexagon generation must be studied numerically. Matrix elements are obtained for the three-and four-wave interactions as functions of the distance to the feedback mirror, and an equation for the time evolution of the sideband wave amplitudes is derived that describes the hexagon generation. A comparison is made with experimental results for the photorefractive crystals KNbO₃ and BaTiO₃. Zh. éksp. Teor. Fiz. 113, 1122–1146 (March 1998)     

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.