Anisotropic four-wave mixing in cubic photorefractive crystals

The anisotropic four-wave mixing in the scheme recently proposed by S.I. Stepanov and M.P. Petrov (Opt. Commun. vol.53, p.64-8, 1985) is studied. The main feature of this interaction arrangement is that the same phase hologram (index grating) has opposite contrasts for orthogonally polarized, counterpropagating waves. The coupled nonlinear equations, in the case of transmission and reflection gratings, for the π/2 photorefractive phase shift are exactly solved, and their properties are discussed in detail. The numerical evidence of the effects of bistability and self-oscillation is included     

Theory and applications of four-wave mixing in photorefractive media

The development of a theory of four-wave mixing in photo-refractive crystals is described. This theory is solved in the undepleted pumps approximation with linear absorption and without using the undepleted pumps approximation for negligible absorption. Both the transmission and reflection gratings are treated individually. The results are used to analyze several photorefractive phase conjugate mirrors, yielding reflectivities and thresholds. The use of photorefractive crystals as optical distortion correction elements and experimental demonstrations of several of the passive phase conjugate mirrors are described.     

多通道简并的四波混频

使用脉冲调QNd:YAG倍频激光辐射,香豆素152染料二氯乙烷溶液作混频介质,研究了四通道简并的四波混频。各通道后向波转换效率为4％左右。     

Theory of degenerate four-wave mixing in picosecond excitation-probe experiments

A comparative theoretical study of the transient grating coherent effects in resonant picosecond excitation-probe experiments is presented. Signals in both the probe and conjugate directions are discussed. The effects of recombination, nonradiative scattering, and spatial and orientational diffusion are included. The analysis is applied to both a molecular and a semiconductor model. Signal contributions from concentration and orientational gratings are distinguished and their temporal natures discussed. From the solid-state point of view, we show that state-filling, and in particular, anisotropic state-filling, can be identified from the configurational and time dependence of the detected signal, and thereby establish a theoretical explanation for our recent observations in germanium.     

Transient coherent degenerate four-wave mixing

A set of coupled equations is derived and used to analyze transient coherent degenerate four-wave mixing (DFWM) in a two-level system. The numerical results show that in the case of near-resonance, intense pumping, and short pulses, the properties of degenerate four-wave mixing have interesting coherent interaction characteristics, such as quasi-periodicity in the pump pulse area, probe pulse areas, and energy reflectivity, oscillatory behavior of the DFWM pulse, and generation of a DFWM signal in the case of delayed incidence, where the three incident pulses do not overlap in the medium     

Thermally induced degenerate four-wave mixing

Time-dependent aspects of thermally stimulated degenerate four-wave mixing (DFWM) in absorbing liquid solutions have been theoretically investigated through a coupled electromagnetic-hydrodynamic theory originally formulated to study stimulated scattering processes. The various time scales involved in the interaction (including those characteristic of acoustic modes and thermalization effects) are identified and relevant laser and media parametrical relations are sorted out. Suitable approximation regimes are then outlined, corresponding to specific experimental situations of interest and allowing for relatively simple and tractable analytic relations to be derived. In particular, the effects of finite rise time of thermalization were studied and found to lead to a possibly strong angular dependence in the conjugate reflectivity. Acoustic modes and their influence on the process efficiency were also investigated. The calculations culminate in a set of guidelines for optimizing conjugation efficiencies, through judicious choice of dye-solvent combinations, "read" pump time delays, experimental arrangements, and laser pulse parameters.     

瞬态简并四波混频中的弛豫效应

引入唯像弛豫方程组描述介质中的光栅建立和衰变过程.在理论和实验上研究了介质弛豫对四波混频瞬态特性的影响,通过考察后向波波形的变化,观察到光栅的“积累效应”和“光滑效应”.实验结果得到满意的理论解释.     

Propagation analysis of forward degenerate four-wave mixing

We discuss the propagation problem associated with the forward four-wave degenerate mixing induced by the third-order non-linear susceptibilitychi_{(-omega; omega, omega, -omega)}^{(3)} = chi_{1}^{(3)} + ichi_{2}^{(3)}. Exact analytical solutions are presented of two-photon resonances, evidencing the influence of the Kerr effect on the efficiency of the process. Around a two-photon resonance, we solve the problem of the nearly parallel propagation of two beams undergoing auto and induced two-photon absorption (TPA). The resonant interaction is studied in detail and analytical solutions are provided with operational accuracy for current experimental conditions. We show by the way that in the two-beam two-photon experiments, when the phase matching condition is fulfilled, although TPA is governed bychi_{2}^{(3)}, the real part ofchi^{(3)}must be considered in a substantial way. All the above solutions are put in a form simple enough that the numerical computations can be performed on a programmable calculator.     

Experimental investigations of thermally stimulated degenerate four-wave mixing

Results of experimental investigations aimed at testing efficiency-related aspects of thermally induced degenerate four-wave mixing in absorbing solutions are reported. The effects of fluorescence, read beam time delay, and forward beam angle variations are measured and shown to strongly influence the achievable thermal grating diffraction efficiency. In particular, a strong decrease of conjugation efficiency is observed as a function of increasing angle between the forward beams. Conjugate beam diffraction efficiencies as high as 17 percent were measured for the dye RhB in acetone. Based on our observations, we predict that still higher conjugation efficiencies will be feasible under optimal conditions with the thermal grating mechanism.     

利用铁电晶体四波混频的光学无损检测

本文描述了一种利用铁电晶体简并四波混频的实时二次曝光法。该方法利用这种晶体的介电弛豫时间检测相位物体的不均匀性。文中给出了较详细的有关理论分析和公式推导,并且对实际玻璃样品进行了测量,验证了该方法的可行性及实用性。     

利用四波混频消除图像畸变的局限性

一、引言 在大多数理论研究中,人们仅在平面泵浦和探测波的条件下研究四波混频产生位相共扼波的机理、手段。然而在实际应用简并四波混频共轭波补偿大气干扰时,入射到位相共轭镜上的探测波不可能是理想平面波。但是在大多用相位共轭消畸变的方案中都忽略了畸变探测波在简并四波混频中产生什么样的“共轭波”这个问题。本文将讨论利用简并四波混频消除通过湍流大气传输图像的畸变问题。     

Observation of higher-order diffraction components in degenerate four-wave mixing experiments in Bi12GeO20 crystals

Higher-order diffraction components have been observed from the phase volume grating formed in photorefractive crystals Bi12GeO20 via degenerate four-wave mixing. Brief explanations based on the conventional grating theory and the dynamic theory of volume holography are given.     

Collinear nearly degenerate four-wave mixing in intracavity amplifying media

Intracavity nearly degenerate four-wave mixing in amplifying media has been demonstrated to be a powerful technique to get very high conjugated reflectivities. A physical interpretation of this process is given in terms of interactions among pump (ω), probe (omega- deltaomega), or conjugated (omega + deltaomega) waves with optically induced refractive index modulations or gratings. Mixing experiments performed at the milliwatt level inside a (GaAl)As semiconductor laser operating above or below threshold have demonstrated very high conjugated reflectivities (a factor of 10³-10⁴) together with a 10 percent energy conversion efficiency. The appearance of additional peaks related to the ac Stark effect and observation of bistability on probe and conjugated beams also make this mixing process interesting for the study of instabilities occurring in lasers.     

Transient effects in degenerate four-wave mixing in saturable absorbers

The transient behavior of degenerate four-wave mixing (DFWM) in a three-level saturable absorber is analyzed and verified experimentally. A sharp peak of phase-conjugated reflectivity is predicted and observed at high pump intensities for pulsed beams. The influence of the time-dependent behavior of the conjugate wave signal on results of pulsed-beam experiments is studied. It is shown that transient effects could account for discrepancies between previous experimental results and steady-state theory.     

Phase conjugation by degenerate four-wave mixing in absorbing media

A theory of degenerate four-wave mixing in absorbing media is developed in terms of a general nonlinear susceptibility. The predictions of the theory are examined in both high and low reflectivity regimes and the specific nonlinearity-inducing mechanisms of thermally induced refractive index changes, the Kerr effect, and saturable absorption are considered. Such a theory is of particular relevance to degenerate four-wave mixing experiments in the ultraviolet and the predictions of the theory are compared with results obtained from such experiments.     

Theory and experiment of degenerate six-wave mixing in bothisotropic and anisotropic saturable absorbers

Theoretical and experimental characterization of degenerate six-wave mixing (DSWM) in bulk media composed of isotropic or anisotropic saturable absorbers is presented. The ratio of the χ⁽⁵⁾ tensor components has been calculated and measured for both types of media. The authors have also demonstrated that, using DSWM, two-photon absorption coefficients can be evaluated when one-photon absorption is important     

Nearly degenerate four-wave mixing enhanced by the ac Stark effect

A model is developed to describe nondegenerate four-wave mixing in a medium characterized by a single strong atomic resonance. The nonlinear response is calculated using the density-matrix formalism, and propagation effects are included by solving coupled-wave equations. This model predicts large resonant responses for signals detuned from the pump frequency by approximately the generalized Rabi frequency. Potential applications of the effects predicted by this model include construction of tunable bandpass filters and four-wave parametric oscillators.     

Theory of degenerate four-wave mixing in saturable absorbing media with the inclusion of pump propagation effects

The phase-conjugate reflectivity attainable by degenerate four-wave mixing in an idealized saturable absorbing medium is calculated for arbitrary values of the laser intensity, laser frequency, and absorption path-length of the nonlinear medium. The influence of pump-wave absorption, including saturation and standing-wave effects, is included in the theory. The treatment is based on an analytic expression for the intensity distribution of the counterpropagating waves. The theoretical predictions differ substantially from those based on theories that ignore pump absorption effects. The results of the present calculation are used to predict the minimum laser intensity, absorption path-length, and detuning required to obtain unit reflectivity and self-oscillation.     

Laser mirror by degenerate four-wave mixing in a saturable amplifier

A phase conjugate mirror by degenerate four-wave mixing in a saturable gain medium has been successfully operated in a pulsed laser cavity. This mirror works with low-intensity pump beams when they are resonant with the nonlinear medium. The pump beams can thus be delivered by a continuous-wave, frequency stable laser of low power. In such a device, the pulsed laser emission displays automatic frequency locking to the pump waves without cavity length stabilization.     

Investigation of retroreflection scheme for optical phaseconjugation by degenerate four-wave mixing

The authors present theoretical and experimental data which show that the value of the phase conjugate reflectivity of degenerate four-wave mixing depends on whether the retroreflection or counterpropagating schemes are used. It is also shown that the retroflection method may result in decay constants which are not related to the decay of the gratings formed in the nonlinear medium