Mixing In Photorefractive Crystals Research Articles

Enhancement of two-wave mixing gain coefficient by resonant mechanism in photorefractive semiconductor

In this paper, two-wave mixing in photorefractive semiconductors at large modulation depth is theoretically analyzed and discussed. An analytic expression of space-charge field normalized to the weak externally applied dc electric field value is presented and a one center-two band model which includes both temperature and electron-hole is considered. The variations of space-charge field with dc field and Fe2+ concentration are investigated. Furthermore, the variations of the gain coefficient with temperature, intensity beam ratio, incident angle, and incident light intensity are analyzed. The results show that both the space-charge field and gain coefficient can increase with a stronger dc field. When the dc field is less than 10 kV/cm, applying a strong dc field can significantly improve the space charge filed and gain coefficient. As the incident intensity rises, under the influence of the intensity-dependent resonant effect, a maximum gain coefficient is achieved for an optimum incident intensity which increases with the temperature. Besides, an optimal angle of incidence is obtained at which the gain coefficient is maximum. It is demonstrated that the optimal incident intensity of 21 mW/cm2 and the optimal angle of 5° can be obtained under the temperature of 300 K and the dc field of 10 kV/cm conditions. The present work can provide theoretical guidance for the practical application of two-wave mixing in photorefractive crystals.

Optical amplification of Airy beams by photorefractive two-wave mixing.

We propose and demonstrate nonlinear amplifications of self-accelerating Airy beams by two-wave mixing in photorefractive crystals both numerically and experimentally. By employing a broad Gaussian beam as the pump beam, we show that weak signal Airy beams can be significantly amplified under both diffusion and drift mechanisms. It is revealed that not only higher optical gains but also faster response time can be achieved in the presence of an external electric field, where the drift mechanism dominates. We verify that the self-accelerating and self-healing characteristics of the Airy beams are well preserved during the nonlinear amplification.

Uniformity of image amplification by two-wave mixing in photorefractive crystals

A model of two-wave mixing in the photorefractive crystal, which takes account of the difference in spatial frequency in a beam, has been built to study the uniformity of image amplification. Based on the theoretical analysis of the model, the gain distribution for each pixel in the signal beam has been obtained. It shows that the unevenness of the gain is induced by the difference in spatial frequency in the beam. The factors that impact on the uniformity of image amplification have been analyzed. As an example, the effects of these factors in a given photorefractive crystal have been studied through simulation.

Non-steady-state photoelectromotive force and two-wave mixing in photorefractive crystals under frequency modulated illumination

We report the excitation of non-steady-state photoelectromotive force and two-wave mixing signals using uniformly accelerated motion of the recording light pattern. Such illumination is created by linear frequency modulation of the interfering light beams. The pulse response is predicted theoretically and observed experimentally in GaAs and Bi12TiO20 crystals at λ=633  nm. The evolution of the pulse shape versus sweep rate is demonstrated and explained in the frames of the developed theory. The application of the effects in laser Doppler velocimeters and accelerometers is discussed as well.

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.

Beamsplitter testing using the photorefractive effect

A new technique is proposed to test beamsplitters using two- wave mixing in photorefractive crystal. The method uses the diffraction efficiency of two-wave mixing in Bi 12TiO20 (bismuth titanium oxide). De-

High-modulation-depth effects in photorefractive wave mixing: influence on pattern formation and physical foundations

Spatio-temporal pattern formation in contra-directional two-wave mixing in photorefractive crystals is investigated both numerically and analytically, taking high-modulation-depth effects into account. We use a modified two-wave-mixing model that includes a correction function f( m), which is introduced as a phenomenological modification. Transverse instabilities arise only if the modulation depth at one side of the crystal is high (near unity). Therefore, high-modulation-depth effects are both relevant and important. In the near field, transverse running waves appear above the instability threshold. The gain of the signal beam then exhibits an unexpected saturation. Furthermore, the physical justifications of the correction function f( m) are investigated by exactly integrating the nonlinear Kukhtarev equations. We do not neglect the phases of the counter-propagating beams. For static gratings we obtain real and superlinear correction functions, whereas for running gratings they change to complex correction functions.

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.

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.

Adaptive optical array receivers for detection of surface acoustic waves

Adaptive interferometric detection systems based on two-wave mixing in photorefractive crystals have been configured as distributed optical receivers. The spatial distribution of the detection laser power on the sample surface is controlled by use of phase gratings and amplitude masks. The responses of point, line, array, and chirped optical receivers to propagating surface acoustic waves (SAW's) are discussed theoretically and demonstrated experimentally. It is shown that by use of different object beam footprints it is possible to configure adaptive holographic SAW receivers that are either broadband or narrow band and that are preferentially sensitive to SAW's propagating in given directions. The receivers also allow for the distribution of laser power over the sample, eliminating the excessive heating or surface damage that can occur in some materials when high power, point-focused, detection lasers are used.

Real-time holographic interferometry with double two-wave mixing in photorefractive crystals

We present a real-time holographic interferometer for which two reference waves of different phases are created by two-wave mixing with a stationary signal wave in a photorefractive crystal. These waves are reconstructions of the stationary signal wave and interfere with the momentary (changing) signal wave in the manner of a holographic real-time interferometer. A fast change (phase or intensity) of the signal wave leads to different intensity changes in both interferograms that are jointly used for evaluation. With an electric dc field applied to the crystal, a high sensitivity for measuring phase changes (down to lambda/50, lambda = 633 nm) is found, and the sign of the phase change can be determined.

Multiline coherent oscillation in photorefractive crystals with two species of movable carriers

The coherent oscillation, because of nearly degenerate four-wave mixing in photorefractive crystals with two types of movable charge carriers, occurs at two spectral lines symmetrically shifted with respect to the pump frequency. Consequently the output oscillation exhibits the high contrast intensity modulation. The frequency separation of two oscillation modes (and modulation frequency of the output intensity) depend on the incident light intensity and spatial frequency of the developing grating. A model is presented explaining this type of oscillation by the two-maxima shape of the gain spectrum in crystals with sufficiently different relaxation times of two space-charge gratings, one formed by movable electrons and the other one by movable holes. The experimental data for coherent oscillator with tin hypothiodiphosphate (Sn2P2S6) are in reasonable quantitative agreement with the calculations.

Spatial fidelity of externally pumped phase conjugation in photorefractive crystals

The spatial fidelity and the reflectivity of the externally pumped phase conjugation by four-wave mixing in photorefractive crystals are numerically studied by a three-dimensional analysis. The results are given for both the case that the input one-dimensional rectangular amplitude of the image-bearing beam has a finite extent in the plane of incidence of the four extraordinarily polarized beams and the case that the amplitude has a finite extent in the orthogonal plane. The fidelity and the reflectivity versus the input pump ratio, the moving velocity of the crystal, and the externally applied electric field are analyzed. Although one can enhance the reflectivity by moving the crystal or by applying an electric field, the output phase deviates increasingly from the conjugate phase.

Heterodyne interferometer with two-wave mixing in photorefractive crystals for ultrasound detection on rough surfaces

Heterodyne interferometers using two-wave mixing in photorefractive cubic crystals for ultrasound detection on rough surfaces are demonstrated. The speckled scattered beam from a rough surface sample interferes with a planar coherent pump beam inside a photorefractive crystal. A third frequency-shifted beam is used to read the grating. The diffracted readout beam and the transmitted signal beam are wavefront matched, resulting in an optimal heterodyne interference signal. The signal to noise ratio for the two commonly used crystallographic configurations with cubic crystals, G∥〈110〉∥ and G∥〈001〉, where G is the grating wave vector, are investigated. Very good sensitivity is demonstrated for the detection of small amplitude ultrasonic surface displacements.

Dynamic holography with nonplane waves in sillenites

A three-dimensional model describing two-wave mixing in photorefractive crystals with finite beams of arbitrary shape is presented. The well-known longitudinal and transverse geometries are generalized by allowing an arbitrary orientation of the local grating vector. The coupled equations for the wave amplitudes are solved numerically in the small-angle approximation by introducing the light paths as characteristics. The influence of amplitude distributions and phase-front curvatures as well as the influence of geometrical arrangements and crystal properties (i.e. optical activity, externally applied voltage) on the energy exchange and the evolution of the polarization states is investigated. It is demonstrated that scanning the cross-section of the finite signal beam behind the crystal allows analysis of the coupling process inside the crystal which cannot be studied directly. The results of experiments with finite beams carried out on a BSO crystal are in good agreement with the numerical calculations.

Exact solution to photorefractive two-wave mixing with arbitrary modulation depth

We obtain analytical solution to the slowly varying envelope wave equations describing two-wave mixing in photorefractive crystals with arbitrary dependence of the gain and absorption on the two-wave fringe modulation depth. We introduce a novel form of the correction function for the space charge field that offers an improved agreement with the experiment.

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.

Positive and negative feedback effects of four-wave mixing in photorefractive crystals with two active centres

Based on a two-level model of optical transitions, the problem of positive and negative feedback effects during simultaneous reading and writing of dynamic holograms in photorefractive crystals has been solved analytically. The diffraction efficiency and the gain coefficient are shown to be nonlinear functions of the readout beam intensity and are nonreciprocal with respect to the readout from the two input ports. The readout beam intensity value that affects a previously recorded grating is shown to depend on microscopic parameters such as the cross-section of photoionization, the recombination coefficient and the concentration of photorefractive centres. An analysis of the amplitude of the overall shared grating has shown that with increasing readout beam intensity the holographic grating thickness decreases. In this case, under negative feedback the grating amplitude decreases, while with positive feedback it increases. The possibility is shown of achieving (under positive feedback) a maximum value of diffraction efficiency and complete energy transfer in a finite thickness of the photorefractive crystal, in contrast to the infinite thickness required in the standard two-beam coupling case.

BIFURCATION AND CHAOS OF UNIDIRECTIONAL PHOTOREFRACTIVE RING OSCILLATORS

摘要 Abstract 作者及机构信息 庄军2, 谭维翰1 (1)上海科学技术大学物理系,上海201800; (2)中国科学院上海光学精密机械研究所,上海201800 Authors and contacts ZHUANG JUN2, TAN WEI-HAN1 (1)上海科学技术大学物理系,上海201800; (2)中国科学院上海光学精密机械研究所,上海201800 参考文献 施引文献

Implementation of an optical multiwavelength full adder with a polarization encoding scheme

We propose and demonstrate an optical multiwavelength full adder that uses polarization encoding and fourwave mixing in photorefractive crystals. Optical wavelengths are employed to encode the different bits of binary numbers. By exploiting the spectral parallelism of optics, we can perform multibit operations simultaneously in photorefractive crystals. The polarization encoding scheme permits an easy, accurate implementation of multiwavelength SUM operations. A carry-save full adder also is demonstrated to improve system speed further during multinumber addition and subtraction.