Four-wave Mixing In Photorefractive Crystals Research Articles

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.

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.

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.

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.

Optical implementation of carry generation for a multiwavelength full adder

We propose the implementation of an optical multiwavelength full adder. Several optical wavelengths are used to encode the bits of the binary numbers to be added so that the broad spectral bandwidth of optical systems can be utilized. We demonstrate the carry generation for the proposed optical multiwavelength full adder, using a novel scheme of four-wave mixing in photorefractive crystals.

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.

Phase conjugation via unequal amplitude multiple gratings in photorefractives: A simple shooting method for numerical solution

We present a simple shooting method to obtain numerical solutions of the nonlinear coupled-wave equations for degenerate four-wave mixing in photorefractive crystals when four different types of the index gratings of unequal amplitudes are responsible for phase-conjugation. Our analysis includes the effects of pump depletion and absorption in the medium. Intensities of the four beams, both inside and at the output surface, are obtained as a function of four unequal coupling strengths and absorption coefficient. Intensity of the generated phase-conjugate beam is shown as a function of both the small and wide ranges of signal beam intensity. It is found that the multigrating operation with a careful choice of coupling constants and their combinations may improve the phase-conjugate wave generation. Also the presence of absorption reduces the phase-conjugate intensity more significantly when all the gratings are operative than when a single grating is allowed. Numerical results obtained from the computer calculations are presented in graphical form.

Stability analysis and temporal behavior of four-wave mixing in photorefractive crystals

The stability of the steady-state solutions of four-wave mixing in photorefractive crystals has been studied. Two complementary methods have been used: linear stability analysis and time integration of the nonlinear equations. A critical dependence of the stability on the phase of the perturbation has been revealed. The existence of two stable solutions for certain values of some parameters has been found. Also, regimes of unstable behavior in cases with a unique steady-state solution for large values of the pump ratio have been found.

Temporal instabilities in single-grating photorefractive four-wave mixing

The temporal behavior of optical phase conjugation by single-grating anisotropic four-wave mixing in photorefractive crystals is studied. Numerical evidence for optical instabilities of the phase-conjugate wave amplitude is shown.

Four-wave mixing in photorefractive crystals with depleted pumps: an analytical treatment

We present an analytical approximative solution of four-wave mixing in photorefractive crystals with depleted pumps for the case of a negative coupling coefficient and then discuss the solution.

Four-wave mixing in photorefractive crystals with depleted pumps

We present an analytical solution and experimental results for four-wave mixing in photorefractive crystals with depleted pumps. The approximation that we introduce permits a theoretical treatment without numerical computation. The measurements, which were performed using a BaTiO3 crystal, are compared with this model.

Phase conjugation via multiple gratings in photorefractive crystals.

We consider phase conjugation via degenerate four-wave mixing in photorefractive crystals when more than one grating mechanism is operative. A method for exact solution of the steady-state wave equations which include pump depletion is presented. It is discovered that equal-strength multigrating operation does not allow signal amplification.

Nearly degenerate four-wave mixing in photorefractive crystals, an analytical treatment

We extend the standard model of four-wave mixing in photorefractive crystals to the case where the Bragg-condition is broken by a slight departure from degeneracy. Our analytical treatment shows that for this conditions an increased phase conjugate reflectivity can be obtained.

Image amplification by two- and four-wave mixing in BaTiO<inf>3</inf>photorefractive crystals

A theoretical and experimental study of two- and four-wave mixing in photorefractive crystals (BaTiO 3 ) will be presented, giving special priority to image amplification in optical information processing systems.

Theory of self-frequency detuning of oscillations by wave mixing in photorefractive crystals

We present a theory of the frequency-detuning properties of various oscillators formed by four-wave mixing in photorefractive crystals. It is shown that the detuning originates from the self-induced grating dynamics in the mixing crystal, governed by phase conditions of the optical paths and several other parameters, such as external and internal electric fields in the mixing crystal.

Exact solution to the stationary holographic four-wave mixing in photorefractive crystals

An exact solution to the stationary holographic degenerate four-wave mixing in both transmission and reflection geometry for photorefractive media is obtained. The effects of pump depletion and light absorption in the non-linear dynamic medium are rigorously taken into account. The case of the transmission geometry is treated in more detail, with an emphasis on the energy transfer. The numerical steps in the procedure are reduced to the solution of one simple first-order differential equation, or are absent altogether for the case of no absorption.

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.

NEW STUDY AND APPLICATION OF PHASE CONJUGATION WITH PHOTOREFRACTIVE CRYSTALS

A theoretical and experimental study of four-wave mixing in photorefractive crystals like SBN and BaTiO₃ will be presented. A detailed theoretical analysis of the beam coupling as well as new experiments and applications will be described through a distortion ; among them, oneway optical field imaging, a passive (no external pumps) phase conjugate mirror which is pumped by the signal and its use in a laser resonator.