Four-wave Mixing In Photorefractive Media Research Articles

Asymptotic behavior of the boundary value problem of four-wave mixing in photorefractive media

Solutions to the four-wave mixing problem asymptotically approach a spatial steady state over large interaction distances. In this limit, intensities of the two-point boundary value problem may be found from solutions to quadratic equations. The different limiting behavior exhibited for positive and negative gain has important implications for applications in which linearity of system response is important. In the regime studied, positive gain leads quickly to maximally depleted pumps with increasing input signal. For negative gain, such depletion does not occur until higher signal levels are reached.

Degenerate four-wave mixing in photorefractive media in the presence of biasing incoherent illumination

The effect of biasing illumination on the degenerate four-wave mixing (DFWM) in absorbing photorefractive (PR) media has been investigated. The input beams are considered to be spatially uniform. The analysis has been made both for transmission and reflection geometry. Considering pump beam depletion and the slowly varying amplitude approximation, nonlinear coupled wave equations are obtained and have been solved numerically by a shooting method. The effect of different parameters such as input beam intensities ratio, thickness of the interacting medium on the phase conjugate reflectively (PCR) has been investigated. It has been observed that PCR can be controlled to a large extent by controlling the biasing intensity.

Optical wavelet-matched filtering by four-wave mixing in photorefractive media

A novel real-time optical processor is proposed for implementing wavelet-matched filtering that uses four-wave mixing in photorefractive media. An edge enhancement property of the wavelet transform and an improved pattern recognition capability of the proposed method are demonstrated experimentally. The results verify the usefulness of the proposed method compared to the conventional matched filtering by four-wave mixing.

Wave mixing in photorefractive crystals with saturable couplings: stable solutions and instabilities

Two-wave and four-wave mixing in photorefractive media with saturable gain and saturable absorption is analyzed. Solutions to wave equations are found in terms of quadratures and implicitly given functions. Different models of saturation are compared. It is found that for weak couplings energy transfer between waves is less effective in the strong unsaturated regime as compared to the saturated, while for strong couplings both regimes are equally effective. The existence of multiple solutions in four-wave mixing is established. It is shown that the unsaturated system is more stable than the saturated.

Influence of the fanning on the characteristics of self-pumped four-wave mixing in photorefractive media

A review is given of theoretical and experimental investigations of the role of the fanning in the operation of self-pumped four-wave mixing systems. It is shown that in some cases the fanning determines the dynamics of such systems and their final steady states.

Two- and four-wave mixing with saturable absorption and gain

An exact solution to a model of two- and four-wave mixing in photorefractive media with saturable gain and absorption is presented. Pump depletion effects are accounted for, and the procedure for matching two-point boundary conditions is given. Possibilities of multistable solutions are investigated, and procedures on how to deal with such situations are outlined. It is found that the energy transfer between waves is less effective in the nonsaturated regime as compared to the saturated regime. It is also established that the nonsaturated system is more stable than the saturated under the same conditions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Investigation of stability of four-wave mixing in photorefractive media

The stability of the different four-wave mixing (FWM) configurations in photorefractive media for drift-diffusion nonlinearity and nonlocal response is investigated. All the configurations considered are shown to be unstable in some range of parameters, the stability region boundaries are found.

Theory of four-wave mixing in photorefractive media when the response of a medium is nonlinear in respect of the modulation parameter

A theoretical model is constructed for four-wave mixing in a photorefractive crystal where a transmission grating is formed by the drift–diffusion nonlinearity mechanism in the absence of an external electrostatic field and the response of the medium is nonlinear in respect of the modulation parameter. A comparison is made with a model in which the response of the medium is linear in respect of the modulation parameter. Theoretical models of four-wave and two-wave mixing are also compared with experiments.

Exact solution of degenerate four-wave mixing in photorefractive media

A novel method for the exact solution of four-wave mixing in photorefractive media is presented. This method allows us to treat exactly the effects of nonequal angles of incidence, different refractive-index modulation of interacting waves, and external incoherent illumination of the photorefractive crystal.

Multigrating phase conjugation: exact results

Multigrating operation of degenerate four-wave mixing in photorefractive media is considered in the strong pump regime. Closed-form expressions for the reflectivity are obtained for the cases of absorption and no absorption. An arbitrary phase mismatch between the intensity interference fringes and the refractive-index gratings is allowed.

Simple theory for degenerate four-wave mixing in photorefractive media

A simple analytic theory for degenerate four-wave mixing in photorefractive media is presented. The theory is valid when the backward pump-beam intensity is much smaller than the forward pump-beam and probe-beam intensities.

Optical matrix-vector multiplication via four-wave mixing in photorefractive media: errata

Optical matrix-vector multiplication via four-wave mixing in photorefractive media: errata

Optical matrix–vector multiplication through four-wave mixing in photorefractive media

We propose and describe a new method of optical matrix-vector multiplication by using four-wave mixing in photorefractive media. Using a BaTiO(3) crystal, we have demonstrated such a parallel multiplication. The results are presented and discussed.

Simple computational model of image correlation by four-wave mixing in photorefractive media

A simple systems-oriented model of image correlation by nondegenerate four-wave mixing in photorefractive media is discussed, and its computational implementation is described. The model is based on a linear-incomplex modulation index formulation and is capable of describing the correlation product in a wide range of experimental conditions. Bragg matching effects on the test and reference images are explicitly included. The comparison of calculated results with experimental results is excellent, and a discussion of higher-order theories of the photorefractive effect is given. The model is currently being used to optimize the performance of experimental correlators.

Forward phase-conjugate wave in four-wave mixing in photorefractive media

We show that a transmitted phase-conjugate wave should be expected in degenerate four-wave mixing. This prediction is confirmed in experiments using a BSO crystal.

Multistability in reflection grating real-time holography

In this paper, four-wave mixing in photorefractive media for the case of a reflection geometry is investigated. The exact solutions of appropriate nonlinear equations for a zero phase shift between the refractive index grating and interference pattern of the optical beams have been found. The existence of multistability in the process has been shown. In addition, numerical evidence of the effect is included.

Nonlinear vectorial two-beam coupling and forward four-wave mixing in photorefractive materials

We present an exact solution of a nonlinear vector analysis of two-beam coupling and forward four-wave mixing in photorefractive media.

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.