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Journal of Optics

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

N Birla, K.N. Tripathi, Avinashi Kapoor, Amitava Roy

Published May 1, 1996• 0 citations
Publisher

Abstract

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.

DOI
10.1088/0150-536x/27/3/004

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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.
Effects of cross-polarization coupling have been investigated in the case of degenerate four-wave mixing (DFWM) in absorbing semi-insulating compound semiconductor photorefractive (PR) crystals in transmission geometry. Considering pump beam depletion, and the slowly varying approximation, nonlinear coupled wave equations are obtained and have been solved numerically by a shooting method. Numerical results obtained from computer calculation are presented in graphical form. It is seen that if all the input beams are of the same polarization, cross-polarization coupling generates a phase-conjugate beam which is polarized in a plane orthogonal to that of the input beam.
Optical bistability based on the theory of photorefractive nearly degenerate four-wave mixing (DFWM) is considered for the case of transmission geometry with orthogonally polarized pump beams. The coupled wave equations are solved to obtain a nonlinear algebraic equation. This equation is being solved iteratively using Muller's method. The effect of different parameters pump ratio (r), probe ratio (q), coupling strength ( Gamma ) and frequency shift ( Omega ) on the phase conjugate reflectivity (PCR) have been investigated and the results are reported.
Co-polarised degenerate four-wave mixing (DFWM), in which all the four interacting beams have the same direction of polarisation, has been utilised to generate high phase conjugate reflectivities (~ 2500) recently [1]. In the co-polarised geometries six gratings are written in the material in which each beam forms a grating with another beam. Several theoretical models have been used to describe this co-polarised DFWM process in gain media [2]-[3]. However, all of them involve the use of small probe approximation and hence not all gratings are present in these models. Moreover, the effect of pump depletion has been neglected. A novel approach using the underlying symmetry is described recently to solve the co-polarised DFWM problem [4]. This approach allows us to take into account the effect of pump depletion, although the two standing gratings between the pumps and between the probe and the conjugate beams are ignored.
Using perturbation theory, we examine the fidelity of the photorefractive degenerate four-wave mixing (DFWM) phase conju- gator when the probe wave is spatially and temporally varying. Previous theories are based on linearized undepleted pump approximation and Laplace transform technique. Fully nonlinear solutions assume a single monochromatic plane wave probe. We have considered instead the more general case in which the probe is spatially varying (a beam) and/or temporally varying (a pulse), and the pumps are allowed to deplete. The probe wave is expanded as a sum of monochromatic plane waves of frequencies ω j = ω p + Ω j , wavevectors k j , and complex amplitudes A j (Ω j , k j ), where ω p is the frequency of the pumps. Using a perturbation approach up to the third order, we found that the components of the probe interact in pairs, so that the component of the conjugate wave at −Ω l −k l is H(Ω l , k l ) is the linearized response, ρ(Ω l , k l ; Ω j , k j ) represents crosstalk when j ≠ l, and self-nonlinear effect otherwise. Both functions exhibit resonance behavior. We use Eq. (1) to determine the response of the conjugate to pulsed beams.
A method for exact solution of the stationary holographic degenerate four-wave mixing in reflection geometry in photorefractive media is presented. The effects of pump depletion and light absorption in the nonlinear dynamic medium are rigorously taken into account. Numerical steps in the procedure are reduced to the solution of one simple nonlinear first-order differential equation, or are absent altogether when the equation is linearized, or for the case of no absorption. The method of solution is applicable to other wave-mixing geometries as well.