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Journal of the Optical Society of America B

Multigrating optical phase conjugation: numerical results

Milivoj R. Belić, Wieslaw Z. Krolikowski

Published May 1, 1989• 14 citations
Publisher

Abstract

Multigrating optical phase conjugation in photorefractive media in the case of pump depletion and for arbitrary relationships among different coupling strengths is studied numerically. The role of linear absorption as well as the role of all the coupling mechanisms and their competition in the wave mixing process is examined. It is found that multigrating operation with accidental values of coupling constants leads to a decrease in the efficiency of the process. It is also shown that the presence of absorption, which is in principle detrimental, sometimes exerts a beneficial influence on multigrating phase conjugation.

DOI
10.1364/josab.6.000901

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Journal of the Optical Society of America B•Oct 1, 1996•2 citations
Multigrating optical phase conjugation in photorefractive media in the case of pump depletion and for arbitrary relationships among different coupling strengths is studied numerically. The role of linear absorption as well as the role of all the coupling mechanisms and their competition in the wave mixing process is examined. It is found that multigrating operation with accidental values of coupling constants leads to a decrease in the efficiency of the process. It is also shown that the presence of absorption, which is in principle detrimental, sometimes exerts a beneficial influence on multigrating phase conjugation.
A numerical simulation for studying the kinetics of phase-conjugate beams generated by multigrating four-wave mixing has been developed. It has been applied to investigate the four-wave mixing process in BaTiO3 by use of realistic coupling coefficients. The role of the distinct gratings has been analyzed. Depending on the experimental conditions, constructive as well as destructive interference of the different contributions was obtained. Moreover, because of grating competition effects, π-phase changes in the phase-conjugate beam can occur during the kinetics. For large values of the coupling strength and specific regions of the physical parameters, unstable four-wave mixing dynamics were obtained. The analysis of the results provides some criteria for predicting the phase conjugator’s behavior in multigrating conditions.
While the interaction of optical beams in photorefractive crystals can often be accurately described in terms of 1-D plane-wave approximation, 2-D models are sometimes more suitable, as suggested by recent work.1 Here we discuss some aspects of photorefractive interaction of finite size optical beams. We have solved the system of partial differential equations governing two- and four-wave mixing numerically by using iterative procedures. Simulations of beam amplification in two-beam coupling show strong beam deformation even without any spatial information imposed on them. Spatially nonuniform energy transfer is responsible for this effect. The pump beam loses energy during propagation and at the end of its passage through the beam intersection region (which was completely inside the crystal) it is strongly depleted and cannot contribute significantly to beam amplification. As the pump beam crosses through the probe, it amplifies most strongly that side of the probe that it meets first. By the time the pump has reached the far side of the probe, it is strongly depleted and less effective at probe amplification. In the case of phase conjugation through four-wave mixing, we found that the conjugate beam is strongly deformed only when the coupling constant is negative (corresponding to deamplification of the probe input beam). For positive coupling constants the output conjugate beam is a good replica of the input probe beam.
The effects of linear absorption on the degenerate and nondegenerate self-oscillation of a photorefractive phase-conjugate mirror under condition of anisotropic four-wave mixing are considered. The phase conjugation results from nonlinear mixing of two strong undepleted orthogonally polarized counterpropagating pump waves with a probe wave. We consider two types of situation for orthogonally polarized pump beams corresponding to two crystal families: one such as the Bi12SiO20 crystal family (sillenite family) and the other such as the BaTiO3 and strontium barium niobate crystal family. In both of these crystal families the degenerate and nondegenerate self-oscillations are shown to occur in the presence of linear absorption, which tends to increase the value of the coupling coefficient required for self-oscillation. Numerical results are presented that exhibit various features of degenerate and nondegenerate self-oscillation in both crystal families for different values of the phase ϕb of the backward grating.