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Physical Review A

Photorefractive phase-conjugate reflectivity enhancement due to linear absorption

Nitin C. Kothari

Published Dec 1, 1996• 3 citations
Publisher

Abstract

The undepleted-pump photorefractive four-wave mixing equations for the case of orthogonally polarized pumps are solved taking into account the linear absorption of the medium. A phenomenon of the enhancement of the phase conjugate reflectivity due to linear absorption is found to occur for a certain range of the phase conjugator parameters. This phenomenon is shown to occur as a consequence of the existence of the self-oscillatory modes in the presence of linear absorption. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.5313

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The undepleted-pump photorefractive four-wave mixing equations for the case of orthogonally polarized pumps are solved taking into account the linear absorption of the medium. A phenomenon of the enhancement of the phase conjugate reflectivity due to linear absorption is found to occur for a certain range of the phase conjugator parameters. This phenomenon is shown to occur as a consequence of the existence of the self-oscillatory modes in the presence of linear absorption. \textcopyright{} 1996 The American Physical Society.
We describe the steady-state enhancement of the phase-conjugate reflectivity that occurs with linear absorption near self-oscillation in four-wave mixing systems. Using a simplified general model, we show that this effect can arise in a variety of phase conjugators including those based on photorefractive and Kerr media. A new expression is introduced for the optimal reflectivity condition, which occurs if the transfer of energy from the strong forward pump to the weak probe is maximized at the entrance to the nonlinear medium.
Using numerical simulations of the fully nonlinear equations that describe the steady-state optical fields that develop within photorefractive phase-conjugate mirrors, we have shown that the phase-conjugate reflectivity can be enhanced in the presence of linear absorption. Our investigations focused on the development of the optical fields that arise when the reflectivity is nonmonotonically dependent on the linear absorption both near and away from self-oscillation. We have identified several significant features associated with the enhancement. Near self-oscillation and with strong pumps, an increase in the loss can lead to a more efficient energy transfer to the probe by altering the phase of the coupling, resulting in an increase in the index grating amplitude. Away from self-oscillation and with strong pumps, the loss alters the distribution of the grating within the crystal, and maximum reflectivity is associated with an optimum distribution. Reflectivity enhancement that is due to linear absorption was shown to occur even in the weak-pump case, thus providing unequivocal evidence of the veracity of this phenomenon.
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.
The effects of linear absorption on the degenerate and nondegenerate self-oscillation conditions of a photorefractive phase-conjugate mirror are explored. In this study, phase-conjugation results from nonlinear mixing of two strong undepleted parallel-polarized counterpropagating pump waves with a probe wave. Numerical results are presented that illustrate that the linear absorption tends to increase the value of the coupling coefficient required for self-oscillation. It is also found that the pump intensity ratio r is almost independent of the linear absorption for positive normalized detuning Δωτ between the probe and the pump frequencies and of the zero phase shift, ϕ, between the gratings and the light interference patterns when the gratings are stationary. For ϕ = ±π/2, the variation of r with respect to absorption is symmetric for positive and negative detunings.
We analyze the phase-conjugate reflectivity and the amplification property of cross-polarized four-wave mixing with a photorefractive BaTiO3 crystal in consideration of the pump-beam depletion. The coupled-wave equations of cross-polarized four-wave mixing with ordinary writing beams and an extraordinary reading beam are derived and solved with the grating-integral method. The results of calculations of the reflectivity and the amplification factors will be compared with the result under the undepleted-pumps approximation. In addition, to achieve high conversion efficiency, the optimum conditions for the intensity ratio and the angle configurations of the probe and pump beams are also discussed.