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Journal of the Optical Society of America B

Reflectivity enhancement due to linear absorption in photorefractive phase-conjugate mirrors with depleted pumps

Abdul-Azeez R. Al-Rashed, J. A. Tataronis, Bradley M. Jost, Nitin C. Kothari, Bahaa E. A. Saleh

Published Aug 1, 1997• 2 citations
Publisher

Abstract

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.

DOI
10.1364/josab.14.002059

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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.
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.
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.
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 have developed a theory for nondegenerate oscillations in optical resonators containing an intracavity phase-conjugate element. The phase-conjugate element consists of a nonlinear transparent medium that is pumped externally by a pair of counterpropagating laser beams of the same frequency and intensity. Phase conjugation of an input beam of slightly different frequency occurs because of nondegenerate four-wave mixing. The theory takes into account linear absorption (or gain) in the medium and is applied to study the threshold behavior of phase-conjugate oscillators. For the special case of no conventional mirrors, the phase-conjugate oscillator reduces to an ordinary phase-conjugate mirror, and our general formulation yields the results of previous studies. Our analysis shows that the parametric gain required for oscillation increases (or decreases) as a result of linear absorption (or gain) in the medium, and oscillation can occur at a frequency different from that of the pump beams in the presence of large linear gain (or loss). The effects of linear absorption (or gain) on the filter operation are also examined.
We have studied both experimentally and numerically the role of resonant refractive index gratings in a self-pumped phase conjugate mirror based on an Nd:YAG amplifier with nonreciprocal feedback loop. In experiment the generation of the phase-conjugating laser was delayed with respect to recording of a holographic nonlinear mirror by an external beam. An increase in the phase-conjugate reflectivity at a delay time of about 3 microseconds was measured. The numerical calculation confirmed the additional contribution of the resonant refractive-index grating, which is formed in the pumped Nd:YAG crystal due to excitation of a higher-lying level of Nd3+ ions, to efficiency of phase conjugation.