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Soviet Journal of Quantum Electronics

Transient wavefront reversal in four-wave interaction in resonant media

V. N. Abrashin, Pavel A Apanasevich, Anatolii A Afanas'ev, V V Drits, А. И. Урбанович

Published Mar 31, 1985• 7 citations
Publisher

Abstract

Equations describing a transient degenerate four-wave interaction in a resonant medium are derived and solved numerically. The approximation of a "following" nonlinear polarization state is used to determine the range of values of the parameters of the medium and the radiation field in which the efficiency of a transient four-wave interaction is higher than that of the steady-state process. It is found that amplification of weak radiation as a result of transient energy exchange can only be achieved in the four-wave interaction for different pump wave intensities.

DOI
10.1070/qe1985v015n03abeh006329

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Equations describing a transient degenerate four-wave interaction in a resonant medium are derived and solved numerically. The approximation of a "following" nonlinear polarization state is used to determine the range of values of the parameters of the medium and the radiation field in which the efficiency of a transient four-wave interaction is higher than that of the steady-state process. It is found that amplification of weak radiation as a result of transient energy exchange can only be achieved in the four-wave interaction for different pump wave intensities.
An investigation is made of wavefront reversal of optical radiation in a nondegenerate four-wave interaction in a resonant medium. It is shown that for a pump intensity comparable with the saturation intensity of the absorption line of the resonant medium, the reversed wave spectrum has two side peaks positioned symmetrically relative to the central peak which corresponds to a degenerate interaction. These side peaks are attributable to regions of negative absorption (amplification) of weak radiation by the resonant medium situated in a high-power field of opposite pump waves. The dependences of the magnitudes and positions of these peaks on the pump intensity can be used to control the spectral and energy characteristics of the reflected radiation. The conditions for self-excitation of a reversing system based on resonant four-wave interaction are determined. In particular, the ranges of the pump intensity and the optical density of the resonant medium in which self-excitation of the reversing system may occur, are determined for a degenerate interaction.
A theoretical analysis is made of the efficiency of wavefront reversal under conditions of a degenerate form of the four-wave interaction in a resonantly absorbing (amplifying) medium allowing for changes in the pump waves as a result of their natural resonant absorption (amplification). The coefficient of reflection into a reversed wave is obtained as a function of the optical thickness of a layer of the medium, the boundary values of the pump wave intensity, and the shift of the field frequency from the line center. The optimal values of these parameters and the corresponding maximum reflection coefficient are determined.
A wavefront reversal system is proposed for high-power optical radiation. This system is based on a resonant four-wave interaction without recourse to external pump waves. Stimulated scattering of the wave being reversed in a resonant medium placed inside a resonator creates two opposite pump waves and a parametric interaction between them generates reversed radiation. The efficiency of such self-reversal is comparable with the efficiency of conventional wavefront reversal as a result of a four-wave interaction in nonresonant media with a phase nonlinearity and it may reach 10 −3 .
A theory is developed of an opposed degenerate four-wave interaction in resonant two-level media subjected to fields of arbitrary intensity. An allowance is made for the transient nature of the response of a relaxing medium. An infinite chain of equations is used to describe the interaction in such fields, the cases of steady-state and transient interactions are discussed separately, and the results of numerical calculations illustrating the theory are given. It is shown that in the steady-state case the equations derived in the present study reduce directly to the familiar equations of a small-signal theory. A qualitative analysis of the equations for the transient degenerate four-wave interaction shows clearly that in strong fields this interaction may be more effective than the steady-state interaction.
A theoretical analysis is made of wavefront reversal which is not sensitive to the optical quality of the nonlinear wavefront-reversing medium when complex-conjugate reference waves are formed spontaneously. An investigation is made of the linear and nonlinear stages of reversed wave generation in various nonlinear media using feedback in degenerate and nondegenerate four-wave interaction. It is shown that in nonamplifying nonlinear media this method can only be achieved by additional amplification of the radiation reflected from the nonlinear medium.
The two-level approximation is used to make a theoretical analysis of four-wave mixing in the active medium of a laser whose radiation wavefront is to be reversed. Explicit allowance is made for changes in the amplitudes of the pump waves as a result of their amplification during propagation in the active medium. Both the completely degenerate case, when the frequencies of all four waves are the same, and the case of a small detuning of the signal wave frequency relative to the pump waves are considered. For the completely degenerate case a system of reduced equations allowing for saturation of the inversion was solved by computer using an iterative method. It was found that, under optimum conditions in the saturation regime, the power of the wave reflected from a four-wave mixer may be higher than that of the signal wave.