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Soviet Journal of Quantum Electronics

Four-wave resonant parametric interaction accompanied by reversal of the signal wavefront in a nonmonochromatic pump field

N. A. Iskanderov, Vladimir A. Kudryashov, N E Tuvaev

Published Apr 30, 1985• 1 citation
Publisher

Abstract

A theoretical analysis is made of a four-wave parametric interaction accompanied by reversal of the signal wavefront in a thin layer of a two-level medium as a result of a two-photon resonance of opposite waves of randomly modulated pumping. An allowance is made for the inertia of the interaction, saturation of the transition involved in the interaction, Stark shift of the levels, and width of the pump spectrum. A study is made of the influence of random modulation of the pump waves on the average value and relative variance of the intensity of the reversed wave. It is shown that the relative amplitude of the intensity fluctuations of the reversed wave is minimal when the maximum average intensity is reached.

DOI
10.1070/qe1985v015n04abeh006998

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A theoretical analysis is made of a four-wave parametric interaction accompanied by reversal of the signal wavefront in a thin layer of a two-level medium as a result of a two-photon resonance of opposite waves of randomly modulated pumping. An allowance is made for the inertia of the interaction, saturation of the transition involved in the interaction, Stark shift of the levels, and width of the pump spectrum. A study is made of the influence of random modulation of the pump waves on the average value and relative variance of the intensity of the reversed wave. It is shown that the relative amplitude of the intensity fluctuations of the reversed wave is minimal when the maximum average intensity is reached.
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.
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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.
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.
A theoretical investigation is made of the influence of the asymmetry of the intensities of pump waves on the spectrum of weak radiation participating in a nondegenerate four-wave interaction in a resonant medium with a homogeneously broadened absorption line. It is shown that a difference between the intensities of pump waves results in additional modulation of the spectrum of reflected and transmitted waves. In particular, an increase in the asymmetry of the pump wave intensities increases the phase mismatch between the waves and reduces the central maximum in the weak radiation spectrum. When the difference between the intensities of the pump waves becomes sufficiently large, this central maximum of the reflected radiation disappears completely and the side maxima acquire a doublet structure. It is shown that the position of the maxima in the reflected radiation spectrum corresponds exactly to the minima of the phase matching between the waves. An analysis is made of the characteristics of a reflecting narrow-band optical filter based on a nondegenerate four-wave interaction in a resonant medium.
Six-photon parametric up-conversion under conditions of two-, three-, and four-photon resonance of a constant nonmonochromatic pump field is analyzed allowing for population migration, transient response of the medium, Stark shift of the levels, and width of the frequency spectrum of the the pump field. It is found that in the steady-state conversion regime, the maximum average conversion efficiency in the four-photon resonance case differs only negligibly from the maximum conversion efficiency in a monochromatic field, whereas in the two-photon and three-photon resonance cases it is higher than the maximum efficiency in a monochromatic pump field. An analysis is made of the influence of optically induced relaxation on the average conversion efficiency under conditions of pulsed excitation of two-, three-, and four-photon resonances.