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Vestnik of Samara University Natural Science Series

THE POINT SPREAD FUNCTION OF A FOUR-WAVE CONVERTER IN A RESONANT MEDIUM WITH ALLOWANCE FOR PUMP WAVE DIVERGENCE

A.A. Akimov, Elena Vorobeva, Valery V. Ivakhnik

Published Jun 16, 2011• 0 citations
Publisher

Abstract

An expression for point spread function has been obtained for a four-waveconverter in resonant medium modelled by four-level energy scheme. The dependences of point spread function width from pumping wave intensity and resonantmedium parameters have been found.
DOI
10.18287/2541-7525-2011-17-2-141-147

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Quality of the wavefront reversal by a four-wave radiation converter in a parabolic waveguide with resonant nonlinearity have been analyzed using the point spread function. Medium with resonant nonlinearity have been modeled by an ensemble of particles described by a two-level energy scheme. It has been shown that over time, the half-width of the point spread function module decreases, reaching a stationary value, the magnitude of which is determined by the first pump wave intensity in the case of a long waveguide. A decrease in the pump radius at low intensity of the first pump wave leads to a decrease in the half-width of the point spread function modulus (the quality of the wavefront reversal improves), and at high intensity leads to an increase in the half-width of the point spread function modulus (the quality of the wavefront reversal deteriorates) in the stationary case with distribution on the back waveguide face depending on the transverse coordinate of the second pump wave amplitude of the according to the Gaussian law.
Spatial and temporal characteristics of a degenerate four-wave converter in a multimode waveguide with resonant nonlinearity in a scheme with counter-pumping waves are analyzed using the time response function and the point spread function. For single-mode pump waves with equal mode numbers, the dependences of the time response width on the waveguide length, the intensity of the first pump waves, and the mode number in the mode expansion of the object wave amplitude are obtained for the four-wave converter. The greatest contribution to the object wave amplitude is shown to be from the waveguide mode whose number coincides with the mode number of single-mode pump waves. For the stationary model, taking into account the spatial structure of the Gaussian pump wave leads to a monotonous decrease with a decrease in the pump beam width, followed by a constant value of the PSF module width. With single-mode pump waves with equal mode numbers, An increase in the mode number of the pump waves leads to a redistribution of energy concentrated in the side maxima of the point signal image and improvement in the quality of the wavefront reversal for a model with single-mode pump waves with equal mode numbers.
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.
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.