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Soviet Journal of Quantum Electronics

Dynamic reflection range in the case of four-wave interaction in resonant media at the wavelength of 10.6 μ

Nicolai G. Basov, Valeri I. Kovalev, F S Faĭzullov

Published Jun 30, 1983• 2 citations
Publisher

Abstract

It was found experimentally that the dynamic reflection range was ~107 for a four-wave interaction in SF6 and BCl3 gases absorbing resonantly at 10.6 μ. In an optically dense nonlinear medium the power efficiency of reflection of a signal wave was independent of its intensity right up to the value comparable with the intensity of the first reference wave. On the side of low signal intensities the dynamic range was limited by the scattering of the reference waves on the windows of a gas cell.

DOI
10.1070/qe1983v013n06abeh004328

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It was found experimentally that the dynamic reflection range was ~107 for a four-wave interaction in SF6 and BCl3 gases absorbing resonantly at 10.6 μ. In an optically dense nonlinear medium the power efficiency of reflection of a signal wave was independent of its intensity right up to the value comparable with the intensity of the first reference wave. On the side of low signal intensities the dynamic range was limited by the scattering of the reference waves on the windows of a gas cell.
An investigation is made of the reflection of a mulitfrequency signal in connection with wavefront reversal in four-wave interaction. When the signal and reference waves are generated by a single source and their optical paths are matched, it has been established experimentally and theoretically that if the length of the medium is greater than the coherence length, the reflection efficiency is the same as that for monochromatic waves of the same intensity. For a short medium, fluctuations of the intensity of many nonphase-matched spectral components should increase the reflection efficiency up to sixfold.
A system of equations is derived to describe a transient opposed degenerate four-wave interaction (FWI) in fields of arbitrary intensity in gaseous media exhibiting resonant and thermal nonlinearity mechanisms. A system of closed equations describing an opposed degenerate FWI in fields of arbitrary intensity is obtained for the steady-state case. It is found that, unlike linearly absorbing media, the optimal reflection coefficients of a signal wave in nonlinearly absorbing media are only achieved at reference wave intensities comparable with the saturation intensity of the resonant medium. Numerical calculations illustrate a fall in the reflection coefficient as the amplitude of the signal wave is increased.
The optical density of a resonant medium significantly affects the output signal in time resolved nonlinear optical interactions. The resonant interaction with a medium reshapes any propagating short pulse, and the mutual interaction of several such pulses, as in four-wave mixing, must be treated self-consistently. We present a theoretical framework for the proper handling of the propagation of all pulses, input as well as generated, in the small area limit. For optically thick resonant absorbers, negative time delay signals are observed, and the apparent decay rate of the induced polarization is faster than the rate observed for thin samples. We experimentally measure degenerate four-wave mixing in an atomic medium as an example, and demonstrate the quality of the theoretical model by the excellent fit to measured signals over several orders of magnitude. The improved understanding enables us to provide a simple, but surprisingly accurate, estimate for the apparent decay rate in homogeneously broadened optically thick media: If the absorption is given by \ensuremath{\alpha}, the propagation length is L, and the transverse relaxation time is T2{\mathit{T}}_{2}T2​, the apparent decay rate 2/Ta{\mathit{T}}_{\mathit{a}}Ta​ of a time resolved four-wave mixing signal is given by 2/Ta{\mathit{T}}_{\mathit{a}}Ta​=(2/T2{\mathit{T}}_{2}T2​)(1+\ensuremath{\alpha}L/2).
We show that four-wave mixing in optically dense media is very different than in an optically thin medium. In time-resolved degenerate four-wave mixing we experimentally observe ``negative'' time delay response, fast decay rates at short delay times, and broad shoulders at long delays. The observations are explained very well in terms of pulse propagation effects, and a theoretical framework is presented for the analysis of the nonlinear interaction. We treat both the incident and generated fields self-consistently, and solve for the interaction of short pulses with a resonantly absorbing medium. The implications for the extraction of relaxation rates from four-wave-mixing experiments involving ultrashort pulses in optically dense matter are discussed.
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.
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.