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Soviet Journal of Quantum Electronics

Degenerate four-wave mixing of multifrequency radiation in resonant media due to cascade transitions in diatomic molecules

Igor' M Bel'dyugin, A. A. Stepanov, Vladimir A. Shcheglov

Published Jul 31, 1988• 1 citation
Publisher

Abstract

The example of two-frequency radiation is used in an analysis of a resonant antiparallel degenerate four-wave interaction of multifrequency radiation involving cascade transitions in diatomic molecules. The approximation of homogeneous broadening of spectral lines is used in the derivation of equations describing transient interaction of waves in fields of arbitrary intensity allowing for the diffusion of particles in a gas. Numerical calculations illustrate some characteristics of the two-frequency four-wave interaction in resonant media.

DOI
10.1070/qe1988v018n07abeh012332

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The example of two-frequency radiation is used in an analysis of a resonant antiparallel degenerate four-wave interaction of multifrequency radiation involving cascade transitions in diatomic molecules. The approximation of homogeneous broadening of spectral lines is used in the derivation of equations describing transient interaction of waves in fields of arbitrary intensity allowing for the diffusion of particles in a gas. Numerical calculations illustrate some characteristics of the two-frequency four-wave interaction in resonant media.
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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 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.
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 analysis is made of nondegenerate four-wave interaction (FWI) in a resonant medium (two-level model) with Doppler line broadening allowing for nonlinear absorption of the weak radiation. The cubic approximation with respect to the field is used to derive expressions for the coefficients of parametric coupling and absorption of the mixed waves. The angular dependences of the reflection coefficient are studied for quasicollinear and orthogonal FWI geometries. It is shown that, as a result of the thermal motion of the particles, the dependence of the reflection coefficient on the angle θ between the interacting waves results in considerable limitation of the angular width of the reversed beams. This limitation is greater for degenerate FWI. In the case of nondegenerate FWI, as a result of the selective action of waves on groups of atoms having a specific velocity projection, the reversal efficiency may increase on increase in θ.
The interaction of two closely spaced resonances in degenerate four-wave-mixing spectra is investigated theoretically. Degenerate four-wave-mixing spectra for the phase-conjugate geometry (counterpropagating pump beams) are calculated by integrating the time-dependent density-matrix equations at numerous grid points along the phase-matching axis and summing the polarization contribution from each of these grid points. Both purely homogeneously broadened resonances and resonances that are both collision and Doppler broadened are considered. The homogeneously broadened results are found to agree with the results of the widely used Abrams–Lind expression for the case of stationary absorbers exposed to a steady-state excitation. We examine the effects of power broadening, pressure broadening, transition dipole moment, and population on the spectra of two neighboring homogeneously broadened resonances. As the laser power is increased, the real parts of the resonance susceptibilities destructively interfere with each other in the region between the lines, resulting in a significant and persistent dip in reflectivity. When Doppler broadening is included in the calculations, similar interference effects are observed, although at first the interference dip begins to disappear until the homogeneous part of the line shapes is broadened significantly by saturation. Using this numerical approach, we obtain good agreement with experimental results of primarily Doppler-broadened neighboring resonances.