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Soviet Journal of Quantum Electronics

Theory of an opposed four-wave interaction in arbitrary-intensity fields applied to media with resonant and thermal nonlinearity mechanisms

Igor' M Bel'dyugin, А. А. Степанов, Vladimir A. Shcheglov

Published Jan 31, 1989• 5 citations
Publisher

Abstract

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.

DOI
10.1070/qe1989v019n01abeh007710

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Soviet Journal of Quantum Electronics•Jul 31, 1988•1 citation
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.
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.
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.
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 typical ring systems of phase-conjugating mirrors utilizing a degenerate four-wave interaction in media with a thermal nonlinearity. The analysis is made for steady-state conditions taking into account wave saturation effects in an amplifier situated in a positive feedback circuit. It is shown that the reflection coefficient in these systems is extremely sensitive to the level of the phase-conjugate signal (as the ratio of the signal intensity to the saturation intensity of the amplifier active medium is increased, the reflection coefficient of the ring phase-conjugating mirror decreases sharply). It is also found that at a high level of the nonlinearity and for an appreciable gain per pass, these systems exhibit multistability (i.e., several different steady states exist).
The phase-conjugate reflectivity attainable by degenerate four-wave mixing in an idealized saturable absorbing medium is calculated for arbitrary values of the laser intensity, laser frequency, and absorption path-length of the nonlinear medium. The influence of pump-wave absorption, including saturation and standing-wave effects, is included in the theory. The treatment is based on an analytic expression for the intensity distribution of the counterpropagating waves. The theoretical predictions differ substantially from those based on theories that ignore pump absorption effects. The results of the present calculation are used to predict the minimum laser intensity, absorption path-length, and detuning required to obtain unit reflectivity and self-oscillation.
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.