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Soviet Journal of Quantum Electronics

Spatial resonance in four-photon interaction between concurrent waves in a cubic medium

Leonid A Bol'shov, D. V. Vlasov, R A Garaev

Published Jan 31, 1982• 6 citations
Publisher

Abstract

An analysis is made of the conditions for efficient nonlinear interaction during propagation of four concurrent waves in a cubic medium. It is found that the evolution of the energy distribution between the waves depends on their phase relationships. An investigation is made of the influence of thermal nonlinearity on the time dependence of the four-photon scattering process. Possible variants of the application of this effect in physical research are described.

DOI
10.1070/qe1982v012n01abeh005264

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An analysis is made of the conditions for efficient nonlinear interaction during propagation of four concurrent waves in a cubic medium. It is found that the evolution of the energy distribution between the waves depends on their phase relationships. An investigation is made of the influence of thermal nonlinearity on the time dependence of the four-photon scattering process. Possible variants of the application of this effect in physical research are described.
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Theoretical and experimental investigations were made of a four-wave interaction of middle-infrared radiation based on a thermal nonlinearity of absorbing liquids and gases. A study was made of the influence of parasitic effects associated with heating of a nonlinear medium (such as the thermal lens effect, frequency sweeping of interacting waves, thermal expansion of the medium, and convection) on the efficiency of the four-wave interaction and the quality of phase conjugation utilizing this interaction. The conditions under which this influence is minimal were identified. An experimental study was made of phase conjugation of CO 2 laser radiation by a four-wave interaction in CCl 4 with a high reflection coefficient (up to 20% in the cw regime). The attained phase conjugation was limited the thermal lens effect, but this could be compensated.
An investigation is made of four-photon sum and difference frequency generation under two-photon resonance conditions allowing for population migration accompanying incoherent processes and for the possibility of a one-photon quasiresonance with the emitted radiation in inverted and uninverted media. A study is made of parametric bleaching of the medium and phase locking of the interacting waves, their stability, and influence on the conversion quantum efficiency η . It is established that resonant parametric processes have a larger region of stability than nonresonant ones. An analysis is made of bifurcation, typical of resonant processes, that strongly influences η . Accurate analytic expressions are derived for the maximum attainable values of η and it is shown that there is an optimum frequency detuning from a one-photon resonance.
The transition regimes of solitons in four-photon resonant processes in the case of two-photon absorption of the fundamental radiation are numerically investigated. The standard system of equations for the amplitudes of probability of finding the system in state with certain energy is used to derive the expression for the induced polarization in the nonlinear medium. As for the equations for the amplitudes of the optical pulses, the general case is considered in which both the amplitudes and phases are space-time dependent. We focus on the finite difference methods and the case of simultaneously propagating solitons at all frequencies of the interacting waves (simultons). The obtained results indicate that upon certain threshold conditions all interacting pulses become the solitons of Lorentzian shape. The numerical analysis has also shown that the soliton amplitudes significantly depend on the ratio between the nonlinear polarizability at the fundamental frequency ω0 and that of combination of ω0 and the trigger-field frequency ω1(2ω0 + ω1). In the second part of the paper, we apply the method of phase planes to show that at typical values of parameters, the solitons are stable.
An expression is obtained for the nonlinear susceptibility governing the addition of frequencies under resonance conditions. Allowance is made for the Stark shift, changes in populations, and transient response of the medium. Analysis is made of the stimulated emission of the third harmonic as a result of two-photon resonance in parallel and focused beams. It is shown that the saturation effect limits seriously the conversion coefficient of a nonlinear medium of fixed length. Optimal intensities of the fundamental-frequency radiation are found. It is shown that when a beam is focused sharply in a nonlinear medium, the saturation effect and Stark shift make it possible to add frequencies in media with normal dispersion. The relationship between four-photon parametric effects and coherent resonant processes such as self-induced transparency is established for ultrashort pulses.
A theoretical investigation is made of the characteristics of wavefront reversal in the course of a degenerate four-wave interaction in moving slow-response media. It is shown that the displacement (by a moving medium) of amplitude and phase gratings, and also diffusion of excited particles may influence greatly the parameters of a reversed wave. The characteristics of a nonlinear mechanism of light-induced heat evolution in thermodynamic-nonequilibrium media are determined for spatially inhomogeneous radiation.