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Soviet Journal of Quantum Electronics

Nondegenerate four-wave interaction in a resonant medium with Doppler broadening of the absorption line

Anatolii A Afanas'ev, А. П. Войтович, M V Dotsenko

Published Mar 31, 1987• 0 citations
Publisher

Abstract

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.

DOI
10.1070/qe1987v017n03abeh007613

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Journal de physique•Jan 1, 1981•74 citations
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.
Third-order susceptibilities are calculated for a Doppler-broadened two-level system. The dependence of four-wave mixing on the angle θ between the pump and signal fields is studied, and the reflection coefficient is shown to have a narrow field of view that is inversely proportional to the ratio of the Doppler width to the homogeneous linewidth. For the collinear geometry, θ = 0°, the frequency dependence of the nondegenerate case is analyzed and shown capable of yielding a real-time narrow-bandwidth optical filter whose bandwidth is limited by the homogeneous linewidth.
A theoretical investigation is made of the influence of the asymmetry of the intensities of pump waves on the spectrum of weak radiation participating in a nondegenerate four-wave interaction in a resonant medium with a homogeneously broadened absorption line. It is shown that a difference between the intensities of pump waves results in additional modulation of the spectrum of reflected and transmitted waves. In particular, an increase in the asymmetry of the pump wave intensities increases the phase mismatch between the waves and reduces the central maximum in the weak radiation spectrum. When the difference between the intensities of the pump waves becomes sufficiently large, this central maximum of the reflected radiation disappears completely and the side maxima acquire a doublet structure. It is shown that the position of the maxima in the reflected radiation spectrum corresponds exactly to the minima of the phase matching between the waves. An analysis is made of the characteristics of a reflecting narrow-band optical filter based on a nondegenerate four-wave interaction in a resonant medium.
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.
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.
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.
We present in this paper a theoretical study of the angular dependence of phase-conjugate emission via resonant degenerate four-wave mixing (FWM) in Doppler-broadened gas media. The nonlinear optical polarization is calculated through an expansion of the atomic density matrix up to the third order in the incident fields. One finds that, when the incident frequency is resonant for a single-photon transition, both strength and lineshape of the phase-conjugate emission strongly depend on the angle 0 between standing pump wave and probe wave. The emission intensity, maximum at grazing incidences, decreases rapidly by several orders of magnitude when 0 increases. Simultaneously the emission linewidth increases from homogeneous to Doppler width. Similar effects are predicted for nearly-degenerate FWM (different pump and probe frequencies). In particular, one shows that the bandwidth of the equivalent optical reflection filter undergoes a Doppler-broadening linearly increasing with sin θ. On the opposite, none of the above effects is predicted in two-photon-resonant FWM which does not exhibit any angular dependence.