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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Splitting effects and power saturation in cw resonant four-wave mixing with two strong fields

Sergei A Babin, Sergey I. Kablukov, U. Hinze, E. Tiemann, B. Wellegehausen

Published Mar 2, 2001• 0 citations
Publisher

Abstract

Investigations of resonant spectral structures of four wave mixing (FWM) in molecular sodium are presented. For a double- (Lambda) configuration with strong-weak-strong-weak fields, split components in FWM spectra induced by the strong pump fields are observed. It is shown, that the split components merge into a single peak for a certain ratio of the strong field intensities. A strong correlation between the level splitting effect and saturation behavior of the FWM-signal is experimentally demonstrated.

DOI
10.1117/12.417724

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Investigations of resonant spectral structures of four wave mixing (FWM) in molecular sodium are presented. For a double- (Lambda) configuration with strong-weak-strong-weak fields, split components in FWM spectra induced by the strong pump fields are observed. It is shown, that the split components merge into a single peak for a certain ratio of the strong field intensities. A strong correlation between the level splitting effect and saturation behavior of the FWM-signal is experimentally demonstrated.
A nonperturbative theoretical study of four-wave-mixing processes in four-level systems is presented. Using the density-matrix formalism, numerical results are obtained for two arbitrarily intense pump fields with the third field a weak probe. The fourth wave, radiated by the system, is obtained analytically for some special cases. We find, for different frequency detunings, Rabi frequencies, and relaxation rates that the line shapes exhibit: (i) dynamic Stark splitting and shifting, and merging of resonances; (ii) power broadening with two-photon antiresonance behavior resulting from a destructive interference between different contributions to the optical polarization; and (iii) extra resonances induced by field intensities and saturation processes.
The explicit solution is obtained for Raman four-wave mixing ω4=ω1−ω2+ω3\omega_4=\omega_1-\omega_2+\omega_3ω4​=ω1​−ω2​+ω3​ of two strong fields E1,E3E_1, E_3E1​,E3​ and two weak fields E2,E4E_2, E_4E2​,E4​ in a four-level system with the large Doppler broadening. The resonance of the mixing coefficient vs intensity is found near equal Rabi frequencies of strong fields and interpreted as an intersection of quasi-energy levels. Up to 6 peaks appear in the dependence of conversion coefficient on the detuning of the probe field. An unexpected additional pair of peaks is a result of averaging over velocities and disappears at low temperature. The effects allow explaining saturation behavior in recent experiments on the mixing in sodium molecular vapor.
A nonperturbative semiclassical theory is presented for the treatment of four-wave mixing (FWM) in a four-level system. This treatment is based on a transformation to a generalized rotating frame followed by a numerical diagonalization of the resulting time-independent Hamiltonian. For strong fields, all resonant frequencies are shifted from the atomic (molecular) frequencies. Lines are split up in a way similar to the ac Stark effect for a two-level system, and for even stronger fields, the effect of stirring is observed for the first time in four-wave mixing. In addition, a new extra resonance appears which is induced by the saturating field. This field-induced resonance is the new member in the family of extra resonances (pressure induced, or stochastic fluctuation induced), and it should be observed whenever saturating fields interact with a multilevel atomic or molecular system.
Summary form only given. Various schemes of resonant frequency conversion using four-wave mixing (FWM) have been investigated recently. For example, sum-frequency FWM in Hg atoms has been used for generation of CW radiation at 121.56 nm, corresponding to the Lyman-/spl alpha/ line of hydrogen and efficient difference frequency mixing has been demonstrated in double-/spl Lambda/ level configurations of Na/sub 2/ molecules. We present novel investigations on the resonance structure of the FWM-spectra in the case of up-conversion in a double-/spl Lambda/ scheme realized in Na/sub 2/.
An explicit solution is obtained for the four-wave frequency mixing ${\ensuremath{\omega}}_{d}={\ensuremath{\omega}}_{a}\ensuremath{-}{\ensuremath{\omega}}_{b}+{\ensuremath{\omega}}_{c}$ of two strong fields a and c and two weak fields b and d in a four-level system with large Doppler broadening in collinear geometry, where the frequencies of weak fields are nearly equal, ${\ensuremath{\omega}}_{b}\ensuremath{\simeq}{\ensuremath{\omega}}_{d},$ and the medium is optically thin. Without weak fields there are two independent two-level systems. A pair of weak fields probes two other allowed transitions. A peak of the mixing coefficient as a function of intensity is found around an equal Rabi splitting of both two-level systems. The effect is based on a resonance between two closed cycles of four-wave mixing via different dressed states. Three, four, or six peaks are predicted in the dependence of the mixing coefficient on the frequency of the weak field; two of them are a consequence of averaging over velocities. The model allows an interpretation of the dependence of the output wave power on the intensity and detuning in recent experiments on frequency mixing in sodium vapor.