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Physical Review A

Strong-field theory of four-wave mixing

Alfred M. Levine, N. Chencinski, W. M. Schreiber, Andrei N. Weiszmann, Yehiam Prior

Published Mar 1, 1987• 29 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.35.2550

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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.
Nonlinear perturbative susceptibilities have been used successfully to analyze experiments in nonlinear optics for two decades. By its very nature, a perturbative approach is limited to a small value of the expansion parameter, and nonlinear susceptibilities are not useful for strong saturating fields. Presently, a theory is presented for the treatment of FWM which is applicable to arbitrary strength of the input fields, both on and off resonance. The field harmonic time dependences are removed by a transformation to the proper rotating frame, and the resulting eigenvalue problem is solved numerically. Several new effects are predicted. For strong fields resonance frequencies are shifted and lines are split (similar to the ac Stark effect). When such a split line is acted on by another strong field (a phenomenon not studied so far), a new effect of stirring is observed, which results in the broadening and merging of the two separate components. A new extra resonance appears which is induced by the strong field and is present even in the absence of any collisions or other dephasing processes or of laser phase fluctuation. This new extra resonance is a new member in the family of extra resonances which were discussed in various previous publications.
A nonperturbative density-matrix formalism is used for the analysis of strong-field four-wave mixing, allowing the treatment of relaxation processes, including lifetime as well as dephasing. The combined role of proper dephasing and level saturation in the generation of extra resonances is studied. It is shown that, whereas in the absence of proper dephasing there is no pressure-induced resonance, there is always a nonzero contribution to the field-induced resonance. For increasing field intensity, a characteristic double saturation is predicted as a function of the field strength. The dependence on the various parameters is investigated, and the conditions under which these effects should be observable are identified.
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.