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Physical Review A

Four-wave mixing in a three-level system interacting with an intense two-frequency pump wave

Motowo Tsukakoshi

Published Sep 1, 1989• 2 citations
Publisher

Abstract

A semiclassical treatment of four-wave mixing is presented for the case for which a two-frequency pump wave of arbitrary intensity and a weak probe wave interact with a three-level system. Numerical, as well as analytical, results for the emission spectra are obtained from the steady-state response. At high pump power, the spectra are strongly modified by the ac Stark effect.

DOI
10.1103/physreva.40.2428

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Japanese Journal of Applied Physics•Jul 1, 1982•1 citation
A semiclassical treatment of four-wave mixing is presented for the case for which a two-frequency pump wave of arbitrary intensity and a weak probe wave interact with a three-level system. Numerical, as well as analytical, results for the emission spectra are obtained from the steady-state response. At high pump power, the spectra are strongly modified by the ac Stark effect.
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.
Summary form only given. It is well-known that the steady-state four-wave mixing (FWM) spectrum, obtained when a two-level atomic system interacts with a coherent pump of arbitrary intensity and a weak probe, is symmetrical and consists of three peaks: a central peak and two Rabi sidebands. Previously, we showed for temporally nonoverlapping pulses, that the spectrum becomes extremely asymmetrical and that only the Rabi sideband near the resonance frequency survives, in the case where the probe precedes the pump. For the opposite case, where the pump precedes the probe, no FWM spectrum is obtained at all. It should be noted that these results hold true provided the pump and probe pulses are much shorter than the transverse relaxation time T/sub 2/ and the pump-probe time delay /spl Delta/t/sub 0/ (/spl Delta/t/sub 0/<0 when the probe precedes the pump). We have also shown that T/sub 2/ can be determined from the slope of the semilog plot of the FWM intensity, near the resonance sideband, versus the pump-probe time delay /spl Delta/t/sub 0/ (for the case /spl Delta/t/sub 0/<0).
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.
The interaction of a strong nearly resonant cw pump laser and a weak cw probe laser in a medium consisting of two-level atoms was studied by numerical integration of the Maxwell-Bloch equations. With propagation into the optically thick medium, the numerically calculated probe gain spectrum deviates substantially from one calculated by a four-wave-mixing formulation of coupled-wave theory with an undepleted pump. For probe frequencies inside the modified gain region, the laser field, initially in an unstable steady-state condition, evolves to a stable solution of the sine-Gordon equation.
We have presented a semiclassical analysis of four-wave mixing in a system of two-level atoms interacting with a single-mode self-consistent classical electromagnetic field in the presence of a weak probe field. The relevant response functions for the probe wave as well as for the field generated by the four-wave mixing have been calculated over a wide-range coupling constant for the self-consistent field and the atoms. The significant departures from the spectral characteristics associated with the usual four-wave mixing with an external strong pump field arise. The probe wave and the four-wave mixing spectra have been interpreted in terms of simple excitation transfer in the atom--self-consistent-field coupled oscillator model.