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Europhysics Letters (EPL)

Optical Stark Splitting in Doppler-Broadened, Nondegenerate Multiwave Mixing

J. W. R. Tabosa, S. Le Boiteux, Pierre Simoneau, Daniel Bloch, M. Ducloy

Published Aug 15, 1987• 8 citations
Publisher

Abstract

We report on the first observation of optical Stark splitting in noncollinear, nondegenerate multiwave mixing, in Doppler-broadened gas media. We demonstrate this optical line splitting to be the dominant wave mixing process at large e.m. field intensities. Polarization characteristics of this type of high-order mixing processes are investigated, and applications to methods of optical phase conjugation with frequency up-conversion are outlined.

DOI
10.1209/0295-5075/4/4/009

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We report on the first observation of optical Stark splitting in noncollinear, nondegenerate multiwave mixing, in Doppler-broadened gas media. We demonstrate this optical line splitting to be the dominant wave mixing process at large e.m. field intensities. Polarization characteristics of this type of high-order mixing processes are investigated, and applications to methods of optical phase conjugation with frequency up-conversion are outlined.
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Our semiclassical theory of two-photon multiwave mixing1 is a generalization of the degenerate four-wave mixing case2 to treat nondegenerate pump/signal/conjugate frequencies. We apply that theory to four-wave mixing in two-photon media. We present explicit formulas for the nondegenerate signal/conjugate absorption and coupling coefficients for cases for which the two-photon Stark shifts are sufficiently small compared to the homogeneous linewidths. More general cases require that the spatial hole burning averages be performed numerically. We find intricate dependencies of the transmission and reflection spectra on the pump intensity and on dynamic Stark shifts. In particular, the reflection coefficients do not necessarily bleach to zero as the pump intensity is increased indefinitely, and interferences occur between pure index and mixed absorption/index contributions
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.
In nonlinear atomic gaseous media the interference between independent macroscopic polarizations of different ensembles within the atomic velocity distribution can lead to anomalous behavior of the multiwave mixing spectra. For phase-conjugate six-wave mixing (SWM) in a Doppler-broadened N-type four-level system, it is found that the SWM spectrum can be either Doppler-free or very broad, depending on the directions of the incident beams and the ratios between the magnitudes of the wave vectors. This polarization interference can be controlled by the strong coupling field which, on the other hand, can induce Autler-Townes (AT) splitting when the SWM spectrum is Doppler-free. This technique may find special applications as an improved form of AT spectroscopy with higher resolution.