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Journal of Crystal Growth

Intensity dependence of signals obtained in four-wave-mixing geometry: influence of higher-order contributions

Björn Haase, U. Neukirch, J. Meinertz, J. Gutowski, V. M. Axt, Georg Bartels, A Stahl, J. Nürnberger, Wolfgang Faschinger

Published Jun 1, 2000• 9 citations
Publisher
DOI
10.1016/s0022-0248(00)00207-4

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An analytical expression for the degenerate four-wave mixing signal produced in a medium composed of two-level atoms by pump and probe lasers of arbitrary intensities and parallel linear polarization, suffering negligible absorption and depletion, has been derived. The Abrams–Lind approach [Opt. Lett.2, 94 and 3, 205 (1978)] for deriving the phase-matched polarization has been extended to find all the other higher-order polarization terms contributing to the signal. The signal field amplitude is expressed as an infinite series whose convergence rate depends on the intensity of the input fields and their detuning from resonance. The solution is successfully verified by comparison with a full numerical nonperturbative calculation and is found to be equivalent to the Abrams–Lind result in the limit of weak probe intensity. The result is used to calculate the saturation effects on spectral line shape that are relevant to simulation of molecular spectra obtained by degenerate four-wave mixing with saturating pump and probe fields. The result is extended to treat atomic motion in the case of forward geometry of the input beams.
Four-wave-mixing signals from excitons under linear-circular polarized excitation exhibit an elliptical polarization, depending on both the pulse delay and the spectral position. Besides the resonances corresponding to excitons and exciton-biexciton transitions, a breakup of the exciton line is found reflecting the influence of correlations on the four-point level. An analysis accounting for the exciton density, the bound biexciton, and the exciton-exciton scattering continuum reveals that these features are not due to an antibound two-exciton state. Instead, they result from an interference of the correlated exciton continuum with the exciton density. In addition, the modeling shows that the signals ellipticity is highly sensitive to the influences of different correlations and, therefore, allows for a discrimination of their contributions.
We present a theoretical analysis of the spatial shape of two symmetric signals of degenerate four-wave mixing induced by Gaussian beams in a thin sample of two-level atoms. Our calculations take into account the full spatial and spectral dependences of the relevant nonlinear susceptibilities that govern the two processes. This reveals two interesting effects. The first one is that the total power of incident beams affects the transverse profile of the four-wave-mixing signals at the medium exit and their free propagation. The second one is the influence of the spectral characteristics of the medium on the longitudinal profile of both generated signals upon free propagation. We argue that the first effect can be seen as the saturation of the medium in regions of higher intensity, while the second can be understood as the result of a nonlinear contribution to the refractive index inside the atomic medium. These effects can be symmetric between the two signals, with asymmetries induced by different detunings from the resonance of the incident fields.