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IEEE Journal of Quantum Electronics

Effects of unequal pump intensity in resonantly enhanced degenerate four-wave mixing

Gilmore J. Dunning, Duncan G. Steel

Published Jan 1, 1982• 39 citations
Publisher

Abstract

Experiments performed in SF6using a CO2laser show the effect of unequal pump intensity in resonantly enhanced degenerate four-wave mixing (DFWM). A two-level saturable absorber model was extended to include the effects of unequal pump intensity and the results show significant departure from typical nonsaturating behavior. The experimental results and theory show qualitative agreement.

DOI
10.1109/jqe.1982.1071360

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Conference on Lasers and Electro-Optics•Jan 1, 1982•0 citations
Experiments performed in SF6using a CO2laser show the effect of unequal pump intensity in resonantly enhanced degenerate four-wave mixing (DFWM). A two-level saturable absorber model was extended to include the effects of unequal pump intensity and the results show significant departure from typical nonsaturating behavior. The experimental results and theory show qualitative agreement.
Detailed measurements have been made of degenerate four-wave mixing (DFWM) in a resonant homogeneously broadened gas. The measurements were performed in SF6{\mathrm{F}}_{6}F6​ using a pulsed CO2{\mathrm{O}}_{2}O2​ laser operated on the 10.4-\ensuremath{\mu} m branch. A pulse width of 1.2 nsec was used to reduce effects of collisional relaxation. Data are also presented for pulse widths of 140 nsec. At high-energy fluences (\ensuremath{\sim}0.1 J/cm2{\mathrm{cm}}^{2}cm2) pulse breakup is observed and is believed to arise from multiple-photon effects. The data obtained with the short pulse width are compared to a four-level saturable-absorber model where excellent agreement is obtained when pump absorption is included. The qualitative behavior of DFWM due to dispersion is also demonstrated in the wings of the SF6{\mathrm{F}}_{6}F6​ absorption spectrum. Peak reflectivities of 38% were readily obtained. In addition contributions due to a coherent three-level nonlinearity are presented showing a contribution equal to the measured saturable contribution.
The transient behavior of degenerate four-wave mixing (DFWM) in a three-level saturable absorber is analyzed and verified experimentally. A sharp peak of phase-conjugated reflectivity is predicted and observed at high pump intensities for pulsed beams. The influence of the time-dependent behavior of the conjugate wave signal on results of pulsed-beam experiments is studied. It is shown that transient effects could account for discrepancies between previous experimental results and steady-state theory.
The effects of finite laser bandwidth on resonant degenerate four-wave mixing (DFWM) are calculated with use of a model in which the intense, counterpropagating pump beams are characterized by a chaotic field, the probe beam is weak and monochromatic, and the medium consists of a gas of two-level atoms. We present a steady-state solution in the limit where the pump-laser bandwidth exceeds all other atomic relaxation rates. Although the mean intensity due to the fluctuating fields is spatially independent (no steady-state standing-wave pattern is established), the analytic results indicate that, for intensities above the saturation intensity Isat{I}_{\mathrm{sat}}Isat​, spatially periodic saturation effects are important. Increasing bandwidth is shown to lead to an increase in the effective saturation intensity resulting in lower phase-conjugate reflectivity for IIsat{I}_{\mathrm{sat}}Isat​ than for coherent pump fields, in contrast to the results for narrow-bandwidth chaotic fields. The resonant DFWM line shape is also calculated and compared to the coherent result. We comment on the application of the model to other four-wave-mixing processes employing broad-bandwidth lasers.
The steady-state theory of degenerate four-wave mixing (DFWM) with broad-bandwidth lasers is extended to treat the time dependence of the interaction allowing calculation of the intensity dependence and saturation behavior of DFWM with pulsed lasers. An experimental study of this intensity dependence as a function of laser bandwidth is reported, showing qualitative agreement with the theory. The line shape of DFWM induced by broad-bandwidth pump fields, probed by a monochromatic probe, is shown to have a Doppler-broadened profile in agreement with the theoretical predictions.
We present a revision of the theory of finite laser bandwidth effects on degenerate four-wave mixing (DFWM) of Alber, Cooper, and Ewart (ACE) [Phys. Rev. A 31, 2344 (1985)]. The same model is used for intense, broad-bandwidth pump lasers interacting with a weak monochromatic probe in a medium composed of two-level atoms. The density-matrix equations describing the time evolution of the atomic polarization coupled to fluctuating fields are solved using an appropriate decorrelation approximation. A steady-state analytical solution is found for resonant and near-resonant DFWM, for intensities that do not saturate the medium. For more intense fields it is found to be necessary to form a more complicated set of differential equations for all products of the field and atomic density-matrix elements. The results show that as in the ACE theory, increasing the bandwidth b leads to an increased effective saturation intensity. However, we find the DFWM reflectivity scales as 1/b2{b}^{2}b2 when the probe is monochromatic and not 1/b as in the ACE theory. Furthermore, the saturation behavior of nonresonant DFWM is found to differ from the predictions of ACE. Atomic motion effects are shown to yield a Doppler-broadened line shape and also to affect the saturation behavior of the signal.