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Physical Review Letters

Suppression of Amplified Spontaneous Emission by the Four-Wave Mixing Process

Michelle S. Malcuit, Daniel J. Gauthier, Robert W. Boyd

Published Sep 2, 1985• 108 citations
Publisher

Abstract

Two-photon-resonant excitation of the sodium $3d$ level can lead to the generation of new frequencies either by amplified spontaneous emission at the $3d\ensuremath{\rightarrow}3p$ transition frequency or by a resonantly enhanced four-wave mixing process. Competition between these two processes has been observed. The four-wave mixing process can suppress amplified spontaneous emission by preventing the excitation of the $3d$ level due to an interference between two different pathways connecting the ground ($3s$) and $3d$ states.

DOI
10.1103/physrevlett.55.1086

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Two-photon-resonant excitation of the sodium 3d3d3d level can lead to the generation of new frequencies either by amplified spontaneous emission at the 3d\ensuremath→3p3d\ensuremath{\rightarrow}3p3d\ensuremath→3p transition frequency or by a resonantly enhanced four-wave mixing process. Competition between these two processes has been observed. The four-wave mixing process can suppress amplified spontaneous emission by preventing the excitation of the 3d3d3d level due to an interference between two different pathways connecting the ground (3s3s3s) and 3d3d3d states.
Competition between amplified spontaneous emission (ASE) and the four-wave-mixing (FWM) process has been observed under conditions of two-photon resonant excitation of the sodium 3d level. The nature of the competition is that the FWM process is able to prevent the occurrence of ASE, even though the gain of the ASE process calculated in the absence of competition effects is much larger than that of FWM. The ASE is suppressed because the fields generated by the FWM process create a new excitation pathway connecting the ground and 3d levels, and under quite general conditions this pathway interferes destructively with that due solely to the applied laser field. These effects are modeled theoretically by solving perturbatively the density-matrix equations of the atomic system, thereby determining the population in the upper level and the nonlinear polarization of the medium. The coupling between the various optical fields due to the nonlinear polarization is described by coupled amplitude equations. The solution to these equations predicts that when the wave-vector mismatch is not too large the fields evolve spatially to reach steady-state values, and that the population excited to the 3d level by the total steady-state optical field is much smaller than that due to the incident laser field alone. We have observed experimentally the suppression of ASE by FWM and have observed that this suppression does not occur when the medium is excited with counterpropagating beams that cannot efficiently excite the FWM process. In addition, we have conducted a series of experiments that shows that the degree of suppression of ASE depends on the intensity and focusing characteristics of the incident laser as expected on the basis of our theoretical model.
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The interference between two different quantum-mechanical pathways for four-wave mixing in sodium vapor has been observed. The four-wave mixing was enhanced by two-photon resonance with the 5s state, for one pathway, and the 4d state, for the other. The phase of the interference could be varied continuously by varying laser frequencies, and constructive and destructive interference effects were studied. A model based on third-order perturbation theory gives a good description of the features observed.