Analysis of four wave mixing under the undepleted pump approximation

Germán J. de Valcárcel, Fernando Silva, A. Esteban-Martín +1 more

Abstract We theoretically consider photorefractive degenerate four-wave mixing oscillators and show that, for this particular system, the linear stability analysis technique leads to incorrect results. The reason for this astonishing failure lies in the unphysical predictions of the undepleted-pump approximation, which appear naturally during the linearization process of the full model. As a consequence, photorefractive four-wave mixing does not seem to permit a perturbative treatment that allows the derivation of mean-field models, and one is forced to use the full model in order to make sensible predictions.

Yanpeng Zhang, Zhiqiang Nie, Min Xiao

Ying Wu, Xiaoxue Yang, C. P. Sun +2 more

Starting from the Gross-Pitaevskii nonlinear Schr\"odinger equation, we derive a set of nonlinear coupled equations describing four-wave mixing with matter waves and solve them analytically without utilizing the undepleted pump approximation.

W. J. Firth

Chun-Ching Shih

An analytical solution of the short-pulse four-wave mixing phenomenon is obtained in the undepleted-pump approximation for an instantaneously responding Kerr medium.

Z. A. Tagiev, Rena J. Kasumova, R. A. Salmanova