Transient four-wave mixing and coherent transient optical phenomena

The general formalism of transient four-wave mixing is developed using the diagrammatic technique of Yee and Gustafson, and applied systematically to two-, three-, and four-level systems. The results predict all possible photon-echo phenomena including free-induction decay in the low-intensity limit. Connections to transient saturation spectroscopy and other coherent transient effects can also be made. The treatment can be readily extended to the more general problem of coherent transient optical effects with n waves.