Diagrammatic density matrix theory of transient four-wave mixing and the measurement of transient phenomena

A diagrammatic density matrix perturbation technique is applied to describe transient third-order nonlinear optical processes and their applications to the measurement of transient phenomena. Using this approach, pump probe, parametric scattering, and three-pulse scattering are analyzed in a computationally simple and unified manner. The density matrix allows the description of a wide variety of dynamical processes including population and dephasing relaxation as well as orientational randomization and spatial diffusion. In addition, the diagrams provide a physical interpretation for the density matrix terms that they represent, and the effect of varying experimental parameters for the measurement of transient behavior can often be determined directly from the diagrams. Finally, topological similarities between diagrams provide a unified description of several different transient four-wave mixing measurement techniques.