Diagrammatic analysis of third order nonlinear optical processes

We apply a diagrammatic density matrix perturbation technique to analyze third order nonlinear optical processes. The diagrammatic approach is shown to yield a significant simplification in the computation of both steady state and transient response while including the effects of damping and linewidth. The topology of the diagrams is stressed in identifying and interpreting their associated perturbation terms as well as predicting frequency resonance and transient behavior. We demonstrate the practical utility of the technique by presenting a detailed analysis and discussion of the processes of stimulated Raman scattering, hot luminescence, and pressure induced resonances in four wave mixing.