Abstract

A diagrammatic density matrix technique is developed and applied to study nonlinear optical processes involving responses from weak probe fields interacting with a system under strong excitation. These diagrams consist of lowest-order double-Feynman diagrams which represent the density matrix perturbation terms describing the system response to the weak probe fields^1,2 combined with dressed propagators which represent the density matrix elements of the system under strong excitation. The dressed propagators are described by a set of linear equations which, in most cases, may be derived in inspection. The methodology is similar to the bare-atom approach.² The advantages of using this diagrammatic technique are that (1) it allows one to select and express analytically the dominant and appropriate density matrix elements (diagrams and dressed propagators); (2) analytical expressions may be constructed directly from the diagrams and thus lengthy calculations needed to obtain closed-form solutions are greatly reduced; (3) it provides a physical interpretation for the density matrix solutions and nonlinear optical processes; and (4) it may be generalized to more complicated, multilevel systems. We demonstrate the application of this technique to describe gain saturation, Stark splitting, and Raman scattering.

© 1985 Optical Society of America