Computational Toolbox for Modeling Nonlinear Optical Coherence Phenomena

We present a simple and versatile computational approach for simulating ultrafast nonlinear optical processes in coupled systems. This approach is based on the numerical time propagation of the density-matrix equations of motion describing interacting optical two-level systems. This method bridges the gap between the high-speed dynamics of decay modes and oscillation frequencies and the low-speed modulation of heterodyned optical mixing. Through the use of a pulse train, modes of interest such as four-wave or three-wave mixing signals can be selected and isolated, allowing for the robust simulation of realistic practical systems such as coupled excitons and plasmons. Applications of this process are then discussed and compared with existing low order models traditionally used to describe nonlinear optical processes.