The focusing algorithm for the PLDM 2DES simulation requires an stochastic sampling of the "element" {n j , ñj }, based on the weight of the absolute magnitude of the μρ , and re-weight each trajectory based on the phase of μρ . This is done by using the important sampling procedure outlined in the previous work. The application of a laser at a given time on the system can be represented by the dipole operator acting on the system density matrix estimator. We can expand this as