Self-interaction-free approaches for self-consistent solution of the Maxwell-Liouville equations

We propose two complementary approaches for solution of the coupled Maxwell-Liouville equations within the finite-difference time domain (FDTD) framework. The two methods are specifically designed to eliminate self-interaction, which often appears spuriously in simulation of the coupled Maxwell-Liouville equations, and hence can be used for modeling of single as well as ensembles of quantum emitters (such as molecules or quantum dots) in an arbitrary dielectric environment. One approach borrows from the familiar total field-scattered field technique that has been applied in the past in a different context. The second recognizes an opportunity to average over the electric field at a set of specifically chosen points around the quantum emitter. The methods introduced are applied to two problems of growing current interest that also present useful test cases. One is the modeling of spontaneous emission, where comparison with an analytical solution illustrates the accuracy and efficiency of the methodology. The second is quantum-emitter-induced transparency in a resonator formed by two gold ellipsoids, where Fano interferences suggest interesting potential applications.