Analysis of dense quantum dot systems using a self-consistent maxwell-bloch framework

Quantum dot systems have shown numerous applications in random lasing and light localization phenomena. Conventional simulations of radiation in quantum dot systems rely heavily on a differential formulation of Maxwell's equations to compute dynamics. Unfortunately, the computational costs incurred by the underlying differencing mechanism inherent in such models renders them infeasible for simulations in three dimensions. We propose an integral-equation framework to self-consistently describe the dynamics of a disordered system of quantum dots driven by an incident laser pulse. By adopting an integral formulation of Maxwell's equations, we remove the “radiation grid” in favor of highly optimized point-to-point communication of fields through integral equations. By adopting a semiclassical approximation of the quantum dot system, we partition the computational problem into two distinct parts: (1) determination of source polarizations through evolution of the optical Bloch equations, and (2) evaluation of radiation patterns with electric field integral equation techniques. The solution of each part proceeds explicitly in time, facilitating a complete description of both quantum dots and electromagnetic fields at each timestep, giving rise to phenomena such as localization, photon echo effects, and nonlinear response patterns.