Numerical Simulations of Laser Pulse Propagation in Quantum Active Media: Using a semiclassical model

Active media are materials that consist of quantum systems, such as atoms, impurities, or quantum dots, and are characterized by strong resonant absorption and re-emission of radiation. In this article, we present a general framework for the numerical simulation and analysis of time-dependent radiation-induced phenomena in active media. The formulation used is based on the solution of semiclassical Maxwell–Bloch equations describing the evolution of each quantum element under the effect of external and re-emitted radiation. Within these Maxwell–Bloch equations, the coupling of quantum systems to classical Maxwellian fields poses computational challenges due to the strong nonlinearities involved. In contrast to traditional mesh-based solvers, we adopt an electric field integral-operator approach that can reliably account for near-field effects—including self-radiation—and is scalable to large systems. We then focus on media based on large numbers of quantum dots and demonstrate various physical effects arising from the near-field coupling, including polarization modulations and superradiance.