A new modeling formalism to compute the time-dependent behavior of combined electromagnetic (EM) and quantum mechanical (QM) systems is proposed. The method is geared towards highly multiscale geometries, which is vital for the future design of nanoelectronic devices. The advocated multiphysics modeling formalism leverages the alternating-direction hybrid implicit-explicit (ADHIE) finite-difference time-domain (FDTD) method for the EM fields and is combined with a novel ADHIE method for the EM potentials. Additionally, we tackle the QM problem using a new split real and imaginary part formulation that includes higher-order spatial differences and arbitrary time-dependent EM potentials. The validity of the proposed formalism is theoretically discussed by deriving its stability condition and calculating the numerical dispersion relation. Furthermore, the applicability of our modeling approach is proven through several numerical experiments, including a single-particle Maxwell-Schrödinger (MS) system as well as a many-particle Maxwell-Kohn-Sham (MKS) system within the time-dependent density-functional theory (TDDFT) framework. These experiments confirm that the novel ADHIE method drastically decreases the computation time while retaining the accuracy, leading to efficient and accurate simulations of light-matter interactions in multiscale nanoelectronic devices.
A new modeling formalism to compute the time-dependent behavior of combined electromagnetic (EM) and quantum mechanical (QM) systems is proposed. The method is geared towards