Time propagation method for the coupled Maxwell and Schrodinger equations on the same atomistic

We implement a semi-classical, hybrid simulation to investigate the interaction of electromagnetic fields and matter on the atomic scale using Density Functional Theory (DFT) calculations coupled to Maxwell’s equations. We present two approaches to simulate the time propagation of the Maxwell equations on the atomic scale, using a simplified quantum mechanical system, jellium, as the target for the incident electromagnetic pulse. The first approach implements finite difference time domain, which employs finite differences as approximations to both spatial and temporal derivatives that appear in Maxwell’s equations. However, FDTD is shown to be numerically unstable, so a new method must be implemented. The second approach implements the Riemann-Silberstein vector, a complex vector composed of the electric and magnetic fields, to propagate Maxwell’s equations. Using the Riemann-Silberstein formalism, we can track both the Maxwell and Schrodinger equations on the same atomistic scale and observe induced excitations in jellium. The next step is to use real atoms and nanostructures in place of jellium as the target of the electromagnetic pulse.