Finite-Difference Time-Domain Simulation of the Maxwell–Schrödinger System

A thorough studyon the finite-difference time-domain (FDTD) simulation of the Maxwell-Schrödinger system in the semiclassical regime is given. For the Maxwell part which is treated classically, this novel approach directly using the vector and scalar potentials (A and Φ) is taken. This approach is stable in the long-wavelength regime and removes the need to extract the potentials at every time step. The perfectly matched layer important for FDTD simulations is developed for this new approach. For the Schrodinger and quantum mechanical part, minimal coupling is applied to couple the charges to the electromagnetic potentials. FDTD stability is analyzed for the whole system and simulation results agree with the properties of quantum coherent states.