A High-Order Symplectic FDTD Scheme for the Maxwell-Schrodinger System

In the finite-difference time-domain simulation of the Maxwell–Schrodinger system it is necessary to analyze multi-physics phenomena ruled by more than one governing equation. In this paper, a novel approach was proposed to solve the hybrid simulation. Using fourth-order spatial differences for the whole system and third-order symplectic integrators for the Schrodinger equation, the simulation was high-order-accurate and energy-conserving. This hybrid simulation is well suited to study the long-term light-matter interaction between electromagnetic radiation and charged particles in the semi-classical regime and can save computer resources with large time steps and coarse spatial grids.