Dual-Potential Finite-Difference Technique for Computational Electrodynamics

We present a finite-difference time-domain (FDTD) technique suitable for coupling with quantum-transport solvers. We derive first-order equations for the electric and magnetic vector potentials and the electric scalar potential which, upon the adoption of the Coulomb gauge, decouple into solenoidal and irrotational equation sets and are sourced by the solenoidal and irrotational parts of the current density, respectively. The solenoidal electric and magnetic vector potentials obey equations analogous to the normal curl equations for the electric and magnetic fields, a fact we exploit to develop an effective absorbing boundary layer used to simulate unbounded regions in a way identical to standard FDTD. We demonstrate coupling to a simple quantum transport technique known as the Usuki transfer matrix technique.