Including Quantum Effects in Electromagnetic System--An FDTD Solution to Maxwell-Schrödinger Equations

In this paper a novel approach to include quantum effects, described by Schrodinger equation in tempo and spatial domains, into electromagnetic system analysis, which uses an extended finite-difference time-domain (FDTD) technique to solve the Maxwell´s equations. An iterative numerical scheme that marches in time provides a complete solution that describes the interactions between electromagnetic field and electron movement under quantum effects. An example is given to include electron tunneling current through a potential barrier and the good agreement between the extended FDTD method and the analytical solution proves its accuracy. This technique is expected to become an important tool analyzing nanoscale circuit.