Universal Vector–Scalar Potential Framework for Inhomogeneous Electromagnetic System and Its Application in Semiclassical Quantum Electromagnetics

In this work, numerical solution to a general electromagnetic (EM) system is studied using a formalism based on the formulas for the E–B–A–
$\phi $
formulas with different gauge conditions. The finite-difference time-domain (FDTD) method is employed to discretize these formulas. In addition, the convolutional perfectly matched layer (CPML) technique is successfully applied to absorb outgoing scattered waves described by the proposed formulas. The gauge invariance of EM fields in inhomogeneous environment is demonstrated by numerical examples. Moreover, the proposed EM framework integrated with the Schrödinger equation is introduced to investigate the mesoscopic phenomenon for light–matter interaction, which is useful to design laser pulses for controlling discrete quantum states. The work offers a simple and general numerical EM framework, which is essential to bridge the classical EM and quantum mechanical systems.