Nanoscale electromagnetic boundary conditions based on Maxwell’s equations

Abstract

The electromagnetic boundary conditions have great important applications in many physical branchs. Here, the nanoscale electromagnetic boundary conditions are derived by using the integral Maxwell’s equations through constructing the dielectric transition layer across the interface between the two materials. The two interface response functions are obtained to reflect the electromagnetic field response characteristics of the interface. Based on the Maxwell’s equations, the physical meanings of the interface response functions are given as the position of the equivalent interfacial polarization charge and the gradient position of interfacial polarization current density, respectively. The influence of the dielectric constant of the medium, the transition line shape of the electric field and the frequency on the interface response functions are analyzed. When the material scale is large, the interface response function can be ignored, and the nanoscale electromagnetic boundary conditions degenerate to the classical boundary conditions given by the abrupt junction. On this basis, the interface electric dipole moment, the equivalent interfacial polarization charge area density, the equivalent interfacial polarization current density and the equivalent interfacial magnetic current density are introduced, leading to three forms of nanoscale electromagnetic boundary conditions. The results provide a clear physical picture and necessary theoretical basis for nanoscale electromagnetism and interface optics.