Electromagnetic boundary conditions at deep nanoscale based on anisotropic interface

A transition interface model with gradient optical parameter is constructed for the anisotropic media interface in this paper. The electromagnetic boundary conditions suitable for deep nanoscale are derived from the integral form of Maxwell’s equations by introducing six interface response functions that capture the variations of electromagnetic field quantities in the transition region. The physical meaning of the interface response functions are clarified based on Maxwell’s equations and material constitutive relations; An equivalent anisotropic abrupt interface model corresponding to the transition interface model was proposed, where electric dipole moments and magnetic dipole moments are distributed on the interface, and then the electromagnetic boundary conditions in the form with the interfacial electric and magnetic dipole moment are obtained through derivation. The results indicate that the obtained electromagnetic boundary conditions, based on anisotropic interface model, degenerate into traditional ones when the interface response functions can be negligible. This work provides a theoretical foundation and physical insight for the study of the optical or electromagnetic properties of deep nanoscale anisotropic interfaces.