  Classical electromagnetic boundary conditions (EMBCs) fail to describe
quantum interface phenomena at nanoscale. Here, we construct the interface
model with a transition layer describing the electromagnetic field
inhomogeneity across the interface. Generalized nanoscale EMBCs are derived by
introducing the magnetic interfacial response functions (IRFs) and are
rewritten as three different forms based on Maxwell's equations in first order
approximation. The corresponding Fresnel formula are further used to analyze
the interfacial photonic phenomenon, demonstrating interesting behaviors of
Brewster angle shifting, non-extinction at Brewster angle and distinctive
non-classical absorption or gain effect at Brewster angle and the total
internal reflection angles. IRFs-controlled GH-shifts of Gaussian beam near
Brewster angle are generated by the non-classical interface. These unique
phenomena give us some guidance to measure the IRFs and expand interface
photonics in nanoscale.
