Electromagnetic reflection, transmission and energy density at boundaries of nonlocal media

Abstract

We consider a semi-infinite spatially dispersive dielectric with unequal transverse and longitudinal susceptibilities. The effect of the boundary is characterized by arbitrary reflection coefficients for polarization waves in the material that propagate to the surface. Specific values of these coefficients correspond to various additional boundary conditions (ABC) for Maxwell's equations. We derive the electromagnetic reflection and transmission coefficients at the boundary and investigate their dependence on material parameters and ABC. We also investigate the electromagnetic zero-point and thermal spectral energy density outside the dielectric. The nonlocal response removes the boundary divergence of the spectral energy density that is present in a local model. The spectral energy density shows a large dependence on the difference between the transverse and longitudinal susceptibilities, even at distances up to 10nm from the boundary.