Generalized laws of Snell, Fresnel and energy balance for a charged planar interface between lossy media

Abstract

The generalized laws of Snell, Fresnel and energy balance are derived for the harmonic inhomogeneous plane waves (HIPW) that are incident upon a charged plane interface between two absorbing media. Excess surface charges impact the Fresnel coefficients by the surface conductivity which is the ratio of the surface current to the tangential component of the electric field. The surface current introduces an extra term of Joule heat loss in the generalized energy balance besides the usual terms of reflection, transmission and interference. The reflection and transmission coefficients are calculated by the equations we derived, and the validity of the results is verified by comparison with those calculated by the finite-difference time-domain method. In addition, we identify a charge-induced increase of (pseudo) Brewster angle for the harmonic homogeneous plane waves (HHPW), a significant influence of the incident angles for amplitude propagation vector on optical properties for HIPW, and a strong increase of Joule heat loss due to the interaction between the incident HIPW and the surface charges.