The Fresnel equations for lossy dielectrics and conservation of energy

摘要

The well-known relation for energy conservation at the boundary of two dielectrics R + T = 1 does not hold in the case of lossy systems, if for R and T the conventional relations are used. It has to be corrected to R + T = 1 + Δ. The additional term is derived for the s- and p-components from Maxwell’s equations by proper use of the Poynting vectors. Δ depends on the angle of incidence, the complex refractive indices and the polarization. The correct transmission factor for lossy transitions reads T = T - Δ. The correction term is very small for dielectrics used in thin film technology, but becomes important for metallic layers.