GENERALIZATION OF COMPLEX SNELL-DESCARTES AND FRESNEL LAWS

Generalized Snell-Descartes and Fresnel laws are derived for harmonic inhomogeneous plane waves that are incident upon a static interface be tween two continuous absorbing dielectric media that are macroscopical ly characterized by their electric and magnetic permittivities and the ir conductivities. A coordinate-free formalism based on complex vector algebra is used to carry out all discussions. Surprisingly, the usual complex Snell-Descartes laws for reflection and refraction and Fresne l laws for polarization are recovered only in the special case in whic h the vector characterizing the direction of inhomogeneity is in the p lane of incidence. In the more general case a new deflection angle bet ween planes of incidence and refraction has to be introduced. An exper iment is proposed to test this prediction. A generalized form of the T E and TM modes (with respect to the interface), which are elliptically polarized and which are called parallel electric and parallel magneti c modes, also emerges.