Reflected and refracted electromagnetic fields in a semi-infinite body

We compute the reflected and refracted electromagnetic fields for an ideal semi-infinite body (either a plasma or a dielectric), as well as the reflection coefficient, by using a general approach based on the polarization equation of motion and electromagnetic potentials. The method consists of representing the charge disturbances by a displacement field in the positions of the moving charges. The propagation of an electromagnetic wave in matter is treated by means of the retarded electromagnetic potentials, and the resulting integral equations are solved. Generalized Fresnel's relations are thereby obtained for any incidence angle and polarization and the angles of total polarization and total reflection are derived (the latter for the plasma). Bulk and surface plasmon-polariton modes are also identified for the plasma. As it is well known, the field inside the plasma is either damped (evanescent) or propagating (transparency regime), and the reflection coefficient exhibits an abrupt enhancement on passing from the propagating regime to the damped one (total reflection).