Light propagation in dielectric materials

Abstract: We present a pedagogic derivation of the electromagnetic field established in a dielectric material by an impinging external field. We consider the problem from the point of view of the physical mechanism involved at the microscopic level. The internal field emerges when the material is thought of as an assembly of atoms in vacuum, each of them being polarized by the external incident field and by the re-radiated fields of all the other polarized atoms of the material. In this way, each atom becomes itself a source of secondary radiation that adds and interferes with all the other internal fields (including the internal extension of the externally impinging field), contributing to build up the total internal field within the dielectric material as well as the externally scattered field. This picture naturally leads to a connection between the microscopic properties of the material and its index of refraction, that describes the dielectric response to the applied electromagnetic field. Calculations also show that the incident radiation is extinguished inside the dielectric by an equal but opposite field generated by the total induced polarization currents, and is substituted by a macroscopic electric field which propagates with the new speed c/n.