Mode Analysis and Mode Coupling of Electromagnetic Fields in Spatially Dispersive Media

Abstract

The electrodynamics of a spatially dispersive medium filling the whole space has been the subject of many investigations. Pekar[1] in 1957 predicted many remarkable properties associated with such a medium. He showed that in a spatially dispersive medium the macroscopic polarization is connected to the electric field by a certain differential equation in spatial coordinates. Maxwell’s equations along with this new differential constitutive relation showed clearly the possibility of several waves being propagated in the medium with the same polarization and frequency but with different velocities. In such media, longitudinal waves with nonzero group velocity may also be generated. These and other interesting properties of spatial dispersion attracted a good deal of attention from both theoretical and experimental physicists. The works of Agranovich, Ginzburg[2], Pekar[1], Hopfield and Thomas[3] and others, show the connection of the theory of excitons with the theory of spatial dispersion. However the electrodynamics for bounded spatially dispersive media has been only poorly understood. The need for additional boundary conditions (a.b.c’s) to take account of the appearance of new waves in the medium resulted in a different set of a.b.c.’s, depending on various models employed.

Research supported by the U.S. Army Research Office (Durham).