On the Group Velocity, Wave Path and their Relations to the Poynting Vector of the Electromagnetic Field in an Absorbing Medium

Abstract

The physical meanings of concepts such as group velocity and wave path, are first carefuly examined and mathematically founded, and it is then investigated whether the significant concepts of group velocity and wave path do exist or not, when the Maxwell field energy is lost in a medium. It is concluded that, in a rigorous sense, they generally do not exist in absorbing non-uniform medium, and that, when the energy loss in a medium is sufficiently small that only the first order changes in group velocity and wave path due to the energy loss are required to be taken into account, they approximately exist and are concordant with the ones obtained when the field energy is not lost in that medium, so that it is anyhow meaningless to discuss their changes due to the energy loss in a medium.