Group Velocity and Energy Velocity In Lossless,Isotropic and Homogeneous Dielectric Slab Guide

Abstract

When a uniform E.M. Plane wave travels in a dense perfect dieletric incident on the boundary of a less dense perfect dielectric, total reflection will occur, if the incident angle is greater than the critical angle. If both dielectrics are lossless, isotropic, and homogeneous, then the reflected plane wave in the denser medium will still be uniform and the transmitted wave in the less dense material will be nonuniform. Let us consider a slab guide immersed in air. The geometry of the slab is assumed to be infinitely wide, but with finite thickness. The dielectric in the slab is lossless, isotropic, and homogeneous where its permittivity is larger than that in air and its permeability is not less than that in air. Thus the uniform plane waves propagating in the slab possess the property of total reflection as stated in the preceeding paragraph. The investigations of dielectric slab guide have been largely based on the graphical method while in this paper, the analytic method is adopted. The field distribution is describedfirst, and then the phase, group and energy velocity are derived, finally the relationship among them is established.