The equations of propagation of electromagnetic waves in a stratified medium (i.e. a medium in which the refractive index is a function of one Cartesian coordinate only—in practice the height) are obtained first from Maxwell's equations for a material medium, and secondly from the treatment of the refracted wave as the sum of the incident wave and the wavelets scattered by the particles of the medium. The equations for the propagation in the presence of an external magnetic field are also derived by a simple extension of the second method.The significance of a reflection coefficient for a layer of stratified medium is discussed and a general formula for the reflection coefficient is found in terms of any two independent solutions of the equations of propagation in a given stratified medium.Three special cases are worked out, for waves with the electric field in the plane of incidence, viz.(1) A finite, sharply bounded, medium which is “totally reflecting” at the given angle of incidence.(2) Two media of different refractive index with a transition layer in which μ2 varies linearly from the value in one to the value in the other.(3) A layer in which μ2 is a minimum at a certain height and increases linearly to 1 above and below, at the same rate.For cases (2) and (3) curves are drawn showing the variation of reflection coefficient with thickness of the stratified layer.Case (3) may be of some importance as a first approximation to the conditions in the Heaviside layer.
Electromagnetic Waves in a Time Periodic Medium With Step-Varying Refractive Index
