THE REFLECTION OF WAVES IN A GENERALIZED EPSTEIN PROFILE

Abstract

Epstein (1930) and Rawer (1939) studied the reflection of waves in a stratified medium by transforming the hypergeometric equation into the wave equation. A particular case of the Epstein profile is a symmetrical layer. Considerable attention has been given in the literature to this case as well as to symmetrical layers with certain other profiles of the refractive index. In the present paper a generalized Epstein profile is considered and the reflection and transmission coefficients are obtained. The special case in which the refractive index tends to the same constant value on either side of a layer is then discussed. The symmetrical Epstein profile is a special case of this layer which, in general, is asymmetrical. Particular attention is given to a layer differing only slightly from the symmetrical Epstein layer, a simple approximate formula for the reflection coefficient being derived.