A general analysis of the propagation of electromagnetic waves through a stratified medium, applicable to the entire class of problems of plane multilayer systems, is developed. The medium is assumed to be divided into m plane-parallel layers, the first and mth of which are semi-infinite. The electromagnetic properties of the m layers are unrestricted and dissimilar, and the thicknesses of the (m-2) finite layers are also different in general. A steady-state monochromatic wave, generated in the mth layer, is assumed to be incident at any angle upon the (m-1) th layer. Formulas for the resulting reflection and transmission are derived. The methods which are employed in the paper facilitate application of these formulas, with a minimum of algebraic complications, to specific problems.
BERNARD SALZBERG, "Propagation of Electromagnetic Waves through a Stratified Medium. I," J. Opt. Soc. Am. 40, 465-470 (1950)