Effective medium approximation for the effective optical constants of a bilayer and a multilayer structure based on the characteristic matrix technique

This article presents a derivation of the effective optical constants of a bilayer using the characteristic matrix technique. The derivation is simple, and in essence, adds an extra step to an approximate treatment of near-normal incidence spectroscopy, based on the characteristic matrix technique for stratified media. By this method, the effective optical constants of a bilayer consisting of two thin layers, each with a thickness much less than the wavelength of the incident radiation, are determined. This step leads to a modified procedure for calculating the optical properties of a layered stack that consists of thin bilayer units. The method, though still an effective medium approximation, is distinct from previous approximations. It introduces a more consistent parallelism to the fundamental theory of the characteristic matrix technique, and leads to a simplified analog of a multilayer viewed as one system of definite effective optical constants. Such a task has been difficult to achieve for structures with an arbitrary number of layers.