Review of the characteristic effective medium approximation: Fundamentals and use in calculating the optical properties of ultrathin layer structures

This article presents a review of several aspects of the characteristic effective medium approximation that has been used to calculate the optical properties of ultrathin multilayer systems treated as one uniform layer with a single set of effective optical constants. The method, applied for normal incidence, enables one to represent any layer stack by one characteristic matrix whose elements are functions of the structure effective optical constants, stack thickness, and wavelength of the incident light wave. The error between values of the optical properties of a layer system calculated by the standard characteristic matrix technique and those calculated by the characteristic effective matrix approximation can be used as a criterion for establishing a limit beyond which the validity of the approximation could be compromised. As part of this grand review, calculations of the optical properties for normal incidence for numerous layer systems that were reported earlier in separate communications, are reviewed and analyzed.