The transformation S = jω, ω = —cotφ of the interference phase angle φ = 2πnhλ-1 is applied to the matrix of a thin dielectric film. This brings the complex coefficients of reflection and transmission to the form of rational functions, whose coefficients are built up from the refractive indices. Matching to a given spectral characteristic may be performed by any of the approximation methods of network theory. An algorithm is derived for the computation of the refractive indices from the coefficients of these rational functions. Connection with other synthetic methods for thin films is also indicated. Illustrative examples are included.
Zdenoěk Knittl, "A Rational Function Approach to Multilayer Synthesis," Appl. Opt. 6, 331-340 (1967)