A theoretical examination of the optical properties of layered structures is performed by means of signal flow graphs. Analytical expressions for reflectivity, transmissivity, reflectance, and transmittance are obtained for one-, two-, and three-layer media by using Mason's rule. We also derive alternative formulations of the bilinear transformed reflectance expressed as functions of the Fresnel reflectivity coefficients between the interfaces of the various layers. Under the assumption of lossless materials and normal incidence, these formulas are expressed as functions of refractive indices. These expressions are coincident with those obtained in the past when using the matrix technique. The study of transmittance for layered structures proves, however, that information about thickness and refractive index steps between layers is also available by applying similar digital signal processing techniques to the inverse transmittance.
Gustavo E. Aizenberg,
Pieter L. Swart,
Beatrys M. Lacquet,
"Flow graph analysis of spectral properties of multilayered media," Optical Engineering 33(9), (1 September 1994). https://doi.org/10.1117/12.175694