Influence of coating thickness on the performance of a Fabry-Perot interferometer

The effects of the coating thickness on the physical performance of a Fabry-erot interferometer (FP) are investigated. The FP is modeled as three media separated by two thin films and not merely by two interfaces. We show that the transmitted intensity obeys an Airy function, but not the reflected intensity because of the appearance of a complex factor accounting for the coupling between the reflected waves in the coatings. The Stokes relations are generalized for this model. We study the dependence of the phase lag of reflection in the coatings on the angle of incidence, which causes a shift in the position of the intensity maxima. We discuss as well the properties of the FP with an absorbing medium in the cavity, defining a merit function that optimizes the compromise between peak transmission and finesse.