Coherent and incoherent reflection and transmission of multilayer structures

The complex-amplitude reflection and transmission coefficientsr andt of a pile of films are represented as a product of matrices. The matrices describe the transformation of two plane waves travelling in opposite directions between the films, and their development within the films.If one of the films is significantly thicker than the other layers (e.g., several films on a substrate), the calculated reflectanceR=rr^* and transmittanceTt^* show narrow Fabry-Perot oscillations which, in a lot of cases, are not observed in the experiment. Since the matrix method is equivalent to the representation of the amplitudesr andt as a coherent superposition of multiple reflected waves within the thick slab, we are able to suppress, in the calculation, the interference within this thick film by adding the absolute squares of the partial waves corresponding to an incoherent treatment. This procedure is shorter and more simple than averaging over an appropriate interval of frequency or thickness, which, in most cases, leads to the same results.