Reflectivity
of a Multi-layer
System

Using the single transfer matrix defined in the previous section we can consolidate a number transfer matrices into a single matrix M for any number of layers by simply defining a transfer matrix for each layer and calculating the product.

To obtain the reflectivity of the combination of layers,

where

since b/a represents the ratio of incident light to the amount reflected back. The power reflectivity is given by:

It is a simple task to program a computer to use this method to calculate the reflectivity against wavelength for a layered structure, but if you would like a very friendly version then Wah has written a GUI controlled program which runs in Matlab. Check it out here