Admittance of rugate filters derived from a 2 × 2 inhomogeneous matrix.

Admittance diagrams are used to analyze qualitatively and quantitatively the behavior of inhomogeneous thin films with an arbitrary refractive-index function. From this study it follows that one can treat the behavior of rugate filters by using the concept of effective refractive indices, which are associated with the phase integral in a simple way. These results are applied to the study of periodic systems, and, as expected, one can consider high and low effective refractive indices to determine the important parameters of these stop bands. With these ideas it is possible that one can deal with rugate filters more closely as homogeneous periodic systems by taking advantage of the existing theory.