State transition matrix of inhomogeneous planar layers

In this study, the computation and properties of the state transition matrix of inhomogeneous planar layered media are investigated. Furthermore, non-reciprocity of inhomogeneous planar layered media is shown using the transition matrix method. This theorem says that the plane wave transmission coefficients for a slab with inhomogeneity along the direction perpendicular to the interfaces are the same when the wave incidences on the slab from left or from right, but that the reflection coefficients usually differ. The validation of the results is studied finally through some typical examples.