Reflection of waves by imperfectly periodic layered media

In order to facilitate the numerical evaluation of the grating effects of imperfectly periodic layered media, we introduce the extended local wave number concept, and we describe how the reflected wave is determined from the spatial behavior of the extended local wave number. A numerical method based on this concept is presented, which proves to be useful for structures with more than ten layers with the nonuniform period. Numerical comparisons with the invariant imbedding approach show the validity and utility of the method. Two specific structures are analyzed using this method.