Title  Explicit formulas for the reflection and transmission coefficients of onecomponent waves through a stack of an arbitrary number of layers 
Publication Type  Journal Article 
Year of Publication  2015 
Authors  Vinh, PChi, Tuan, TThanh, Capistran, MA 
Journal  Wave Motion 
Volume  54 
Pagination  134144 
Abstract  The transmission and reflection of onecomponent elastic, acoustic, optical waves on a stack of arbitrary number of different homogeneous layers have been intensively studied in the literature. However, all obtained formulas for the reflection and transmission coefficients are in implicit form. In this paper, we provide the explicit formulas for them. From these formulas we immediately arrive at the explicit formulas for the reflection and transmission coefficients of onecomponent waves through an FGM layer. Based on the obtained exact formulas, approximate formulas for the reflection and transmission coefficients are established for a stack of thin layers and for a thin FGM layer. It is numerically shown that they are good approximations. Since the obtained formulas are totally explicit, they are useful in evaluating, not only numerically but also analytically, the transmission and reflection coefficients of onecomponent waves.
