Wave propagation through cascading screens of finite thickness with periodic distribution of openings

We develop an analytical approach to study normal penetration of a scalar plane wave into an arbitrary number of parallel, equidistant screens of finite thickness; on each screen, there is a periodic distribution of rectangular openings. After reducing the problem to a system of integral equations and then to an algebraic linear system, suitable assumptions on the physical and geometrical parameters lead to explicit representations for the scattered wave field and the relevant parameters. Some figures are given to reflect the peculiar wave properties of the cascading structure under consideration.