On the three-dimensional wave propagation through cascading screens having a periodic system of arbitrary openings

In a genuine three-dimensional context, an analytical approach to study the propagation of scalar waves through an arbitrary number of parallel screens is developed. Each screen contains a periodic distribution of openings with arbitrary shape. By using results previously established for the single screen, both the problems for equally spaced and differently spaced screens are studied, reaching in any case an explicit representation with respect to frequency for the relevant scattering parameters. Some figures are given which reflect the peculiar physical properties of the cascading structure in the two types considered.