Explicit results for scattering parameters in three-dimensional wave propagation through a doubly periodic system of arbitrary openings |
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Authors: | E Scarpetta V Tibullo |
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Affiliation: | (1) D.I.I.M.A, University of Salerno, 84084 Fisciano, (SA), Italy |
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Abstract: | Summary In the present paper, an analytical approach previously formulated for two-dimensional scattering problems is further developed
to study three-dimensional problems. A scalar plane wave is assumed to (normally) penetrate into a plane screen having identical
openings of arbitrary shape which are periodically distributed. This problem is first described by an integral equation holding
over the typical openings' domain. Then, by applying simple approximations (uniformly) valid in the assumed regime of propagation,
some auxiliary integral equations are deduced which are independent of the wave frequency. A linear algebraic system is finally
set up whose solution provides explicit analytical formulas for the main scattering parameters. By solving numerically this
system of equations for assigned obstacle shapes, several graphs are obtained which show comparison between such explicit
formulas and the corresponding rigorous numerical solution of the original integral equation. |
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