Wave scattering from a periodic surface with finite extent: A periodic approach

As a method of analyzing the wave scattering from a finite periodic surface , this paper introduces a periodic approach. The approach first considers t he wave diffraction by a periodic surface that is a superposition of surfac e profiles generated by displacing the finite periodic surface by every int eger multiple of the period A. It is pointed out that the Floquet solution for such a periodic case becomes an integral representation of the scattere d field from the finite periodic surface when the period Lambda goes to inf inity. A mathematical relation estimating the scattering amplitude for the finite periodic surface from the diffraction amplitude for the periodic sur face is proposed, From some numerical examples, it is concluded that the sc attering cross section for the finite periodic surface can be well estimate d from the diffraction amplitude for a sufficiently large Lambda.