Periodic Fourier Transform and Its Application to Wave Scattering from a Finite Periodic Surface: Two-Dimensional Case

Junichi NAKAYAMA

Publication
IEICE TRANSACTIONS on Electronics   Vol.E88-C    No.5    pp.1025-1032
Publication Date: 2005/05/01
Online ISSN: 
DOI: 10.1093/ietele/e88-c.5.1025
Print ISSN: 0916-8516
Type of Manuscript: PAPER
Category: Electromagnetic Theory
Keyword: 
bigrating,  diffraction beam,  periodic Fourier transform,  harmonic series representation,  s-periodic spectrum,  harmonic spectrum,  

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Summary: 
In this paper, the previously introduced periodic Fourier transform concept is extended to a two-dimensional case. The relations between the periodic Fourier transform, harmonic series representation and Fourier integral representation are also discussed. As a simple application of the periodic Fourier transform, the scattering of a scalar wave from a finite periodic surface with weight is studied. It is shown that the scattered wave may have an extended Floquet form, which is physically considered as the sum of diffraction beams. By the small perturbation method, the first order solution is given explicitly and the scattering cross section is calculated.