Periodic Fourier Transform and Its Application to Wave Scattering from a Finite Periodic Surface

Junichi NAKAYAMA

Publication
IEICE TRANSACTIONS on Electronics   Vol.E83-C    No.3    pp.481-487
Publication Date: 2000/03/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8516
Type of Manuscript: PAPER
Category: Electromagnetic Theory
Keyword: 
periodic Fourier transform,  wave scattering,  finite periodic surface,  

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Summary: 
As a new idea for analyzing the wave scattering and diffraction from a finite periodic surface, this paper proposes the periodic Fourier transform. By the periodic Fourier transform, the scattered wave is transformed into a periodic function which is further expanded into Fourier series. In terms of the inverse transformation, the scattered wave is shown to have an extended Floquet form, which is a 'Fourier series' with 'Fourier coefficients' given by band-limited Fourier integrals of amplitude functions. In case of the TE plane wave incident, an integral equation for the amplitude functions is obtained from the the boundary condition on the finite periodic surface. When the surface corrugation is small, in amplitude, compared with the wavelength, the integral equation is approximately solved by iteration to obtain the scattering cross section. Several properties and examples of the periodic Fourier transform are summarized in Appendix.