Scattering of TE Plane Wave from Periodic Grating with Single Defect

Kazuhiro HATTORI
Junichi NAKAYAMA

Publication
IEICE TRANSACTIONS on Electronics   Vol.E90-C    No.2    pp.312-319
Publication Date: 2007/02/01
Online ISSN: 1745-1353
DOI: 10.1093/ietele/e90-c.2.312
Print ISSN: 0916-8516
Type of Manuscript: Special Section PAPER (Special Section on Recent Progress in Electromagnetic Theory and Its Application)
Category: Periodic Structures
Keyword: 
scattering,  periodic grating,  defect,  TE plane wave,  rectangular grooves,  single scattering approximation,  

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Summary: 
This paper deals with the scattering of TE plane wave from a periodic grating with single defect, of which position is known. The surface is perfectly conductive and made up with a periodic array of rectangular grooves and a defect where a groove is not formed. By use of the modal expansion method, the field inside grooves is expressed as a sum of guided modes with unknown amplitudes. The mode amplitudes are regarded as a sum of the base component and the perturbed component due to the defect, where the base component is the solution in case of the perfectly periodic grating. An equation for the base component is obtained in the first step. By use of the base component, a new equation for the perturbed component is derived in the second step. A new representation of the optical theorem, relating the total scattering cross section with the reduction of the scattering amplitude is obtained. Also, a single scattering approximation is proposed to express the scattered field. By use of truncation, we numerically obtain the base component and the perturbed component, in terms of which the total scattering cross section and the differential scattering cross section are calculated and illustrated in figures.