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Guided waves by electromagnetic gratings and non‐uniqueness examples for the diffraction problem
Author(s) -
BonnetBendhia AnneSophie,
Starling Felipe
Publication year - 1994
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670170502
Subject(s) - uniqueness , diffraction , scalar (mathematics) , grating , plane wave , plane (geometry) , diffraction grating , optics , dielectric , physics , electromagnetic radiation , mathematical analysis , mathematics , geometry , optoelectronics
Abstract We consider the two‐dimensional scalar problem of the diffraction of a plane wave by an infinite grating of conducting bodies immersed in a periodical dielectric medium. A Fredholm‐type formulation is derived and studied. The existence of a solution is proved and some uniqueness results are established. A detailed description of the guided modes of the grating is carried out. Finally, various non‐uniqueness examples for the diffraction problem are exhibited.