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Asymptotic of the Green function for the diffraction by a perfectly conducting plane perturbed by a sub‐wavelength rectangular cavity
Author(s) -
Bonnetier E.,
Triki F.
Publication year - 2010
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.1194
Subject(s) - diffraction , wavelength , planar , helmholtz equation , dipole , plane (geometry) , helmholtz free energy , function (biology) , optics , electromagnetic radiation , mathematics , plane wave , mathematical analysis , operator (biology) , physics , geometry , quantum mechanics , boundary value problem , chemistry , biochemistry , computer graphics (images) , repressor , evolutionary biology , computer science , transcription factor , gene , biology
This work is aimed at understanding the amplification and confinement of electromagnetic fields in open sub‐wavelength metallic cavities. We present a theoretical study of the electromagnetic diffraction by a perfectly conducting planar interface, which contains a sub‐wavelength rectangular cavity. We derive a rigorous asymptotic of the Green function associated with the Helmholtz operator when the width of the cavity shrinks to zero. We show that the limiting Green function is that of a perfectly conducting plane with a dipole in place of the cavity. We give an explicit description of the effective dipole in terms of the wavelength and of the geometry of the cavity. Copyright © 2009 John Wiley & Sons, Ltd.