Asymptotic of the Green function for the diffraction by a perfectly conducting plane perturbed by a sub‐wavelength rectangular cavity | Zendy

Bonnetier E. | Zendy; Triki F. | Zendy

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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.

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