Resonant frequencies for diffraction gratings

This note is devoted to a study of resonance phenomena in electromagnetic gratings. In particular, a characterization of the scattering frequencies (the complex values of the frequency inducing resonant behaviors) is given by using a variational method. After the diffraction problem is reduced to a...

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Bibliographic Details
Published in:Applied mathematics letters 2002-08, Vol.15 (6), p.755-760
Main Authors: Bao, G., Ramdani, K.
Format: Article
Language:English
Subjects:
Applied classical electromagnetism
Diffraction
Electromagnetic wave propagation, radiowave propagation
Electromagnetics
Electromagnetism
electron and ion optics
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Gratings
Physics
Resolvant
Resonance
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Summary:This note is devoted to a study of resonance phenomena in electromagnetic gratings. In particular, a characterization of the scattering frequencies (the complex values of the frequency inducing resonant behaviors) is given by using a variational method. After the diffraction problem is reduced to a bounded domain, we extend it to complex values of the frequency. The existence of the resolvant of the diffraction problem is established in the upper complex half-plane. It is shown that this resolvant can be extended meromorphically to the domain C/ R +. In addition, the scattering frequencies, which correspond to the poles of this extension, solve a nonlinear eigenvalue problem.
ISSN:0893-9659
1873-5452
DOI:10.1016/S0893-9659(02)00038-1