Local transformation leading to an efficient Fourier modal method for perfectly conducting gratings

We present an efficient Fourier modal method for wave scattering by perfectly conducting gratings (in the two polarizations). The method uses a geometrical transformation, similar to the one used in the C-method, that transforms the grating surface into a flat surface, thus avoiding to question the...

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Bibliographic Details
Published in:Journal of the Optical Society of America. A, Optics, image science, and vision Optics, image science, and vision, 2014-10, Vol.31 (10), p.2249-2255
Main Authors: Félix, Simon, Maurel, Agnès, Mercier, Jean-François
Format: Article
Language:English
Subjects:
Computation
Conduction
Criteria
Diffraction gratings
Fourier analysis
Gratings (spectra)
Grooves
Polarization
Transformations
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Summary:We present an efficient Fourier modal method for wave scattering by perfectly conducting gratings (in the two polarizations). The method uses a geometrical transformation, similar to the one used in the C-method, that transforms the grating surface into a flat surface, thus avoiding to question the Rayleigh hypothesis; also, the transformation only affects a bounded inner region that naturally matches the outer region; this allows applying a simple criterion to select the ingoing and outgoing waves. The method is shown to satisfy reciprocity and energy conservation, and it has an exponential rate of convergence for regular groove shapes. Besides, it is shown that the size of the inner region, where the solution is computed, can be reduced to the groove depth, that is, to the minimal computation domain.
ISSN:1084-7529
1520-8532
DOI:10.1364/JOSAA.31.002249