Abstract
We observe that the transmission and reflection efficiencies of a one-dimensional
metallic grating under transverse-magnetic illumination calculated using the Fourier modal method
(FMM) with the Fourier factorization rules have peculiar fluctuations, albeit small in magnitude, as
the number of field harmonics increases. It is shown that when the number of Fourier terms for the
electromagnetic field is increased from that in the conventional FMM, the fluctuations due to
non-convergent highly evanescent eigenmodes can be eliminated. Our examination reveals that the
fluctuations originate from the Gibbs phenomenon inherent in the Fourier-series representation of a
permittivity function with discontinuities, and from non-convergence of highly evanescent internal
Bloch eigenmodes.
© 2012 Optical Society of Korea
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