Journal of the Optical Society of Korea

Optical Society of Korea (한국광학회)
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Investigation of the Convergence Behavior with Fluctuation Features in the Fourier Modal Analysis of a Metallic Grating

  • Kim, Hwi (Department of Electronics and Information Engineering, College of Science and Technology, Korea University, Sejong Campus) ;
  • Park, Gwanwoo (Department of Electronics and Information Engineering, College of Science and Technology, Korea University, Sejong Campus) ;
  • Kim, Changsoon (Graduate School of Convergence Science and Technology, Seoul National University)
  • Received : 2012.08.27
  • Accepted : 2012.09.05
  • Published : 2012.09.25
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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.

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