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B-spline modal method: a polynomial approach compared to the Fourier modal method.

Michael Walz1, Thomas Zebrowski, Jens Küchenmeister

  • 1Institut für Theoretische Festkörperphysik (TFP) and DFG-Center for Functional Nanostructures (CFN), Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Str. 1, 76131 Karlsruhe, Germany.

Optics Express
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PubMed
Summary

The B-spline Modal Method (BMM) offers superior accuracy and efficiency for diffraction grating analysis compared to the Fourier Modal Method (FMM). BMM effectively handles discontinuities, improving electromagnetic field profile computations.

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Area of Science:

  • Optics and Photonics
  • Computational Electromagnetics
  • Diffractive Optics

Background:

  • The Fourier Modal Method (FMM) is widely used for diffraction grating analysis but suffers from the Gibbs phenomenon due to its inability to accurately resolve discontinuities.
  • This limitation complicates accurate eigenmode and field profile computations, especially for complex grating structures.

Purpose of the Study:

  • To present a detailed analysis and comparison of the B-spline Modal Method (BMM) against the FMM for one- and two-dimensional diffraction gratings.
  • To demonstrate the advantages of BMM in handling discontinuities and improving computational efficiency.

Main Methods:

  • Analysis of the B-spline Modal Method (BMM) for one- and two-dimensional diffraction gratings.
  • Comparison of BMM with the Fourier Modal Method (FMM).
  • Development and application of a novel Galerkin approach with a scattering-matrix algorithm for improved field matching in BMM.

Main Results:

  • BMM effectively resolves discontinuities, avoiding the Gibbs phenomenon inherent in FMM.
  • BMM demonstrates significantly more efficient eigenmode computations.
  • The novel Galerkin approach enhances field matching between layers, outperforming traditional point-wise methods.
  • This Galerkin approach enables a competitive extension of BMM to two-dimensional gratings.

Conclusions:

  • BMM provides a more accurate and efficient alternative to FMM for diffraction grating analysis.
  • The developed Galerkin approach is crucial for extending BMM's capabilities, particularly for 2D gratings.
  • These advancements are beneficial for high-accuracy grating computations and electromagnetic field profile analysis.