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Chebyshev collocation Dirichlet-to-Neumann map method for diffraction gratings.

Dawei Song1, Ya Yan Lu

  • 1Joint Advanced Research Center of the University of Science and Technology of China, Hefei, Anhui, China 2City University of Hong Kong, Suzhou, Jiangsu, China.

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|September 2, 2009
PubMed
Summary
This summary is machine-generated.

We present an efficient Dirichlet-to-Neumann (DtN) map method for analyzing diffraction gratings with layered structures. This approach avoids computationally expensive eigenvalue problems, particularly beneficial for absorptive media.

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Area of Science:

  • Optics and Photonics
  • Computational Electromagnetics
  • Nanophotonics

Background:

  • Fourier Modal Method (FMM) is standard for layered diffraction gratings.
  • FMM requires computationally intensive eigenmode calculations, especially for absorptive materials.
  • Existing methods lack efficiency for complex layered structures.

Purpose of the Study:

  • To develop an efficient computational method for analyzing diffraction gratings with layered refractive index profiles.
  • To overcome the computational cost associated with traditional eigenmode calculations in FMM.
  • To provide a robust alternative for structures involving absorptive media.

Main Methods:

  • Developed a novel method based on the Dirichlet-to-Neumann (DtN) map, avoiding eigenvalue problems.
  • Approximated the DtN map as a matrix operator for each layer.
  • Employed a Chebyshev collocation method for uniform discretization.
  • Utilized a fourth-order finite difference method for periodic direction discretization.

Main Results:

  • The DtN map method significantly reduces computational cost compared to traditional FMM.
  • Numerical examples demonstrate the efficiency and accuracy of the developed method.
  • The method effectively handles layered structures, including those with absorptive media.

Conclusions:

  • The DtN map approach offers an efficient and accurate alternative for analyzing diffraction gratings.
  • This method is particularly advantageous for complex layered structures and absorptive materials.
  • The findings pave the way for faster simulations in nanophotonics and optical device design.