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Modal method based on subsectional Gegenbauer polynomial expansion for nonperiodic structures: complex coordinates

Kofi Edee1, Brahim Guizal

  • 1Université Blaise Pascal, LASMEA, UMR-6602-CNRS, BP 10448, Clermont-Ferrand, France. kofi.edee@univ‑bpclermont.fr

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|April 19, 2013
PubMed
Summary
This summary is machine-generated.

The modal method by Gegenbauer expansion (MMGE) effectively handles nonperiodic electromagnetic problems using perfectly matched layers (PMLs). This robust approach avoids issues with spurious modes, unlike other numerical methods.

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Area of Science:

  • Computational electromagnetics
  • Numerical methods for wave propagation

Background:

  • The modal method by Gegenbauer expansion (MMGE) is a numerical technique for electromagnetic problems.
  • Nonperiodic structures pose challenges for traditional electromagnetic simulation methods.
  • Perfectly matched layers (PMLs) are commonly used to truncate computational domains in electromagnetic simulations.

Purpose of the Study:

  • To extend the modal method by Gegenbauer expansion (MMGE) for analyzing nonperiodic electromagnetic problems.
  • To investigate the integration of perfectly matched layers (PMLs) within the MMGE framework.
  • To assess the robustness and stability of the extended MMGE with PMLs.

Main Methods:

  • Extension of the modal method by Gegenbauer expansion (MMGE).
  • Introduction of nonperiodicity using perfectly matched layers (PMLs) via coordinate transformation or uniaxial anisotropic medium.
  • Analysis of electromagnetic field behavior and numerical scheme convergence.

Main Results:

  • The MMGE with PMLs demonstrates robustness in handling nonperiodic electromagnetic problems.
  • The method exhibits natural immunity to spurious modes, a common issue in other techniques like the Fourier modal method.
  • PMLs, when implemented, can introduce field irregularities but do not compromise the MMGE's stability.

Conclusions:

  • The extended MMGE provides a stable and reliable numerical tool for nonperiodic electromagnetic simulations.
  • The MMGE's inherent properties make it superior to methods susceptible to spurious modes when using PMLs.
  • This work validates the MMGE with PMLs as a powerful approach for complex electromagnetic field analysis.