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Comparison of vector finite-difference techniques for modal analysis.

Magnus Wik1, Derek Dumas, David Yevick

  • 1Department of Physics, University of Waterloo, Waterloo, Ontario N2L 3G7, Canada.

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|August 2, 2005
PubMed
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Accurate boundary condition application in finite-difference methods is less critical than refractive index assignment for waveguides. Local averaging of refractive index significantly improves accuracy in finite-difference models.

Area of Science:

  • Computational electromagnetics
  • Waveguide theory
  • Numerical methods

Background:

  • Finite-difference methods are widely used for simulating electromagnetic phenomena.
  • Accurate application of boundary conditions is crucial for reliable numerical simulations.
  • Previous studies have focused on improving boundary condition handling in numerical methods.

Purpose of the Study:

  • To compare the impact of exact vs. approximate boundary conditions on finite-difference simulations of dielectric waveguides.
  • To investigate the influence of refractive index assignment schemes on simulation accuracy.
  • To evaluate the performance of different field formalisms (H- and E-field).

Main Methods:

  • Vector finite-difference method implementation.

Related Experiment Videos

  • Comparison of algorithms with exact and approximate boundary condition satisfaction.
  • Analysis of refractive index assignment strategies, including local averaging.
  • Evaluation of both H- and E-field formalisms.

    • Main Results:

    • For strongly guiding waveguides, boundary condition accuracy has a minor effect on field distributions compared to refractive index assignment.
    • Locally averaging the refractive index at grid points significantly enhances the precision of basic finite-difference models.
    • Both H- and E-field formalisms yield identical accuracy.

    Conclusions:

    • The method of assigning refractive index values at grid points is a dominant factor in the accuracy of finite-difference waveguide simulations.
    • Simple local averaging techniques can achieve high accuracy, rivaling more complex methods.
    • The choice between H- and E-field formalisms does not impact the accuracy of these finite-difference methods.