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Optics Letters

Optics Letters

| RAPID, SHORT PUBLICATIONS ON THE LATEST IN OPTICAL DISCOVERIES

  • Editor: Alan E. Willner
  • Vol. 33, Iss. 14 — Jul. 15, 2008
  • pp: 1590–1592

Hybridization of electromagnetic numerical methods through the G-matrix algorithm

J. P. Hugonin, M. Besbes, and P. Lalanne  »View Author Affiliations


Optics Letters, Vol. 33, Issue 14, pp. 1590-1592 (2008)
http://dx.doi.org/10.1364/OL.33.001590


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Abstract

For the sake of numerical performance, we hybridize two common approaches often used in electromagnetic computations, namely the finite-element method and the aperiodic Fourier modal method. To that end, we propose an extension of the classical S-matrix formalism to numerical situations, which requires handling different mathematical representations of the electromagnetic fields. As shown with a three-dimensional example, the proposed G-matrix formalism is stable and allows for an enhanced performance in terms of numerical accuracy and efficiency.

© 2008 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(050.1960) Diffraction and gratings : Diffraction theory
(050.1755) Diffraction and gratings : Computational electromagnetic methods

ToC Category:
Diffraction and Gratings

History
Original Manuscript: March 12, 2008
Revised Manuscript: June 11, 2008
Manuscript Accepted: June 13, 2008
Published: July 11, 2008

Citation
J. P. Hugonin, M. Besbes, and P. Lalanne, "Hybridization of electromagnetic numerical methods through the G-matrix algorithm," Opt. Lett. 33, 1590-1592 (2008)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-33-14-1590


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References

  1. J. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (Wiley, 2002).
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  10. With the MATLAB software, we have implemented several methods using LU and QR factorizations for the Gauss-Jordan elimination; see W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, 1989), Chap. 3.
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  13. We note that accurately calculating the W1 modal field on the hole discontinuities is crucial for estimating the inevitable extrinsic loss in the slow-light regime, see L. C. Andreani and D. Gerace, Phys. Status Solidi B 244, 3528 (2007). [CrossRef]
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