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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 26 — Dec. 20, 2010
  • pp: 27511–27524

Fourier factorization with complex polarization bases in the plane-wave expansion method applied to two-dimensional photonic crystals

Roman Antos and Martin Veis  »View Author Affiliations

Optics Express, Vol. 18, Issue 26, pp. 27511-27524 (2010)

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We demonstrate an enhancement of the plane wave expansion method treating two-dimensional photonic crystals by applying Fourier factorization with generally elliptic polarization bases. By studying three examples of periodically arranged cylindrical elements, we compare our approach to the classical Ho method in which the permittivity function is simply expanded without changing coordinates, and to the normal vector method using a normal–tangential polarization transform. The compared calculations clearly show that our approach yields the best convergence properties owing to the complete continuity of our distribution of polarization bases. The presented methodology enables us to study more general systems such as periodic elements with an arbitrary cross-section or devices such as photonic crystal waveguides.

© 2010 Optical Society of America

OCIS Codes
(050.1755) Diffraction and gratings : Computational electromagnetic methods
(050.5298) Diffraction and gratings : Photonic crystals

ToC Category:
Photonic Crystals

Original Manuscript: November 4, 2010
Revised Manuscript: December 10, 2010
Manuscript Accepted: December 10, 2010
Published: December 14, 2010

Roman Antos and Martin Veis, "Fourier factorization with complex polarization bases in the plane-wave expansion method applied to two-dimensional photonic crystals," Opt. Express 18, 27511-27524 (2010)

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