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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 19, Iss. 5 — May. 1, 2002
  • pp: 1021–1024

Analysis for the convergence problem of the plane-wave expansion method for photonic crystals

Linfang Shen and Sailing He  »View Author Affiliations


JOSA A, Vol. 19, Issue 5, pp. 1021-1024 (2002)
http://dx.doi.org/10.1364/JOSAA.19.001021


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Abstract

The convergence feature of two types of plane-wave expansion methods commonly used for photonic crystals is analyzed. It is shown that the reason for the slow convergence of these plane-wave expansion methods is not the slow convergence of the Fourier series for the permittivity profile of the photonic crystal but the inappropriate formulation of the eigenproblem. A new formulation of the eigenproblem is presented to improve the convergence in the one-dimensional case.

© 2002 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(070.2590) Fourier optics and signal processing : ABCD transforms
(260.2030) Physical optics : Dispersion
(260.2110) Physical optics : Electromagnetic optics

History
Original Manuscript: July 5, 2001
Manuscript Accepted: October 24, 2001
Published: May 1, 2002

Citation
Linfang Shen and Sailing He, "Analysis for the convergence problem of the plane-wave expansion method for photonic crystals," J. Opt. Soc. Am. A 19, 1021-1024 (2002)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-19-5-1021

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