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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

  • Editor: Stephen A. Burns
  • Vol. 24, Iss. 12 — Dec. 1, 2007
  • pp: 3772–3780

Removal of the Gibbs phenomenon and its application to fast-Fourier-transform-based mode solvers

J. G. Wangüemert-Pérez, R. Godoy-Rubio, A. Ortega-Moñux, and I. Molina-Fernández  »View Author Affiliations


JOSA A, Vol. 24, Issue 12, pp. 3772-3780 (2007)
http://dx.doi.org/10.1364/JOSAA.24.003772


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Abstract

A simple strategy for accurately recovering discontinuous functions from their Fourier series coefficients is presented. The aim of the proposed approach, named spectrum splitting (SS), is to remove the Gibbs phenomenon by making use of signal-filtering-based concepts and some properties of the Fourier series. While the technique can be used in a vast range of situations, it is particularly suitable for being incorporated into fast-Fourier-transform-based electromagnetic mode solvers (FFT-MSs), which are known to suffer from very poor convergence rates when applied to situations where the field distributions are highly discontinuous (e.g., silicon-on-insulator photonic wires). The resultant method, SS-FFT-MS, is exhaustively tested under the assumption of a simplified one-dimensional model, clearly showing a dramatic improvement of the convergence rates with respect to the original FFT-based methods.

© 2007 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(130.2790) Integrated optics : Guided waves
(230.7370) Optical devices : Waveguides

ToC Category:
Optical Devices

History
Original Manuscript: March 9, 2007
Revised Manuscript: July 23, 2007
Manuscript Accepted: September 24, 2007
Published: November 21, 2007

Citation
J. G. Wangüemert-Pérez, R. Godoy-Rubio, A. Ortega-Moñux, and I. Molina-Fernández, "Removal of the Gibbs phenomenon and its application to fast-Fourier-transform-based mode solvers," J. Opt. Soc. Am. A 24, 3772-3780 (2007)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-24-12-3772

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