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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 22 — Oct. 31, 2005
  • pp: 9078–9084

Application of the Fixed Point Theorem for the solution of the 1D wave equation: Comparison with exact Mathieu solutions

L. Carretero, M. Perez-Molina, S. Blaya, R. Madrigal, P. Acebal, and A. Fimia  »View Author Affiliations


Optics Express, Vol. 13, Issue 22, pp. 9078-9084 (2005)
http://dx.doi.org/10.1364/OPEX.13.009078


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Abstract

A method based in the application of Fixed Point Theorem (FPT) techniques to the solution of the 1D wave equation at normal incidence for materials that present a continuous (real or complex) dielectric constant is presented. As an example, the method is applied for the calculation of the electric field, reflection and transmission spectra in volume holographic gratings. It is shown that the solution obtained using this method agrees with the exact Mathieu solutions also obtained in this paper for volume holographic reflection gratings.

© 2005 Optical Society of America

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(050.7330) Diffraction and gratings : Volume gratings
(090.0090) Holography : Holography
(090.2900) Holography : Optical storage materials
(260.2110) Physical optics : Electromagnetic optics
(350.5500) Other areas of optics : Propagation

ToC Category:
Research Papers

History
Original Manuscript: June 22, 2005
Revised Manuscript: October 6, 2005
Published: October 31, 2005

Citation
L. Carretero, M. Perez-Molina, S. Blaya, R. Madrigal, P. Acebal, and A. Fimia, "Application of the Fixed Point Theorem for the solution of the 1D wave equation: comparison with exact Mathieu solutions," Opt. Express 13, 9078-9084 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-22-9078


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