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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 25, Iss. 1 — Jan. 1, 2008
  • pp: 211–218

Summing Pauli asymptotic series to solve the wedge problem

Riccardo Borghi  »View Author Affiliations

JOSA A, Vol. 25, Issue 1, pp. 211-218 (2008)

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The use of the asymptotic treatment for the wedge diffraction problem established long ago by Pauli [Phys. Rev. 54, 924 (1938)] is here revisited and proposed in the character of a powerful computational tool for accurately retrieving the total electromagnetic field even in the near zone. After proving its factorial divergent character, the Pauli series is summed through the Weniger transformation, a nonlinear resummation scheme particularly efficient in the case of factorial divergence. Numerical results are carried out to show the accuracy and effectiveness of the proposed approach.

© 2008 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(260.0260) Physical optics : Physical optics
(260.1960) Physical optics : Diffraction theory

ToC Category:
Physical Optics

Original Manuscript: October 4, 2007
Manuscript Accepted: October 29, 2007
Published: December 20, 2007

Riccardo Borghi, "Summing Pauli asymptotic series to solve the wedge problem," J. Opt. Soc. Am. A 25, 211-218 (2008)

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  28. When z is a real negative, the integral in Eq. must be intended in the Cauchy principal value sense. This is related to the fact that the line arg z=π represents a branch cut for the exponential integral function .
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  32. M. A. Alonso and R. Borghi, "Complete far-field asymptotic series for free fields," Opt. Lett. 31, 3028-3030 (2006). [CrossRef] [PubMed]

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