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Optics Letters

Optics Letters


  • Editor: Xi-Cheng Zhang
  • Vol. 39, Iss. 9 — May. 1, 2014
  • pp: 2727–2730

Generalized image principle for cylindrical waves

Fabrizio Frezza and Nicola Tedeschi  »View Author Affiliations

Optics Letters, Vol. 39, Issue 9, pp. 2727-2730 (2014)

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In this Letter, we analyze the reflection of cylindrical waves (CWs) at planar interfaces. We consider the reflected CW proposed in the literature as a spectral integral. We present a Laurent series expansion of the Fresnel coefficient convergent on the whole real axis and we use it to solve analytically the reflected-wave integral. We found a solution that involves both Bessel functions and Anger–Weber functions, i.e., solutions of both the homogeneous and inhomogeneous Bessel differential equations. We compare the analytical solution with the numerical results obtained with a quadrature formula presented in the literature. Moreover, we present a physical interpretation that connects our solution to the image principle.

© 2014 Optical Society of America

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(260.2110) Physical optics : Electromagnetic optics
(050.1755) Diffraction and gratings : Computational electromagnetic methods
(290.2558) Scattering : Forward scattering

ToC Category:
Diffraction and Gratings

Original Manuscript: February 24, 2014
Revised Manuscript: March 31, 2014
Manuscript Accepted: April 3, 2014
Published: April 28, 2014

Fabrizio Frezza and Nicola Tedeschi, "Generalized image principle for cylindrical waves," Opt. Lett. 39, 2727-2730 (2014)

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