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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 22, Iss. 3 — Mar. 1, 2005
  • pp: 481–490

Differential theory of diffraction by finite cylindrical objects

Nicolas Bonod, Evgeny Popov, and Michel Nevière  »View Author Affiliations

JOSA A, Vol. 22, Issue 3, pp. 481-490 (2005)

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We present a differential theory for solving Maxwell equations in cylindrical coordinates, projecting them onto a Fourier–Bessel basis. Numerical calculations require the truncation of that basis, so that correct rules of factorization have to be used. The convergence of the method is studied for different cases of dielectric and metallic cylinders of finite length. Applications of such a method are presented, with a special emphasis on the near-field map inside a hole pierced in a plane metallic film.

© 2005 Optical Society of America

OCIS Codes
(050.1220) Diffraction and gratings : Apertures
(050.1960) Diffraction and gratings : Diffraction theory
(260.1960) Physical optics : Diffraction theory
(260.2110) Physical optics : Electromagnetic optics

Original Manuscript: June 16, 2004
Revised Manuscript: September 16, 2004
Manuscript Accepted: October 1, 2004
Published: March 1, 2005

Nicolas Bonod, Evgeny Popov, and Michel Nevière, "Differential theory of diffraction by finite cylindrical objects," J. Opt. Soc. Am. A 22, 481-490 (2005)

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  1. P. Vincent, “Differential methods,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), Chap. 4.
  2. M. Nevière, E. Popov, Light Propagation in Periodic Medias: Differential Theory and Design (Marcel Dekker, New York, 2003).
  3. E. Popov, M. Nevière, “Maxwell equations in Fourier space: fast converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media,” J. Opt. Soc. Am. A 18, 2886–2894 (2001). [CrossRef]
  4. B. Guizal, D. Barchiesi, D. Felbacq, “Electromagnetic beam diffraction by a finite lamellar structure: an aperiodic coupled-wave method,” J. Opt. Soc. Am. A 20, 2274–2280 (2001). [CrossRef]
  5. J. D. Jackson, Classical Electromagnetism, 3rd ed. (Wiley, New York, 1998), Chap. 3.
  6. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870–1876 (1996). [CrossRef]
  7. E. Popov, M. Nevière, N. Bonod, “Factorization of products of discontinuous functions applied to Fourier–Bessel basis,” J. Opt. Soc. Am. A 21, 46–52 (2004). [CrossRef]
  8. L. W. Davis, “Theory of electromagnetism beams,” Phys. Rev. A 19, 1177–1179 (1979). [CrossRef]
  9. M. Abramovitz, I. A. Stegun, eds., Handbook of Mathematical Functions [9th printing (1970).] National Bureau of Standards Applied Mathematics Series 55 (U.S. Government Printing Office, Washington, D.C., 1964).
  10. E. Popov, B. Chernov, M. Nevière, N. Bonod, “Differential theory: application to highly conducting gratings,” J. Opt. Soc. Am. A 21, 199–206 (2004). [CrossRef]
  11. A. Degiron, H. J. Lezec, N. Yamamoto, T. W. Ebbesen, “Optical transmission properties of a single subwavelength aperture in a real metal,” Opt. Commun. 239, 61–66 (2004). [CrossRef]

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