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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: Franco Gori
  • Vol. 27, Iss. 1 — Jan. 1, 2010
  • pp: 109–115

Fictitious diffracted waves in the diffraction theory of Kirchhoff

Yusuf Z. Umul  »View Author Affiliations


JOSA A, Vol. 27, Issue 1, pp. 109-115 (2010)
http://dx.doi.org/10.1364/JOSAA.27.000109


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Abstract

The diffraction theory of Kirchhoff is applied to the semi-infinite aperture of a black half-screen. The derivative of the spherical Green’s function is taken into account without any approximation. The uniformly evaluated scattering integral is compared with the physical optics solution. It is shown that the non-omitted term causes the existence of fictitious diffracted waves.

© 2009 Optical Society of America

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(260.0260) Physical optics : Physical optics
(260.1960) Physical optics : Diffraction theory

ToC Category:
Physical Optics

History
Original Manuscript: October 6, 2009
Revised Manuscript: November 17, 2009
Manuscript Accepted: November 20, 2009
Published: December 11, 2009

Citation
Yusuf Z. Umul, "Fictitious diffracted waves in the diffraction theory of Kirchhoff," J. Opt. Soc. Am. A 27, 109-115 (2010)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-1-109


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References

  1. T. Young, “The Bakerian lecture: On the theory of light and colors,” Philos. Trans. R. Soc. London 92, 12-48 (1802). [CrossRef]
  2. J. B. Keller, “Geometrical theory of diffraction,” J. Opt. Soc. Am. 52, 116-130 (1962). [CrossRef] [PubMed]
  3. A. J. Fresnel, “Mémoire sur la diffraction de la lumière,” Ann. Chim. Phys. 1, 239-281 (1816).
  4. G. A. Kirchhoff, “Zur Theorie der Lichtstrahlen,” Ann. Phys. 254, 663-695 (1883). [CrossRef]
  5. S. V. Kukhlevsky, M. Mechler, O. Samek, and K. Janssens, “Analytical model of the enhanced light transmission through subwavelength metal slits: Green's function formalism versus Rayleigh's expansion,” Appl. Phys. B: Photophys. Laser Chem. 84, 19-24 (2006). [CrossRef]
  6. W. C. Elmore and M. A. Heald, Physics of Waves (McGraw-Hill, 1969).
  7. C. Tai, “Kirchhoff theory: Scalar, vector or dyadic?” IEEE Trans. Antennas Propag. 20, 114-115 (1972). [CrossRef]
  8. E. Hecht, Optics (Addison-Wesley, 2002).
  9. R. Kumar, “Structure of boundary diffraction wave revisited,” Appl. Phys. B: Photophys. Laser Chem. 90, 379-382 (2008). [CrossRef]
  10. H. M. MacDonald, “The effect produced by an obstacle on a train of electric waves,” Philos. Trans. R. Soc. London, Ser. A 212, 299-337 (1913). [CrossRef]
  11. G. A. Maggi, “Sulla propagazione libera e perturbata delle onde luminose in un mezzo isotropo,” Ann. Mat. Pura Appl. 16, 21-48 (1888).
  12. A. Rubinowicz, “Die Beugungswelle in der Kirchhoffschen Theorie der Beugungserscheinungen,” Ann. Phys. 358, 257-278 (1917). [CrossRef]
  13. H. Poincaré, Théorie Mathématique de la Lumière (De la Faculté des Sciences de Paris, 1892).
  14. N. Mukunda, “Consistency of Rayleigh's diffraction formulas with Kirchhoff's boundary conditions,” J. Opt. Soc. Am. 52, 336-337 (1962). [CrossRef]
  15. F. Kottler, “Zur Theorie der Beugung an schwarzen Schirmen,” Ann. Phys. 375, 405-456 (1923). [CrossRef]
  16. F. Kottler, “Elektromagnetische Theorie der Beugung an schwarzen Schirmen,” Ann. Phys. 376, 457-508 (1923). [CrossRef]
  17. J. S. Asvestas, “Diffraction by a black screen,” J. Opt. Soc. Am. 65, 155-158 (1975). [CrossRef]
  18. E. W. Marchand and E. Wolf, “Consistent formulation of Kirchhoff's diffraction theory,” J. Opt. Soc. Am. 56, 1712-1721 (1966). [CrossRef]
  19. S. Ganci, “Equivalence between two consistent formulations of Kirchhoff's diffraction theory,” J. Opt. Soc. Am. A 5, 1626-1628 (1988). [CrossRef]
  20. S. Ganci, “A note on the Kirchhoff formulation of diffraction by a plane screen,” J. Mod. Opt. 45, 873-876 (1998). [CrossRef]
  21. S. Ganci, “A general scalar solution for the half-plane problem,” J. Mod. Opt. 42, 1707-1711 (1995). [CrossRef]
  22. S. Ganci, “Half-plane diffraction in a case of oblique incidence,” J. Mod. Opt. 43, 2543-2551 (1996). [CrossRef]
  23. Y. Z. Umul, “Modified theory of physical optics,” Opt. Express 12, 4959-4972 (2004). [CrossRef] [PubMed]
  24. Y. Z. Umul, “Modified diffraction theory of Kirchhoff,” J. Opt. Soc. Am. A 25, 1850-1860 (2008). [CrossRef]
  25. A. Sommerfeld, “Mathematische Theorie der Diffraction,” Math. Ann. 47, 317-374 (1896). [CrossRef]
  26. T. Gravelsaeter and J. J. Stamnes, “Diffraction by circular apertures. 1. Method of linear phase and amplitude approximation,” Appl. Opt. 21, 3644-3651 (1982). [CrossRef] [PubMed]
  27. A. Rubinowicz, “Zur Kirchhoffschen Beugungstheorie,” Ann. Phys. 378, 339-364 (1924). [CrossRef]
  28. A. Rubinowicz, “On the anomalous propagation of phase in the focus,” Phys. Rev. 54, 931-936 (1938). [CrossRef]
  29. W. B. Gordon, “Vector potentials and physical optics,” J. Math. Phys. 16, 448-454 (1975). [CrossRef]
  30. G. A. Forbes and A. A. Asatryan, “Reducing canonical diffraction problems into singularity-free one-dimensional integrals,” J. Opt. Soc. Am. A 15, 1320-1328 (1998). [CrossRef]
  31. A. S. Marathay and J. F. McCalmont, “On the usual approximation used in the Rayleigh-Sommerfeld diffraction theory,” J. Opt. Soc. Am. A 21, 510-516 (2004). [CrossRef]
  32. Y. Z. Umul, “Rubinowicz transform of the MTPO surface integrals,” Opt. Commun. 281, 5641-5646 (2008). [CrossRef]
  33. M. Born and E. Wolf, Principles of Optics (Cambridge Univ. Press, 2003).
  34. Y. Z. Umul, “The relation between the boundary diffraction wave theory and physical optics,” Opt. Commun. 281, 4844-4848 (2008). [CrossRef]
  35. Y. Z. Umul, “Simplified uniform theory of diffraction,” Opt. Lett. 30, 1614-1616 (2005). [CrossRef] [PubMed]
  36. G. L. James, Geometrical Theory of Diffraction for Electromagnetic Waves (IEE, 1983).
  37. S. W. Lee and G. Deschamps, “A uniform asymptotic theory of electromagnetic diffraction by a curved wedge,” IEEE Trans. Antennas Propag. AP-24, 25-34 (1976).

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