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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. 3 — Mar. 1, 2010
  • pp: 622–631

Discontinuity-free edge-diffraction model for characterization of focused wave fields

Andrey G. Sedukhin  »View Author Affiliations


JOSA A, Vol. 27, Issue 3, pp. 622-631 (2010)
http://dx.doi.org/10.1364/JOSAA.27.000622


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Abstract

A model of discontinuity-free edge diffraction is proposed that is valid in the framework of the scalar Debye approximation and describes the formation process and approximate structure of the stationary diffracted field of a monochromatic converging spherical wave of limited angular opening throughout the whole space about the focus. The field is represented semianalytically in terms of the sum of a direct quasi-spherical wave and two edge quasi-conical waves of the zeroth and first order. The angular spectrum amplitudes of all these waves have smooth continuous variations of the real and imaginary parts in polar angle and radius, the separable nonanalytic functions defining the polar-angle variations of the amplitudes being found by optimization techniques.

© 2010 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(050.1220) Diffraction and gratings : Apertures
(050.1960) Diffraction and gratings : Diffraction theory
(260.1960) Physical optics : Diffraction theory

ToC Category:
Physical Optics

History
Original Manuscript: November 5, 2009
Revised Manuscript: January 16, 2010
Manuscript Accepted: January 17, 2010
Published: February 26, 2010

Citation
Andrey G. Sedukhin, "Discontinuity-free edge-diffraction model for characterization of focused wave fields," J. Opt. Soc. Am. A 27, 622-631 (2010)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-3-622


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References

  1. M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed.(Cambridge Univ. Press, 1999), Sect. 8.
  2. T. Young, “On the theory of light and colours,” Philos. Trans. R. Soc. London 92, 12-48 (1802). [CrossRef]
  3. P. Debye, “Das verhalten von lichtwellen in der nahe eines brennpuktes oder iener brennlinie,” Ann. Phys. 30, 755-776 (1909). [CrossRef]
  4. W. H. Carter, “Band-limited angular-spectrum approximation to a spherical scalar wave field,” J. Opt. Soc. Am. 65, 1054-1058 (1975). [CrossRef]
  5. H. Weyl, “Ausbreitung elektromagnetischer wellen über einem ebenen leiter,” Ann. Phys. 60, 481-500 (1919). [CrossRef]
  6. G. A. Maggi, “Sulla propagazione libera e perturbata delle onde luminose in un mezzo isotropo,” Ann. Matem. 16, 21-48 (1888). [CrossRef]
  7. A. Rubinowicz, “Die beugungswelle in der Kirchhoffschen theorie der beugungserscheinungen,” Ann. Phys. 53, 257-278 (1917). [CrossRef]
  8. A. Sommerfeld, “Mathematische theorie der diffraction,” Math. Ann. 47, 317-374 (1896). [CrossRef]
  9. J. B. Keller, “Geometrical theory of diffraction,” J. Opt. Soc. Am. 52, 116-130 (1962). [CrossRef] [PubMed]
  10. K. Miyamoto and E. Wolf, “Generalization of the Maggi-Rubinowicz theory of the boundary diffraction wave—Part I,” J. Opt. Soc. Am. 52, 615-625 (1962). [CrossRef]
  11. K. Miyamoto and E. Wolf, “Generalization of the Maggi-Rubinowicz theory of the boundary diffraction wave—Part lI,” J. Opt. Soc. Am. 52, 626-637 (1962). [CrossRef]
  12. S. Ganci, “An experiment on the physical reality of edge-diffracted waves,” Am. J. Phys. 57, 370-373 (1989). [CrossRef]
  13. R. Kumar, “Structure of boundary diffraction wave revisited,” Appl. Phys. B 90, 379-382 (2008). [CrossRef]
  14. A. I. Khizhnyak, S. P. Anokhov, R. A. Lyramenko, M. S. Soskin, and M. V. Vasnetsov, “Structure of an edge-dislocation wave originating in plane wave diffraction by a half-plane,” J. Opt. Soc. Am. A 17, 2199-2207 (2000). [CrossRef]
  15. Y. Z. Umul, “Alternative interpretation of the edge-diffraction phenomenon,” J. Opt. Soc. Am. A 25, 582-586 (2008). [CrossRef]
  16. G. C. Sherman and W. C. Chew, “Aperture and far-field distributions expressed by the Debye integral representation of focused fields,” J. Opt. Soc. Am. 72, 1076-1083 (1982). [CrossRef]
  17. J. J. Stamnes, “Waves, rays, and the method of stationary phase,” Opt. Express 10, 740-751 (2002). [PubMed]
  18. W. Wang, A. T. Friberg, and E. Wolf, “Structure of focused fields in systems with large Fresnel numbers,” J. Opt. Soc. Am. A 12, 1947-1953 (1995). [CrossRef]
  19. E. Wolf and Y. Li, “Conditions for the validity of the Debye integral representation of focused fields,” Opt. Commun. 39, 205-209 (1981). [CrossRef]
  20. A. Papoulis, Systems and Transforms with Applications in Optics, 1st ed. (McGraw-Hill, 1968), Chap. 7.
  21. A. G. Sedukhin, “Marginal phase correction of truncated Bessel beams,” J. Opt. Soc. Am. A 17, 1059-1066 (2000). [CrossRef]
  22. A. G. Sedukhin, “Refinement of a discontinuity-free edge-diffraction model describing focused wave fields,” J. Opt. Soc. Am. A 26, 632-636 (2010). [CrossRef]
  23. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253, 358-379 (1959). [CrossRef]

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