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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

  • Vol. 15, Iss. 4 — Apr. 1, 1998
  • pp: 857–867

Free-space beam propagation between arbitrarily oriented planes based on full diffraction theory: a fast Fourier transform approach

N. Delen and B. Hooker  »View Author Affiliations


JOSA A, Vol. 15, Issue 4, pp. 857-867 (1998)
http://dx.doi.org/10.1364/JOSAA.15.000857


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Abstract

A fast and accurate numerical method for free-space beam propagation between arbitrarily oriented planes is developed. The only approximation made in the development of the method was that the vector nature of light was ignored. The method is based on evaluating the Rayleigh–Sommerfeld diffraction integral by use of the fast Fourier transform with a special transformation to handle tilts and offsets of planes. The fundamental aspects of a software package based on the developed method are presented. A numerical example realized with the software package is presented to establish the validity of the method.

© 1998 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(050.1960) Diffraction and gratings : Diffraction theory
(070.2590) Fourier optics and signal processing : ABCD transforms
(350.5500) Other areas of optics : Propagation

History
Original Manuscript: July 3, 1997
Revised Manuscript: November 17, 1997
Manuscript Accepted: December 1, 1997
Published: April 1, 1998

Citation
N. Delen and B. Hooker, "Free-space beam propagation between arbitrarily oriented planes based on full diffraction theory: a fast Fourier transform approach," J. Opt. Soc. Am. A 15, 857-867 (1998)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-4-857


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References

  1. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), p. 382.
  2. R. E. Wagner, W. J. Tomlinson, “Coupling efficiency of optics in single-mode fiber components,” Appl. Opt. 21, 2671–2688 (1982). [CrossRef] [PubMed]
  3. H. Kogelnik, T. Li, “Laser beams and resonators,” Proc. IEEE 54, 1312–1329 (1966). [CrossRef]
  4. S. Ganci, “Fourier diffraction through a tilted slit,” Eur. J. Phys. 2, 158–160 (1981). [CrossRef]
  5. K. Patorski, “Fraunhofer diffraction patterns of tilted planar objects,” Opt. Acta 30, 673–679 (1983). [CrossRef]
  6. H. J. Rabal, N. Bolognini, E. E. Sicre, “Diffraction by a tilted aperture, coherent and partially coherent cases,” Opt. Acta 32, 1309–1311 (1985). [CrossRef]
  7. D. Leseberg, C. Frère, “Computer generated holograms of 3-D objects composed of tilted planar segments,” Appl. Opt. 27, 3020–3024 (1988). [CrossRef] [PubMed]
  8. C. Frère, D. Leseberg, “Large objects reconstructed from computer-generated holograms,” Appl. Opt. 28, 2422–2425 (1989). [CrossRef] [PubMed]
  9. T. Tommasi, B. Bianco, “Frequency analysis of light diffraction between rotated planes,” Opt. Lett. 17, 556–558 (1992). [CrossRef] [PubMed]
  10. T. Tommasi, B. Bianco, “Computer-generated holograms of tilted planes by a spatial frequency approach,” J. Opt. Soc. Am. A 10, 299–305 (1993). [CrossRef]
  11. B. Bianco, T. Tommasi, “Space-variant optical interconnection through the use of computer-generated holograms,” Appl. Opt. 34, 7573–7580 (1995). [CrossRef] [PubMed]
  12. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), p. 1.
  13. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), p. 17.
  14. A. Sommerfeld, Optics: Lectures on Theoretical Physics (Academic, New York, 1964), p. 197.
  15. J. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 3.
  16. E. Lalor, “Conditions for the validity of the angular spectrum of plane waves,” J. Opt. Soc. Am. 58, 1235–1237 (1968). [CrossRef]
  17. E. A. Sziklas, A. E. Siegman, “Mode calculations in unstable resonators with flowing saturable gain,” Appl. Opt. 14, 1874–1889 (1975). [CrossRef] [PubMed]
  18. W. H. Southwell, “Validity of the Fresnel approximations in the near field,” J. Opt. Soc. Am. 71, 7–14 (1981). [CrossRef]
  19. G. Thomas, R. Finney, Calculus and Analytic Geometry, 7th ed. (Addison-Wesley, New York, 1990), p. 780.
  20. G. Arfken, Mathematical Methods for Physicists, 3rd ed. (Academic, New York, 1985), p. 195.
  21. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), p. 195.
  22. A. Louri, M. Major, “Generalized methodology for modeling and simulating optical interconnection networks using diffraction analysis,” Appl. Opt. 34, 4052–4064 (1995). [CrossRef] [PubMed]
  23. J. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 2.
  24. W. Press, S. Teukolsky, W. Vetterling, B. Flannery, Numerical Recipes in fortran, 2nd ed. (Cambridge U. Press, New York, 1992), p. 497.

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