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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. 30, Iss. 4 — Apr. 1, 2013
  • pp: 640–644

Gaussian beam propagation: comparison of the analytical closed-form Fresnel integral solution to the simulations of the Huygens, Fresnel, and Rayleigh–Sommerfeld I approximations

Seyed M. Azmayesh-Fard  »View Author Affiliations


JOSA A, Vol. 30, Issue 4, pp. 640-644 (2013)
http://dx.doi.org/10.1364/JOSAA.30.000640


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Abstract

Simulations of the Huygens, Fresnel, and Rayleigh–Sommerfeld I approximations in the case of free-space propagation of a Gaussian beam are compared with analytical solutions. The most accurate results were obtained by the Rayleigh–Sommerfeld I approximation. The study reveals that the approximations are not uniform throughout the propagation region. While the accuracies of the Huygens and Fresnel methods generally increase as the propagation distance increases, the accuracy of the Rayleigh–Sommerfeld I approximation at first starts to diminish and later recovers as the propagation distance is further increased.

© 2013 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(050.1960) Diffraction and gratings : Diffraction theory

ToC Category:
Diffraction and Gratings

History
Original Manuscript: January 17, 2013
Manuscript Accepted: February 2, 2013
Published: March 18, 2013

Citation
Seyed M. Azmayesh-Fard, "Gaussian beam propagation: comparison of the analytical closed-form Fresnel integral solution to the simulations of the Huygens, Fresnel, and Rayleigh–Sommerfeld I approximations," J. Opt. Soc. Am. A 30, 640-644 (2013)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-4-640


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References

  1. M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975).
  2. A. E. Siegman, Lasers (University Science, 1986).
  3. C. Huygens, Treatise on Light (Dover, 1962).
  4. A. Sommerfeld, Optics, Vol. 3 of Lectures on Theoretical Physics (Academic, 1964).
  5. M. Totzeck, “Validity of the scalar Kirchhoff and Rayleigh-Sommerfeld diffraction theories in the near field of small phase objects,” J. Opt. Soc. Am. A 8, 27–32 (1991). [CrossRef]
  6. C. J. Bouwkamp, “Diffraction theory,” Rep. Prog. Phys. 17, 35–100 (1954). [CrossRef]
  7. L. Eyges, The Classical Electromagnetic Field (Addison-Wesley, 1972), p. 263.
  8. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 7th ed. (National Bureau of Standards, 1968).

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