OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 31, Iss. 3 — Mar. 1, 2014
  • pp: 591–602

Efficient semi-analytical propagation techniques for electromagnetic fields

Daniel Asoubar, Site Zhang, Frank Wyrowski, and Michael Kuhn  »View Author Affiliations

JOSA A, Vol. 31, Issue 3, pp. 591-602 (2014)

View Full Text Article

Enhanced HTML    Acrobat PDF (1217 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



In this work, four fast and rigorous methods for the simulation of light propagation in a homogenous medium are introduced. It is shown that in free-space propagation, the analytical handling of smooth but strong phase terms is very efficient in reducing the computational effort. Therefore, the angular spectrum of plane waves (SPW) operator is reformulated to handle linear, spherical, and general smooth phase terms without limiting the application of the fast-Fourier-transformation algorithm. Especially for nonparaxial field propagation, the proposed techniques can significantly reduce the required number of sampling points. Numerical results are presented to demonstrate the efficiency and the accuracy of the new methods.

© 2014 Optical Society of America

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(220.2560) Optical design and fabrication : Propagating methods
(260.1960) Physical optics : Diffraction theory
(070.7345) Fourier optics and signal processing : Wave propagation

ToC Category:
Optical Design and Fabrication

Original Manuscript: November 5, 2013
Revised Manuscript: January 10, 2014
Manuscript Accepted: January 13, 2014
Published: February 14, 2014

Daniel Asoubar, Site Zhang, Frank Wyrowski, and Michael Kuhn, "Efficient semi-analytical propagation techniques for electromagnetic fields," J. Opt. Soc. Am. A 31, 591-602 (2014)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. F. Wyrowski and M. Kuhn, “Introduction to field tracing,” J. Mod. Opt. 58, 449–466 (2011). [CrossRef]
  2. J. A. C. Veerman, J. J. Rusch, and H. P. Urbach, “Calculation of the Rayleigh-Sommerfeld diffraction integral by exact integration of the fast oscillating factor,” J. Opt. Soc. Am. A 22, 636–646 (2005). [CrossRef]
  3. J. J. M. Braat, S. van Haver, A. J. E. M. Janssen, and P. Dirksen, “Assessment of optical systems by means of point-spread functions,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2008), Vol. 51.
  4. D. Asoubar, S. Zhang, F. Wyrowski, and M. Kuhn, “Parabasal field decomposition and its applications to non-paraxial propagation,” Opt. Express 20, 23502–23517 (2012). [CrossRef]
  5. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  6. M. Mansuripur, “Certain computational aspects of vector diffraction problems,” J. Opt. Soc. Am. A 6, 786–805 (1989). [CrossRef]
  7. C. van der Avoort, J. J. M. Braat, P. Dirksen, and A. J. E. M. Janssen, “Aberration retrieval from the intensity point-spread function in the focal region using the extended Nijboer Zernike approach,” J. Mod. Opt. 52, 1695–1728 (2005). [CrossRef]
  8. E. Wolf, “A scalar representation of electromagnetic fields: II,” Proc. Phys. Soc. London 74, 269–280 (1959). [CrossRef]
  9. J. Turunen, “Elementary-field representations in partially coherent optics,” J. Mod. Opt. 58, 509–527 (2011). [CrossRef]
  10. J. W. Cooley and J. W. Tukey, “An algorithm for the machine calculation of complex Fourier series,” Math. Comput. 19, 297–301 (1965). [CrossRef]
  11. W. Goodmann, Introduction to Fourier Optics (McGraw-Hill, 1968).
  12. K. Matsushima, “Shifted angular spectrum method for off-axis numerical propagation,” Opt. Express 18, 18453–18463 (2010). [CrossRef]
  13. Y. M. Engelberg and S. Ruschin, “Fast method for physical optics propagation of high-numerical-aperture beams,” J. Opt. Soc. Am. A 21, 2135–2145 (2004). [CrossRef]
  14. C. J. R. Sheppard and M. Hrynevych, “Diffraction by a circular aperture: a generalization of Fresnel diffraction theory,” J. Opt. Soc. Am. A 9, 274–281 (1992). [CrossRef]
  15. E. O. Brigham, The Fast Fourier Transform and Its Applications (Prentice-Hall, 1988).
  16. J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, R. R. Shannon and J. C. Wyant, eds. (Academic, 1992), Vol. XI, Chap. 1.
  17. R. J. Hanson and C. L. Lawson, Solving Least Squares Problems (Society for Industrial and Applied Mathematics, 1995).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited