OSA's Digital Library

Optics Express

Optics Express

  • Editor: J. H. Eberly
  • Vol. 8, Iss. 13 — Jun. 18, 2001
  • pp: 705–722

Limits of scalar diffraction theory and an iterative angular spectrum algorithm for finite aperture diffractive optical element design

Stephen D. Mellin and Gregory P. Nordin  »View Author Affiliations

Optics Express, Vol. 8, Issue 13, pp. 705-722 (2001)

View Full Text Article

Enhanced HTML    Acrobat PDF (540 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We have designed high-efficiency finite-aperture diffractive optical elements (DOE’s) with features on the order of or smaller than the wavelength of the incident illumination. The use of scalar diffraction theory is generally not considered valid for the design of DOE’s with such features. However, we have found several cases in which the use of a scalar-based design is, in fact, quite accurate. We also present a modified scalar-based iterative design method that incorporates the angular spectrum approach to design diffractive optical elements that operate in the near-field and have sub-wavelength features. We call this design method the iterative angular spectrum approach (IASA). Upon comparison with a rigorous electromagnetic analysis technique, specifically, the finite difference time-domain method (FDTD), we find that our scalar-based design method is surprisingly valid for DOE’s having sub-wavelength features.

© Optical Society of America

OCIS Codes
(050.1970) Diffraction and gratings : Diffractive optics
(230.1950) Optical devices : Diffraction gratings

ToC Category:
Research Papers

Original Manuscript: April 16, 2001
Published: June 18, 2001

Stephen Mellin and Gregory Nordin, "Limits of scalar diffraction theory and an iterative angular spectrum algorithm for finite aperture diffractive optical element design," Opt. Express 8, 705-722 (2001)

Sort:  Journal  |  Reset  


  1. M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon Press, New York, 1965).
  2. J. Goodman, Introduction to Fourier Optics (McGraw-Hill., New York, 1968).
  3. G.S. Smith. An Introduction to Classical Electromagnetic Radiation (Cambridge University Press, Cambridge, 1997).
  4. D. A. Gremaux and N. C. Gallagher, "Limits of scalar diffraction theory for conducting gratings," Appl. Opt. 32, 1948-1953 (1993). [CrossRef] [PubMed]
  5. D.A. Pommet, M.G. Moharam, and E.B. Grann, "Limits of scalar diffraction theory for diffractive phase elements", Opt. Lett. 11, 1827-1834 (1995).
  6. M. G. Moharam and T. K. Gaylord, "Diffraction analysis of surface-relief gratings," J. Opt. Soc. Am. A 72, 1385-1392 (1982). [CrossRef]
  7. R.W. Gerchberg, W.O. Saxton. "A practical algorithm for the determination of phase from image and diffraction plane pictures" Optik 35, 237-246 (1971).
  8. Pierre St. Hilaire, "Phase profiles for holographic stereograms," Opt. Eng. 34, 83-89 (1995). [CrossRef]
  9. N.C. Gallagher and B. Liu, "Method for computing kinoforms that reduces image reconstruction error," Appl. Opt. 12, 2328-2335 (1973). [CrossRef] [PubMed]
  10. J.R. Fienup, "Iterative method applied to image reconstruction and to computer-generated holograms," Opt. Eng. 19, 297-306 (1980).
  11. F. Wyrowski, "Iterative Fourier-transform algorithm applied to computer holography," J. Opt. Soc. Am. A 5, 1058-1065 (1988). [CrossRef]
  12. F. Wyrowski and O. Bryngdahl, "Digital holography as part of diffractive optics," Rep. Prog. Phys. 54, 1481-1571 (1991). [CrossRef]
  13. J. N. Mait, "Understanding diffractive optic design in the scalar domain," J. Opt. Soc. Am. A 12, 2145- 2158 (1995). [CrossRef]
  14. I.O. Bohachevsky, M.E. Johnson, M.L. Stein, "Generalized simulated annealing for function optimization," Technometrics 28, 209-217 (1986). [CrossRef]
  15. Y. Lin, T.J. Kessler, G.N. Lawrence, "Design of continuous surface-relief phase plates by surface-based simulated annealing to achieve control of focal-plane irradiance," Opt. Lett. 21, 1703-1705 (1996). [CrossRef] [PubMed]
  16. B. K. Jennison, J. P. Allebach, and D. W. Sweeney, "Iterative approaches to computer-generated holog-raphy," Opt. Eng. 28, 629-637 (1989).
  17. J. Turunen, A. Vasara, and J. Westerholm, "Kinoform phase relief synthesis: a stochastic method," Opt. Eng. 28, 1162-1167 (1989).
  18. M.R. Feldman and C.C. Guest, "High-efficiency hologram encoding for generation of spot arrays," Opt. Lett. 14, 479-481 (1989). [CrossRef] [PubMed]
  19. J. Jiang and G. Nordin, "A rigorous unidirectional method for designing finite aperture diffractive optical elements," Opt. Express 7, 237-242 (2000), http://www.opticsexpress.org/oearchive/source/23164.htm. [CrossRef]
  20. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, 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