OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 24, Iss. 8 — Aug. 1, 2007
  • pp: 2280–2295

Theory of optimal beam splitting by phase gratings. I. One-dimensional gratings

Louis A. Romero and Fred M. Dickey  »View Author Affiliations

JOSA A, Vol. 24, Issue 8, pp. 2280-2295 (2007)

View Full Text Article

Enhanced HTML    Acrobat PDF (232 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We give an analytical basis for the theory of optimal beam splitting by one-dimensional gratings. In particular, we use methods from the calculus of variations to derive analytical expressions for the optimal phase function.

© 2007 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.2770) Diffraction and gratings : Gratings
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(230.1950) Optical devices : Diffraction gratings

ToC Category:
Diffraction and Gratings

Original Manuscript: November 1, 2006
Manuscript Accepted: February 14, 2007
Published: July 11, 2007

Louis A. Romero and Fred M. Dickey, "Theory of optimal beam splitting by phase gratings. I. One-dimensional gratings," J. Opt. Soc. Am. A 24, 2280-2295 (2007)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. G. H. Dammann and K. Görtler, "High efficiency in-line multiple imaging by means of multiple phase holograms," Opt. Commun. 3, 312-315 (1971). [CrossRef]
  2. L. P. Boivin, "Multiple imaging using various types of phase gratings," Appl. Opt. 11, 1782-1792 (1972). [CrossRef] [PubMed]
  3. H. Dammann and E. Klotz, "Coherent optical generation and inspection of two-dimensional periodic structures," Opt. Acta 24, 505-515 (1977). [CrossRef]
  4. T. Lizotte, R. Rosenberg, and O. Obar, "Actual performance vs. modeled performance of diffractive beam splitters," Proc. SPIE 5876, 505-515 (2005).
  5. W. H. Lee, "High efficiency multiple beam gratings," Appl. Opt. 18, 2152-2158 (1979). [CrossRef] [PubMed]
  6. J. Jahns, M. M. Downs, M. E. Price, N. Streibl, and S. J. Walker, "Dammann gratings for laser beam shaping," Opt. Eng. (Bellingham) 28, 1267-1275 (1989).
  7. J. N. Mait, "Design for two dimensional non-separable array generators," Proc. SPIE 1555, 43-52 (1991). [CrossRef]
  8. J. Turunen, A. Vasara, J. Westrholm, G. Jin, and A. Salin, "Optimization and fabrication of beam splitters," J. Phys. D 21, s202-s205 (1988). [CrossRef]
  9. M. P. Dames, R. J. Dowling, P. McKee, and D. Wood, "Efficient optimization elements to generate intensity weighted spot arrays: design and fabrication," Appl. Opt. 30, 2685-2691 (1991). [CrossRef] [PubMed]
  10. D. C. O'Shea, "Reduction of the zero-order intensity in binary Dammann gratings," Appl. Opt. 34, 6533-6537 (1995). [CrossRef] [PubMed]
  11. F. M. Dickey and S. C. Holswade, Laser Beam Shaping: Theory and Technique (CRC Press, 2000). [CrossRef]
  12. F. M. Dickey, S. C. Holswade, and D. L. Shealy, Laser Beam Shaping: Applications (CRC Press, 2005). [CrossRef]
  13. F.M.Dickey and D.L.Shealy, eds., Laser Beam Shaping VI, Proc. SPIE 5876, 380 pp. (2005).
  14. T. E. Lizotte, "Beam shaping for microvia drilling," Printed Circuit Fabr. 26, 28-33 (2003).
  15. F. M. Dickey, "Laser beam shaping," Opt. Photonics News 14, 30-35 (2003). [CrossRef]
  16. I. M. Gelfand and S. V. Fomin, The Calculus of Variations (Prentice Hall, 1963).
  17. L. A. Romero and F. M. Dickey, "Theory for optimal beam splitting by phase gratings. II. Square and hexagonal gratings," J. Opt. Soc. Am. A 24, 2296-2312 (2007). [CrossRef]
  18. J. Tervo and J. Turunen, "Paraxial-domain diffractive elements with 100% efficiency based on polarization gratings," Opt. Lett. 25, 785-786 (2000). [CrossRef]
  19. F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Cincotti, and E. DiFabrizio, "Analytical derivation of the optimum triplicator," Opt. Commun. 157, 13-16 (1998). [CrossRef]
  20. R. Borghi, G. Cincotti, and M. Santarsiero, "Diffractive variable beam splitter: optimal design," J. Opt. Soc. Am. A 17, 63-67 (2000). [CrossRef]
  21. D. Prongue, H. P. Herzig, R. Dandliker, and M. T. Gale, "Optimized kinoform structures for highly efficient fan-out elements," Appl. Opt. 31, 5706-5711 (1992). [CrossRef] [PubMed]
  22. F. Wyrowski, "Upper bound of the diffractive efficiency of diffractive phase elements," Opt. Lett. 16, 1915-1917 (1991). [CrossRef] [PubMed]
  23. U. Krackhardt, J. N. Mait, and N. Streibl, "Upper bound on the diffraction efficiency of phase-only fan out elements," Appl. Opt. 31, 27-37 (1992). [CrossRef] [PubMed]
  24. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  25. F. Gori, "Diffractive optics and introduction," in Diffractive Optics and Optical Microsystems, S.Martellucci and A.N.Chester, eds. (Plenum, 1997).
  26. E. Hecht and A. Zajac, Optics (Addison Wesley, 1974).

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