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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 23, Iss. 4 — Apr. 1, 2006
  • pp: 858–865

Nonparaxial scalar treatment of sinusoidal phase gratings

James E. Harvey, Andrey Krywonos, and Dijana Bogunovic  »View Author Affiliations

JOSA A, Vol. 23, Issue 4, pp. 858-865 (2006)

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Scalar diffraction theory is frequently considered inadequate for predicting diffraction efficiencies for grating applications where λ d > 0.1 . It has also been stated that scalar theory imposes energy upon the evanescent diffracted orders. These notions, as well as several other common misconceptions, are driven more by an unnecessary paraxial approximation in the traditional Fourier treatment of scalar diffraction theory than by the scalar limitation. By scaling the spatial variables by the wavelength, we have previously shown that diffracted radiance is shift invariant in direction cosine space. Thus simple Fourier techniques can now be used to predict a variety of wide-angle (nonparaxial) diffraction grating effects. These include (1) the redistribution of energy from the evanescent orders to the propagating ones, (2) the angular broadening (and apparent shifting) of wide-angle diffracted orders, and (3) nonparaxial diffraction efficiencies predicted with an accuracy usually thought to require rigorous electromagnetic theory.

© 2006 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.1940) Diffraction and gratings : Diffraction
(050.1950) Diffraction and gratings : Diffraction gratings
(050.2770) Diffraction and gratings : Gratings
(260.1960) Physical optics : Diffraction theory

ToC Category:
Diffraction and Gratings

Original Manuscript: May 2, 2005
Revised Manuscript: August 19, 2005
Manuscript Accepted: August 24, 2005

James E. Harvey, Andrey Krywonos, and Dijana Bogunovic, "Nonparaxial scalar treatment of sinusoidal phase gratings," J. Opt. Soc. Am. A 23, 858-865 (2006)

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  1. R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, 1980), p. 98.
  2. P. Beckman and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, 1963).
  3. J. M. Bennett and L. Mattsson, Introduction to Surface Roughness and Scattering, 2nd ed. (Optical Society of America, 1999).
  4. J. C. Stover, Optical Scattering, Measurement and Analysis, 2nd ed. (SPIE, 1995). [CrossRef]
  5. D. A. Gremaux and N. C. Gallager, "Limits of scalar diffraction theory for conducting gratings," Appl. Opt. 32, 1048-1953 (1993). [CrossRef]
  6. D. A. Pommet, M. G. Moharam, and E. B. Grann, "Limits of scalar diffraction theory for diffractive phase elements," J. Opt. Soc. Am. A 11, 1827-1834 (1994). [CrossRef]
  7. E. G. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, 1997).
  8. S. D. Mellin and G. P. 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). [CrossRef] [PubMed]
  9. D. Maystre, "Rigorous vector theories of diffraction gratings," in Progress in Optics XXI, E.Wolf, ed. (Elsevier Science, 1984). [CrossRef]
  10. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  11. M. Born and E. Wolf, Principles of Optics (Pergamon, 1980), p. 598.
  12. T. K. Gaylord and M. G. Moharam, "Analysis and applications of optical diffraction by gratings," Proc. IEEE 73, 894-937 (1985).
  13. C. V. Raman and N. S. N. Nath, "The diffraction of light by high frequency sound waves," Proc. Ind. Acad. Sci. A 2, 406-413 (1935).
  14. C. Palmer, Diffraction Grating Handbook, 4th ed. (Richardson Grating Laboratory, 2000), p. 15.
  15. J. E. Harvey, "Fourier treatment of near-field scalar diffraction theory," Am. J. Phys. 47, 974-980 (1979). [CrossRef]
  16. J. E. Harvey, C. L. Vernold, A. Krywonos, and P. L. Thompson, "Diffracted radiance: a fundamental quantity in a nonparaxial scalar diffraction theory," Appl. Opt. 38, 6469-6481 (1999). [CrossRef]
  17. J. E. Harvey, C. L. Vernold, A. Krywonos, and P. L. Thompson, "Diffracted radiance: a fundamental quantity in a nonparaxial scalar diffraction theory: errata," Appl. Opt. 39, 6374-6375 (2000). [CrossRef]
  18. J. A. Ratcliff, "Some aspects of diffraction theory and their application to the ionosphere," in Reports on Progress in Physics, A.C.Strickland, ed. (Physical Society, 1956), Vol. XIX.
  19. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, 1978).
  20. J. E. Harvey and R. V. Shack, "Aberrations of diffracted wave fields," Appl. Opt. 17, 3003-3009 (1978). [CrossRef] [PubMed]
  21. J. E. Harvey, A. Krywonos, and D. Bogunovic, "Tolerance on defocus precisely locates the far field (exactly where is that far field anyway?)" Appl. Opt. 41, 2586-2588 (2002). [CrossRef] [PubMed]
  22. R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Philos. Mag. 4, 396-410 (1902).
  23. J. E. Harvey and C. L. Vernold, "Description of diffraction grating behavior in direction cosine space," Appl. Opt. 37, 8158-8160 (1998). [CrossRef]
  24. J. E. Harvey and E. A. Nevis, "Angular grating anomalies: effects of finite beam size upon wide-angle diffraction phenomena," Appl. Opt. 31, 6783-6788 (1992). [CrossRef] [PubMed]
  25. A. Hessel and A. A. Oliner, "A new theory of Wood's anomalies on optical gratings," Appl. Opt. 4, 1275-1297 (1965). [CrossRef]

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