OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 22, Iss. 6 — Jun. 1, 2005
  • pp: 1115–1126

Effective grating theory for resonance domain surface-relief diffraction gratings

Michael A. Golub and Asher A. Friesem  »View Author Affiliations

JOSA A, Vol. 22, Issue 6, pp. 1115-1126 (2005)

View Full Text Article

Acrobat PDF (410 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



An effective grating model, which generalizes effective-medium theory to the case of resonance domain surface-relief gratings, is presented. In addition to the zero order, it takes into account the first diffraction order, which obeys the Bragg condition. Modeling the surface-relief grating as an effective grating with two diffraction orders provides closed-form analytical relationships between efficiency and grating parameters. The aspect ratio, the grating period, and the required incidence angle that would lead to high diffraction efficiencies are predicted for TE and TM polarization and verified by rigorous numerical calculations.

© 2005 Optical Society of America

OCIS Codes
(050.1380) Diffraction and gratings : Binary optics
(050.1950) Diffraction and gratings : Diffraction gratings
(050.1970) Diffraction and gratings : Diffractive optics
(050.2770) Diffraction and gratings : Gratings
(260.1960) Physical optics : Diffraction theory
(260.2110) Physical optics : Electromagnetic optics

Michael A. Golub and Asher A. Friesem, "Effective grating theory for resonance domain surface-relief diffraction gratings," J. Opt. Soc. Am. A 22, 1115-1126 (2005)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1999).
  2. D. H. Raguin and G. M. Morris, "Antireflection structured surfaces for the infrared spectral region," Appl. Opt. 32, 1154-1167 (1993).
  3. N. Bokor, R. Shechter, N. Davidson, A. A. Friesem, and E. Hasman, "Achromatic phase retarder by slanted illumination of a dielectric grating with period comparable with the wavelength," Appl. Opt. 40, 2076-2080 (2001).
  4. J. Turunen, M. Kuittinen, and F. Wyrowski, "Diffractive optics: electromagnetic approach," in Progress in Optics, Vol. XL, E.Wolf, ed. (Elsevier North-Holland, Amsterdam, 2000), pp. 343-388.
  5. T. Shiono, T. Hamamoto, and K. Takahara, "High-efficiency blazed diffractive optical elements for the violet wavelength fabricated by electron-beam lithography," Appl. Opt. 41, 2390-2393 (2002).
  6. E. Noponen, A. Vasara, J. Turunen, J. M. Miller, and M. R. Taghizadeh, "Synthetic diffractive optics in the resonance domain," J. Opt. Soc. Am. A 9, 1206-1213 (1992).
  7. Y. Sheng, D. Feng, and S. Larochelle, "Analysis and synthesis of circular diffractive lens with local linear grating model and rigorous coupled wave theory," J. Opt. Soc. Am. A 14, 1562-1568 (1997).
  8. D. Meshulach, D. Yelin, and Y. Silberberg, "Adaptive real-time femtosecond pulse shaping," J. Opt. Soc. Am. B 15, 1615-1619 (1998).
  9. R. Shechter, Y. Amitai, and A. A. Friesem, "Compact beam expander with linear gratings," Appl. Opt. 41, 1236-1240 (2002).
  10. S. J. Walker, U. Jahns, L. Li, W. M. Mansfield, P. Mulgrew, D. M. Tennant, C. W. Roberts, L. C. West, and N. K. Ailawadi, "Design and fabrication of high-efficiency beam splitters and beam deflectors for integrated planar micro-optic systems," Appl. Opt. 32, 2494-2501 (1993).
  11. A. Sharon, D. Rosenblatt, A. A. Friesem, H. G. Weber, H. Engel, and R. Steingrueber, "Light modulation with resonant grating-waveguide structures," Opt. Lett. 21, 1564-1566 (1996).
  12. I. Nee, O. Beyer, M. Muller, and K. Buse, "Multichannel wavelength-division multiplexing with thermally fixed Bragg gratings in photorefractive lithium niobate crystals," J. Opt. Soc. Am. A 20, 1593-1602 (2003).
  13. G. W. Stroke, "Ruling, testing and use of optical gratings for high resolution spectroscopy," in Progress in Optics, Vol. II, E.Wolf, ed. (Elsevier North-Holland, Amsterdam, 1963), pp. 343-388.
  14. M. G. Moharam and T. K. Gaylord, "Diffraction analysis of dielectric surface-relief gratings," J. Opt. Soc. Am. 72, 1385-1392 (1982).
  15. L. Li, "Multilayer modal method for diffraction gratings of arbitrary profile, depth, and permittivity," J. Opt. Soc. Am. A 10, 2581-2591 (1993).
  16. K. Yokomori, "Dielectric surface-relief gratings with high diffraction efficiency," Appl. Opt. 23, 2303-2310 (1984).
  17. D. M. Pai and K. A. Awada, "Analysis of dielectric gratings of arbitrary profiles and thicknesses," J. Opt. Soc. Am. A 8, 755-762 (1991).
  18. M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, "Stable implementation of the rigorous coupled wave analysis for surface-relief gratings: enhanced transmittance matrix approach," J. Opt. Soc. Am. A 12, 1077-1086 (1995).
  19. S. Peng and G. M. Morris, "Efficient implementation of rigorous coupled-wave analysis for surface-relief gratings," J. Opt. Soc. Am. A 12, 1087-1096 (1995).
  20. L. Li, J. Chandezon, G. Granet, and J.-P. Plumey, "Rigorous and efficient grating-analysis method made easy for optical engineers," Appl. Opt. 38, 304-313 (1999).
  21. R.Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
  22. E. Popov and E. G. Loewen, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997), Chap. 4, Sect. 4.2.3.
  23. M. Nevière and E. Popov, Light Propagation in Periodic Media (Marcel Dekker, New York, 2003).
  24. H. J. Gerritsen, D. K. Thornton, and S. R. Bolton, "Application of Kogelnik's two-wave theory to deep, slanted, highly efficient, relief transmission gratings," Appl. Opt. 30, 807-814 (1991).
  25. M. A. Golub and A. A. Friesem, "Analytical theory for efficient surface relief gratings in the resonance domain," in The Art and Science of Holography: A Tribute to Emmett Leith and Yuri Denisyuk, H.J.Caulfield, ed. (SPIE Press, Bellingham, Wash., 2004), Chap. 19, pp. 307-328.
  26. M. A. Golub, A. A. Friesem, and L. Eisen, "Bragg properties of efficient surface relief gratings in the resonance domain," Opt. Commun. 235, 261-267 (2004).
  27. H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969).
  28. R. Magnusson and T. K. Gaylord, "Analysis of multiwave diffraction of thick gratings," J. Opt. Soc. Am. 67, 1165-1170 (1977).
  29. N. Chateau and J.-P. Hugonin, "Algorithm for the rigorous coupled-wave analysis of grating diffraction," J. Opt. Soc. Am. A 11, 1321-1331 (1994).
  30. J.-P. Plumey, B. Guizal, and J. Chandezon, "Coordinate transformation method as applied to asymmetric gratings with vertical facets," J. Opt. Soc. Am. A 14, 610-617 (1997).
  31. J. M. Miller, N. Beaucoudrey, P. Chavel, J. Turunen, and E. Cambril, "Design and fabrication of binary slanted surface-relief gratings for a planar optical interconnection," Appl. Opt. 36, 5717-5727 (1997).
  32. L. Li, "Oblique-coordinate-system-based Chandezon method for modeling one-dimensionally periodic, multilayer, inhomogeneous, anisotropic gratings," J. Opt. Soc. Am. A 16, 2521-2531 (1999).
  33. P. Laakkonen, M. Kuittinen, J. Simonen, and J. Turunen, "Electron-beam-fabricated asymmetric transmission gratings for microspectroscopy," Appl. Opt. 39, 3187-3191 (2000).
  34. M. G. Moharam, T. K. Gaylord, and R. Magnusson, "Criteria for Bragg regime diffraction by phase gratings," Opt. Commun. 32, 14-18 (1980).
  35. M. Breidne and D. Maystre, "Equivalence of ruled, holographic, and lamellar gratings in constant deviation mountings," Appl. Opt. 19, 1812-1821 (1980).
  36. M. A. Golub, "Generalized conversion from the phase function to the blazed surface-relief profile of diffractive optical elements," J. Opt. Soc. Am. A 16, 1194-1201 (1999).

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