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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. 25, Iss. 8 — Aug. 1, 2008
  • pp: 1885–1893

Analysis of the influence of the passive facet of blazed transmission gratings in the intermediate diffraction regime

Oliver Sandfuchs, Daniel Pätz, Stefan Sinzinger, Alexander Pesch, and Robert Brunner  »View Author Affiliations

JOSA A, Vol. 25, Issue 8, pp. 1885-1893 (2008)

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Blazed diffraction gratings are of enormous practical importance for imaging and analyzing hybrid optical systems. The intermediate diffraction regime is characterized by the transition from the scalar to the rigorous electromagnetic theory. An effect known as shadowing occurs and reduces the diffraction efficiency. Based on rigorous calculations for optimized sawtooth-shaped and binary-multilevel blaze profiles, we deduce a semianalytical model describing the shadowing phenomenon for the general case of oblique incidence. We discuss illumination both from air and from the substrate. Though a multilevel blaze possesses a discrete substructure, our shadowing model remains valid, if substructural effects are neglected. We find that electromagnetic effects due to the passive blaze facet lead to the efficiency reduction, and the blazing efficiency shows a linear dependence on the ratio of blaze wavelength to grating period. Our shadowing model is applied to predict the performance of a Littrow-like blazing condition in transmission geometry as, e.g., for a diffractive solid immersion lens.

© 2008 Optical Society of America

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(110.0110) Imaging systems : Imaging systems
(220.0220) Optical design and fabrication : Optical design and fabrication

ToC Category:
Diffraction and Gratings

Original Manuscript: December 14, 2007
Revised Manuscript: April 25, 2008
Manuscript Accepted: April 26, 2008
Published: July 3, 2008

Oliver Sandfuchs, Daniel Pätz, Stefan Sinzinger, Alexander Pesch, and Robert Brunner, "Analysis of the influence of the passive facet of blazed transmission gratings in the intermediate diffraction regime," J. Opt. Soc. Am. A 25, 1885-1893 (2008)

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  1. M. D. Missig and G. M. Morris, “Diffractive optics applied to eyepiece design,” Appl. Opt. 34, 2452-2461 (1995). [CrossRef] [PubMed]
  2. W. Knapp, G. Blough, K. Khajurival, R. Michaels, B. Tatian, and B. Volk, “Optical design comparison of 60° eyepieces: One with a diffractive surface and one with aspherics,” Appl. Opt. 34, 4756-4760 (1997). [CrossRef]
  3. I. M. Barton, J. A. Britten, S. N. Dixit, L. J. Summers, I. M. Thomas, M. C. Rushford, K. Lu., R. A. Hyde, and M. D. Perry, “Fabrication of large-aperture lightweight diffractive lenses for use in space,” Appl. Opt. 40, 447-451 (2001). [CrossRef]
  4. R. Brunner, R. Steiner, K. Rudolf, and H.-J. Dobschal, “Diffractive-refractive hybrid microscope objective for 193 nm inspection systems,” Proc. SPIE 5177, 9-15 (2003). [CrossRef]
  5. R. Brunner, A. Menck, R. Steiner, G. Buchda, S. Weissenberg, U. Horn, and A. M. Zibold, “Immersion mask inspection with hybrid-microscopic systems at 193 nm,” Proc. SPIE 5567, 887-893 (2004). [CrossRef]
  6. S. Sinzinger and M. Testorf, “Transition between diffractive and refractive micro-optical components,” Appl. Opt. 34, 5970-5976 (1995). [CrossRef] [PubMed]
  7. M. B. Fleming and M. C. Hutley, “Blazed diffractive optics,” Appl. Opt. 36, 4635-4643 (1997). [CrossRef] [PubMed]
  8. E. Noponen, J. Turunen, and A. Vasara, “Electromagnetic theory and design of diffractive-lens arrays,” J. Opt. Soc. Am. A 10, 434-443 (1993). [CrossRef]
  9. R. Brunner, R. Steiner, H.-J. Dobschal, D. Martin, M. Burkhardt, and M. Helgert, “New solutions to realize complex optical systems by a combination of diffractive and refractive optical components,” Proc. SPIE 5183, 47-55 (2003). [CrossRef]
  10. R. Brunner, M. Burkhardt, A. Pesch, O. Sandfuchs, M. Ferstl, S. Hohng, and J. O. White, “Diffraction-based solid immersion lens,” J. Opt. Soc. Am. A 21, 1186-1191 (2004). [CrossRef]
  11. C. G. Blough, M. Rossi, S. K. Mack, and R. L. Michaels, “Single-point diamond turning and replication of visible and near-infrared diffractive optical elements,” Appl. Opt. 36, 4648-4654 (1997). [CrossRef] [PubMed]
  12. T. Hessler, M. Rossi, R. E. Kunz, and M. T. Gale, “Analysis and optimization of fabrication of continuous-relief diffractive optical elements,” Appl. Opt. 37, 4069-4079 (1998). [CrossRef]
  13. U. Levy, E. Marom, and D. Mendlovic, “Thin element approximation for the analysis of blazed gratings: Simplified model and validity limits,” Opt. Commun. 229, 11-21 (2004). [CrossRef]
  14. M. S. L. Lee, Ph. Lalanne, J. C. Rodier, P. Chavel, E. Cambril, and Y. Chen, “Imaging with binary diffractive elements,” J. Opt. A, Pure Appl. Opt. 4, S119-S124 (2002). [CrossRef]
  15. Ph. Lalanne, S. Astilean, P. Chavel, E. Cambril, and H. Launois, “Design and fabrication of blazed binary diffractive elements with sampling periods smaller than the structural cutoff,” J. Opt. Soc. Am. A 16, 1143-1156 (1999). [CrossRef]
  16. G. J. Swanson, “Binary optics technology: Theoretical limits on the diffraction efficiency of multilevel diffractive optical elements,” MIT Tech. Rep. 914, Massachusetts Institute of Technology Lincoln Laboratory, Cambridge, Massachusetts, 1991.
  17. A. v. Pfeil, F. Wyrowski, A. Drauschke, and H. Aagedal, “Analysis of optical elements with the local plane-interface approximation,” Appl. Opt. 39, 3304-3313 (2000). [CrossRef]
  18. B. H. Kleemann, A. Mitreiter, and F. Wyrowski, “Integral equation method with parametrization of grating profile. Theory and experiments,” J. Mod. Opt. 43, 1323-1349 (1996). [CrossRef]
  19. A. Rathsfeld, G. Schmidt, and B. H. Kleemann, “On a fast integral equation method for diffraction gratings,” Comm. Comp. Phys. 1, 984-1009 (2006).
  20. 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]
  21. O. Sandfuchs, R. Brunner, D. Pätz, S. Sinzinger, and J. Ruoff, “Rigorous analysis of shadowing effects in blazed transmission gratings,” Opt. Lett. 31, 3638-3640 (2006). [CrossRef] [PubMed]
  22. M. 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). [CrossRef]
  23. S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615-2616 (1990). [CrossRef]
  24. T. Delort, D. Maystre, and J. P. Laude, “Perfect blazing for transmission gratings: Generalized and numerical verification,” J. Opt. Soc. Am. A 13, 2034-2040 (1996). [CrossRef]
  25. O. Sandfuchs, A. Pesch, and R. Brunner, “Rigorous modeling of dielectric and metallic blaze gratings in the intermediate structure regime,” Proc. SPIE 6675, 66750I-1-8 (2007).
  26. S.-Y. Kim, J.-W. Ra, and S.-Y. Shin, “Edge diffraction by dielectric wedge of arbitrary angle,” Electron. Lett. 19, 851-853 (1983). [CrossRef]
  27. P.-K. Wei, H.-L. Chou, and W.-L. Chang, “Diffraction-induced near-field optical images in mesoscale air-dielectric structures,” J. Opt. Soc. Am. B 20, 1503-1507 (2003). [CrossRef]

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