OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 16, Iss. 5 — May. 1, 1999
  • pp: 1143–1156

Design and fabrication of blazed binary diffractive elements with sampling periods smaller than the structural cutoff

Philippe Lalanne, Simion Astilean, Pierre Chavel, Edmond Cambril, and Huguette Launois  »View Author Affiliations


JOSA A, Vol. 16, Issue 5, pp. 1143-1156 (1999)
http://dx.doi.org/10.1364/JOSAA.16.001143


View Full Text Article

Acrobat PDF (526 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We report here on the theoretical performance of blazed binary diffractive elements composed of pillars carefully arranged on a two-dimensional grid whose period is smaller than the structural cutoff. These diffractive elements operate under unpolarized light. For a given grating geometry, the structural cutoff is a period value above which the grating no longer behaves like a homogeneous thin film. Because the grid period is smaller than this value, effective-medium theories can be fully exploited for the design, and straightforward procedures are obtained. The theoretical performance of the blazed binary elements is investigated through electromagnetic theories. It is found that these elements substantially outperform standard blazed échelette diffractive elements in the resonance domain. The increase in efficiency is explained by a decrease of the shadowing effect and by an unexpected sampling effect. The theoretical analysis is confirmed by experimental evidence obtained for a 3λ-period prismlike grating operating at 633 nm and for a 20°-off-axis diffractive lens operating at 860 nm.

© 1999 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

History
Original Manuscript: July 30, 1998
Revised Manuscript: January 5, 1999
Manuscript Accepted: December 17, 1998
Published: May 1, 1999

Citation
Philippe Lalanne, Simion Astilean, Pierre Chavel, Edmond Cambril, and Huguette 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)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-5-1143


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. L. d’Auria, J. P. Huignard, A. M. Roy, E. Spitz, “Photolithographic fabrication of thin film lenses,” Opt. Commun. 5, 232–235 (1972). [CrossRef]
  2. G. J. Swanson, “Binary optics technology: the theory and design of multilevel diffractive optical elements,” (MIT, Cambridge, Mass., 1989).
  3. B. Goebel, L. L. Wang, T. Tschudi, “Multilayer technology for diffractive optical elements,” Appl. Opt. 35, 4490–4493 (1996). [CrossRef] [PubMed]
  4. J. M. Finlan, K. M. Flood, R. J. Bojko, “Efficient f/1 binary-optics microlenses in fused silica designed using vector diffraction theory,” Opt. Eng. 34, 3560–3564 (1995). [CrossRef]
  5. M. T. Gale, M. Rossi, J. Pedersen, H. Schütz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33, 3556–3566 (1994). [CrossRef]
  6. C. G. Blough, M. Rossi, S. K. Mack, 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]
  7. F. Fujita, H. Nishihara, J. Koyama, “Blazed gratings and Fresnel lenses fabricated by electron-beam lithography,” Opt. Lett. 7, 578–580 (1982). [CrossRef] [PubMed]
  8. J. M. Stauffer, Y. Oppliger, P. Régnault, L. Baraldi, M. T. Gale, “Electron beam writing of continuous resist profiles for optical applications,” J. Vac. Sci. Technol. B 10, 2526–2529 (1992). [CrossRef]
  9. T. Shiono, H. Ogawa, “Diffraction-limited blazed reflection diffractive microlenses for oblique incidence fabricated by electron-beam lithography,” Appl. Opt. 30, 3643–3649 (1991). [CrossRef] [PubMed]
  10. A. F. Harvey, Microwave Engineering (Academic, London, 1963), Sect. 13.3.
  11. W. E. Kock, “Metallic delay lenses,” Bell Syst. Tech. J. 27, 58–82 (1948). [CrossRef]
  12. W. M. Farn, “Binary gratings with increased efficiency,” Appl. Opt. 31, 4453–4458 (1992). [CrossRef] [PubMed]
  13. W. Stork, N. Streibl, H. Haidner, P. Kipfer, “Artificial distributed-index media fabricated by zero-order gratings,” Opt. Lett. 16, 1921–1923 (1991). [CrossRef] [PubMed]
  14. H. Haidner, J. T. Sheridan, N. Streibl, “Dielectric binary blazed gratings,” Appl. Opt. 32, 4276–4278 (1993). [CrossRef] [PubMed]
  15. Z. Zhou, T. J. Drabik, “Optimized binary, phase-only, diffractive optical element with subwavelength features for 1.55 µm,” J. Opt. Soc. Am. A 12, 1104–1112 (1995). [CrossRef]
  16. E. Noponen, J. Turunen, “Binary high-frequency-carrier diffractive optical elements: electromagnetic theory,” J. Opt. Soc. Am. A 11, 1097–1109 (1994). [CrossRef]
  17. M. Schmitz, O. Bryngdahl, “Rigorous concept for the design of diffractive microlenses with high numerical apertures,” J. Opt. Soc. Am. A 14, 901–906 (1997). [CrossRef]
  18. M. Kuittinen, J. Turunen, P. Vahimaa, “Rigorous analysis and optimization of subwavelength-structured binary dielectric beam deflector gratings,” J. Mod. Opt. 45, 133–142 (1998). [CrossRef]
  19. J. N. Mait, D. W. Prather, M. S. Mirtoznik, “Binary subwavelength diffractive-lens design,” Opt. Lett. 23, 1343–1345 (1998). [CrossRef]
  20. H. Haidner, P. Kipfer, J. T. Sheridan, J. Schwider, N. Streibl, M. Collischon, J. Hutfless, M. Marz, “Diffraction grating with rectangular grooves exceeding 80% diffraction efficiency,” Infrared Phys. 34, 467–475 (1993). [CrossRef]
  21. P. Kipfer, M. Collischon, H. Haidner, J. Schwider, “Subwavelength structures and their use in diffractive optics,” Opt. Eng. 35, 726–731 (1996). [CrossRef]
  22. M. E. Warren, R. E. Smith, G. A. Vawter, J. R. Wendt, “High-efficiency subwavelength diffractive optical element in GaAs for 975 nm,” Opt. Lett. 20, 1441–1443 (1995). [CrossRef] [PubMed]
  23. F. T. Chen, H. G. Craighhead, “Diffractive phase elements on two-dimensional artificial dielectrics,” Opt. Lett. 20, 121–123 (1995). [CrossRef] [PubMed]
  24. F. T. Chen, H. G. Craighead, “Diffractive lens fabricated with mostly zeroth-order gratings,” Opt. Lett. 21, 177–179 (1996). [CrossRef] [PubMed]
  25. J. M. Miller, N. de Beaucoudrey, P. Chavel, E. Cambril, H. Launois, “Synthesis of subwavelength-pulse-width spatially modulated array illuminator for 0.633 µm,” Opt. Lett. 21, 1399–1401 (1996). [CrossRef] [PubMed]
  26. S. Astilean, Ph. Lalanne, P. Chavel, E. Cambril, H. Launois, “High-efficiency subwavelength diffractive element patterned in a high-refractive-index material for 633 nm,” Opt. Lett. 23, 552–554 (1998). [CrossRef]
  27. Ph. Lalanne, S. Astilean, P. Chavel, E. Cambril, H. Launois, “Blazed binary subwavelength gratings with efficiencies larger than those of conventional échelette gratings,” Opt. Lett. 23, 1081–1083 (1998). [CrossRef]
  28. We believe that, with current technologies, the fabrication in glass of blazed binary diffractive elements is extremely difficult and probably impossible. Moreover, note that the use of a high-index material also has a beneficial effect on the theoretical performance (see Ref. 26).
  29. M. G. Moharam, E. B. Grann, D. A. Pommet, T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995). [CrossRef]
  30. Ph. Lalanne, G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779–784 (1996). [CrossRef]
  31. G. Granet, B. Guizal, “Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization,” J. Opt. Soc. Am. A 13, 1019–1023 (1996). [CrossRef]
  32. L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14, 2758–2767 (1997). [CrossRef]
  33. Ph. Lalanne, “Effective properties and band structures of lamellar subwavelength crystals: plane-wave method revisited,” Phys. Rev. B 58, 9801–9807 (1998). [CrossRef]
  34. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870–1876 (1996). [CrossRef]
  35. D. A. Pommet, M. G. Moharam, E. B. Grann, “Limits of scalar diffraction theory for diffractive phase elements,” J. Opt. Soc. Am. A 11, 1827–1834 (1994). [CrossRef]
  36. W. Singer, H. Tiziani, “Born approximation for the nonparaxial scalar treatment of thick phase gratings,” Appl. Opt. 37, 1249–1255 (1997). [CrossRef]
  37. G. J. Swanson, “Binary optics technology: theoretical limits on the diffraction efficiency of multilevel diffractive optical elements,” (MIT, Cambridge, Mass., 1991).
  38. See, for example, A. Bensoussan, J. L. Lions, G. Papanicolaou, “Asymptotic analysis for periodic structures,” in Study in Mathematics and Its Applications, J. L. Lions, G. Papanicolaou, eds. (North-Holland, Amsterdam, 1978), Chap. 4.
  39. Ph. Lalanne, D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43, 2063–2085 (1996). [CrossRef]
  40. One can qualitatively understand this by considering that the pillar surrounded by the low-index material (in our case, air) may be seen as the core of a 2D waveguide. For a given grating period and from well-known results on 1D waveguides, multimode operations are obtained for large core widths, i.e., for large fill factors, by analogy. Conversely, for a given fill factor and a given grating period, it is intuitively clear that the structure supports an increasing number of modes for increasing values of the core refractive index.
  41. H. Kikuta, Y. Ohira, H. Kubo, K. Iwata, “Effective medium theory of two-dimensional subwavelength gratings in the non-quasi-static limit,” J. Opt. Soc. Am. A 15, 1577–1585 (1998). [CrossRef]
  42. The computation was performed by the modal theory of Ref. 32, with square truncation. Nineteen orders along each periodicity axis were retained for the computation. No convergence problems were encountered, and the numerical results can be considered as exact. These numerical results strongly differ from those obtained by Chen and Craighead (see Fig. 1 of Ref. 24). For pillar sizes of approximately 400 nm, the zeroth-order diffraction efficiency is 65%, a value 15% smaller than that reported in Ref. 24. This difference is due to the fact that the numerical results of Ref. 24 are obtained for 16 retained orders by a slowly converging numerical method. We believe that our lower-efficiency prediction may explain the 12% discrepancy, observed by the authors of Ref. 24, between their experimental results and their numerical predictions. In our opinion, the existence of the higher-order modes is responsible for the drop in efficiency denoted by the multiplication signs; because of their oscillatory form, these modes appreciably excite the nonzero orders diffracted by the grating.
  43. E. B. Grann, M. G. Moharam, D. A. Pommet, “Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings,” J. Opt. Soc. Am. A 11, 2695–2703 (1994). [CrossRef]
  44. In our opinion, the pillar structure offers the advantage of open ridges that are suitable for removing material during the RIE process.
  45. The depth h is chosen such that a 2π-phase change occurs at normal incidence between two homogeneous thin films coated on a glass substrate and whose refractive indices are 1-(nmax-1)/(2N-2) and nmax+(nmax-1)/(2N-2). This phase change is straightforwardly obtained by use of the Airy formula [see M. Born, E. Wolf, Principles of Optics, 6th ed. (Macmillan, New York, 1964), p. 62], for homogeneous thin films. The resulting formula for h is rather complex, and it turns out that, for the values of nmax considered hereafter, the simple expression given in Eq. (4) is valid.
  46. The value of 66.5% was computed by electromagnetic theory and holds for a grating etched into glass (refractive index, ng=1.52), with an optimized grating depth slightly larger than λ/(ng-1), and for unpolarized light at normal incidence from air. It is 1% larger than that obtained in Fig. 1 for a grating depth equal to λ/(ng-1).
  47. Also note that the maximum pillar aspect ratio is increased from 4.6, reported in Ref. 27, to 8.8 in this study because of the use of a smaller sampling period.
  48. Strictly speaking, the Airy formula for thin films has to be used, as mentioned above.
  49. The diffractive components designed along the lines of procedures 1 and 2 are weakly polarization dependent. In general, we found that the first-order diffraction efficiency is a few percent larger for TE than for TM (see, e.g., Table 1).
  50. B. Layet, M. R. Taghizadeh, “Electromagnetic analysis of fan-out gratings and diffractive lens arrays by field stitching,” J. Opt. Soc. Am. A 14, 1554–1561 (1997). [CrossRef]
  51. Y. Sheng, D. Feng, 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). [CrossRef]
  52. Since the width of the shadowing zone of the blazed échelette gratings decreases as the value of n increases, the performance is expected to improve with the refractive index.

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