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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • 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)

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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

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

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)

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  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.
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  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.
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  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).
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  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.

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