Abstract

Antireflection coatings fabricated between the substrate and the diffractive microstructure are shown to reduce Fresnel losses effectively, especially for high-index substrates used in the infrared region, if the diffractive structure and the antireflection stack are designed simultaneously. A substantial reduction of the Fabry-Perot effect caused by the high-index substrate is observed by using antireflection layers with films thicker than the normal quarter-wave films.

© 2004 Optical Society of America

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References

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  1. J. Turunen and F. Wyrowski, eds., Diffractive Optics for Industrial and Commercial Applications (Wiley-VCH, Berlin, 1997).
  2. J. Turunen, M. Kuittinen, and F.Wyrowski, ???Diffractive optics: electromagnetic approach,??? in Progress in Optics, Vol. XL, E. Wolf, ed. (Elsevier, Amsterdam, 2000), pp. 343???388.
    [CrossRef]
  3. H. A. Macleod, Thin-Film Optical Filters, (Hilger, Bristol, 1986).
    [CrossRef]
  4. L. Li, ???Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,??? J. Opt. Soc. Am. A 13, 1024???1035 (1996).
    [CrossRef]
  5. See for example: Umicore Advanced Materials, <a href="http://www.advancedmaterials.umicore.com/Substrates/SilWaf.htm">http://www.advancedmaterials.umicore.com/Substrates/SilWaf.htm</a>.
  6. M. Moll, ???Silicon wafer: producers and suppliers,??? (URL collection), <a href="http://mmoll.web.cern.ch/mmoll/links/silicon.htm">http://mmoll.web.cern.ch/mmoll/links/silicon.htm</a>.
  7. M. R. Taghizadeh and J. Turunen, ???Synthetic diffractive elements for optical interconnection,??? Optical Computing and Processing 2, 221???242 (1992).
  8. L. Li, ???Use of Fourier series in the analysis of discontinuous periodic structures,??? J. Opt. Soc. Am. A 13, 1870???1876 (1996).
    [CrossRef]
  9. H. Dammann and K. Görtler,???High-efficiency in-line multiple imaging by means of multiple phase holograms,??? Opt. Commun. 3, 312???315 (1971).
    [CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

H. Dammann and K. Görtler,???High-efficiency in-line multiple imaging by means of multiple phase holograms,??? Opt. Commun. 3, 312???315 (1971).
[CrossRef]

Optical Computing and Processing (1)

M. R. Taghizadeh and J. Turunen, ???Synthetic diffractive elements for optical interconnection,??? Optical Computing and Processing 2, 221???242 (1992).

Progress in Optics, Vol. XL (1)

J. Turunen, M. Kuittinen, and F.Wyrowski, ???Diffractive optics: electromagnetic approach,??? in Progress in Optics, Vol. XL, E. Wolf, ed. (Elsevier, Amsterdam, 2000), pp. 343???388.
[CrossRef]

Other (4)

H. A. Macleod, Thin-Film Optical Filters, (Hilger, Bristol, 1986).
[CrossRef]

See for example: Umicore Advanced Materials, <a href="http://www.advancedmaterials.umicore.com/Substrates/SilWaf.htm">http://www.advancedmaterials.umicore.com/Substrates/SilWaf.htm</a>.

M. Moll, ???Silicon wafer: producers and suppliers,??? (URL collection), <a href="http://mmoll.web.cern.ch/mmoll/links/silicon.htm">http://mmoll.web.cern.ch/mmoll/links/silicon.htm</a>.

J. Turunen and F. Wyrowski, eds., Diffractive Optics for Industrial and Commercial Applications (Wiley-VCH, Berlin, 1997).

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Figures (5)

Fig. 1.
Fig. 1.

Two alternative ways to combine a diffractive microstructure with a thin-film AR structure: (a) the microstructure is over-coated with a thin film and (b) the AR coating is fabricated underneath the microstructure.

Fig. 2.
Fig. 2.

Transmission of a perfectly flat Si substrate (dashed line) as a function of its thickness and the influence of AR-coatings on both sides. Green line: Design 1. Red line: Design 2. Blue line: design 3.

Fig. 3.
Fig. 3.

Diffraction efficiencies of central transmitted orders of the 1→2 beam-splitter. Substrate is AR-coated on the both sides. Blue bars: Grating without AR-layers. Green bars: Optimal AR stack with a standard grating. Red bars: Simultaneously optimized AR and grating layer thicknesses.

Fig. 4.
Fig. 4.

Diffraction efficiencies ηm of the central orders of 1→5 beam splitters. Substrate is AR-coated on the both sides. Blue bars: SiO2 grating on a Si substrate without AR-layers. Green bars: Optimal AR-layer stack with a standard grating. Red bars: Simultaneously optimized AR and grating layer thicknesses.

Fig. 5.
Fig. 5.

Transmitted diffraction efficiencies of 4-level staircase gratings. Substrate is AR-coated on the both sides. Blue: Grating without AR-layers. Green: Optimized AR stacks. Red: AR-layers and grating thickness scale optimized simultaneously.

Tables (1)

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Table 1. Three AR coating designs consisting of a Al2O3 layer with n=1.6 and thickness h 1, and a HfO2 layer (located next to the Si-substrate) with n=1.9 and thickness h 2.

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