Abstract

Artificial index gratings, which are composed of binary microstructures of sizes less than the incident wavelength, are analyzed as functions of the filling factor or duty cycle of the microstructures. Different models for calculating the optimum duty cycles to produce high blazed diffraction efficiency are compared. Blazed binary grating designs in a material with a refractive index n = 2 show theoretical diffraction efficiencies as high as η = 80%. In the semiconductor material silicon, which has a refractive index n = 3.4, theoretical diffraction efficiencies as high as η = 70% are predicted.

© 1993 Optical Society of America

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References

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  1. H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Höchstfrequente Gitter als Gradienten-Index-Elemente,” presented at the Conference of the Deutschen Gesellschaft für Angewandte Optik (DGAO), Oldenburg, Germany, 1991).
  2. 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]
  3. S. Babin, H. Haidner, P. Kipfer, A. Lang, J. T. Sheridan, W. Stork, N. Streibl, “Artificial index surface relief diffraction optical elements,” in Miniature and Micro-Optics: Fabrication, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. and Instrum. Eng.1751, 202–213 (1992).
  4. W. M. Farn, “Binary gratings with increased efficiency,” Appl. Opt. 32, 4453–4458 (1992).
    [CrossRef]
  5. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), p. 705.
  6. R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
    [CrossRef]

1992 (1)

W. M. Farn, “Binary gratings with increased efficiency,” Appl. Opt. 32, 4453–4458 (1992).
[CrossRef]

1991 (1)

Babin, S.

S. Babin, H. Haidner, P. Kipfer, A. Lang, J. T. Sheridan, W. Stork, N. Streibl, “Artificial index surface relief diffraction optical elements,” in Miniature and Micro-Optics: Fabrication, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. and Instrum. Eng.1751, 202–213 (1992).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), p. 705.

Farn, W. M.

W. M. Farn, “Binary gratings with increased efficiency,” Appl. Opt. 32, 4453–4458 (1992).
[CrossRef]

Haidner, H.

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]

S. Babin, H. Haidner, P. Kipfer, A. Lang, J. T. Sheridan, W. Stork, N. Streibl, “Artificial index surface relief diffraction optical elements,” in Miniature and Micro-Optics: Fabrication, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. and Instrum. Eng.1751, 202–213 (1992).

H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Höchstfrequente Gitter als Gradienten-Index-Elemente,” presented at the Conference of the Deutschen Gesellschaft für Angewandte Optik (DGAO), Oldenburg, Germany, 1991).

Kipfer, P.

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]

S. Babin, H. Haidner, P. Kipfer, A. Lang, J. T. Sheridan, W. Stork, N. Streibl, “Artificial index surface relief diffraction optical elements,” in Miniature and Micro-Optics: Fabrication, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. and Instrum. Eng.1751, 202–213 (1992).

H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Höchstfrequente Gitter als Gradienten-Index-Elemente,” presented at the Conference of the Deutschen Gesellschaft für Angewandte Optik (DGAO), Oldenburg, Germany, 1991).

Lang, A.

S. Babin, H. Haidner, P. Kipfer, A. Lang, J. T. Sheridan, W. Stork, N. Streibl, “Artificial index surface relief diffraction optical elements,” in Miniature and Micro-Optics: Fabrication, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. and Instrum. Eng.1751, 202–213 (1992).

Petit, R.

R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
[CrossRef]

Sheridan, J. T.

S. Babin, H. Haidner, P. Kipfer, A. Lang, J. T. Sheridan, W. Stork, N. Streibl, “Artificial index surface relief diffraction optical elements,” in Miniature and Micro-Optics: Fabrication, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. and Instrum. Eng.1751, 202–213 (1992).

Stork, W.

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]

S. Babin, H. Haidner, P. Kipfer, A. Lang, J. T. Sheridan, W. Stork, N. Streibl, “Artificial index surface relief diffraction optical elements,” in Miniature and Micro-Optics: Fabrication, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. and Instrum. Eng.1751, 202–213 (1992).

H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Höchstfrequente Gitter als Gradienten-Index-Elemente,” presented at the Conference of the Deutschen Gesellschaft für Angewandte Optik (DGAO), Oldenburg, Germany, 1991).

Streibl, N.

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]

S. Babin, H. Haidner, P. Kipfer, A. Lang, J. T. Sheridan, W. Stork, N. Streibl, “Artificial index surface relief diffraction optical elements,” in Miniature and Micro-Optics: Fabrication, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. and Instrum. Eng.1751, 202–213 (1992).

H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Höchstfrequente Gitter als Gradienten-Index-Elemente,” presented at the Conference of the Deutschen Gesellschaft für Angewandte Optik (DGAO), Oldenburg, Germany, 1991).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), p. 705.

Appl. Opt. (1)

W. M. Farn, “Binary gratings with increased efficiency,” Appl. Opt. 32, 4453–4458 (1992).
[CrossRef]

Opt. Lett. (1)

Other (4)

S. Babin, H. Haidner, P. Kipfer, A. Lang, J. T. Sheridan, W. Stork, N. Streibl, “Artificial index surface relief diffraction optical elements,” in Miniature and Micro-Optics: Fabrication, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. and Instrum. Eng.1751, 202–213 (1992).

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), p. 705.

R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
[CrossRef]

H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Höchstfrequente Gitter als Gradienten-Index-Elemente,” presented at the Conference of the Deutschen Gesellschaft für Angewandte Optik (DGAO), Oldenburg, Germany, 1991).

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Figures (4)

Fig. 1
Fig. 1

AIG with period d1 made up of M microstructures, each of size d2. The grating depth is h. Each microstructure is different because of the variation iii the filled part of the microstructure d3,m.

Fig. 2
Fig. 2

Duty cycle as a function of phase: F, SPA, and DM predictions are presented for a microstructure with d2 = 0.4 μm, h = 1 μm, n1 = 1, n2 = 2, λ = 1 μm, and normal incidence.

Fig. 3
Fig. 3

Diffraction efficiency of the +1.0 order as a function of depth. The three gratings consist of M = 10 microstructures. The duty cycles tm of the microstructures were chosen with the help of the SPA, DM, and F functions in Fig. 2. The physical parameters of the microstructures are the same as those in Fig. 2.

Fig. 4
Fig. 4

Diffraction efficiency of +1.0 diffraction order as a function of depth: d1 = 30 μm, d2 = 3 μm, n1= 1, n2 = 3.4, λ = 10.6 μm, and normal incidence. Three gratings with M = 10 microstructures, designed using the F, DM, and SPA methods to choose the optimum duty cycles, are compared.

Equations (3)

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av , m = n 1 2 ( 1 t m ) + n 2 2 t m .
φ d , m = ( 2 π h / λ ) [ n 1 2 ( 1 t m ) + n 2 2 t m ] 1 / 2 2 π h n 1 / λ .
t m = m / ( M + 1 ) .

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