Abstract

We report the use of rigorous coupled-wave diffraction analysis in conjunction with the simulated annealing optimization method for performing optimal design of binary-level surface-relief diffractive elements with subwavelength, submicrometer features that exhibit quasi-linear-phase transmittance. An element designed for operation at 1.55 μm has been fabricated and is characterized.

© 1995 Optical Society of America

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References

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  1. E. Gluch, H. Haidner, P. Kipfer, W. Stork, N. Streibl, “High frequency grating used as graded index medium,” Tech. Rep. (Physikalisches Institut der Universität Erlangen-Nürnberg, Erlangen, Germany, 1990).
  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 and System Applications II, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1751, 202–213 (1993).
    [CrossRef]
  4. H. Haidner, P. Kipfer, J. T. Sheridan, J. Schwider, N. Striebl, M. Collischon, J. Hutfless, M. Marz, “Diffraction grating with rectangular grooves exceeding 80% diffraction efficiency,” Infrared Phys. 34, 467–475 (1993).
    [CrossRef]
  5. M. Moharam, T. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981).
    [CrossRef]
  6. M. Moharam, T. Gaylord, “Rigorous coupled-wave analysis of grating diffraction—E-mode polarization and losses,” J. Opt. Soc. Am. 73, 451–455 (1983).
    [CrossRef]
  7. T. Gaylord, M. Moharam, “Planar dielectric grating diffraction theories,” Appl. Phys. B 28, 1–14 (1982).
    [CrossRef]
  8. W. B. Veldkamp, G. J. Swanson, S. A. Gaither, C. L. Chen, T. R. Osborne, “Binary optics: a diffraction analysis,” MIT Lincoln Lab. Tech. Rep. (Lincoln Laboratory, Lexington, Mass., 1989).
  9. S. Kirkpatrick, J. C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
    [CrossRef] [PubMed]
  10. P. J. M. Laarhoven, Theoretical and Computational Aspects of Simulated Annealing (Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands, 1988).
  11. E. A. Taft, “Characterization of silicon nitride film,” J. Electrochem. Soc. 118, 1341–1346 (1971).
    [CrossRef]
  12. E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985), Subpart 3, p. 771.

1993 (1)

H. Haidner, P. Kipfer, J. T. Sheridan, J. Schwider, N. Striebl, M. Collischon, J. Hutfless, M. Marz, “Diffraction grating with rectangular grooves exceeding 80% diffraction efficiency,” Infrared Phys. 34, 467–475 (1993).
[CrossRef]

1991 (1)

1983 (2)

1982 (1)

T. Gaylord, M. Moharam, “Planar dielectric grating diffraction theories,” Appl. Phys. B 28, 1–14 (1982).
[CrossRef]

1981 (1)

1971 (1)

E. A. Taft, “Characterization of silicon nitride film,” J. Electrochem. Soc. 118, 1341–1346 (1971).
[CrossRef]

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 and System Applications II, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1751, 202–213 (1993).
[CrossRef]

Chen, C. L.

W. B. Veldkamp, G. J. Swanson, S. A. Gaither, C. L. Chen, T. R. Osborne, “Binary optics: a diffraction analysis,” MIT Lincoln Lab. Tech. Rep. (Lincoln Laboratory, Lexington, Mass., 1989).

Collischon, M.

H. Haidner, P. Kipfer, J. T. Sheridan, J. Schwider, N. Striebl, M. Collischon, J. Hutfless, M. Marz, “Diffraction grating with rectangular grooves exceeding 80% diffraction efficiency,” Infrared Phys. 34, 467–475 (1993).
[CrossRef]

Gaither, S. A.

W. B. Veldkamp, G. J. Swanson, S. A. Gaither, C. L. Chen, T. R. Osborne, “Binary optics: a diffraction analysis,” MIT Lincoln Lab. Tech. Rep. (Lincoln Laboratory, Lexington, Mass., 1989).

Gaylord, T.

Gelatt, J. C. D.

S. Kirkpatrick, J. C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Gluch, E.

E. Gluch, H. Haidner, P. Kipfer, W. Stork, N. Streibl, “High frequency grating used as graded index medium,” Tech. Rep. (Physikalisches Institut der Universität Erlangen-Nürnberg, Erlangen, Germany, 1990).

Haidner, H.

H. Haidner, P. Kipfer, J. T. Sheridan, J. Schwider, N. Striebl, M. Collischon, J. Hutfless, M. Marz, “Diffraction grating with rectangular grooves exceeding 80% diffraction efficiency,” Infrared Phys. 34, 467–475 (1993).
[CrossRef]

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]

E. Gluch, H. Haidner, P. Kipfer, W. Stork, N. Streibl, “High frequency grating used as graded index medium,” Tech. Rep. (Physikalisches Institut der Universität Erlangen-Nürnberg, Erlangen, Germany, 1990).

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 and System Applications II, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1751, 202–213 (1993).
[CrossRef]

Hutfless, J.

H. Haidner, P. Kipfer, J. T. Sheridan, J. Schwider, N. Striebl, M. Collischon, J. Hutfless, M. Marz, “Diffraction grating with rectangular grooves exceeding 80% diffraction efficiency,” Infrared Phys. 34, 467–475 (1993).
[CrossRef]

Kipfer, P.

H. Haidner, P. Kipfer, J. T. Sheridan, J. Schwider, N. Striebl, M. Collischon, J. Hutfless, M. Marz, “Diffraction grating with rectangular grooves exceeding 80% diffraction efficiency,” Infrared Phys. 34, 467–475 (1993).
[CrossRef]

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 and System Applications II, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1751, 202–213 (1993).
[CrossRef]

E. Gluch, H. Haidner, P. Kipfer, W. Stork, N. Streibl, “High frequency grating used as graded index medium,” Tech. Rep. (Physikalisches Institut der Universität Erlangen-Nürnberg, Erlangen, Germany, 1990).

Kirkpatrick, S.

S. Kirkpatrick, J. C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Laarhoven, P. J. M.

P. J. M. Laarhoven, Theoretical and Computational Aspects of Simulated Annealing (Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands, 1988).

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 and System Applications II, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1751, 202–213 (1993).
[CrossRef]

Marz, M.

H. Haidner, P. Kipfer, J. T. Sheridan, J. Schwider, N. Striebl, M. Collischon, J. Hutfless, M. Marz, “Diffraction grating with rectangular grooves exceeding 80% diffraction efficiency,” Infrared Phys. 34, 467–475 (1993).
[CrossRef]

Moharam, M.

Osborne, T. R.

W. B. Veldkamp, G. J. Swanson, S. A. Gaither, C. L. Chen, T. R. Osborne, “Binary optics: a diffraction analysis,” MIT Lincoln Lab. Tech. Rep. (Lincoln Laboratory, Lexington, Mass., 1989).

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985), Subpart 3, p. 771.

Schwider, J.

H. Haidner, P. Kipfer, J. T. Sheridan, J. Schwider, N. Striebl, M. Collischon, J. Hutfless, M. Marz, “Diffraction grating with rectangular grooves exceeding 80% diffraction efficiency,” Infrared Phys. 34, 467–475 (1993).
[CrossRef]

Sheridan, J. T.

H. Haidner, P. Kipfer, J. T. Sheridan, J. Schwider, N. Striebl, M. Collischon, J. Hutfless, M. Marz, “Diffraction grating with rectangular grooves exceeding 80% diffraction efficiency,” Infrared Phys. 34, 467–475 (1993).
[CrossRef]

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 and System Applications II, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1751, 202–213 (1993).
[CrossRef]

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 and System Applications II, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1751, 202–213 (1993).
[CrossRef]

E. Gluch, H. Haidner, P. Kipfer, W. Stork, N. Streibl, “High frequency grating used as graded index medium,” Tech. Rep. (Physikalisches Institut der Universität Erlangen-Nürnberg, Erlangen, Germany, 1990).

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]

E. Gluch, H. Haidner, P. Kipfer, W. Stork, N. Streibl, “High frequency grating used as graded index medium,” Tech. Rep. (Physikalisches Institut der Universität Erlangen-Nürnberg, Erlangen, Germany, 1990).

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 and System Applications II, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1751, 202–213 (1993).
[CrossRef]

Striebl, N.

H. Haidner, P. Kipfer, J. T. Sheridan, J. Schwider, N. Striebl, M. Collischon, J. Hutfless, M. Marz, “Diffraction grating with rectangular grooves exceeding 80% diffraction efficiency,” Infrared Phys. 34, 467–475 (1993).
[CrossRef]

Swanson, G. J.

W. B. Veldkamp, G. J. Swanson, S. A. Gaither, C. L. Chen, T. R. Osborne, “Binary optics: a diffraction analysis,” MIT Lincoln Lab. Tech. Rep. (Lincoln Laboratory, Lexington, Mass., 1989).

Taft, E. A.

E. A. Taft, “Characterization of silicon nitride film,” J. Electrochem. Soc. 118, 1341–1346 (1971).
[CrossRef]

Vecchi, M. P.

S. Kirkpatrick, J. C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Veldkamp, W. B.

W. B. Veldkamp, G. J. Swanson, S. A. Gaither, C. L. Chen, T. R. Osborne, “Binary optics: a diffraction analysis,” MIT Lincoln Lab. Tech. Rep. (Lincoln Laboratory, Lexington, Mass., 1989).

Appl. Phys. B (1)

T. Gaylord, M. Moharam, “Planar dielectric grating diffraction theories,” Appl. Phys. B 28, 1–14 (1982).
[CrossRef]

Infrared Phys. (1)

H. Haidner, P. Kipfer, J. T. Sheridan, J. Schwider, N. Striebl, M. Collischon, J. Hutfless, M. Marz, “Diffraction grating with rectangular grooves exceeding 80% diffraction efficiency,” Infrared Phys. 34, 467–475 (1993).
[CrossRef]

J. Electrochem. Soc. (1)

E. A. Taft, “Characterization of silicon nitride film,” J. Electrochem. Soc. 118, 1341–1346 (1971).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Lett. (1)

Science (1)

S. Kirkpatrick, J. C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Other (5)

P. J. M. Laarhoven, Theoretical and Computational Aspects of Simulated Annealing (Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands, 1988).

E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985), Subpart 3, p. 771.

E. Gluch, H. Haidner, P. Kipfer, W. Stork, N. Streibl, “High frequency grating used as graded index medium,” Tech. Rep. (Physikalisches Institut der Universität Erlangen-Nürnberg, Erlangen, Germany, 1990).

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 and System Applications II, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1751, 202–213 (1993).
[CrossRef]

W. B. Veldkamp, G. J. Swanson, S. A. Gaither, C. L. Chen, T. R. Osborne, “Binary optics: a diffraction analysis,” MIT Lincoln Lab. Tech. Rep. (Lincoln Laboratory, Lexington, Mass., 1989).

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Figures (17)

Fig. 1
Fig. 1

Comparison of the different grating structures.

Fig. 2
Fig. 2

Transition from prism to type-II grating.

Fig. 3
Fig. 3

(a) Type-I grating. The period is Λ = 10λ = 6.328 μm, and the height h of the grating is 2.495 μm. (b) Equivalent linear blazed grating with same period as (a), with h= 1.2656 μm.

Fig. 4
Fig. 4

Optimized profile of transmissive type-I grating with Λ = 6.328 μm and h = 2.495 μm.

Fig. 5
Fig. 5

Optimized profile of λ = 2λ = 3.1 μm transmissive type-I grating for a silicon substrate. The grating height is chosen as h = 0.2 μm.

Fig. 6
Fig. 6

Optimized profile of Λ = 2λ = 1.2656 μm type-II grating with h = 2.085 μm.

Fig. 7
Fig. 7

Optimized profile of Λ = 10λ = 6.328 μm type-II grating with h = 2.435 μm.

Fig. 8
Fig. 8

Optimized profile of Λ = 10λ = 6.328 μm type-II grating for maximum second-order diffraction. The grating height is chosen as h = 2.435 μm.

Fig. 9
Fig. 9

Optimized profile of Λ = 10λ = 6.328 μm type-III grating with h = 2.41 μm.

Fig. 10
Fig. 10

Optimized profile of Λ = 10λ = 6.328 μm type-III grating that diffracts two main orders, the first and the fourth. The grating height is h = 2.545 μm.

Fig. 11
Fig. 11

Relationship between the incident angle and the first-order diffraction efficiency in a silicon type-I grating (see Fig. 5). Solid curve, reflection; dotted curve, transmission.

Fig. 12
Fig. 12

Relationship between the incident angle and the first-order diffraction efficiency in a glass type-II grating (see Fig. 7). Solid curve, reflection; dotted curve, transmission.

Fig. 13
Fig. 13

Relationship between the incident angle and the first-order and the fourth-order transmission efficiencies in a glass type-III grating (see Fig. 10).

Fig. 14
Fig. 14

Chromium type-I grating lifted off on top of a silicon substrate.

Fig. 15
Fig. 15

SEM photograph of the fabricated type-I grating on a silicon substrate.

Fig. 16
Fig. 16

Experimental configuration for characterizing the type-I grating.

Fig. 17
Fig. 17

Relationship between the incident angle and the first-order diffraction in silicon type-I grating.

Tables (5)

Tables Icon

Table 1 Parameters for Binary Gratings with Localized Subwavelength, Submicrometer Feature Design

Tables Icon

Table 2 Diffraction Efficiencies for the Type-III Grating with the First and the Fourth Orders Optimized

Tables Icon

Table 3 Diffraction Efficiencies for the Type-I and the Linear Blazed Gratings, with Maximum Transmission at First Order

Tables Icon

Table 4 Diffraction Efficiencies for the Type-II and the Type-III Gratings, with Maximum Transmission at First Order

Tables Icon

Table 5 Parameters for E-Beam Direct Writing

Equations (5)

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Δ S = p d M = p p d Λ = p 2 d Λ ,
Δ w i = S ma S mi M .
h = Δ S Δ w i .
η n = P n / P 0 ,
sin ( θ t ) = sin ( θ i ) + ( m λ / Λ ) ,

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