Abstract

A modulation scheme that uses pulse-position modulation of a high-frequency binary grating to increase the diffraction efficiency of the elements is presented. These elements are designed and fabricated with both one- and two-dimensional signals for operation in transmission or reflection modes in the visible and the infrared regions of the spectrum. A direct electron-beam lithography fabrication process capable of realizing features of ~280 nm with a resolution of 15 nm is described in detail. Experimental results show that diffraction efficiencies of >80% are attainable.

© 1995 Optical Society of America

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References

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  1. T. W. Weidman, A. M. Josi, “New photodefinable glass etch masks for entirely dry photolithography—plasma deposited organosilican hydride polymers,” Appl. Phys. Lett. 62, 372–374 (1993).
    [CrossRef]
  2. J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
    [CrossRef]
  3. J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, “Multilevel grating array generators: fabrication error analysis and experiments,” Appl. Opt. 32, 2519–2525 (1993).
    [CrossRef] [PubMed]
  4. M. Ekberg, M. Larsson, S. Hård, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, “Multilevel grating array illuminators manufactured by electron-beam lithography,” Opt. Commun. 88, 37–41 (1992).
    [CrossRef]
  5. J. Turunen, P. Blair, J. M. Miller, M. R. Taghizadeh, E. Noponen, “Bragg holograms with binary synthetic surface-relief profile,” Opt. Lett. 18, 1022–1024 (1993).
    [CrossRef] [PubMed]
  6. 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]
  7. H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Zero-order gratings used as artificial distributed index medium,” Optik 89, 107–112 (1992).
  8. M. W. Farn, “Binary gratings with increased efficiency,” Appl. Opt. 31, 4953–4488 (1992).
    [CrossRef]
  9. O. Bryngdahl, F. Wyrowski, “Digital holography—computer-generated holograms,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam1990), Vol. XXVIII, pp. 1–86.
    [CrossRef]
  10. R. Petit, Ed, Electromagnetic Theory of Gratings (Springer, Berlin, 1980), pp. 14–15, 31–33.
  11. A. Vasara, E. Noponen, J. Turunen, J. M. Miller, M. R. Taghizadeh, J. Tuovinen, “Rigorous diffraction theory of binary optical interconnects,” in Holographic Optics III: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum Eng.1507, 224–238 (1991).
  12. E. Noponen, A. Vasara, J. Turunen, J. M. Miller, M. R. Taghizadeh, “Synthetic diffractive optics in the resonance domain,” J. Opt. Soc. Am. A 9, 1206–1213 (1992).
    [CrossRef]
  13. J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).
  14. F. Wyrowski, O. Bryngdahl, “Iterative Fourier transform algorithm applied to computer holography,” J. Opt. Soc. Am. A 5, 1058–1065 (1988).
    [CrossRef]
  15. B. Robertson, J. Turunen, H. Ichikawa, J. M. Miller, M. R. Taghizadeh, A. Vasara, “Hybrid kinoform fanout holograms in dichromated gelatin,” Appl. Opt. 30, 3711–3720 (1991).
    [CrossRef] [PubMed]
  16. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, eds., Numerical Recipes in Fortran (Cambridge U. Press, Cambridge, 1992), pp. 395–399.
  17. A. W. Lohmann, D. P. Paris, “Binary Fraunhofer holograms, generated by computer,” Appl. Opt. 6, 1739–1748 (1967).
    [CrossRef] [PubMed]
  18. S. P. Beaumont, P. G. Bower, T. Tamamura, C. D. W. Wilkinson, “Sub-20nm-wide metal lines by electron-beam exposure of thin poly(methyl methacrylate) films and lift off,” Appl. Phys. Lett. 38, 436–439 (1981).
    [CrossRef]
  19. W. Parkes, S. Thom, C. D. W. Wilkinson, “Applications of electron beam lithography to pattern submicron features in a beam-forming grating,” Micro. Eng. 23, 465–468 (1994).
    [CrossRef]

1994

W. Parkes, S. Thom, C. D. W. Wilkinson, “Applications of electron beam lithography to pattern submicron features in a beam-forming grating,” Micro. Eng. 23, 465–468 (1994).
[CrossRef]

1993

J. Turunen, P. Blair, J. M. Miller, M. R. Taghizadeh, E. Noponen, “Bragg holograms with binary synthetic surface-relief profile,” Opt. Lett. 18, 1022–1024 (1993).
[CrossRef] [PubMed]

T. W. Weidman, A. M. Josi, “New photodefinable glass etch masks for entirely dry photolithography—plasma deposited organosilican hydride polymers,” Appl. Phys. Lett. 62, 372–374 (1993).
[CrossRef]

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[CrossRef]

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, “Multilevel grating array generators: fabrication error analysis and experiments,” Appl. Opt. 32, 2519–2525 (1993).
[CrossRef] [PubMed]

1992

M. Ekberg, M. Larsson, S. Hård, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, “Multilevel grating array illuminators manufactured by electron-beam lithography,” Opt. Commun. 88, 37–41 (1992).
[CrossRef]

H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Zero-order gratings used as artificial distributed index medium,” Optik 89, 107–112 (1992).

M. W. Farn, “Binary gratings with increased efficiency,” Appl. Opt. 31, 4953–4488 (1992).
[CrossRef]

E. Noponen, A. Vasara, J. Turunen, J. M. Miller, M. R. Taghizadeh, “Synthetic diffractive optics in the resonance domain,” J. Opt. Soc. Am. A 9, 1206–1213 (1992).
[CrossRef]

1991

1989

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).

1988

1981

S. P. Beaumont, P. G. Bower, T. Tamamura, C. D. W. Wilkinson, “Sub-20nm-wide metal lines by electron-beam exposure of thin poly(methyl methacrylate) films and lift off,” Appl. Phys. Lett. 38, 436–439 (1981).
[CrossRef]

1967

Beaumont, S. P.

S. P. Beaumont, P. G. Bower, T. Tamamura, C. D. W. Wilkinson, “Sub-20nm-wide metal lines by electron-beam exposure of thin poly(methyl methacrylate) films and lift off,” Appl. Phys. Lett. 38, 436–439 (1981).
[CrossRef]

Blair, P.

Bower, P. G.

S. P. Beaumont, P. G. Bower, T. Tamamura, C. D. W. Wilkinson, “Sub-20nm-wide metal lines by electron-beam exposure of thin poly(methyl methacrylate) films and lift off,” Appl. Phys. Lett. 38, 436–439 (1981).
[CrossRef]

Bryngdahl, O.

F. Wyrowski, O. Bryngdahl, “Iterative Fourier transform algorithm applied to computer holography,” J. Opt. Soc. Am. A 5, 1058–1065 (1988).
[CrossRef]

O. Bryngdahl, F. Wyrowski, “Digital holography—computer-generated holograms,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam1990), Vol. XXVIII, pp. 1–86.
[CrossRef]

Ekberg, M.

M. Ekberg, M. Larsson, S. Hård, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, “Multilevel grating array illuminators manufactured by electron-beam lithography,” Opt. Commun. 88, 37–41 (1992).
[CrossRef]

Farn, M. W.

M. W. Farn, “Binary gratings with increased efficiency,” Appl. Opt. 31, 4953–4488 (1992).
[CrossRef]

Haidner, H.

H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Zero-order gratings used as artificial distributed index medium,” Optik 89, 107–112 (1992).

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]

Hård, S.

M. Ekberg, M. Larsson, S. Hård, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, “Multilevel grating array illuminators manufactured by electron-beam lithography,” Opt. Commun. 88, 37–41 (1992).
[CrossRef]

Ichikawa, H.

Josi, A. M.

T. W. Weidman, A. M. Josi, “New photodefinable glass etch masks for entirely dry photolithography—plasma deposited organosilican hydride polymers,” Appl. Phys. Lett. 62, 372–374 (1993).
[CrossRef]

Kipfer, P.

H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Zero-order gratings used as artificial distributed index medium,” Optik 89, 107–112 (1992).

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]

Larsson, M.

M. Ekberg, M. Larsson, S. Hård, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, “Multilevel grating array illuminators manufactured by electron-beam lithography,” Opt. Commun. 88, 37–41 (1992).
[CrossRef]

Lohmann, A. W.

Miller, J. M.

Noponen, E.

J. Turunen, P. Blair, J. M. Miller, M. R. Taghizadeh, E. Noponen, “Bragg holograms with binary synthetic surface-relief profile,” Opt. Lett. 18, 1022–1024 (1993).
[CrossRef] [PubMed]

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[CrossRef]

E. Noponen, A. Vasara, J. Turunen, J. M. Miller, M. R. Taghizadeh, “Synthetic diffractive optics in the resonance domain,” J. Opt. Soc. Am. A 9, 1206–1213 (1992).
[CrossRef]

A. Vasara, E. Noponen, J. Turunen, J. M. Miller, M. R. Taghizadeh, J. Tuovinen, “Rigorous diffraction theory of binary optical interconnects,” in Holographic Optics III: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum Eng.1507, 224–238 (1991).

Paris, D. P.

Parkes, W.

W. Parkes, S. Thom, C. D. W. Wilkinson, “Applications of electron beam lithography to pattern submicron features in a beam-forming grating,” Micro. Eng. 23, 465–468 (1994).
[CrossRef]

Robertson, B.

Ross, N.

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[CrossRef]

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, “Multilevel grating array generators: fabrication error analysis and experiments,” Appl. Opt. 32, 2519–2525 (1993).
[CrossRef] [PubMed]

Stork, W.

H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Zero-order gratings used as artificial distributed index medium,” Optik 89, 107–112 (1992).

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]

Streibl, N.

H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Zero-order gratings used as artificial distributed index medium,” Optik 89, 107–112 (1992).

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]

Taghizadeh, M. R.

J. Turunen, P. Blair, J. M. Miller, M. R. Taghizadeh, E. Noponen, “Bragg holograms with binary synthetic surface-relief profile,” Opt. Lett. 18, 1022–1024 (1993).
[CrossRef] [PubMed]

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[CrossRef]

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, “Multilevel grating array generators: fabrication error analysis and experiments,” Appl. Opt. 32, 2519–2525 (1993).
[CrossRef] [PubMed]

M. Ekberg, M. Larsson, S. Hård, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, “Multilevel grating array illuminators manufactured by electron-beam lithography,” Opt. Commun. 88, 37–41 (1992).
[CrossRef]

E. Noponen, A. Vasara, J. Turunen, J. M. Miller, M. R. Taghizadeh, “Synthetic diffractive optics in the resonance domain,” J. Opt. Soc. Am. A 9, 1206–1213 (1992).
[CrossRef]

B. Robertson, J. Turunen, H. Ichikawa, J. M. Miller, M. R. Taghizadeh, A. Vasara, “Hybrid kinoform fanout holograms in dichromated gelatin,” Appl. Opt. 30, 3711–3720 (1991).
[CrossRef] [PubMed]

A. Vasara, E. Noponen, J. Turunen, J. M. Miller, M. R. Taghizadeh, J. Tuovinen, “Rigorous diffraction theory of binary optical interconnects,” in Holographic Optics III: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum Eng.1507, 224–238 (1991).

Tamamura, T.

S. P. Beaumont, P. G. Bower, T. Tamamura, C. D. W. Wilkinson, “Sub-20nm-wide metal lines by electron-beam exposure of thin poly(methyl methacrylate) films and lift off,” Appl. Phys. Lett. 38, 436–439 (1981).
[CrossRef]

Thom, S.

W. Parkes, S. Thom, C. D. W. Wilkinson, “Applications of electron beam lithography to pattern submicron features in a beam-forming grating,” Micro. Eng. 23, 465–468 (1994).
[CrossRef]

Tuovinen, J.

A. Vasara, E. Noponen, J. Turunen, J. M. Miller, M. R. Taghizadeh, J. Tuovinen, “Rigorous diffraction theory of binary optical interconnects,” in Holographic Optics III: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum Eng.1507, 224–238 (1991).

Turunen, J.

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, “Multilevel grating array generators: fabrication error analysis and experiments,” Appl. Opt. 32, 2519–2525 (1993).
[CrossRef] [PubMed]

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[CrossRef]

J. Turunen, P. Blair, J. M. Miller, M. R. Taghizadeh, E. Noponen, “Bragg holograms with binary synthetic surface-relief profile,” Opt. Lett. 18, 1022–1024 (1993).
[CrossRef] [PubMed]

M. Ekberg, M. Larsson, S. Hård, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, “Multilevel grating array illuminators manufactured by electron-beam lithography,” Opt. Commun. 88, 37–41 (1992).
[CrossRef]

E. Noponen, A. Vasara, J. Turunen, J. M. Miller, M. R. Taghizadeh, “Synthetic diffractive optics in the resonance domain,” J. Opt. Soc. Am. A 9, 1206–1213 (1992).
[CrossRef]

B. Robertson, J. Turunen, H. Ichikawa, J. M. Miller, M. R. Taghizadeh, A. Vasara, “Hybrid kinoform fanout holograms in dichromated gelatin,” Appl. Opt. 30, 3711–3720 (1991).
[CrossRef] [PubMed]

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).

A. Vasara, E. Noponen, J. Turunen, J. M. Miller, M. R. Taghizadeh, J. Tuovinen, “Rigorous diffraction theory of binary optical interconnects,” in Holographic Optics III: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum Eng.1507, 224–238 (1991).

Vasara, A.

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[CrossRef]

M. Ekberg, M. Larsson, S. Hård, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, “Multilevel grating array illuminators manufactured by electron-beam lithography,” Opt. Commun. 88, 37–41 (1992).
[CrossRef]

E. Noponen, A. Vasara, J. Turunen, J. M. Miller, M. R. Taghizadeh, “Synthetic diffractive optics in the resonance domain,” J. Opt. Soc. Am. A 9, 1206–1213 (1992).
[CrossRef]

B. Robertson, J. Turunen, H. Ichikawa, J. M. Miller, M. R. Taghizadeh, A. Vasara, “Hybrid kinoform fanout holograms in dichromated gelatin,” Appl. Opt. 30, 3711–3720 (1991).
[CrossRef] [PubMed]

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).

A. Vasara, E. Noponen, J. Turunen, J. M. Miller, M. R. Taghizadeh, J. Tuovinen, “Rigorous diffraction theory of binary optical interconnects,” in Holographic Optics III: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum Eng.1507, 224–238 (1991).

Weidman, T. W.

T. W. Weidman, A. M. Josi, “New photodefinable glass etch masks for entirely dry photolithography—plasma deposited organosilican hydride polymers,” Appl. Phys. Lett. 62, 372–374 (1993).
[CrossRef]

Westerholm, J.

M. Ekberg, M. Larsson, S. Hård, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, “Multilevel grating array illuminators manufactured by electron-beam lithography,” Opt. Commun. 88, 37–41 (1992).
[CrossRef]

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).

Wilkinson, C. D. W.

W. Parkes, S. Thom, C. D. W. Wilkinson, “Applications of electron beam lithography to pattern submicron features in a beam-forming grating,” Micro. Eng. 23, 465–468 (1994).
[CrossRef]

S. P. Beaumont, P. G. Bower, T. Tamamura, C. D. W. Wilkinson, “Sub-20nm-wide metal lines by electron-beam exposure of thin poly(methyl methacrylate) films and lift off,” Appl. Phys. Lett. 38, 436–439 (1981).
[CrossRef]

Wyrowski, F.

F. Wyrowski, O. Bryngdahl, “Iterative Fourier transform algorithm applied to computer holography,” J. Opt. Soc. Am. A 5, 1058–1065 (1988).
[CrossRef]

O. Bryngdahl, F. Wyrowski, “Digital holography—computer-generated holograms,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam1990), Vol. XXVIII, pp. 1–86.
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

S. P. Beaumont, P. G. Bower, T. Tamamura, C. D. W. Wilkinson, “Sub-20nm-wide metal lines by electron-beam exposure of thin poly(methyl methacrylate) films and lift off,” Appl. Phys. Lett. 38, 436–439 (1981).
[CrossRef]

T. W. Weidman, A. M. Josi, “New photodefinable glass etch masks for entirely dry photolithography—plasma deposited organosilican hydride polymers,” Appl. Phys. Lett. 62, 372–374 (1993).
[CrossRef]

J. Mod. Opt.

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[CrossRef]

J. Opt. Soc. Am. A

Micro. Eng.

W. Parkes, S. Thom, C. D. W. Wilkinson, “Applications of electron beam lithography to pattern submicron features in a beam-forming grating,” Micro. Eng. 23, 465–468 (1994).
[CrossRef]

Opt. Commun.

M. Ekberg, M. Larsson, S. Hård, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, “Multilevel grating array illuminators manufactured by electron-beam lithography,” Opt. Commun. 88, 37–41 (1992).
[CrossRef]

Opt. Eng.

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).

Opt. Lett.

Optik

H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Zero-order gratings used as artificial distributed index medium,” Optik 89, 107–112 (1992).

Other

O. Bryngdahl, F. Wyrowski, “Digital holography—computer-generated holograms,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam1990), Vol. XXVIII, pp. 1–86.
[CrossRef]

R. Petit, Ed, Electromagnetic Theory of Gratings (Springer, Berlin, 1980), pp. 14–15, 31–33.

A. Vasara, E. Noponen, J. Turunen, J. M. Miller, M. R. Taghizadeh, J. Tuovinen, “Rigorous diffraction theory of binary optical interconnects,” in Holographic Optics III: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum Eng.1507, 224–238 (1991).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, eds., Numerical Recipes in Fortran (Cambridge U. Press, Cambridge, 1992), pp. 395–399.

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Figures (7)

Fig. 1
Fig. 1

(a) Binary high-frequency grating illuminated at Bragg incidence, (b) PP-modulated binary grating.

Fig. 2
Fig. 2

Grating height against (minus) first-order (normalized) diffraction efficiency for (a) quartz, (b) polyimide, (c) epoxy. Illumination is at Bragg incidence, TE polarization, d/λ = 0.9, and c/d = 0.5.

Fig. 3
Fig. 3

Fabrication steps involved in producing a binary grating with submicrometer features for operation in both reflection and transmission modes. (a) The prepared samples are patterned by an electron-beam pattern generator, and (b) the resist is developed. (c) The relevant material is deposited, and (d) for a reflection grating the unwanted deposits are removed. (e) For a transmission grating the deposited material acts as a mask when transferring the pattern into the substrate.

Fig. 4
Fig. 4

Cleaved section of a reflection element.

Fig. 5
Fig. 5

Scanning electron micrograph of a transmission element.

Fig. 6
Fig. 6

Polyimide transmission element; note the vertical, but rough, sidewall geometry.

Fig. 7
Fig. 7

Suppressed-order signal HWU: η = 85%, Δr = 0.4%. Open circles, suppressed orders; filled circles, unsuppressed orders.

Tables (1)

Tables Icon

Table 1 Results of Parametric Optimization of (Minus) First-Order Diffraction Efficiency for a Range of Possible Materials that form the Substrate of a PP-Modulated Transmission Grating a

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

sin θ = λ 2 n s d ,
( 1 / 2 ) < ( d / λ ) < ( 3 / 2 ) .
| s m , n s m + 1 , n | d .
θ G ( x , y ) = ϕ t , p + T × ( ϕ t + 1 , p + ϕ t , p ) ( x t T ) { x [ t T , ( t + 1 ) T ] y [ p P , ( p + 1 ) P ] ,
θ Q G ( x , y ) = θ G ( x , y ) + 2 π Q x .
h ( x , y ) = { h , if 2 k π θ Q G ( x , y ) < ( 2 k + 1 ) π 0 , otherwise ,

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