Abstract

Polarization-selective gratings are designed by use of rigorous electromagnetic diffraction theory. The polarizing effects are attained by special surface-relief structures. We present a scheme for coding two different optical functions in one diffractive element. It is based on a combination of the scalar diffraction theory and the effective-medium theory. The diffractive element may be regarded as a combination of a phase element and a subwavelength grating.

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. L. Roumiguieres, “The rectangular-groove grating used as an infrared polarizer,” Opt. Commun. 19, 76–78 (1976).
    [CrossRef]
  2. K. Knop, “Reflection grating polarizer for the infrared,” Opt. Commun. 26, 281–283 (1978).
    [CrossRef]
  3. G. J. Sonek, D. K. Wagner, J. M. Ballantyne, “Ultraviolet grating polarizers,” J. Vac. Sci Technol. 19, 921–923 (1981).
    [CrossRef]
  4. L. H. Cescato, E. Gluch, N. Streibl, “Holographic quarterwave plates,” Appl. Opt. 29, 3286–3290 (1990).
    [CrossRef] [PubMed]
  5. C. W. Haggans, L. Li, T. Fujita, R. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mod. Opt. 40, 675–686 (1993).
    [CrossRef]
  6. S. J. Wilson, M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” Opt. Acta 29, 993–1009 (1982).
    [CrossRef]
  7. D. A. Pommet, M. G. Moharam, E. B. Grann, “Limits of scalar diffraction theory for diffractive phase elements,” J. Opt. Soc. Am. A 11, 1827–1834 (1994).
    [CrossRef]
  8. J. Hossfeld, D. Columbus, H. Sprave, T. Tschudi, W. Dultz, “Polarizing computer-generated holograms,” Opt. Eng. 32, 1835–1838 (1993).
    [CrossRef]
  9. Q. W. Song, M. C. Lee, P. J. Talbot, “Polarization sensitivity of birefringent photorefractive holograms and its applications to binary switching,” Appl. Opt. 31, 6240–6246 (1992).
    [CrossRef] [PubMed]
  10. F. Xu, J. E. Ford, Y. Fainman, “Polarization-selective computer-generated holograms: design, fabrication, and applications,” Appl. Opt. 34, 256–266 (1995).
    [CrossRef] [PubMed]
  11. A. Ohba, Y. Kimura, S. Sugama, Y. Urino, Y. Ono, “Holographic optical-element with analyzer function for magneto-optical disk head,” Jpn. J. Appl. Phys. 28, Suppl. 28-3, 359–361 (1989).
  12. M. W. Farn, “Binary gratings with increased efficiency,” Appl. Opt. 31, 4453–4458 (1992).
    [CrossRef] [PubMed]
  13. M. Collischon, H. Haidner, P. Kipfer, A. Lang, J. T. Sheridan, J. Schwider, N. Streibl, J. Lindolf, “Binary blazed reflection gratings,” Appl. Opt. 33, 3572–3577 (1994).
    [CrossRef] [PubMed]
  14. R. Bräuer, O. Bryngdahl, “Design of antireflection gratings with approximate and rigorous methods,” Appl. Opt. 33, 7875–7882 (1994).
    [CrossRef] [PubMed]
  15. C. B. Burckhardt, “Diffraction of a plane wave at a sinusoidally stratified dielectric grating,” J. Opt. Soc.Am. 56, 1502–1509 (1966).
    [CrossRef]
  16. F. G. Kaspar, “Diffraction by thick, periodically stratified gratings with complex dielectric constant,” J. Opt. Soc. Am. 63, 37–45 (1973).
    [CrossRef]
  17. K. Knop, “Rigorous diffraction theory for transmission phase gratings with deep rectangular grooves,” J. Opt. Soc. Am. 68, 1206–1210 (1978).
    [CrossRef]
  18. W. J. Dallas, Computer-Generated Holograms, Vol. 41 of Topics in Applied Physics (Springer-Verlag, Berlin, 1980).
  19. W. H. Lee, “Computer generated holograms: techniques and applications,” in Progress in Optics, E. Wolf, ed. (North-Holland, New York, 1978), Vol. 16, Chap. 3, pp. 119–223.
    [CrossRef]
  20. H. Lüpken, T. Pauka, R. Bräuer, F. Wyrowski, O. Bryngdahl, “On the design of Dammann gratings,” Opt. Commun. 100, 415–420 (1993).
    [CrossRef]
  21. F. Wyrowski, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Physics 54, 1481–1571 (1991).
    [CrossRef]
  22. P. B. Fischer, S. Y. Chou, “Sub-50 nm high aspect-ratio silicon pillars, ridges, and trenches fabricated using ultra-high resolution electron beam lithography and reactive ion etching,” Appl. Phys. Lett. 62, 1414–1416 (1993).
    [CrossRef]

1995 (1)

1994 (3)

1993 (4)

P. B. Fischer, S. Y. Chou, “Sub-50 nm high aspect-ratio silicon pillars, ridges, and trenches fabricated using ultra-high resolution electron beam lithography and reactive ion etching,” Appl. Phys. Lett. 62, 1414–1416 (1993).
[CrossRef]

C. W. Haggans, L. Li, T. Fujita, R. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mod. Opt. 40, 675–686 (1993).
[CrossRef]

J. Hossfeld, D. Columbus, H. Sprave, T. Tschudi, W. Dultz, “Polarizing computer-generated holograms,” Opt. Eng. 32, 1835–1838 (1993).
[CrossRef]

H. Lüpken, T. Pauka, R. Bräuer, F. Wyrowski, O. Bryngdahl, “On the design of Dammann gratings,” Opt. Commun. 100, 415–420 (1993).
[CrossRef]

1992 (2)

1991 (1)

F. Wyrowski, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Physics 54, 1481–1571 (1991).
[CrossRef]

1990 (1)

1989 (1)

A. Ohba, Y. Kimura, S. Sugama, Y. Urino, Y. Ono, “Holographic optical-element with analyzer function for magneto-optical disk head,” Jpn. J. Appl. Phys. 28, Suppl. 28-3, 359–361 (1989).

1982 (1)

S. J. Wilson, M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” Opt. Acta 29, 993–1009 (1982).
[CrossRef]

1981 (1)

G. J. Sonek, D. K. Wagner, J. M. Ballantyne, “Ultraviolet grating polarizers,” J. Vac. Sci Technol. 19, 921–923 (1981).
[CrossRef]

1978 (2)

1976 (1)

J. L. Roumiguieres, “The rectangular-groove grating used as an infrared polarizer,” Opt. Commun. 19, 76–78 (1976).
[CrossRef]

1973 (1)

1966 (1)

C. B. Burckhardt, “Diffraction of a plane wave at a sinusoidally stratified dielectric grating,” J. Opt. Soc.Am. 56, 1502–1509 (1966).
[CrossRef]

Ballantyne, J. M.

G. J. Sonek, D. K. Wagner, J. M. Ballantyne, “Ultraviolet grating polarizers,” J. Vac. Sci Technol. 19, 921–923 (1981).
[CrossRef]

Bräuer, R.

R. Bräuer, O. Bryngdahl, “Design of antireflection gratings with approximate and rigorous methods,” Appl. Opt. 33, 7875–7882 (1994).
[CrossRef] [PubMed]

H. Lüpken, T. Pauka, R. Bräuer, F. Wyrowski, O. Bryngdahl, “On the design of Dammann gratings,” Opt. Commun. 100, 415–420 (1993).
[CrossRef]

Bryngdahl, O.

R. Bräuer, O. Bryngdahl, “Design of antireflection gratings with approximate and rigorous methods,” Appl. Opt. 33, 7875–7882 (1994).
[CrossRef] [PubMed]

H. Lüpken, T. Pauka, R. Bräuer, F. Wyrowski, O. Bryngdahl, “On the design of Dammann gratings,” Opt. Commun. 100, 415–420 (1993).
[CrossRef]

F. Wyrowski, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Physics 54, 1481–1571 (1991).
[CrossRef]

Burckhardt, C. B.

C. B. Burckhardt, “Diffraction of a plane wave at a sinusoidally stratified dielectric grating,” J. Opt. Soc.Am. 56, 1502–1509 (1966).
[CrossRef]

Cescato, L. H.

Chou, S. Y.

P. B. Fischer, S. Y. Chou, “Sub-50 nm high aspect-ratio silicon pillars, ridges, and trenches fabricated using ultra-high resolution electron beam lithography and reactive ion etching,” Appl. Phys. Lett. 62, 1414–1416 (1993).
[CrossRef]

Collischon, M.

Columbus, D.

J. Hossfeld, D. Columbus, H. Sprave, T. Tschudi, W. Dultz, “Polarizing computer-generated holograms,” Opt. Eng. 32, 1835–1838 (1993).
[CrossRef]

Dallas, W. J.

W. J. Dallas, Computer-Generated Holograms, Vol. 41 of Topics in Applied Physics (Springer-Verlag, Berlin, 1980).

Dultz, W.

J. Hossfeld, D. Columbus, H. Sprave, T. Tschudi, W. Dultz, “Polarizing computer-generated holograms,” Opt. Eng. 32, 1835–1838 (1993).
[CrossRef]

Fainman, Y.

Farn, M. W.

Fischer, P. B.

P. B. Fischer, S. Y. Chou, “Sub-50 nm high aspect-ratio silicon pillars, ridges, and trenches fabricated using ultra-high resolution electron beam lithography and reactive ion etching,” Appl. Phys. Lett. 62, 1414–1416 (1993).
[CrossRef]

Ford, J. E.

Fujita, T.

C. W. Haggans, L. Li, T. Fujita, R. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mod. Opt. 40, 675–686 (1993).
[CrossRef]

Gluch, E.

Grann, E. B.

Haggans, C. W.

C. W. Haggans, L. Li, T. Fujita, R. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mod. Opt. 40, 675–686 (1993).
[CrossRef]

Haidner, H.

Hossfeld, J.

J. Hossfeld, D. Columbus, H. Sprave, T. Tschudi, W. Dultz, “Polarizing computer-generated holograms,” Opt. Eng. 32, 1835–1838 (1993).
[CrossRef]

Hutley, M. C.

S. J. Wilson, M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” Opt. Acta 29, 993–1009 (1982).
[CrossRef]

Kaspar, F. G.

Kimura, Y.

A. Ohba, Y. Kimura, S. Sugama, Y. Urino, Y. Ono, “Holographic optical-element with analyzer function for magneto-optical disk head,” Jpn. J. Appl. Phys. 28, Suppl. 28-3, 359–361 (1989).

Kipfer, P.

Knop, K.

Kostuk, R.

C. W. Haggans, L. Li, T. Fujita, R. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mod. Opt. 40, 675–686 (1993).
[CrossRef]

Lang, A.

Lee, M. C.

Lee, W. H.

W. H. Lee, “Computer generated holograms: techniques and applications,” in Progress in Optics, E. Wolf, ed. (North-Holland, New York, 1978), Vol. 16, Chap. 3, pp. 119–223.
[CrossRef]

Li, L.

C. W. Haggans, L. Li, T. Fujita, R. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mod. Opt. 40, 675–686 (1993).
[CrossRef]

Lindolf, J.

Lüpken, H.

H. Lüpken, T. Pauka, R. Bräuer, F. Wyrowski, O. Bryngdahl, “On the design of Dammann gratings,” Opt. Commun. 100, 415–420 (1993).
[CrossRef]

Moharam, M. G.

Ohba, A.

A. Ohba, Y. Kimura, S. Sugama, Y. Urino, Y. Ono, “Holographic optical-element with analyzer function for magneto-optical disk head,” Jpn. J. Appl. Phys. 28, Suppl. 28-3, 359–361 (1989).

Ono, Y.

A. Ohba, Y. Kimura, S. Sugama, Y. Urino, Y. Ono, “Holographic optical-element with analyzer function for magneto-optical disk head,” Jpn. J. Appl. Phys. 28, Suppl. 28-3, 359–361 (1989).

Pauka, T.

H. Lüpken, T. Pauka, R. Bräuer, F. Wyrowski, O. Bryngdahl, “On the design of Dammann gratings,” Opt. Commun. 100, 415–420 (1993).
[CrossRef]

Pommet, D. A.

Roumiguieres, J. L.

J. L. Roumiguieres, “The rectangular-groove grating used as an infrared polarizer,” Opt. Commun. 19, 76–78 (1976).
[CrossRef]

Schwider, J.

Sheridan, J. T.

Sonek, G. J.

G. J. Sonek, D. K. Wagner, J. M. Ballantyne, “Ultraviolet grating polarizers,” J. Vac. Sci Technol. 19, 921–923 (1981).
[CrossRef]

Song, Q. W.

Sprave, H.

J. Hossfeld, D. Columbus, H. Sprave, T. Tschudi, W. Dultz, “Polarizing computer-generated holograms,” Opt. Eng. 32, 1835–1838 (1993).
[CrossRef]

Streibl, N.

Sugama, S.

A. Ohba, Y. Kimura, S. Sugama, Y. Urino, Y. Ono, “Holographic optical-element with analyzer function for magneto-optical disk head,” Jpn. J. Appl. Phys. 28, Suppl. 28-3, 359–361 (1989).

Talbot, P. J.

Tschudi, T.

J. Hossfeld, D. Columbus, H. Sprave, T. Tschudi, W. Dultz, “Polarizing computer-generated holograms,” Opt. Eng. 32, 1835–1838 (1993).
[CrossRef]

Urino, Y.

A. Ohba, Y. Kimura, S. Sugama, Y. Urino, Y. Ono, “Holographic optical-element with analyzer function for magneto-optical disk head,” Jpn. J. Appl. Phys. 28, Suppl. 28-3, 359–361 (1989).

Wagner, D. K.

G. J. Sonek, D. K. Wagner, J. M. Ballantyne, “Ultraviolet grating polarizers,” J. Vac. Sci Technol. 19, 921–923 (1981).
[CrossRef]

Wilson, S. J.

S. J. Wilson, M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” Opt. Acta 29, 993–1009 (1982).
[CrossRef]

Wyrowski, F.

H. Lüpken, T. Pauka, R. Bräuer, F. Wyrowski, O. Bryngdahl, “On the design of Dammann gratings,” Opt. Commun. 100, 415–420 (1993).
[CrossRef]

F. Wyrowski, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Physics 54, 1481–1571 (1991).
[CrossRef]

Xu, F.

Appl. Opt. (6)

Appl. Phys. Lett. (1)

P. B. Fischer, S. Y. Chou, “Sub-50 nm high aspect-ratio silicon pillars, ridges, and trenches fabricated using ultra-high resolution electron beam lithography and reactive ion etching,” Appl. Phys. Lett. 62, 1414–1416 (1993).
[CrossRef]

J. Mod. Opt. (1)

C. W. Haggans, L. Li, T. Fujita, R. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mod. Opt. 40, 675–686 (1993).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

J. Opt. Soc.Am. (1)

C. B. Burckhardt, “Diffraction of a plane wave at a sinusoidally stratified dielectric grating,” J. Opt. Soc.Am. 56, 1502–1509 (1966).
[CrossRef]

J. Vac. Sci Technol. (1)

G. J. Sonek, D. K. Wagner, J. M. Ballantyne, “Ultraviolet grating polarizers,” J. Vac. Sci Technol. 19, 921–923 (1981).
[CrossRef]

Jpn. J. Appl. Phys. (1)

A. Ohba, Y. Kimura, S. Sugama, Y. Urino, Y. Ono, “Holographic optical-element with analyzer function for magneto-optical disk head,” Jpn. J. Appl. Phys. 28, Suppl. 28-3, 359–361 (1989).

Opt. Acta (1)

S. J. Wilson, M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” Opt. Acta 29, 993–1009 (1982).
[CrossRef]

Opt. Commun. (3)

J. L. Roumiguieres, “The rectangular-groove grating used as an infrared polarizer,” Opt. Commun. 19, 76–78 (1976).
[CrossRef]

K. Knop, “Reflection grating polarizer for the infrared,” Opt. Commun. 26, 281–283 (1978).
[CrossRef]

H. Lüpken, T. Pauka, R. Bräuer, F. Wyrowski, O. Bryngdahl, “On the design of Dammann gratings,” Opt. Commun. 100, 415–420 (1993).
[CrossRef]

Opt. Eng. (1)

J. Hossfeld, D. Columbus, H. Sprave, T. Tschudi, W. Dultz, “Polarizing computer-generated holograms,” Opt. Eng. 32, 1835–1838 (1993).
[CrossRef]

Rep. Prog. Physics (1)

F. Wyrowski, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Physics 54, 1481–1571 (1991).
[CrossRef]

Other (2)

W. J. Dallas, Computer-Generated Holograms, Vol. 41 of Topics in Applied Physics (Springer-Verlag, Berlin, 1980).

W. H. Lee, “Computer generated holograms: techniques and applications,” in Progress in Optics, E. Wolf, ed. (North-Holland, New York, 1978), Vol. 16, Chap. 3, pp. 119–223.
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

(a) Phase grating. (b) The structure details of the phase grating are imprinted by several periods of a subwave-length grating. (c) The optical behavior in these effective-structure details is analogous to that of a birefringent crystal.

Fig. 2
Fig. 2

Geometry and phases of the four effective-structure details.

Fig. 3
Fig. 3

Geometry of a polarization-selective phase grating. The grating period is composed of the first and second effective-structure details (see Fig. 2). TM polarization is diffracted in the odd orders, whereas TE polarization passes through the grating undeflected.

Fig. 4
Fig. 4

Geometry of a subwavelength structured phase grating that diffracts TE and TM polarization in different orders.

Tables (4)

Tables Icon

Table 1 Effective Refractive Indices as a Function of the Filling Factor f

Tables Icon

Table 2 Transmitted Diffraction Efficiencies of the Grating Illustrated in Fig. 3 for Normal Incident Light

Tables Icon

Table 3 Transmitted Diffraction Efficiencies of the Grating Illustrated in Fig. 4 for Normal Incidence

Tables Icon

Table 4 Diffraction Efficiencies of the Original Grating Depicted in Fig. 3 and of Two Gratings with Variations in the Filling Factor and the Grating Depth

Equations (55)

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

U TE , TM ( x , h ) = exp [ i k 0 L TE , TM ( x ) ] ,
L TE , TM ( x ) = 0 h n TE , TM ( x , z ) d z
φ TE , TM ( x ) = k 0 L TE , TM ( x )
L TE , TM ( x ) = 0 h ( n TE , TM ( x , z ) 1 ) d z .
k 0 h 4 ( 3.27 1 ) = π .
k 0 h 2 ( n TE 1 ) = 2 π ,
k 0 h 2 ( n TM 1 ) = π .
2 ( n TM 1 ) = ( n TE 1 ) .
k 0 h 2 ( n TE 1 ) + k 0 h 4 ( 3.27 1 ) = 3 π ,
k 0 h 2 ( n TM 1 ) + k 0 h 4 ( 3.27 1 ) = 2 π .
k x m = m 2 π d eff = 2 m 2 π d .
η 0 III
η 0 , sc III
η ± 1 III
η ± 1 , sc III
η ± 2 III
η ± 2 , sc III
η ± 3 III
η ± 3 , sc III
η ± 4 III
η ± 4 , sc III
η ± 5 III
η ± 5 , sc III
η 6 III
η 6 , sc III
η 5 III
η 5 , sc III
η 4 III
η 4 , sc III
η 3 III
η 3 , sc III
η 2 III
η 2 , sc III
η 1 III
η 1 , sc III
η 0 III
η 0 , sc III
η 1 III
η 1 , sc III
η 2 III
η 2 , sc III
η 3 III
η 3 , sc III
η 4 III
η 4 , sc III
η 5 III
η 5 , sc III
η 6 III
η 6 , sc III
η 0 III
η ± 1 III
η ± 2 III
η ± 3 III
η ± 4 III
η ± 5 III

Metrics