Abstract

Diffraction characteristics of high-spatial-frequency (HSF) gratings are evaluated for application to polarization-selective computer-generated holograms by the use of two different approaches: second-order effective-medium theory (EMT) and rigorous coupled-wave analysis (RCWA). The reflectivities and the phase differences for TE- and TM-polarized waves are investigated in terms of various input parameters, and results obtained with second-order EMT and RCWA are compared. It is shown that although the reflection characteristics can be accurately modeled with the second-order EMT, the phase difference created by form birefringence for TE- and TM-polarized waves requires the use of a more rigorous, RCWA approach. The design of HSF gratings in terms of their form birefringence and reflectivity properties is discussed in conjunction with polarization-selective computer-generated holograms. A specific design optimization example furnishes a grating profile that provides a trade-off between the largest form birefringence and the lowest reflectivities.

© 1995 Optical Society of America

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References

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  1. J. E. Ford, F. Xu, K. Urquhart, Y. Fainman, “Polarization-selective computer-generated holograms,” Opt. Lett. 18, 456–458 (1993).
    [CrossRef] [PubMed]
  2. F. Xu, J. E. Ford, Y. Fainman, “Polarization-selective computer-generated holograms: design, fabrication and applications,” Appl. Opt. 34, 256–266 (1995).
    [CrossRef] [PubMed]
  3. Y. Ono, Y. Kimura, Y. Ohta, N. Nishida, “Antireflection effect in ultrahigh spatial-frequency holographic relief gratings,” Appl. Opt. 26, 1142–1146 (1987).
    [CrossRef] [PubMed]
  4. D. C. Flanders, “Submicron periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42, 492–494 (1983).
    [CrossRef]
  5. E. Gluch, H. Haidner, P. Kipfer, J. T. Sheridan, N. Streibl, “Form birefringence of surface relief gratings and its angular dependence,” Opt. Commun. 89, 173–177 (1992).
    [CrossRef]
  6. R. C. Enger, S. K. Case, “Optical elements with ultrahigh spatial-frequency surface corrugations,” Appl. Opt. 22, 3220–3228 (1983).
    [CrossRef] [PubMed]
  7. M. Born, E. Wolf, Principles of Optics, 2nd ed. (Pergamon, Oxford, 1964), Chap. 14, p. 705.
  8. L. H. Cescato, E. Gluch, N. Streibl, “Holographic quarter-wave plates,” Appl. Opt. 29, 3286–3290 (1990).
    [CrossRef] [PubMed]
  9. 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, Proc. Soc. Photo-Opt. Instrum. Eng.1751, 202–213 (1992).
  10. K. Shiraishi, T. Sato, S. Kawakami, “Experimental verification of a form birefringence polarization splitter,” Appl. Phys. Lett. 58, 211–212 (1991).
    [CrossRef]
  11. S. Aoyama, T. Yamashita, “Grating beam splitting polarizer using multilayer resist method,” in International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1545, 241–250 (1991).
  12. S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).
  13. D. L. Brundrett, E. N. Glytsis, T. K. Gaylord, “Homogeneous layer models for high-spatial frequency dielectric surface-relief gratings: conical diffraction and antireflection designs,” Appl. Opt. 33, 2695–2706 (1994).
    [CrossRef] [PubMed]
  14. R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980). Chaps. 3 and 4.
    [CrossRef]
  15. T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
    [CrossRef]
  16. M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1385–1392 (1982).
    [CrossRef]
  17. M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of grating diffraction—E-mode polarization and losses,” J. Opt. Soc. Am. 73, 451–455 (1983).
    [CrossRef]
  18. D. H. Raquin, G. M. Morris, “Antireflection structured surfaces for the infrared spectral region,” Appl. Opt. 32, 1154–1167 (1993).
    [CrossRef]
  19. D. H. Raquin, G. M. Morris, “Analysis of antireflection-structured surfaces with continuous one-dimensional surface profiles,” Appl. Opt. 32, 2582–2598 (1993).
    [CrossRef]
  20. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), Chap. 4.
  21. M. K. Moaveni, “Plane-wave diffraction by dielectric gratings, finite difference formulation,” IEEE Trans. Antennas Propag. 37, 1026–1031 (1989).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  24. S. T. Han, Y.-L. Tsao, R. M. Walser, M. F. Becker, “Electromagnetic scattering of two-dimensional surface-relief dielectric gratings,” Appl. Opt. 31, 2343–2352 (1992).
    [CrossRef] [PubMed]
  25. E. N. Glytsis, T. K. Gaylord, “Three-dimensional (vector) rigorous coupled-wave analysis of anisotropic grating diffraction,” J. Opt. Soc. Am. A 7, 1399–1420 (1990).
    [CrossRef]
  26. E. N. Glytsis, T. K. Gaylord, “Rigorous 3-D coupled wave diffraction analysis of multiple superposed gratings in anisotropic media,” Appl. Opt. 28, 2401–2421 (1989).
    [CrossRef] [PubMed]
  27. E. N. Glytsis, T. K. Gaylord, “Rigorous three-dimensional coupled-wave diffraction analysis of single and cascaded anisotropic gratings,” J. Opt. Soc. Am. A 4, 2061–2080 (1987).
    [CrossRef]
  28. N. Chateau, J.-P. Hugonin, “Algorithm for the rigorous coupled-wave analysis of grating diffraction,” J. Opt. Soc. Am. A 11, 1321–1331 (1994).
    [CrossRef]
  29. C. W. Haggans, L. Li, R. K. Kostuk, “Effective-medium theory of zeroth-order lamellar gratings in conical mounting,” J. Opt. Soc. Am. A 10, 2217–2225 (1993).
    [CrossRef]
  30. E. N. Glytsis, T. K. Gaylord, “High-spatial-frequency binary and multilevel stairstep gratings: polarization selective mirrors and broadband antireflection surfaces,” Appl. Opt. 31, 4459–4470 (1992).
    [CrossRef] [PubMed]
  31. M. E. Motamedi, W. H. Southwell, W. J. Gunning, “Antireflection surfaces in silicon using binary optics technology,” Appl. Opt. 31, 4371–4376 (1992).
    [CrossRef] [PubMed]

1995

1994

1993

1992

1991

K. Shiraishi, T. Sato, S. Kawakami, “Experimental verification of a form birefringence polarization splitter,” Appl. Phys. Lett. 58, 211–212 (1991).
[CrossRef]

1990

1989

E. N. Glytsis, T. K. Gaylord, “Rigorous 3-D coupled wave diffraction analysis of multiple superposed gratings in anisotropic media,” Appl. Opt. 28, 2401–2421 (1989).
[CrossRef] [PubMed]

M. K. Moaveni, “Plane-wave diffraction by dielectric gratings, finite difference formulation,” IEEE Trans. Antennas Propag. 37, 1026–1031 (1989).
[CrossRef]

1987

1985

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

1983

1982

1981

I. C. Botten, M. S. Craig, R. C. Mcphedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
[CrossRef]

1956

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Adams, J. L.

I. C. Botten, M. S. Craig, R. C. Mcphedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
[CrossRef]

Andrewartha, J. R.

I. C. Botten, M. S. Craig, R. C. Mcphedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
[CrossRef]

Aoyama, S.

S. Aoyama, T. Yamashita, “Grating beam splitting polarizer using multilayer resist method,” in International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1545, 241–250 (1991).

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), Chap. 4.

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, Proc. Soc. Photo-Opt. Instrum. Eng.1751, 202–213 (1992).

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), Chap. 4.

Becker, M. F.

Born, M.

M. Born, E. Wolf, Principles of Optics, 2nd ed. (Pergamon, Oxford, 1964), Chap. 14, p. 705.

Botten, I. C.

I. C. Botten, M. S. Craig, R. C. Mcphedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
[CrossRef]

Brundrett, D. L.

Case, S. K.

Cescato, L. H.

Chateau, N.

Craig, M. S.

I. C. Botten, M. S. Craig, R. C. Mcphedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
[CrossRef]

Delort, T.

Enger, R. C.

Fainman, Y.

Flanders, D. C.

D. C. Flanders, “Submicron periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42, 492–494 (1983).
[CrossRef]

Ford, J. E.

Gaylord, T. K.

D. L. Brundrett, E. N. Glytsis, T. K. Gaylord, “Homogeneous layer models for high-spatial frequency dielectric surface-relief gratings: conical diffraction and antireflection designs,” Appl. Opt. 33, 2695–2706 (1994).
[CrossRef] [PubMed]

E. N. Glytsis, T. K. Gaylord, “High-spatial-frequency binary and multilevel stairstep gratings: polarization selective mirrors and broadband antireflection surfaces,” Appl. Opt. 31, 4459–4470 (1992).
[CrossRef] [PubMed]

E. N. Glytsis, T. K. Gaylord, “Three-dimensional (vector) rigorous coupled-wave analysis of anisotropic grating diffraction,” J. Opt. Soc. Am. A 7, 1399–1420 (1990).
[CrossRef]

E. N. Glytsis, T. K. Gaylord, “Rigorous 3-D coupled wave diffraction analysis of multiple superposed gratings in anisotropic media,” Appl. Opt. 28, 2401–2421 (1989).
[CrossRef] [PubMed]

E. N. Glytsis, T. K. Gaylord, “Rigorous three-dimensional coupled-wave diffraction analysis of single and cascaded anisotropic gratings,” J. Opt. Soc. Am. A 4, 2061–2080 (1987).
[CrossRef]

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of grating diffraction—E-mode polarization and losses,” J. Opt. Soc. Am. 73, 451–455 (1983).
[CrossRef]

M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1385–1392 (1982).
[CrossRef]

Gluch, E.

E. Gluch, H. Haidner, P. Kipfer, J. T. Sheridan, N. Streibl, “Form birefringence of surface relief gratings and its angular dependence,” Opt. Commun. 89, 173–177 (1992).
[CrossRef]

L. H. Cescato, E. Gluch, N. Streibl, “Holographic quarter-wave plates,” Appl. Opt. 29, 3286–3290 (1990).
[CrossRef] [PubMed]

Glytsis, E. N.

Gunning, W. J.

Haggans, C. W.

Haidner, H.

E. Gluch, H. Haidner, P. Kipfer, J. T. Sheridan, N. Streibl, “Form birefringence of surface relief gratings and its angular dependence,” Opt. Commun. 89, 173–177 (1992).
[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, C. Roychoudhuri, W. B. Veldkamp, Proc. Soc. Photo-Opt. Instrum. Eng.1751, 202–213 (1992).

Han, S. T.

Hugonin, J.-P.

Kawakami, S.

K. Shiraishi, T. Sato, S. Kawakami, “Experimental verification of a form birefringence polarization splitter,” Appl. Phys. Lett. 58, 211–212 (1991).
[CrossRef]

Kimura, Y.

Kipfer, P.

E. Gluch, H. Haidner, P. Kipfer, J. T. Sheridan, N. Streibl, “Form birefringence of surface relief gratings and its angular dependence,” Opt. Commun. 89, 173–177 (1992).
[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, C. Roychoudhuri, W. B. Veldkamp, Proc. Soc. Photo-Opt. Instrum. Eng.1751, 202–213 (1992).

Kostuk, R. K.

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, Proc. Soc. Photo-Opt. Instrum. Eng.1751, 202–213 (1992).

Li, L.

Mayestre, D.

Mcphedran, R. C.

I. C. Botten, M. S. Craig, R. C. Mcphedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
[CrossRef]

Moaveni, M. K.

M. K. Moaveni, “Plane-wave diffraction by dielectric gratings, finite difference formulation,” IEEE Trans. Antennas Propag. 37, 1026–1031 (1989).
[CrossRef]

Moharam, M. G.

Morris, G. M.

Motamedi, M. E.

Nishida, N.

Ohta, Y.

Ono, Y.

Petit, R.

R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980). Chaps. 3 and 4.
[CrossRef]

Raquin, D. H.

Rytov, S. M.

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Sato, T.

K. Shiraishi, T. Sato, S. Kawakami, “Experimental verification of a form birefringence polarization splitter,” Appl. Phys. Lett. 58, 211–212 (1991).
[CrossRef]

Sheridan, J. T.

E. Gluch, H. Haidner, P. Kipfer, J. T. Sheridan, N. Streibl, “Form birefringence of surface relief gratings and its angular dependence,” Opt. Commun. 89, 173–177 (1992).
[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, C. Roychoudhuri, W. B. Veldkamp, Proc. Soc. Photo-Opt. Instrum. Eng.1751, 202–213 (1992).

Shiraishi, K.

K. Shiraishi, T. Sato, S. Kawakami, “Experimental verification of a form birefringence polarization splitter,” Appl. Phys. Lett. 58, 211–212 (1991).
[CrossRef]

Southwell, W. H.

Stork, W.

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, Proc. Soc. Photo-Opt. Instrum. Eng.1751, 202–213 (1992).

Streibl, N.

E. Gluch, H. Haidner, P. Kipfer, J. T. Sheridan, N. Streibl, “Form birefringence of surface relief gratings and its angular dependence,” Opt. Commun. 89, 173–177 (1992).
[CrossRef]

L. H. Cescato, E. Gluch, N. Streibl, “Holographic quarter-wave plates,” Appl. Opt. 29, 3286–3290 (1990).
[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, Proc. Soc. Photo-Opt. Instrum. Eng.1751, 202–213 (1992).

Tsao, Y.-L.

Urquhart, K.

Walser, R. M.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 2nd ed. (Pergamon, Oxford, 1964), Chap. 14, p. 705.

Xu, F.

Yamashita, T.

S. Aoyama, T. Yamashita, “Grating beam splitting polarizer using multilayer resist method,” in International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1545, 241–250 (1991).

Appl. Opt.

R. C. Enger, S. K. Case, “Optical elements with ultrahigh spatial-frequency surface corrugations,” Appl. Opt. 22, 3220–3228 (1983).
[CrossRef] [PubMed]

Y. Ono, Y. Kimura, Y. Ohta, N. Nishida, “Antireflection effect in ultrahigh spatial-frequency holographic relief gratings,” Appl. Opt. 26, 1142–1146 (1987).
[CrossRef] [PubMed]

E. N. Glytsis, T. K. Gaylord, “Rigorous 3-D coupled wave diffraction analysis of multiple superposed gratings in anisotropic media,” Appl. Opt. 28, 2401–2421 (1989).
[CrossRef] [PubMed]

S. T. Han, Y.-L. Tsao, R. M. Walser, M. F. Becker, “Electromagnetic scattering of two-dimensional surface-relief dielectric gratings,” Appl. Opt. 31, 2343–2352 (1992).
[CrossRef] [PubMed]

M. E. Motamedi, W. H. Southwell, W. J. Gunning, “Antireflection surfaces in silicon using binary optics technology,” Appl. Opt. 31, 4371–4376 (1992).
[CrossRef] [PubMed]

E. N. Glytsis, T. K. Gaylord, “High-spatial-frequency binary and multilevel stairstep gratings: polarization selective mirrors and broadband antireflection surfaces,” Appl. Opt. 31, 4459–4470 (1992).
[CrossRef] [PubMed]

D. H. Raquin, G. M. Morris, “Analysis of antireflection-structured surfaces with continuous one-dimensional surface profiles,” Appl. Opt. 32, 2582–2598 (1993).
[CrossRef]

D. H. Raquin, G. M. Morris, “Antireflection structured surfaces for the infrared spectral region,” Appl. Opt. 32, 1154–1167 (1993).
[CrossRef]

D. L. Brundrett, E. N. Glytsis, T. K. Gaylord, “Homogeneous layer models for high-spatial frequency dielectric surface-relief gratings: conical diffraction and antireflection designs,” Appl. Opt. 33, 2695–2706 (1994).
[CrossRef] [PubMed]

F. Xu, J. E. Ford, Y. Fainman, “Polarization-selective computer-generated holograms: design, fabrication and applications,” Appl. Opt. 34, 256–266 (1995).
[CrossRef] [PubMed]

L. H. Cescato, E. Gluch, N. Streibl, “Holographic quarter-wave plates,” Appl. Opt. 29, 3286–3290 (1990).
[CrossRef] [PubMed]

Appl. Phys. Lett.

D. C. Flanders, “Submicron periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42, 492–494 (1983).
[CrossRef]

K. Shiraishi, T. Sato, S. Kawakami, “Experimental verification of a form birefringence polarization splitter,” Appl. Phys. Lett. 58, 211–212 (1991).
[CrossRef]

IEEE Trans. Antennas Propag.

M. K. Moaveni, “Plane-wave diffraction by dielectric gratings, finite difference formulation,” IEEE Trans. Antennas Propag. 37, 1026–1031 (1989).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Acta

I. C. Botten, M. S. Craig, R. C. Mcphedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
[CrossRef]

Opt. Commun.

E. Gluch, H. Haidner, P. Kipfer, J. T. Sheridan, N. Streibl, “Form birefringence of surface relief gratings and its angular dependence,” Opt. Commun. 89, 173–177 (1992).
[CrossRef]

Opt. Lett.

Proc. IEEE

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Sov. Phys. JETP

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Other

R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980). Chaps. 3 and 4.
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 2nd ed. (Pergamon, Oxford, 1964), Chap. 14, p. 705.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), Chap. 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, Proc. Soc. Photo-Opt. Instrum. Eng.1751, 202–213 (1992).

S. Aoyama, T. Yamashita, “Grating beam splitting polarizer using multilayer resist method,” in International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1545, 241–250 (1991).

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Figures (12)

Fig. 1
Fig. 1

Schematic diagram of (a) a HSF rectangular surface-relief grating, (b) its equivalent homogeneous layer model.

Fig. 2
Fig. 2

Schematic diagram of (a) HSF sinusoidal surface-relief grating, (b) its equivalent homogeneous multilayer model.

Fig. 3
Fig. 3

Geometry of surface-relief grating and its decomposition into thin rectangular gratings by RCWA.

Fig. 4
Fig. 4

Phase difference between TE- and TM-polarized light at normal incidence as a function of a normalized thickness rectangular-shaped grating of 50% duty cycle, with the normalized grating period as a parameter, with (a) second-order EMT, (b) RCWA. The grating is made of a material with ∊III = 6.25 in air ∊I = 1.0.

Fig. 5
Fig. 5

Phase difference between TE- and TM-polarized light at normal incidence as a function of a rectangular-shaped grating duty cycle, with d/λ = 1.0 and Λ/λ as a parameter, with (a) second-order EMT, (b) RCWA.

Fig. 6
Fig. 6

Phase difference between TE- and TM-polarized light as a function of angle of incidence for a rectangular 50% duty cycle grating with d/λ = 1.0 and Λ/λ = 0.1 and 0.3.

Fig. 7
Fig. 7

Comparison of phase differences between TE- and TM-polarized light at normal incidence as a function of normalized thickness, and normalized grating period as a parameter for a triangular profile grating.

Fig. 8
Fig. 8

Reflectivity of TE- and TM-polarized light at normal incidence as a function of a normalized thickness rectangular-shaped grating of 50% duty cycle for (a) Λ/λ = 0.1, (b) Λ/λ = 0.3.

Fig. 9
Fig. 9

Comparison of reflectivities of TE- and TM-polarized light at normal incidence as a function of a normalized triangular-shaped grating thickness and Λ/λ = 0.1.

Fig. 10
Fig. 10

Schematic drawing of the optimized profile that comprises a large phase difference (curved shape) and a simultaneous low and uniform reflectivity (trapezoidal shape).

Fig. 11
Fig. 11

Phase difference between TE- and TM-polarized light at normal incidence as a function of a normalized thickness optimized profile for Λ/λ = 0.3, obtained by RCWA.

Fig. 12
Fig. 12

Reflectivity of (a) TE- and (b) TM-polarized light at normal incidence as a function of normalized thickness optimized profile for Λ/λ = 0.3, obtained by RCWA.

Equations (2)

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

0 , E K = F III + ( 1 F ) I , 0 , E K = III I F I + ( 1 F ) III ,
2 , E K = 0 , E K + 1 3 ( Λ λ ) 2 π 2 F 2 ( 1 F ) 2 ( III I ) 2 , 2 , E K = 0 , E K + 1 3 ( Λ λ ) 2 π 2 F 2 ( 1 F ) 2 ( 1 III 1 I ) 2 × 0 , E K 3 0 , E K ,

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