Abstract

A formalism is presented for calculating the ordinary and extraordinary refractive indices for a uniaxial film with optical properties equivalent to those of a conically mounted zeroth-order lamellar grating. In the quasi-static limit (grating-period-to-wavelength ratio → 0) this treatment is exact for both dielectric and metallic gratings. For period-to-wavelength ratios approaching unity, the effective anisotropic refractive indices are dependent on the polar and azimuthal incidence angles. The validity of this method as the period-to-wavelength ratio increases is studied by comparison of the method with the predictions of rigorous grating theories. Comparisons are then made with the predictions of other effective-medium theories. Examples of the use of this theory for conically mounted zeroth-order gratings are presented.

© 1993 Optical Society of America

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  1. R. C. Enger, S. K. Case, “Optical elements with ultrahigh spatial-frequency surface corrugations,” Appl. Opt. 22, 3220–3228 (1983).
    [CrossRef] [PubMed]
  2. D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42, 492–494 (1983).
    [CrossRef]
  3. M. L. Minden, G. J. Dunning, “Polarization-dependent phase shift in high-efficiency gratings,” in Periodic Structures, Gratings, Moiré Patterns, and Diffraction Phenomena I, C. H. Chi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.240, 249–254 (1980).
    [CrossRef]
  4. L. H. Cescato, E. Gluch, N. Streibl, “Holographic quarter-wave plates,” Appl. Opt. 29, 3286–3290 (1990).
    [CrossRef] [PubMed]
  5. C. W. Haggans, L. Li, T. Fujita, R. K. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mod. Opt. 40, 675–686 (1993).
    [CrossRef]
  6. G. P. Bryan-Brown, J. R. Sambles, M. C. Hutley, “Polarization conversion through the excitation of surface plasmons on a metallic grating,” J. Mod. Opt. 37, 1227–1232 (1990).
    [CrossRef]
  7. Y.-L. Kok, N. C. Gallagher, “Relative phases of electromagnetic waves diffracted by a perfectly conducting rectangular-grooved grating,” J. Opt. Soc. Am. A 5, 65–73 (1988).
    [CrossRef] [PubMed]
  8. S. S. H. Naqvi, N. C. Gallagher, “Analysis of a strip-grating twist reflector,” J. Opt. Soc. Am. A 7, 1723–1729 (1990).
    [CrossRef]
  9. T. K. Gaylord, W. E. Baird, M. G. Moharam, “Zero-reflectivity high spatial-frequency rectangular-groove dielectric surface-relief gratings,” Appl. Opt. 25, 4562–4567 (1986).
    [CrossRef] [PubMed]
  10. 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]
  11. E. N. Glytsis, T. K. Gaysslord, “Antireflection surface structure: dielectric layer(s) over a high spatial-frequency surface-relief grating on a lossy substrate,” Appl. Opt. 27, 4288–4303 (1988).
    [CrossRef] [PubMed]
  12. 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]
  13. D. H. Raguin, G. M. Morris, “Antireflection structured surfaces for the infrared spectral region,” Appl. Opt. 32, 1154–1167 (1993).
    [CrossRef] [PubMed]
  14. See, for example, Electromagnetic Theory of Gratings, R. Petit, ed., Vol. 22 of Topics in Current Physics (Springer-Verlag, Berlin, 1980).
    [CrossRef]
  15. R. C. McPhedran, L. C. Botten, M. S. Craig, M. Nevière, D. Maystre, “Lossy lamellar gratings in the quasistatic limit,” Opt. Acta 29, P89–312 (1982).
    [CrossRef]
  16. J. M. Bell, G. H. Derrick, R. C. McPhedran, “Diffraction gratings in the quasistatic limit,” Opt. Acta 29, 1475–1489 (1982).
    [CrossRef]
  17. G. Bouchitte, R. Petit, “Homogenization techniques as applied in the electromagnetic theory of gratings,” Electromagnetics 5, 17–36 (1985).
    [CrossRef]
  18. P. Yeh, A. Yariv, C.-S. Hong, “Electromagnetic propagation in periodic stratified media. I. General theory,” J. Opt. Soc. Am. 67, 423–438 (1977); A. Yariv, P. Yeh, “Electromagnetic propagation in periodic stratified media. II. Birefringence, phase matching, and x-ray lasers,”J. Opt. Soc. Am. 67, 438–448 (1977).
    [CrossRef]
  19. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), p. 207.
  20. P. Yeh, “Electromagnetic propagation in birefringent layered media,”J. Opt. Soc. Am. 69, 742–756 (1979).
    [CrossRef]
  21. M. Mansuripur, “Analysis of multilayer thin-film structures containing magneto-optic and anisotropic media at oblique incidence using 2 × 2 matrices,” J. Appl. Phys. 67, 6466–6475 (1990).
    [CrossRef]
  22. S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).
  23. 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. Instrum. Eng.1751, 202–213 (1992).
    [CrossRef]
  24. R. M. A. Azzam, N. M. Bashara, “Polarization characteristics of scattered radiation from a diffraction grating by ellipsometry with application to surface roughness,” Phys. Rev. B 5, 4721–4729 (1972).
    [CrossRef]
  25. L. Cescato, E. Gluch, H. Haidner, N. Streibl, “Form birefringence of dielectric coatings and relief gratings,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 333–334 (1990).
    [CrossRef]
  26. 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]
  27. 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]
  28. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), pp. 24–30.
  29. L. Li, “A modal analysis of lamellar diffraction gratings in conical mountings,” J. Mod. Opt. 40, 553–573 (1993).
    [CrossRef]
  30. L. 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]
  31. L. C. Botten, M. S. Craig, R. C. McPhedran, “Highly conducting lamellar diffraction gratings,” Opt. Acta 28, 1103–1106 (1981).
    [CrossRef]
  32. G. Tayeb, R. Petit, “On the numerical study of deep conducting lamellar diffraction gratings,” Opt. Acta 31, 1361–1365 (1984).
    [CrossRef]
  33. M. G. Moharam, T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffractionJ. Opt. Soc. Am. 73, 1105–1112 (1983).
    [CrossRef]
  34. M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,”J. Opt. Soc. Am. 72, 1385–1392 (1982).
    [CrossRef]
  35. C. W. Haggans, R. K. Kostuk, “Use of rigorous vector coupled-wave theory for designing and tolerancing surface-relief diffractive components for magneto-optical heads,” in Optical Data Storage ’91, J. J. Burke, N. Imamura, T. A. Shull, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1499, 293–302 (1991).
    [CrossRef]
  36. E. Popov, L. Tsonev, D. Maystre, “Gratings: general properties of the Littrow mounting and energy flow distribution,” J. Mod. Opt. 37, 367–377 (1990).
    [CrossRef]

1993 (3)

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

L. Li, “A modal analysis of lamellar diffraction gratings in conical mountings,” J. Mod. Opt. 40, 553–573 (1993).
[CrossRef]

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

1992 (2)

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. 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]

1991 (1)

1990 (5)

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

E. Popov, L. Tsonev, D. Maystre, “Gratings: general properties of the Littrow mounting and energy flow distribution,” J. Mod. Opt. 37, 367–377 (1990).
[CrossRef]

S. S. H. Naqvi, N. C. Gallagher, “Analysis of a strip-grating twist reflector,” J. Opt. Soc. Am. A 7, 1723–1729 (1990).
[CrossRef]

G. P. Bryan-Brown, J. R. Sambles, M. C. Hutley, “Polarization conversion through the excitation of surface plasmons on a metallic grating,” J. Mod. Opt. 37, 1227–1232 (1990).
[CrossRef]

M. Mansuripur, “Analysis of multilayer thin-film structures containing magneto-optic and anisotropic media at oblique incidence using 2 × 2 matrices,” J. Appl. Phys. 67, 6466–6475 (1990).
[CrossRef]

1988 (2)

1987 (1)

1986 (1)

1985 (1)

G. Bouchitte, R. Petit, “Homogenization techniques as applied in the electromagnetic theory of gratings,” Electromagnetics 5, 17–36 (1985).
[CrossRef]

1984 (1)

G. Tayeb, R. Petit, “On the numerical study of deep conducting lamellar diffraction gratings,” Opt. Acta 31, 1361–1365 (1984).
[CrossRef]

1983 (3)

1982 (3)

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

R. C. McPhedran, L. C. Botten, M. S. Craig, M. Nevière, D. Maystre, “Lossy lamellar gratings in the quasistatic limit,” Opt. Acta 29, P89–312 (1982).
[CrossRef]

J. M. Bell, G. H. Derrick, R. C. McPhedran, “Diffraction gratings in the quasistatic limit,” Opt. Acta 29, 1475–1489 (1982).
[CrossRef]

1981 (2)

L. 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]

L. C. Botten, M. S. Craig, R. C. McPhedran, “Highly conducting lamellar diffraction gratings,” Opt. Acta 28, 1103–1106 (1981).
[CrossRef]

1979 (1)

1977 (1)

1972 (1)

R. M. A. Azzam, N. M. Bashara, “Polarization characteristics of scattered radiation from a diffraction grating by ellipsometry with application to surface roughness,” Phys. Rev. B 5, 4721–4729 (1972).
[CrossRef]

1956 (1)

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

Adams, J. L.

L. 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.

L. 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]

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, “Polarization characteristics of scattered radiation from a diffraction grating by ellipsometry with application to surface roughness,” Phys. Rev. B 5, 4721–4729 (1972).
[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, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1751, 202–213 (1992).
[CrossRef]

Baird, W. E.

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, “Polarization characteristics of scattered radiation from a diffraction grating by ellipsometry with application to surface roughness,” Phys. Rev. B 5, 4721–4729 (1972).
[CrossRef]

Bell, J. M.

J. M. Bell, G. H. Derrick, R. C. McPhedran, “Diffraction gratings in the quasistatic limit,” Opt. Acta 29, 1475–1489 (1982).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), pp. 24–30.

Botten, L. C.

R. C. McPhedran, L. C. Botten, M. S. Craig, M. Nevière, D. Maystre, “Lossy lamellar gratings in the quasistatic limit,” Opt. Acta 29, P89–312 (1982).
[CrossRef]

L. 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]

L. C. Botten, M. S. Craig, R. C. McPhedran, “Highly conducting lamellar diffraction gratings,” Opt. Acta 28, 1103–1106 (1981).
[CrossRef]

Bouchitte, G.

G. Bouchitte, R. Petit, “Homogenization techniques as applied in the electromagnetic theory of gratings,” Electromagnetics 5, 17–36 (1985).
[CrossRef]

Bryan-Brown, G. P.

G. P. Bryan-Brown, J. R. Sambles, M. C. Hutley, “Polarization conversion through the excitation of surface plasmons on a metallic grating,” J. Mod. Opt. 37, 1227–1232 (1990).
[CrossRef]

Case, S. K.

Cescato, L.

L. Cescato, E. Gluch, H. Haidner, N. Streibl, “Form birefringence of dielectric coatings and relief gratings,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 333–334 (1990).
[CrossRef]

Cescato, L. H.

Craig, M. S.

R. C. McPhedran, L. C. Botten, M. S. Craig, M. Nevière, D. Maystre, “Lossy lamellar gratings in the quasistatic limit,” Opt. Acta 29, P89–312 (1982).
[CrossRef]

L. 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]

L. C. Botten, M. S. Craig, R. C. McPhedran, “Highly conducting lamellar diffraction gratings,” Opt. Acta 28, 1103–1106 (1981).
[CrossRef]

Derrick, G. H.

J. M. Bell, G. H. Derrick, R. C. McPhedran, “Diffraction gratings in the quasistatic limit,” Opt. Acta 29, 1475–1489 (1982).
[CrossRef]

Dunning, G. J.

M. L. Minden, G. J. Dunning, “Polarization-dependent phase shift in high-efficiency gratings,” in Periodic Structures, Gratings, Moiré Patterns, and Diffraction Phenomena I, C. H. Chi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.240, 249–254 (1980).
[CrossRef]

Enger, R. C.

Flanders, D. C.

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

Fujita, T.

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

Gallagher, N. C.

Gaylord, T. K.

Gaysslord, T. K.

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]

L. Cescato, E. Gluch, H. Haidner, N. Streibl, “Form birefringence of dielectric coatings and relief gratings,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 333–334 (1990).
[CrossRef]

Glytsis, E. N.

Haggans, C. W.

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

C. W. Haggans, R. K. Kostuk, “Use of rigorous vector coupled-wave theory for designing and tolerancing surface-relief diffractive components for magneto-optical heads,” in Optical Data Storage ’91, J. J. Burke, N. Imamura, T. A. Shull, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1499, 293–302 (1991).
[CrossRef]

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]

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]

L. Cescato, E. Gluch, H. Haidner, N. Streibl, “Form birefringence of dielectric coatings and relief gratings,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 333–334 (1990).
[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, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1751, 202–213 (1992).
[CrossRef]

Hong, C.-S.

Hutley, M. C.

G. P. Bryan-Brown, J. R. Sambles, M. C. Hutley, “Polarization conversion through the excitation of surface plasmons on a metallic grating,” J. Mod. Opt. 37, 1227–1232 (1990).
[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]

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. Instrum. Eng.1751, 202–213 (1992).
[CrossRef]

Kok, Y.-L.

Kostuk, R. K.

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

C. W. Haggans, R. K. Kostuk, “Use of rigorous vector coupled-wave theory for designing and tolerancing surface-relief diffractive components for magneto-optical heads,” in Optical Data Storage ’91, J. J. Burke, N. Imamura, T. A. Shull, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1499, 293–302 (1991).
[CrossRef]

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. Instrum. Eng.1751, 202–213 (1992).
[CrossRef]

Li, L.

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

L. Li, “A modal analysis of lamellar diffraction gratings in conical mountings,” J. Mod. Opt. 40, 553–573 (1993).
[CrossRef]

Mansuripur, M.

M. Mansuripur, “Analysis of multilayer thin-film structures containing magneto-optic and anisotropic media at oblique incidence using 2 × 2 matrices,” J. Appl. Phys. 67, 6466–6475 (1990).
[CrossRef]

Maystre, D.

E. Popov, L. Tsonev, D. Maystre, “Gratings: general properties of the Littrow mounting and energy flow distribution,” J. Mod. Opt. 37, 367–377 (1990).
[CrossRef]

R. C. McPhedran, L. C. Botten, M. S. Craig, M. Nevière, D. Maystre, “Lossy lamellar gratings in the quasistatic limit,” Opt. Acta 29, P89–312 (1982).
[CrossRef]

McPhedran, R. C.

R. C. McPhedran, L. C. Botten, M. S. Craig, M. Nevière, D. Maystre, “Lossy lamellar gratings in the quasistatic limit,” Opt. Acta 29, P89–312 (1982).
[CrossRef]

J. M. Bell, G. H. Derrick, R. C. McPhedran, “Diffraction gratings in the quasistatic limit,” Opt. Acta 29, 1475–1489 (1982).
[CrossRef]

L. 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]

L. C. Botten, M. S. Craig, R. C. McPhedran, “Highly conducting lamellar diffraction gratings,” Opt. Acta 28, 1103–1106 (1981).
[CrossRef]

Minden, M. L.

M. L. Minden, G. J. Dunning, “Polarization-dependent phase shift in high-efficiency gratings,” in Periodic Structures, Gratings, Moiré Patterns, and Diffraction Phenomena I, C. H. Chi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.240, 249–254 (1980).
[CrossRef]

Moharam, M. G.

Morris, G. M.

Naqvi, S. S. H.

Nevière, M.

R. C. McPhedran, L. C. Botten, M. S. Craig, M. Nevière, D. Maystre, “Lossy lamellar gratings in the quasistatic limit,” Opt. Acta 29, P89–312 (1982).
[CrossRef]

Nishida, N.

Ohta, Y.

Ono, Y.

Petit, R.

G. Bouchitte, R. Petit, “Homogenization techniques as applied in the electromagnetic theory of gratings,” Electromagnetics 5, 17–36 (1985).
[CrossRef]

G. Tayeb, R. Petit, “On the numerical study of deep conducting lamellar diffraction gratings,” Opt. Acta 31, 1361–1365 (1984).
[CrossRef]

Popov, E.

E. Popov, L. Tsonev, D. Maystre, “Gratings: general properties of the Littrow mounting and energy flow distribution,” J. Mod. Opt. 37, 367–377 (1990).
[CrossRef]

Raguin, D. H.

Rytov, S. M.

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

Sambles, J. R.

G. P. Bryan-Brown, J. R. Sambles, M. C. Hutley, “Polarization conversion through the excitation of surface plasmons on a metallic grating,” J. Mod. Opt. 37, 1227–1232 (1990).
[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, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1751, 202–213 (1992).
[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, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1751, 202–213 (1992).
[CrossRef]

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]

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]

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

L. Cescato, E. Gluch, H. Haidner, N. Streibl, “Form birefringence of dielectric coatings and relief gratings,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 333–334 (1990).
[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, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1751, 202–213 (1992).
[CrossRef]

Tayeb, G.

G. Tayeb, R. Petit, “On the numerical study of deep conducting lamellar diffraction gratings,” Opt. Acta 31, 1361–1365 (1984).
[CrossRef]

Tsonev, L.

E. Popov, L. Tsonev, D. Maystre, “Gratings: general properties of the Littrow mounting and energy flow distribution,” J. Mod. Opt. 37, 367–377 (1990).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), pp. 24–30.

Yariv, A.

Yeh, P.

Appl. Opt. (7)

Appl. Phys. Lett. (1)

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

Electromagnetics (1)

G. Bouchitte, R. Petit, “Homogenization techniques as applied in the electromagnetic theory of gratings,” Electromagnetics 5, 17–36 (1985).
[CrossRef]

J. Appl. Phys. (1)

M. Mansuripur, “Analysis of multilayer thin-film structures containing magneto-optic and anisotropic media at oblique incidence using 2 × 2 matrices,” J. Appl. Phys. 67, 6466–6475 (1990).
[CrossRef]

J. Mod. Opt. (4)

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

G. P. Bryan-Brown, J. R. Sambles, M. C. Hutley, “Polarization conversion through the excitation of surface plasmons on a metallic grating,” J. Mod. Opt. 37, 1227–1232 (1990).
[CrossRef]

L. Li, “A modal analysis of lamellar diffraction gratings in conical mountings,” J. Mod. Opt. 40, 553–573 (1993).
[CrossRef]

E. Popov, L. Tsonev, D. Maystre, “Gratings: general properties of the Littrow mounting and energy flow distribution,” J. Mod. Opt. 37, 367–377 (1990).
[CrossRef]

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (2)

Opt. Acta (5)

L. 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]

L. C. Botten, M. S. Craig, R. C. McPhedran, “Highly conducting lamellar diffraction gratings,” Opt. Acta 28, 1103–1106 (1981).
[CrossRef]

G. Tayeb, R. Petit, “On the numerical study of deep conducting lamellar diffraction gratings,” Opt. Acta 31, 1361–1365 (1984).
[CrossRef]

R. C. McPhedran, L. C. Botten, M. S. Craig, M. Nevière, D. Maystre, “Lossy lamellar gratings in the quasistatic limit,” Opt. Acta 29, P89–312 (1982).
[CrossRef]

J. M. Bell, G. H. Derrick, R. C. McPhedran, “Diffraction gratings in the quasistatic limit,” Opt. Acta 29, 1475–1489 (1982).
[CrossRef]

Opt. Commun. (1)

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. (1)

Phys. Rev. B (1)

R. M. A. Azzam, N. M. Bashara, “Polarization characteristics of scattered radiation from a diffraction grating by ellipsometry with application to surface roughness,” Phys. Rev. B 5, 4721–4729 (1972).
[CrossRef]

Sov. Phys. JETP (1)

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

Other (7)

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. Instrum. Eng.1751, 202–213 (1992).
[CrossRef]

M. L. Minden, G. J. Dunning, “Polarization-dependent phase shift in high-efficiency gratings,” in Periodic Structures, Gratings, Moiré Patterns, and Diffraction Phenomena I, C. H. Chi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.240, 249–254 (1980).
[CrossRef]

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), p. 207.

See, for example, Electromagnetic Theory of Gratings, R. Petit, ed., Vol. 22 of Topics in Current Physics (Springer-Verlag, Berlin, 1980).
[CrossRef]

L. Cescato, E. Gluch, H. Haidner, N. Streibl, “Form birefringence of dielectric coatings and relief gratings,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 333–334 (1990).
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), pp. 24–30.

C. W. Haggans, R. K. Kostuk, “Use of rigorous vector coupled-wave theory for designing and tolerancing surface-relief diffractive components for magneto-optical heads,” in Optical Data Storage ’91, J. J. Burke, N. Imamura, T. A. Shull, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1499, 293–302 (1991).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Grating and incidence geometry. For simplicity, only the zeroth reflected order is shown. Overbars indicate vectors.

Fig. 2
Fig. 2

Detail of the grating region.

Fig. 3
Fig. 3

(a) Phase of the s-polarization component of the zeroth-order beam reflected from a grating at a glass–air interface as a function of grating depth. The grating and incidence parameters are λ = 0.780 μm, Λ = 0.3 μm, Θ = 45°, Φ = 0, D = 0.5, n1 = 1.51, n2 = 1.0, αi = 90°, and δi = 0; (b) same as (a) but for the phase of the p-polarization component with αi = 0 and δi = 0.

Fig. 4
Fig. 4

(a) Phase of the s-polarization component of the zeroth-order beam reflected from a grating at a glass–gold interface as a function of grating depth. The grating and incidence parameters are λ = 0.780 μm, Λ = 0.3 μm, Θ = 45°, Φ = 0, D = 0.5, n1 = 1.51, and n2 = 0.175 + i4.91; s polarization is incident upon the grating (αi = 90° and δi = 0). (b) Same as (a) but for the phase of the p-polarization component.

Fig. 5
Fig. 5

Zeroth reflected order sp phase difference as a function of the period-to-wavelength ratio for the grating of Fig. 3(a) at d = 0.5 μm.

Fig. 6
Fig. 6

(a) Phase of the s-polarization component of the zeroth reflected order as a function of the period-to-wavelength ratio for the grating of Fig. 4(a) at d = 0.1 μm; (b) same as (a) for the p-polarization component.

Fig. 7
Fig. 7

(a) Reflectivity as a function of normalized grating depth (d/λo) for the s-polarization component reflected from a lamellar grating at an air–silicon interface. The grating and incidence parameters are λ = 1.5 μm, Λ = 0.1 μm, Θ = 30°, Φ = 0 D = 0.2, n1 = 1, and n2 = 3.5; s polarization is incident upon the grating (αi = 90° and δi = 0); (b) same as (a) but for the reflectivity of the p-polarization component; (c) δ1,0 (ϕs,1,0ϕp,1,0) versus grating depth for a plane wave reflected from the grating of (a). The incident beam has equal s- and p-polarization components (αi = 45° δi = 0).

Fig. 8
Fig. 8

sp phase difference versus grating depth for the grating of Fig. 3(a) except with αi = 45° and Φ = 90°.

Fig. 9
Fig. 9

Amplitude-ratio angle versus grating depth for the grating of Fig. 3(a) except with αi = 45°, D = 0.7, and Φ = 57°.

Tables (4)

Tables Icon

Table 1 Detail of the Effective-Index Computation for the Grating of Fig. 3

Tables Icon

Table 2 Detail of the Effective-Index Computation for the Grating of Fig. 4

Tables Icon

Table 3 EMT Effective Indices for the Grating of Fig. 7(a)

Tables Icon

Table 4 EMT Effective Indices for the Grating of Fig. 4(a)

Equations (16)

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E m , 0 = p ^ cos α m , 0 + s ^ sin α m , 0 exp ( - i δ m , 0 ) ,
δ m , 0 = ϕ s , m , 0 - ϕ p , m , 0 ,             α m , 0 = arctan ( A s , m , 0 A p , m , 0 ) ,
cos ( γ 1 d 1 ) cos ( γ 2 d 2 ) - 1 2 ( σ 2 γ 1 σ 1 γ 2 + σ 1 γ 2 σ 2 γ 1 ) × sin ( γ 1 d 1 ) sin ( γ 2 d 2 ) = cos ( k x Λ ) ,
σ i = 1 ( E ) ,             σ i = n i 2 ( H ) ,             i = 1 , 2 ,
γ i 2 = ( k i 2 - k z 2 ) - μ ( s ) 2 ,             i = 1 , 2 ,             s = e , h ,
k x = k 1 sin Θ cos Φ ,
k z = k 1 sin Θ sin Φ ,
k 1 = k x x ^ + k 1 cos Θ y ^ + k z z ^ .
k 1 2 = n 1 2 k o 2 ,             k 2 2 = n 2 2 k o 2 ,
d 1 = ( 1 - D ) Λ ,             d 2 = D Λ .
μ ( e ) 2 = - k z 2 - k x 2 + ( k 2 2 - k 1 2 ) D + k 1 2 - O ( Λ 4 ) ,
μ ( h ) 2 = - k z 2 - k x 2 n 1 2 n 2 2 [ ( 1 - D ) n 1 2 + D n 2 2 ] [ ( 1 - D ) n 2 2 + D n 1 2 ] + ( k 2 2 - k 1 2 ) n 1 2 D ( 1 - D ) n 2 2 + D n 1 2 + k 1 2 - O ( Λ 2 ) .
k x 2 n o 2 + μ ( e ) 2 + k z 2 n o 2 = k o 2 ,
n o 2 = n 1 2 ( 1 - D ) + n 2 2 D .
k o 2 = μ ( h ) 2 + k z 2 n e 2 + k x 2 n o 2 ,
n e 2 = n 1 2 n 2 2 ( 1 - D ) n 2 2 + D n 1 2 .

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