Abstract

A goniometric ellipsometer is used to recover the optogeometrical parameters of metallic gratings. The phase difference between TE and TM polarizations in all the diffracted orders is measured as a function of the incidence angle. The groove depth, together with the refractive indices of all the media of the diffracting structure, is determined for a holographic sinusoidal aluminum grating. It is shown that a thin layer of alumina on top of the grating must be considered.

© 1996 Optical Society of America

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References

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  1. R. Petit, M. Cadilhac, D. Maystre, P. Vincent, Electromagnetic Theory of Gratings, R. Petit, ed., Vol. 22 of Topics in Current Physics (Springer-Verlag, Berlin, 1980), pp. 1–121.
    [CrossRef]
  2. M. G. Moharam, T. K. Gaylord, J. Opt. Soc. Am. A 3, 1780 (1986).
    [CrossRef]
  3. A. Roger, Opt. Commun. 32, 11 (1980).
    [CrossRef]
  4. H. R. Giovannini, D. Yeddou, S. J. Huard, M. R. Lequime, C. Froehly, Opt. Lett. 18, 2074 (1993).
    [CrossRef] [PubMed]
  5. H. Giovannini, H. Akhouayri, Opt. Lett. 20, 2255 (1995).
    [CrossRef] [PubMed]
  6. R. M. Azzam, N. M. Bashara, Ellipsometry in Polarized Light (North-Holland, Amsterdam, 1977).
  7. R. M. Azzam, N. M. Bashara, J. Opt. Soc. Am. 62, 1521 (1972).
    [CrossRef]
  8. R. M. Azzam, N. M. Bashara, Phys. Rev. B 5, 4721 (1972).
    [CrossRef]
  9. Y. Cui, R. M. A. Azzam, Appl. Opt. 35, 2235 (1996).
    [CrossRef] [PubMed]
  10. F. Montiel, M. Neviére, J. Opt. Soc. Am. A 11, 3241 (1994).
    [CrossRef]
  11. C. Deumié, H. Giovannini, G. Albrand, H. Akhouayri, C. Amra, in Optical Interference Coatings, Vol. 17 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 255–256.
  12. C. Amra, D. Torricini, P. Roche, Appl. Opt. 32, 5462 (1993).
    [CrossRef] [PubMed]
  13. G. Haas, L. Hardley, in American Institute of Physics Handbook, D. E. Gray, ed. (McGraw-Hill, New York, 1972), pp. 6–40.

1996 (1)

1995 (1)

1994 (1)

1993 (2)

1986 (1)

1980 (1)

A. Roger, Opt. Commun. 32, 11 (1980).
[CrossRef]

1972 (2)

R. M. Azzam, N. M. Bashara, J. Opt. Soc. Am. 62, 1521 (1972).
[CrossRef]

R. M. Azzam, N. M. Bashara, Phys. Rev. B 5, 4721 (1972).
[CrossRef]

Akhouayri, H.

H. Giovannini, H. Akhouayri, Opt. Lett. 20, 2255 (1995).
[CrossRef] [PubMed]

C. Deumié, H. Giovannini, G. Albrand, H. Akhouayri, C. Amra, in Optical Interference Coatings, Vol. 17 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 255–256.

Albrand, G.

C. Deumié, H. Giovannini, G. Albrand, H. Akhouayri, C. Amra, in Optical Interference Coatings, Vol. 17 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 255–256.

Amra, C.

C. Amra, D. Torricini, P. Roche, Appl. Opt. 32, 5462 (1993).
[CrossRef] [PubMed]

C. Deumié, H. Giovannini, G. Albrand, H. Akhouayri, C. Amra, in Optical Interference Coatings, Vol. 17 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 255–256.

Azzam, R. M.

R. M. Azzam, N. M. Bashara, Phys. Rev. B 5, 4721 (1972).
[CrossRef]

R. M. Azzam, N. M. Bashara, J. Opt. Soc. Am. 62, 1521 (1972).
[CrossRef]

R. M. Azzam, N. M. Bashara, Ellipsometry in Polarized Light (North-Holland, Amsterdam, 1977).

Azzam, R. M. A.

Bashara, N. M.

R. M. Azzam, N. M. Bashara, Phys. Rev. B 5, 4721 (1972).
[CrossRef]

R. M. Azzam, N. M. Bashara, J. Opt. Soc. Am. 62, 1521 (1972).
[CrossRef]

R. M. Azzam, N. M. Bashara, Ellipsometry in Polarized Light (North-Holland, Amsterdam, 1977).

Cadilhac, M.

R. Petit, M. Cadilhac, D. Maystre, P. Vincent, Electromagnetic Theory of Gratings, R. Petit, ed., Vol. 22 of Topics in Current Physics (Springer-Verlag, Berlin, 1980), pp. 1–121.
[CrossRef]

Cui, Y.

Deumié, C.

C. Deumié, H. Giovannini, G. Albrand, H. Akhouayri, C. Amra, in Optical Interference Coatings, Vol. 17 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 255–256.

Froehly, C.

Gaylord, T. K.

Giovannini, H.

H. Giovannini, H. Akhouayri, Opt. Lett. 20, 2255 (1995).
[CrossRef] [PubMed]

C. Deumié, H. Giovannini, G. Albrand, H. Akhouayri, C. Amra, in Optical Interference Coatings, Vol. 17 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 255–256.

Giovannini, H. R.

Haas, G.

G. Haas, L. Hardley, in American Institute of Physics Handbook, D. E. Gray, ed. (McGraw-Hill, New York, 1972), pp. 6–40.

Hardley, L.

G. Haas, L. Hardley, in American Institute of Physics Handbook, D. E. Gray, ed. (McGraw-Hill, New York, 1972), pp. 6–40.

Huard, S. J.

Lequime, M. R.

Maystre, D.

R. Petit, M. Cadilhac, D. Maystre, P. Vincent, Electromagnetic Theory of Gratings, R. Petit, ed., Vol. 22 of Topics in Current Physics (Springer-Verlag, Berlin, 1980), pp. 1–121.
[CrossRef]

Moharam, M. G.

Montiel, F.

Neviére, M.

Petit, R.

R. Petit, M. Cadilhac, D. Maystre, P. Vincent, Electromagnetic Theory of Gratings, R. Petit, ed., Vol. 22 of Topics in Current Physics (Springer-Verlag, Berlin, 1980), pp. 1–121.
[CrossRef]

Roche, P.

Roger, A.

A. Roger, Opt. Commun. 32, 11 (1980).
[CrossRef]

Torricini, D.

Vincent, P.

R. Petit, M. Cadilhac, D. Maystre, P. Vincent, Electromagnetic Theory of Gratings, R. Petit, ed., Vol. 22 of Topics in Current Physics (Springer-Verlag, Berlin, 1980), pp. 1–121.
[CrossRef]

Yeddou, D.

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

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

Opt. Commun. (1)

A. Roger, Opt. Commun. 32, 11 (1980).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. B (1)

R. M. Azzam, N. M. Bashara, Phys. Rev. B 5, 4721 (1972).
[CrossRef]

Other (4)

C. Deumié, H. Giovannini, G. Albrand, H. Akhouayri, C. Amra, in Optical Interference Coatings, Vol. 17 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 255–256.

R. M. Azzam, N. M. Bashara, Ellipsometry in Polarized Light (North-Holland, Amsterdam, 1977).

G. Haas, L. Hardley, in American Institute of Physics Handbook, D. E. Gray, ed. (McGraw-Hill, New York, 1972), pp. 6–40.

R. Petit, M. Cadilhac, D. Maystre, P. Vincent, Electromagnetic Theory of Gratings, R. Petit, ed., Vol. 22 of Topics in Current Physics (Springer-Verlag, Berlin, 1980), pp. 1–121.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic of the experimental setup. The mirrors can be translated to select the laser sources. Several detectors can be used, depending on the wavelength of operation. The detector can be rotated around a vertical axis.

Fig. 2
Fig. 2

Phase difference between TE and TM polarizations as a function of the incidence angle. Solid curves, numerical results; dashed curves, experimental results: (a) 0 order, (b) 1 order.

Fig. 3
Fig. 3

Efficiencies as a function of the incidence angle. Solid curves, numerical results; dashed curves, experimental results: (a) 0-order TE polarization, (b) 0-order TM polarization, (c) 1-order TE polarization, (d) 1-order TM polarization.

Equations (2)

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ϕ n = arg ( B n , TE ) arg ( B n , TM ) ,
k = [ n 2 1 + 2 n ( 1 + R / 1 R ) ] 1 / 2 .

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