Abstract

The differences in the curves of the zeroth-order cross-polarization reflection coefficients (ps and sp) versus angle of incidence have remarkable potential for application in scatterometry because, if the differences are larger than the measurement error, they could contribute to a reliable nondestructive technique for detecting asymmetries in grating profiles. The cross-polarization efficiencies of highly conducting metallic gratings with asymmetric trapezoidal profiles are investigated theoretically by means of a rigorous electromagnetic code. The results show that the differences between ps and sp conversion tend to be undetectable for highly conducting materials, a fact that limits, in principle, the application of this potential detection technique.

© 2003 Optical Society of America

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References

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  1. P. C. Logofatu, S. A. Coulombe, B. K. Minhas, J. R. Mc-Neil, “Identity of the cross-reflection coefficients for symmetric surface-relief gratings,” J. Opt. Soc. Am. A 16, 1108–1114 (1999).
    [CrossRef]
  2. L. Li, “Symmetries of cross-polarization diffraction coefficients of gratings,” J. Opt. Soc. Am. A 17, 881–887 (2000).
    [CrossRef]
  3. P. Vincent, M. Nevière, “The reciprocity theorem for corrugated surfaces used in conical diffraction mountings,” Opt. Acta 26, 889–898 (1979).
    [CrossRef]
  4. R. Depine, C. Valencia, “Reciprocity relations for s-p polarization conversion in conical diffraction,” Opt. Commun. 117, 223–227 (1995).
    [CrossRef]
  5. R. Depine, C. Valencia, “Reciprocity relations for s-p polarization conversion in conical diffraction: erratum,” Opt. Commun. 190, 391 (2001).
    [CrossRef]
  6. J. Chandezon, M. Dupuis, G. Cornet, D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region.” J. Opt. Soc. Am. A 72, 839–846 (1982).
    [CrossRef]
  7. L. Li, “Multilayer-coated diffraction gratings: differential method of Chandezon et al. revisited,” J. Opt. Soc. Am. A 11, 2816–2828 (1994).
    [CrossRef]
  8. L. Li, J. Chandezon, “Improvement of the coordinate transformation method for surface-relief gratings with sharp edges,” J. Opt. Soc. Am. A 13, 2247–2255 (1996).
    [CrossRef]
  9. R. Depine, M. Lester, “Internal symmetries in conical diffraction from metallic gratings,” J. Mod. Opt. 48, 1405–1411 (2001).

2001 (2)

R. Depine, C. Valencia, “Reciprocity relations for s-p polarization conversion in conical diffraction: erratum,” Opt. Commun. 190, 391 (2001).
[CrossRef]

R. Depine, M. Lester, “Internal symmetries in conical diffraction from metallic gratings,” J. Mod. Opt. 48, 1405–1411 (2001).

2000 (1)

1999 (1)

1996 (1)

1995 (1)

R. Depine, C. Valencia, “Reciprocity relations for s-p polarization conversion in conical diffraction,” Opt. Commun. 117, 223–227 (1995).
[CrossRef]

1994 (1)

1982 (1)

J. Chandezon, M. Dupuis, G. Cornet, D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region.” J. Opt. Soc. Am. A 72, 839–846 (1982).
[CrossRef]

1979 (1)

P. Vincent, M. Nevière, “The reciprocity theorem for corrugated surfaces used in conical diffraction mountings,” Opt. Acta 26, 889–898 (1979).
[CrossRef]

Chandezon, J.

L. Li, J. Chandezon, “Improvement of the coordinate transformation method for surface-relief gratings with sharp edges,” J. Opt. Soc. Am. A 13, 2247–2255 (1996).
[CrossRef]

J. Chandezon, M. Dupuis, G. Cornet, D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region.” J. Opt. Soc. Am. A 72, 839–846 (1982).
[CrossRef]

Cornet, G.

J. Chandezon, M. Dupuis, G. Cornet, D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region.” J. Opt. Soc. Am. A 72, 839–846 (1982).
[CrossRef]

Coulombe, S. A.

Depine, R.

R. Depine, C. Valencia, “Reciprocity relations for s-p polarization conversion in conical diffraction: erratum,” Opt. Commun. 190, 391 (2001).
[CrossRef]

R. Depine, M. Lester, “Internal symmetries in conical diffraction from metallic gratings,” J. Mod. Opt. 48, 1405–1411 (2001).

R. Depine, C. Valencia, “Reciprocity relations for s-p polarization conversion in conical diffraction,” Opt. Commun. 117, 223–227 (1995).
[CrossRef]

Dupuis, M.

J. Chandezon, M. Dupuis, G. Cornet, D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region.” J. Opt. Soc. Am. A 72, 839–846 (1982).
[CrossRef]

Lester, M.

R. Depine, M. Lester, “Internal symmetries in conical diffraction from metallic gratings,” J. Mod. Opt. 48, 1405–1411 (2001).

Li, L.

Logofatu, P. C.

Maystre, D.

J. Chandezon, M. Dupuis, G. Cornet, D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region.” J. Opt. Soc. Am. A 72, 839–846 (1982).
[CrossRef]

Mc-Neil, J. R.

Minhas, B. K.

Nevière, M.

P. Vincent, M. Nevière, “The reciprocity theorem for corrugated surfaces used in conical diffraction mountings,” Opt. Acta 26, 889–898 (1979).
[CrossRef]

Valencia, C.

R. Depine, C. Valencia, “Reciprocity relations for s-p polarization conversion in conical diffraction: erratum,” Opt. Commun. 190, 391 (2001).
[CrossRef]

R. Depine, C. Valencia, “Reciprocity relations for s-p polarization conversion in conical diffraction,” Opt. Commun. 117, 223–227 (1995).
[CrossRef]

Vincent, P.

P. Vincent, M. Nevière, “The reciprocity theorem for corrugated surfaces used in conical diffraction mountings,” Opt. Acta 26, 889–898 (1979).
[CrossRef]

J. Mod. Opt. (1)

R. Depine, M. Lester, “Internal symmetries in conical diffraction from metallic gratings,” J. Mod. Opt. 48, 1405–1411 (2001).

J. Opt. Soc. Am. A (5)

Opt. Acta (1)

P. Vincent, M. Nevière, “The reciprocity theorem for corrugated surfaces used in conical diffraction mountings,” Opt. Acta 26, 889–898 (1979).
[CrossRef]

Opt. Commun. (2)

R. Depine, C. Valencia, “Reciprocity relations for s-p polarization conversion in conical diffraction,” Opt. Commun. 117, 223–227 (1995).
[CrossRef]

R. Depine, C. Valencia, “Reciprocity relations for s-p polarization conversion in conical diffraction: erratum,” Opt. Commun. 190, 391 (2001).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Asymmetric profile used in the calculations; h/ d ≈ 0.08.

Fig. 2
Fig. 2

Zeroth-order cross-polarization conversion coefficient r ps 0 versus angle of incidence θ for the profile shown in Fig. 1 and for several values of angle ϕ. The grating parameters are h/ d = 0.08, β1 = β2 = 10°, ε = -8.2344 + 0.287i, and λ/d = 1.1.

Fig. 3
Fig. 3

Zeroth-order cross-polarization conversion coefficient r ps 0 versus angle of incidence θ for the profile shown in Fig. 1 and for several values of angle β2. The grating parameters are h/ d = 0.08, β1 = 10°, ε = -8.2344 + 0.287i, ϕ = 45°, and λ/d = 1.1.

Fig. 4
Fig. 4

Same as Fig. 3 but for ϕ = 65°.

Fig. 5
Fig. 5

Absolute value of the difference between zeroth-order cross-polarization reflection coefficients |Δ| = |r ps 0 - r sp 0| versus angle of incidence θ for the profile shown in Fig. 1 and for several values of angle β2. The grating parameters are h/ d = 0.08, β1 = 10°, ε = -8.2344 + 0.287i, ϕ = 65°, and λ/d = 1.1.

Fig. 6
Fig. 6

Same as Fig. 5 but for ε = -14.73 + 9.98i.

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