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  1. Ellipsometry in the Measurement of Surfaces and Thin Films, edited by E. Passaglia, R. R. Stromberg, and J. Kruger, Natl. Bur. Std. (U. S.) Misc. Publ. No. 256 (U. S. Government Printing Office, Washington, D. C., 1962).
  2. Proceedings of the Symposium on Recent Developments in Ellipsometry, edited by N. M. Bashara, A. B. Buckman, and A. C. Hall, (North-Holland, Amsterdam, 1969);also Surface Sci. 16 (1969).
  3. R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 62, 222 (1972).
    [Crossref]
  4. R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 62, 336 (1972).
    [Crossref]
  5. R. M. A. Azzam and N. M. Bashara, Opt. Commun. 5, 5 (1972).
    [Crossref]
  6. The higher-order beams propagate away from the plane of incidence and are not accessible in an ordinary planar ellipsometer (where the axes of the two telescopes are in one plane, the plane of incidence). For the present example of a diffraction grating (with lines oblique to the plane of incidence) and for other possible applications of generalized ellipsometry a more versatile ellipsometer is needed, e.g., one in which the analyzer telescope can be rotated around two axes.
  7. D. Beaglehole, Phys. Rev. Letters 22, 708 (1969);IEEE Trans. ED-17, 240 (1970)
    [Crossref]
  8. J. J. Cowan and E. T. Arakawa, Z. Physik 235, 97 (1970);Phys. Status Solidi 1, 695 (1970).
    [Crossref]
  9. R. M. A. Azzam and N. M. Bashara, Phys. Rev. B 5, 4721 (1972).
    [Crossref]

1972 (4)

R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 62, 222 (1972).
[Crossref]

R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 62, 336 (1972).
[Crossref]

R. M. A. Azzam and N. M. Bashara, Opt. Commun. 5, 5 (1972).
[Crossref]

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

1970 (1)

J. J. Cowan and E. T. Arakawa, Z. Physik 235, 97 (1970);Phys. Status Solidi 1, 695 (1970).
[Crossref]

1969 (1)

D. Beaglehole, Phys. Rev. Letters 22, 708 (1969);IEEE Trans. ED-17, 240 (1970)
[Crossref]

Arakawa, E. T.

J. J. Cowan and E. T. Arakawa, Z. Physik 235, 97 (1970);Phys. Status Solidi 1, 695 (1970).
[Crossref]

Azzam, R. M. A.

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

R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 62, 222 (1972).
[Crossref]

R. M. A. Azzam and N. M. Bashara, Opt. Commun. 5, 5 (1972).
[Crossref]

R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 62, 336 (1972).
[Crossref]

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 62, 336 (1972).
[Crossref]

R. M. A. Azzam and N. M. Bashara, Opt. Commun. 5, 5 (1972).
[Crossref]

R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 62, 222 (1972).
[Crossref]

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

Beaglehole, D.

D. Beaglehole, Phys. Rev. Letters 22, 708 (1969);IEEE Trans. ED-17, 240 (1970)
[Crossref]

Cowan, J. J.

J. J. Cowan and E. T. Arakawa, Z. Physik 235, 97 (1970);Phys. Status Solidi 1, 695 (1970).
[Crossref]

J. Opt. Soc. Am. (2)

Opt. Commun. (1)

R. M. A. Azzam and N. M. Bashara, Opt. Commun. 5, 5 (1972).
[Crossref]

Phys. Rev. B (1)

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

Phys. Rev. Letters (1)

D. Beaglehole, Phys. Rev. Letters 22, 708 (1969);IEEE Trans. ED-17, 240 (1970)
[Crossref]

Z. Physik (1)

J. J. Cowan and E. T. Arakawa, Z. Physik 235, 97 (1970);Phys. Status Solidi 1, 695 (1970).
[Crossref]

Other (3)

Ellipsometry in the Measurement of Surfaces and Thin Films, edited by E. Passaglia, R. R. Stromberg, and J. Kruger, Natl. Bur. Std. (U. S.) Misc. Publ. No. 256 (U. S. Government Printing Office, Washington, D. C., 1962).

Proceedings of the Symposium on Recent Developments in Ellipsometry, edited by N. M. Bashara, A. B. Buckman, and A. C. Hall, (North-Holland, Amsterdam, 1969);also Surface Sci. 16 (1969).

The higher-order beams propagate away from the plane of incidence and are not accessible in an ordinary planar ellipsometer (where the axes of the two telescopes are in one plane, the plane of incidence). For the present example of a diffraction grating (with lines oblique to the plane of incidence) and for other possible applications of generalized ellipsometry a more versatile ellipsometer is needed, e.g., one in which the analyzer telescope can be rotated around two axes.

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Figures (8)

F. 1
F. 1

The magnitude of the complex diagonal (Rpp) and off-diagonal (Rps). zero-order, reflection coefficients of a 610-lines/mm diffraction grating normalized to Rss as functions of the angle α (in degrees) of inclination of the grating lines from the plane of incidence. These are obtained from multiple-null ellipsometric measurements using a 6328-Å He–Ne laser at 65° angle of incidence. The arrows, both here and in the other figures to follow, indicate the positions at which the −1st, 2nd, 3rd, and 4th diffracted orders graze parallel to the surface and mark the onset of the surface-plasmon-excitation anomalies.

F. 2
F. 2

The angles (in degrees) of the reflection coefficients whose magnitudes are plotted in Fig. 1.

F. 3
F. 3

Wave-vector diagram.

F. 4
F. 4

The evolution of the circle locus of incident polarization states that cause the zero-order beam to become linearly polarized as the grating is rotated to scan the 2nd-order anomaly at α =17.35°. The circles a, b, c, d, e, and f correspond to values of α = 10°, 12°, 14°, 15°, 16°, and 20°, respectively. Note that the circle flips twice in the region of the anomaly.

F. 5
F. 5

Variation of the azimuths aτp and aτs (degrees) of the reflected ellipse of polarization when the incident light is p and s polarized, respectively, as the angle of inclination of the grating lines, α, is changed from 0° to 90°, showing the grating anomalies.

F. 6
F. 6

Same as in Fig. 5, except that the ellipticity (e) instead of the azimuth (a) is under consideration.

F. 7
F. 7

The azimuths aE1 and aE2 (degrees) of the two eigenpolarizations E1 and E2 of reflection as functions of α. Note the structure of the curves in the region of the surface-plasmon anomalies.

F. 8
F. 8

Same as in Fig. 7 for the ellipticity of the eigenpolarizations.

Equations (7)

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R = ( R p p 0 0 R s s ) .
R = ( R p p R p s R s p R s s ) .
R p p = | R p p | e j θ p p , R p s = | R p s | e j θ p s , R s p = | R s p | e j θ s p , R s s = 1 .
| K s | = 2 π λ sin ϕ , | K | = 2 π d ,
| K s | 2 = | K s | 2 + | n K | 2 + 2 | K s | | n K | sin α .
| K s | = 2 π / λ .
sin α = [ 1 sin 2 ϕ ( n 2 / d 2 ) ] / 2 ( n / d ) sin ϕ ,