Abstract

If a compensator rotating at exactly one-third the rate of the analyzer is added to a rotating-analyzer ellipsometer (RAE), all four Stokes parameters of a general polarization state can be measured by Fourier analyzing the transmitted flux. This rotating-analyzer/compensator ellipsometer (RACE) retains the high sensitivity of photometric systems while eliminating the measurement ambiguities characteristic of other photometric ellipsometers. It is self-calibrating and, like null systems, its precision does not depend upon the state measured.

© 1975 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Takasaki, Appl. Opt. 5, 759 (1966); I. Wilmanns, Surf. Sci. 16, 147 (1969); H. G. Mathieu, D. E. McClure, and R. H. Muller, Rev. Sci. Instrum. 45, 798 (1974).
    [Crossref] [PubMed]
  2. B. D. Cahan and R. F. Spanier, Surf. Sci. 16, 166 (1969); R. Greef, Rev. Sci. Instrum. 41, 532 (1970); B. D. Cahan, J. Horkans, and E. Yeager, Surf. Sci. 37, 559 (1973); R. W. Stobie, B. Rao, and M. J. Dignam, J. Opt. Soc. Am. 65, 25 (1975).
    [Crossref]
  3. D. E. Aspnes, Opt. Commun. 8, 222 (1973).
    [Crossref]
  4. P. S. Hauge and F. H. Dill, IBM J. Res. Dev. 17, 472 (1973); Y. J. van der Meulen and N. C. Hien, J. Opt. Soc. Am. 64, 804 (1974).
    [Crossref]
  5. D. E. Aspnes and A. A. Studna, Appl. Opt. 14, 220 (1975).
    [Crossref] [PubMed]
  6. S. N. Jasperson and S. E. Schnatterly, Rev. Sci. Instrum. 40, 761 (1969); S. N. Jasperson, D. K. Burge, and R. C. O’Handley, Surf. Sci. 37, 548 (1973); J. I. Treu, A. B. Callendar, and S. E. Schnatterly; Rev. Sci. Instrum. 44, 793 (1973).
    [Crossref]
  7. D. E. Aspnes, Appl. Opt. 14, 1131 (1975).
    [Crossref] [PubMed]
  8. D. E. Aspnes, in Optical Properties of Solids: New Developments, edited by B. O. Seraphin (North–Holland, Amsterdam, 1975).
  9. D. E. Aspnes, J. Opt. Soc. Am. 64, 639 (1974).
    [Crossref]
  10. M. Born and E. Wolf, Principles of Optics, 1st ed, (Pergamon, New York, 1964), pp. 544ff.
  11. D. Clark and J. Grainger, Polarized Light and Optical Measurement (Pergamon, New York, 1971), p. 124.
  12. D. E. Aspnes, J. Opt. Soc. Am. 61, 1077 (1971).
    [Crossref]
  13. R. M. A. Azzam and N. Bashara, J. Opt. Soc. Am. 61, 600, 773 (1971).
    [Crossref]
  14. R. C. O’Handley, J. Opt. Soc. Am. 63, 523 (1973); R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 64, 1459 (1974).
    [Crossref]
  15. D. E. Aspnes, J. Opt. Soc. Am. 64, 812 (1974).
    [Crossref]
  16. Model 33-86-25 high-intensity monochromator, with model 33-86-02 grating with 1350 lines/mm blazed at 500 nm. The source used in the measurement was a model 33-86-39-01 45W quartz-iodine lamp, the light from which was collimated by a single quartz focusing lens. All components were manufactured by Bausch and Lomb, Rochester, N. Y. 14625.
  17. Model 9659 QB photomultiplier, manufactured by EMI Electronics, Ltd., Hayes, Middlesex, England.
  18. Rayleigh, Philos. Mag. 14, 60 (1907).
  19. R. W. Wood, Philos. Mag. 4, 396 (1902); Philos. Mag. 23, 310 (1912).
  20. G. W. Stroke, in Handbuch der Physik, 29, edited by S. Flügge (Springer, Berlin, 1967), p. 426.
    [Crossref]

1975 (2)

1974 (2)

1973 (3)

D. E. Aspnes, Opt. Commun. 8, 222 (1973).
[Crossref]

P. S. Hauge and F. H. Dill, IBM J. Res. Dev. 17, 472 (1973); Y. J. van der Meulen and N. C. Hien, J. Opt. Soc. Am. 64, 804 (1974).
[Crossref]

R. C. O’Handley, J. Opt. Soc. Am. 63, 523 (1973); R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 64, 1459 (1974).
[Crossref]

1971 (2)

1969 (2)

B. D. Cahan and R. F. Spanier, Surf. Sci. 16, 166 (1969); R. Greef, Rev. Sci. Instrum. 41, 532 (1970); B. D. Cahan, J. Horkans, and E. Yeager, Surf. Sci. 37, 559 (1973); R. W. Stobie, B. Rao, and M. J. Dignam, J. Opt. Soc. Am. 65, 25 (1975).
[Crossref]

S. N. Jasperson and S. E. Schnatterly, Rev. Sci. Instrum. 40, 761 (1969); S. N. Jasperson, D. K. Burge, and R. C. O’Handley, Surf. Sci. 37, 548 (1973); J. I. Treu, A. B. Callendar, and S. E. Schnatterly; Rev. Sci. Instrum. 44, 793 (1973).
[Crossref]

1966 (1)

1907 (1)

Rayleigh, Philos. Mag. 14, 60 (1907).

1902 (1)

R. W. Wood, Philos. Mag. 4, 396 (1902); Philos. Mag. 23, 310 (1912).

Aspnes, D. E.

Azzam, R. M. A.

Bashara, N.

Born, M.

M. Born and E. Wolf, Principles of Optics, 1st ed, (Pergamon, New York, 1964), pp. 544ff.

Cahan, B. D.

B. D. Cahan and R. F. Spanier, Surf. Sci. 16, 166 (1969); R. Greef, Rev. Sci. Instrum. 41, 532 (1970); B. D. Cahan, J. Horkans, and E. Yeager, Surf. Sci. 37, 559 (1973); R. W. Stobie, B. Rao, and M. J. Dignam, J. Opt. Soc. Am. 65, 25 (1975).
[Crossref]

Clark, D.

D. Clark and J. Grainger, Polarized Light and Optical Measurement (Pergamon, New York, 1971), p. 124.

Dill, F. H.

P. S. Hauge and F. H. Dill, IBM J. Res. Dev. 17, 472 (1973); Y. J. van der Meulen and N. C. Hien, J. Opt. Soc. Am. 64, 804 (1974).
[Crossref]

Grainger, J.

D. Clark and J. Grainger, Polarized Light and Optical Measurement (Pergamon, New York, 1971), p. 124.

Hauge, P. S.

P. S. Hauge and F. H. Dill, IBM J. Res. Dev. 17, 472 (1973); Y. J. van der Meulen and N. C. Hien, J. Opt. Soc. Am. 64, 804 (1974).
[Crossref]

Jasperson, S. N.

S. N. Jasperson and S. E. Schnatterly, Rev. Sci. Instrum. 40, 761 (1969); S. N. Jasperson, D. K. Burge, and R. C. O’Handley, Surf. Sci. 37, 548 (1973); J. I. Treu, A. B. Callendar, and S. E. Schnatterly; Rev. Sci. Instrum. 44, 793 (1973).
[Crossref]

O’Handley, R. C.

Rayleigh,

Rayleigh, Philos. Mag. 14, 60 (1907).

Schnatterly, S. E.

S. N. Jasperson and S. E. Schnatterly, Rev. Sci. Instrum. 40, 761 (1969); S. N. Jasperson, D. K. Burge, and R. C. O’Handley, Surf. Sci. 37, 548 (1973); J. I. Treu, A. B. Callendar, and S. E. Schnatterly; Rev. Sci. Instrum. 44, 793 (1973).
[Crossref]

Spanier, R. F.

B. D. Cahan and R. F. Spanier, Surf. Sci. 16, 166 (1969); R. Greef, Rev. Sci. Instrum. 41, 532 (1970); B. D. Cahan, J. Horkans, and E. Yeager, Surf. Sci. 37, 559 (1973); R. W. Stobie, B. Rao, and M. J. Dignam, J. Opt. Soc. Am. 65, 25 (1975).
[Crossref]

Stroke, G. W.

G. W. Stroke, in Handbuch der Physik, 29, edited by S. Flügge (Springer, Berlin, 1967), p. 426.
[Crossref]

Studna, A. A.

Takasaki, H.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 1st ed, (Pergamon, New York, 1964), pp. 544ff.

Wood, R. W.

R. W. Wood, Philos. Mag. 4, 396 (1902); Philos. Mag. 23, 310 (1912).

Appl. Opt. (3)

IBM J. Res. Dev. (1)

P. S. Hauge and F. H. Dill, IBM J. Res. Dev. 17, 472 (1973); Y. J. van der Meulen and N. C. Hien, J. Opt. Soc. Am. 64, 804 (1974).
[Crossref]

J. Opt. Soc. Am. (5)

Opt. Commun. (1)

D. E. Aspnes, Opt. Commun. 8, 222 (1973).
[Crossref]

Philos. Mag. (2)

Rayleigh, Philos. Mag. 14, 60 (1907).

R. W. Wood, Philos. Mag. 4, 396 (1902); Philos. Mag. 23, 310 (1912).

Rev. Sci. Instrum. (1)

S. N. Jasperson and S. E. Schnatterly, Rev. Sci. Instrum. 40, 761 (1969); S. N. Jasperson, D. K. Burge, and R. C. O’Handley, Surf. Sci. 37, 548 (1973); J. I. Treu, A. B. Callendar, and S. E. Schnatterly; Rev. Sci. Instrum. 44, 793 (1973).
[Crossref]

Surf. Sci. (1)

B. D. Cahan and R. F. Spanier, Surf. Sci. 16, 166 (1969); R. Greef, Rev. Sci. Instrum. 41, 532 (1970); B. D. Cahan, J. Horkans, and E. Yeager, Surf. Sci. 37, 559 (1973); R. W. Stobie, B. Rao, and M. J. Dignam, J. Opt. Soc. Am. 65, 25 (1975).
[Crossref]

Other (6)

D. E. Aspnes, in Optical Properties of Solids: New Developments, edited by B. O. Seraphin (North–Holland, Amsterdam, 1975).

G. W. Stroke, in Handbuch der Physik, 29, edited by S. Flügge (Springer, Berlin, 1967), p. 426.
[Crossref]

M. Born and E. Wolf, Principles of Optics, 1st ed, (Pergamon, New York, 1964), pp. 544ff.

D. Clark and J. Grainger, Polarized Light and Optical Measurement (Pergamon, New York, 1971), p. 124.

Model 33-86-25 high-intensity monochromator, with model 33-86-02 grating with 1350 lines/mm blazed at 500 nm. The source used in the measurement was a model 33-86-39-01 45W quartz-iodine lamp, the light from which was collimated by a single quartz focusing lens. All components were manufactured by Bausch and Lomb, Rochester, N. Y. 14625.

Model 9659 QB photomultiplier, manufactured by EMI Electronics, Ltd., Hayes, Middlesex, England.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

FIG. 1
FIG. 1

Diagram of the coordinate system and azimuth convention. The reference azimuth A = 0 is determined by a timing or fiducial mark on the rotating analyzer. The relative retardations 1 and e of the compensator slow (fast) and fast (slow) axes are shown explicitly. The field components, x and x, and the propagation direction, z ˆ, of the incident flux are also shown.

FIG. 2
FIG. 2

Relative Stokes parameter, (s0), and normalized Stokes parameters si/s0 for the high-intensity grating monochromator described in the text.

FIG. 3
FIG. 3

Degree of polarization p, azimuth φ, and minor/major axis ratio b/a, of the elliptically polarized component of the emergent flux for the high-intensity grating monochromator described in the text. The values 0° and 90° for φ correspond to the major axis parallel and perpendicular, respectively, to the grating rulings.

Equations (38)

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

I t = s 0 + s 1 [ cos 2 C cos 2 ( A - C ) - cos δ sin 2 C sin 2 ( A - C ) ] + s 2 [ sin 2 C cos 2 ( A - C ) + cos δ cos 2 C sin 2 ( A - C ) ] - s 3 sin δ sin 2 ( A - C ) .
C = A / 3 + C 0 ,
I t = I 0 [ 1 + α 1 cos θ + β 1 sin θ + α 2 cos 2 θ + β 2 sin 2 θ + α 3 cos 3 θ + β 3 sin 3 θ ]
= s 0 + s 1 [ cos 2 ( δ / 2 ) cos 3 θ + sin 2 ( δ / 2 ) cos ( θ - 4 C 0 ) ] + s 2 [ cos 2 ( δ / 2 ) sin 3 θ - sin 2 ( δ / 2 ) sin ( θ - 4 C 0 ) ] - s 3 sin δ sin ( 2 θ - 2 C 0 ) ,
θ = 2 A / 3.
γ i = α i 2 + β i 2 ,
η i = tan - 1 ( β i / α i ) + π sgn ( β i ) u ( - α i ) ,
ξ = tan - 1 ( s 2 / s 1 ) + π sgn ( s 2 ) u ( - s 1 ) ,
s 0 = 4 I t / ( c 0 ) ,
γ 1 = [ ( s 1 2 + s 2 2 ) 1 / 2 / s 0 ] sin 2 ( δ / 2 ) ,
γ 2 = ( s 3 / s 0 ) sin δ ,
γ 3 = [ ( s 1 2 + s 2 2 ) 1 / 2 / s 0 ] cos 2 ( δ / 2 ) ,
η 1 = 4 C 01 - ξ ,
η 2 = 2 C 02 - π / 2 ,
η 3 = ξ ,
h 1 = sgn { cos [ 6 ( C 01 - C 0 ) ] } = sgn { cos ( 6 C 01 ) } ,
h 2 = sgn { cos [ 2 ( C 01 - C 02 ) ] } .
sgn ( sin δ ) = h 1 ,
sgn ( s 3 sin δ ) = h 2 ,
sgn ( s 3 ) = h 1 h 2 ,
C 01 , C 02 = C 0 mod π / 6.
C 01 = ( η 1 + η 3 ) / 4 ,
C 02 = ( η 2 + π / 2 ) / 2 ,
δ = 2 h 1 tan - 1 ( γ 1 / γ 3 ) ,
s 0 = 4 I t / ( c 0 ) ,
s 1 / s 0 = ( γ 1 + γ 3 ) cos η 3 ,
s 2 / s 0 = ( γ 1 + γ 3 ) sin η 3 ,
s 3 / s 0 = γ 2 h 2 / sin δ .
p = [ s 1 2 + s 2 2 + s 3 2 ] 1 / 2 / s 0 = ( γ 1 + γ 3 ) [ 1 + γ 2 2 / ( 4 γ 1 γ 3 ) ] 1 / 2 ,
φ = 1 2 tan - 1 ( s 2 / s 1 ) + ( π / 2 ) sgn ( s 2 ) u ( - s 1 ) = η 3 / 2 ,
b a = tan [ 1 2 sin - 1 ( s 3 s 1 2 + s 2 2 + s 3 2 ) ] = h 1 h 2 γ 2 / ( γ 2 2 + 8 γ 1 γ 3 ) 1 / 2 .
s 0 + 2 γ s 3 cos δ = 4 I t / ( c e 0 ) ,
η 1 = 4 C 01 - ζ - 4 γ cot ( δ / 2 ) .
p = p ( 1 - 2 γ cos δ s 3 / s 0 ) ,
ρ = tan ψ e i Δ = s 2 - i s 3 s 0 - s 1 tan P ,
s 0 2 s 0 2
= s 1 2 + s 2 2 + s 3 2
= 2 ( r p 2 cos 2 P + r s 2 sin 2 P ) .