Abstract

Recent work in which reflection polarizers were used to make ellipsometric measurements in the far uv employed the tacit assumption that the incident light was in a coherent state of polarization. However, since the most general state of light, is that of partial polarization, i.e., a mixture of polarized and unpolarized components, a significant modification to the experimental techniques used hitherto is shown to be necessary.

© 1971 Optical Society of America

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References

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  1. G. Rosenbaum et al., Appl. Opt. 7, 1917 (1968).
    [CrossRef] [PubMed]
  2. M. Schledermann, M. Skibowski, Appl. Opt. 10, 321 (1971).
    [CrossRef] [PubMed]
  3. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1959), p. 550.
  4. Ref. 3, p. 545.
  5. Synchrotron radiation was used as a source, and this is in theory fully elliptically polarized. However, scattering within the system could cause partial depolarization. Furthermore, the results of studies of synchrotron polarization in the visible region [P. Joos, Phys. Rev. Lett. 4, 558 (1960); K. Codling, R. P. Madden, J. Appl. Phys. 36, 380 (1965)] do not exclude the possibility of there being a small unpolarized component in such radiation.
    [CrossRef]
  6. D. G. Avery, Proc. Phys. Soc. B65, 425 (1952).
  7. I. H. Malitson, J. Opt. Soc. Am. 55, 1205 (1965).
    [CrossRef]
  8. S. P. F. Humphreys-Owen, Proc. Phys. Soc. 77, 949 (1961).
    [CrossRef]

1971 (1)

1968 (1)

1965 (1)

1961 (1)

S. P. F. Humphreys-Owen, Proc. Phys. Soc. 77, 949 (1961).
[CrossRef]

1960 (1)

Synchrotron radiation was used as a source, and this is in theory fully elliptically polarized. However, scattering within the system could cause partial depolarization. Furthermore, the results of studies of synchrotron polarization in the visible region [P. Joos, Phys. Rev. Lett. 4, 558 (1960); K. Codling, R. P. Madden, J. Appl. Phys. 36, 380 (1965)] do not exclude the possibility of there being a small unpolarized component in such radiation.
[CrossRef]

1952 (1)

D. G. Avery, Proc. Phys. Soc. B65, 425 (1952).

Avery, D. G.

D. G. Avery, Proc. Phys. Soc. B65, 425 (1952).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1959), p. 550.

Humphreys-Owen, S. P. F.

S. P. F. Humphreys-Owen, Proc. Phys. Soc. 77, 949 (1961).
[CrossRef]

Joos, P.

Synchrotron radiation was used as a source, and this is in theory fully elliptically polarized. However, scattering within the system could cause partial depolarization. Furthermore, the results of studies of synchrotron polarization in the visible region [P. Joos, Phys. Rev. Lett. 4, 558 (1960); K. Codling, R. P. Madden, J. Appl. Phys. 36, 380 (1965)] do not exclude the possibility of there being a small unpolarized component in such radiation.
[CrossRef]

Malitson, I. H.

Rosenbaum, G.

Schledermann, M.

Skibowski, M.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1959), p. 550.

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

Phys. Rev. Lett. (1)

Synchrotron radiation was used as a source, and this is in theory fully elliptically polarized. However, scattering within the system could cause partial depolarization. Furthermore, the results of studies of synchrotron polarization in the visible region [P. Joos, Phys. Rev. Lett. 4, 558 (1960); K. Codling, R. P. Madden, J. Appl. Phys. 36, 380 (1965)] do not exclude the possibility of there being a small unpolarized component in such radiation.
[CrossRef]

Proc. Phys. Soc. (2)

D. G. Avery, Proc. Phys. Soc. B65, 425 (1952).

S. P. F. Humphreys-Owen, Proc. Phys. Soc. 77, 949 (1961).
[CrossRef]

Other (2)

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1959), p. 550.

Ref. 3, p. 545.

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Figures (3)

Fig. 1
Fig. 1

Azimuth angle definitions for reflecting polarizer/analyzer system; XY coordinates represent the laboratory frame. The polarizer plane of incidence (P) is measured with respect to the X axis, and the analyzer plane of incidence (A) is measured with respect to P.

Fig. 2
Fig. 2

Fixed azimuth polarizer form of reflecting ellipsometer. P, polarizer (specimen); T, turntable; A, reflecting analyzer; D, detector. The analyzer/detector assembly shown inside the dashed line rotates around the axis Z as a single unit.

Fig. 3
Fig. 3

The n and k contours within ρ602 and ρ752 axes.

Tables (1)

Tables Icon

Table I Examples of Numerical Determination of (n,k) Values Showing Variation of Accuracy with Position in ρ2 Space (Fig. 3)

Equations (36)

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I ( ψ , ϕ ) = K i = 1 9 A i B i C i ,
E x = E x ( x , y ) exp [ i θ 1 ( x , y ) ]
E y = E y ( x , y ) exp [ i θ 2 ( x , y ) ] ,
U = N - 1 F E y 2 d F ,
V = N - 1 F E x E y cos θ d F ,
W = N - 1 F E x E y sin θ d F ,
N = F E x 2 d F
θ = θ 2 - θ 1 .
E y / E x = U 1 2 exp ( i θ ) ,
V = U 1 2 cos θ , W = U 1 2 sin θ .
I ( ψ , ϕ ) = K [ ( i = 1 9 A i B i C i ) U = 1 θ = ( π / 2 ) + ( i = 1 9 A i B i C i ) U = 1 θ = ( π / 2 ) ] = K [ ( 1 + ρ 1 2 ρ 2 2 ) cos 2 ϕ + ( ρ 1 2 + ρ 2 2 ) sin 2 ϕ ] .
I ( ψ , ϕ ) = ( 1 - m ) K i = 1 11 A i B i C i ,
A 10 B 10 C 10 = [ m / ( 1 - m ) ] ( 1 + ρ 1 2 ρ 2 2 ) cos 2 ϕ
A 11 B 11 C 11 = [ m / ( 1 - m ) ] ( ρ 1 2 + ρ 2 2 ) sin 2 ϕ .
U = 0.042 , V = - 0.011 W = 0.112 } V 2 + W 2 = 0.0127.
I ( ψ , ϕ ) = t = 1 11 Q f i · A i ( ψ , ϕ ) ,
Q = ( 1 - m ) K , f i = f i ( ρ 1 , ρ 2 , δ 1 , U , V , W , m ) = B i C i ,
I ( 0 , 0 ) = ( 1 - m ) K [ ( 1 + U ρ 1 2 ρ 2 2 ) + [ m / ( 1 - m ) ] ( 1 + ρ 1 2 ρ 2 2 ) ] = K ( 1 + M ρ 1 2 ρ 2 2 ) ,
M = m + U ( 1 - m ) ; I ( 0 , π / 2 ) = K ( ρ 2 2 + M ρ 1 2 ) , I ( π / 2 , 0 ) = K ( M + ρ 1 2 ρ 2 2 ) , I ( π / 2 , π / 2 ) = K ( ρ 1 2 + M ρ 2 2 ) .
R 1 = I ( 0 , π 4 ) - I ( 0 , - π 4 ) = ( 1 - m ) K [ 2 ρ 1 ( 1 - ρ 2 2 ) × ( V cos δ 1 - W sin δ 1 ) ] , R 2 = I ( π 2 , π 4 ) - I ( π 2 , - π 4 ) = ( 1 - m ) K [ - 2 ρ 1 ( 1 - ρ 2 2 ) × ( V cos δ 1 + W sin δ 1 ) ] , R 3 = I ( π 4 , 0 ) - I ( - π 4 , 0 ) = ( 1 - m ) K [ 2 ( 1 - ρ 1 2 ρ 2 2 ) V ] ,
( R 1 - R 2 ) / R 3 = [ 2 ρ 1 ( 1 - ρ 2 2 ) / ( 1 - ρ 1 2 ρ 2 2 ) ] · cos δ 1 .
I ( ϕ ) = K [ ( 1 + M ρ 1 2 ρ 2 2 ) cos 2 ϕ + ( ρ 2 2 + M ρ 1 2 ) sin 2 ϕ + ( 1 - m ) U 1 2 ρ 1 ( 1 - ρ 2 2 ) cos ( δ 1 + θ ) sin 2 ϕ ] ,
I ( π / 2 ) / I ( 0 ) = a = ( ρ 2 2 + M ρ 1 2 ) / ( 1 + M ρ 1 2 ρ 2 2 ) .
I ( π / 2 ) / I ( 0 ) = b = ( ρ 2 2 + M ) / ( 1 + M ρ 2 2 ) .
ρ 1 2 = [ ( a - ρ 2 2 ) / ( b - ρ 2 2 ) ] [ ( 1 - b ρ 2 2 ) / ( 1 - a ρ 2 2 ) ] ,
ρ 2 = 1 2 { ( S - 1 ) - [ ( S - 1 ) 2 - 4 ] 1 2 } ,
S = ( 1 + b + a b ) / a .
I ( ϕ ) = A cos 2 ϕ + B sin 2 ϕ + C sin 2 ϕ ,
I ( ϕ ) + I [ ϕ + ( π / 2 ) ] = A + B = const .
r p = ( γ - N 2 cos θ ) / ( γ + N 2 cos θ )
r s = ( cos θ - γ ) / ( cos θ + γ ) ,
γ = γ - i γ = ( N 2 - sin 2 θ ) 1 2 ,
r p / r s = ρ exp ( i δ ) = ( γ - sin θ tan θ ) / ( γ + sin θ tan θ ) .
ρ 2 = [ ( γ - t ) 2 + γ 2 ] / [ ( γ + t ) 2 + γ 2 ] ,
( 1 - ρ 2 ) / ( 1 + ρ 2 ) = 2 t γ / [ ( γ 2 + γ 2 ) + t 2 ] ,
σ ( γ 2 + γ 2 ) - 2 t γ + σ t 2 = 0

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