Abstract

To our knowledge there has been very little work done to establish the theoretical basis of high-NA Mueller matrix polarimetry. We consider how high-NA polarimetry differs from traditional wide-field polarimetry. We show that confocal polarimetry leads to an averaging of the sample Jones matrices, each of which is associated with one of the incident plane waves comprising the incident focused field and that a conventional polarimeter leads to an averaging of sample Mueller matrices. We conclude with an example.

© 2008 Optical Society of America

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References

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2005 (1)

2003 (1)

1998 (1)

T. Wilson, P. Török, and P. D. Higdon, J. Microsc. 189, 12 (1998).
[CrossRef]

1997 (1)

P. Török and T. Wilson, Opt. Commun. 137, 127 (1997).
[CrossRef]

1996 (1)

1995 (2)

S. V. Shatalin, R. C. Juškaitis, J. B. Tan, and T. Wilson, J. Microsc. 179, 241 (1995).
[CrossRef]

T. Wilson and R. Juškaitis, J. Microsc. 179, 238 (1995).
[CrossRef]

1992 (1)

R. Azzam and N. Bashara, Ellipsometry and Polarized Light, 3rd ed. (North Holland, 1992).

1987 (1)

Azzam, R.

R. Azzam and N. Bashara, Ellipsometry and Polarized Light, 3rd ed. (North Holland, 1992).

Bashara, N.

R. Azzam and N. Bashara, Ellipsometry and Polarized Light, 3rd ed. (North Holland, 1992).

Carlini, A. R.

Chipman, R.

Dainty, C.

De Martino, A.

Drévillon, B.

Garcia-Caurel, E.

Higdon, P. D.

T. Wilson, P. Török, and P. D. Higdon, J. Microsc. 189, 12 (1998).
[CrossRef]

Juškaitis, R.

T. Wilson and R. Juškaitis, J. Microsc. 179, 238 (1995).
[CrossRef]

Juškaitis, R. C.

S. V. Shatalin, R. C. Juškaitis, J. B. Tan, and T. Wilson, J. Microsc. 179, 241 (1995).
[CrossRef]

Kim, Y.

Lara, D.

Laude, B.

Lu, S.-Y.

Shatalin, S. V.

S. V. Shatalin, R. C. Juškaitis, J. B. Tan, and T. Wilson, J. Microsc. 179, 241 (1995).
[CrossRef]

Tan, J. B.

S. V. Shatalin, R. C. Juškaitis, J. B. Tan, and T. Wilson, J. Microsc. 179, 241 (1995).
[CrossRef]

Török, P.

T. Wilson, P. Török, and P. D. Higdon, J. Microsc. 189, 12 (1998).
[CrossRef]

P. Török and T. Wilson, Opt. Commun. 137, 127 (1997).
[CrossRef]

Wilson, T.

T. Wilson, P. Török, and P. D. Higdon, J. Microsc. 189, 12 (1998).
[CrossRef]

P. Török and T. Wilson, Opt. Commun. 137, 127 (1997).
[CrossRef]

S. V. Shatalin, R. C. Juškaitis, J. B. Tan, and T. Wilson, J. Microsc. 179, 241 (1995).
[CrossRef]

T. Wilson and R. Juškaitis, J. Microsc. 179, 238 (1995).
[CrossRef]

T. Wilson and A. R. Carlini, Opt. Lett. 12, 227 (1987).
[CrossRef] [PubMed]

J. Microsc. (3)

T. Wilson, P. Török, and P. D. Higdon, J. Microsc. 189, 12 (1998).
[CrossRef]

S. V. Shatalin, R. C. Juškaitis, J. B. Tan, and T. Wilson, J. Microsc. 179, 241 (1995).
[CrossRef]

T. Wilson and R. Juškaitis, J. Microsc. 179, 238 (1995).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

P. Török and T. Wilson, Opt. Commun. 137, 127 (1997).
[CrossRef]

Opt. Lett. (3)

Other (1)

R. Azzam and N. Bashara, Ellipsometry and Polarized Light, 3rd ed. (North Holland, 1992).

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Figures (3)

Fig. 1
Fig. 1

Schematic of a high-NA MMP.

Fig. 2
Fig. 2

Diagram of notation used in this Letter as a simplified polarimeter.

Fig. 3
Fig. 3

(a) Plots of Mueller matrix elements for confocal and conventional polarimeters and (b) plot of Δ for the case of a conventional polarimeter as a function of NA for a sample of Al (refractive index 0.502 + 4.92 i at 405 nm ). For clarity, the notations M ( J ¯ r ) = diag ( m 11 c , m 11 c , m 11 c , m 11 c ) and M ¯ r = diag ( m 11 i , m 22 i , m 22 i , m 44 i ) have been adopted in (a).

Equations (10)

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E o ( θ o , ϕ o ) = D i J ( θ o , ϕ o , θ i , ϕ i ) E i ( θ i , ϕ i ) d S ,
I q c = 1 π NA 2 D o J q E o ( θ o , ϕ o ) d S 2 = J q J ¯ E i 2 ,
I q i = 1 π NA 2 D o J q E o 2 d S = 1 π NA 2 D o J q J E i 2 d S .
J r ( θ , ϕ ) = 1 2 [ r + r + cos 2 ϕ r + sin 2 ϕ r + sin 2 ϕ r + r + cos 2 ϕ ] ,
M r ( θ , ϕ ) = R 4 diag ( 1 , 1 , 1 , 1 ) + 1 4 [ R + 2 A cos 2 ϕ 2 A sin 2 ϕ 0 2 A cos 2 ϕ R + cos 4 ϕ R + sin 4 ϕ 2 B sin 2 ϕ 2 A sin 2 ϕ R sin 4 ϕ R + cos 4 ϕ 2 B cos 2 ϕ 0 2 B sin 2 ϕ 2 B cos 2 ϕ R + ] ,
J ¯ r = 1 2 NA 2 0 α diag ( r , r ) sin 2 θ d θ ,
M ( J ¯ r ) = 0 α r sin 2 θ d θ 2 NA 2 2 diag ( 1 , 1 , 1 , 1 ) ,
M ¯ r = 1 π NA 2 D o M r ( θ , ϕ ) d S ,
= 1 4 NA 2 0 α diag ( R + + R , R , R , R + R ) sin 2 θ d θ ,
Δ = 1 2 0 α R sin 2 θ d θ + 0 α ( R + R ) sin 2 θ d θ 3 0 α ( R + R + ) sin 2 θ d θ .

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