Abstract

This paper describes a Stokes vector measurement method based on a snapshot polarization-sensitive spectral interferometry. We measure perpendicular linearly polarized complex wave information of an anisotropic object in the spectral domain from which an accurate Stokes vector can be extracted. The proposed Stokes vector measurement method is robust to the object plane 3-D pose variation and external noise, and it provides a reliable snapshot solution in numerous spectral polarization-related applications.

© 2014 Optical Society of America

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2013 (1)

2012 (2)

A. Dubois, “Spectroscopic polarization-sensitive full-field optical coherence tomography,” Opt. Express 20(9), 9962–9977 (2012).
[Crossref] [PubMed]

I. Eom, S. Ahn, H. Rhee, and M. Cho, “Single-shot electronic optical activity interferometry: power and phase fluctuation-free measurement,” Phys. Rev. Lett. 108, 103901 (2012).

2011 (2)

2010 (1)

S. P. Ng, C. M. Wu, S. Y. Wu, H. P. Ho, and S. K. Kong, “Differential spectral phase interferometry for wide dynamic range surface plasmon resonance biosensing,” Biosens. Bioelectron. 26(4), 1593–1598 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (2)

2007 (2)

2005 (1)

2004 (2)

H. Huang and F. L. Terry., “Spectroscopic ellipsometry and reflectometry from gratings (Scatterometry) for critical dimension measurement and in situ, real-time process monitoring,” Thin Solid Films 455, 828–836 (2004).
[Crossref]

L. R. Watkins and M. D. Hoogerland, “Interferometric ellipsometer with wavelength-modulated laser diode source,” Appl. Opt. 43(22), 4362–4366 (2004).
[Crossref] [PubMed]

2002 (1)

2001 (1)

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular spectroscopic scatterometry,” IEEE Trans. Semicond. Manuf. 14(2), 97–111 (2001).
[Crossref]

2000 (1)

1999 (2)

1992 (1)

1982 (1)

1973 (1)

H. Hazebroek and A. Holscher, “Interferometric ellipsometry,” J. Phys. E 6(9), 822–826 (1973).
[Crossref]

Abdelsalam, D. G.

Ahn, S.

I. Eom, S. Ahn, H. Rhee, and M. Cho, “Single-shot electronic optical activity interferometry: power and phase fluctuation-free measurement,” Phys. Rev. Lett. 108, 103901 (2012).

Baev, A.

Bao, J.

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular spectroscopic scatterometry,” IEEE Trans. Semicond. Manuf. 14(2), 97–111 (2001).
[Crossref]

Boccara, A. C.

Bouma, B. E.

Cense, B.

Chegal, W.

Cho, H. M.

Cho, M.

I. Eom, S. Ahn, H. Rhee, and M. Cho, “Single-shot electronic optical activity interferometry: power and phase fluctuation-free measurement,” Phys. Rev. Lett. 108, 103901 (2012).

Cho, Y. J.

Chou, C.

Ciprian, D.

de Boer, J. F.

Dubois, A.

Eom, I.

I. Eom, S. Ahn, H. Rhee, and M. Cho, “Single-shot electronic optical activity interferometry: power and phase fluctuation-free measurement,” Phys. Rev. Lett. 108, 103901 (2012).

Fercher, A. F.

Fujimoto, J. G.

Hazebroek, H.

H. Hazebroek and A. Holscher, “Interferometric ellipsometry,” J. Phys. E 6(9), 822–826 (1973).
[Crossref]

Hee, M. R.

Hitzenberger, C. K.

Hlubina, P.

Ho, H. P.

S. P. Ng, C. M. Wu, S. Y. Wu, H. P. Ho, and S. K. Kong, “Differential spectral phase interferometry for wide dynamic range surface plasmon resonance biosensing,” Biosens. Bioelectron. 26(4), 1593–1598 (2010).
[Crossref] [PubMed]

Holscher, A.

H. Hazebroek and A. Holscher, “Interferometric ellipsometry,” J. Phys. E 6(9), 822–826 (1973).
[Crossref]

Hoogerland, M. D.

Huang, D.

Huang, H.

H. Huang and F. L. Terry., “Spectroscopic ellipsometry and reflectometry from gratings (Scatterometry) for critical dimension measurement and in situ, real-time process monitoring,” Thin Solid Films 455, 828–836 (2004).
[Crossref]

Huang, S. L.

Ina, H.

Jakatdar, N.

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular spectroscopic scatterometry,” IEEE Trans. Semicond. Manuf. 14(2), 97–111 (2001).
[Crossref]

Jin, M.

Kabashin, A.

Kato, T.

Kim, D.

Kim, H.

Kim, S.

Kobayashi, S.

Kong, H. J.

Kong, S. K.

S. P. Ng, C. M. Wu, S. Y. Wu, H. P. Ho, and S. K. Kong, “Differential spectral phase interferometry for wide dynamic range surface plasmon resonance biosensing,” Biosens. Bioelectron. 26(4), 1593–1598 (2010).
[Crossref] [PubMed]

Kowalczyk, A.

Law, W. C.

Lee, J.

Lee, Y.

Leitgeb, R.

Lin, C. E.

Lunacek, J.

Magnusson, R.

Markowicz, P. P.

Milner, T. E.

Moneron, G.

Mujat, M.

Nelson, J. S.

Ng, S. P.

S. P. Ng, C. M. Wu, S. Y. Wu, H. P. Ho, and S. K. Kong, “Differential spectral phase interferometry for wide dynamic range surface plasmon resonance biosensing,” Biosens. Bioelectron. 26(4), 1593–1598 (2010).
[Crossref] [PubMed]

Niu, X.

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular spectroscopic scatterometry,” IEEE Trans. Semicond. Manuf. 14(2), 97–111 (2001).
[Crossref]

Oka, K.

Park, B. H.

Patskovsky, S.

Pierce, M. C.

Prasad, P. N.

Rhee, H.

I. Eom, S. Ahn, H. Rhee, and M. Cho, “Single-shot electronic optical activity interferometry: power and phase fluctuation-free measurement,” Phys. Rev. Lett. 108, 103901 (2012).

Spanos, C. J.

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular spectroscopic scatterometry,” IEEE Trans. Semicond. Manuf. 14(2), 97–111 (2001).
[Crossref]

Sticker, M.

Swanson, E. A.

Takeda, M.

Tearney, G. J.

Terry, F. L.

H. Huang and F. L. Terry., “Spectroscopic ellipsometry and reflectometry from gratings (Scatterometry) for critical dimension measurement and in situ, real-time process monitoring,” Thin Solid Films 455, 828–836 (2004).
[Crossref]

Tsai, C. C.

Watkins, L. R.

Wei, H. C.

Wojtkowski, M.

Wu, C. M.

S. P. Ng, C. M. Wu, S. Y. Wu, H. P. Ho, and S. K. Kong, “Differential spectral phase interferometry for wide dynamic range surface plasmon resonance biosensing,” Biosens. Bioelectron. 26(4), 1593–1598 (2010).
[Crossref] [PubMed]

Wu, S. Y.

S. P. Ng, C. M. Wu, S. Y. Wu, H. P. Ho, and S. K. Kong, “Differential spectral phase interferometry for wide dynamic range surface plasmon resonance biosensing,” Biosens. Bioelectron. 26(4), 1593–1598 (2010).
[Crossref] [PubMed]

Yu, C. J.

Yun, S.

Appl. Opt. (3)

Biosens. Bioelectron. (1)

S. P. Ng, C. M. Wu, S. Y. Wu, H. P. Ho, and S. K. Kong, “Differential spectral phase interferometry for wide dynamic range surface plasmon resonance biosensing,” Biosens. Bioelectron. 26(4), 1593–1598 (2010).
[Crossref] [PubMed]

IEEE Trans. Semicond. Manuf. (1)

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular spectroscopic scatterometry,” IEEE Trans. Semicond. Manuf. 14(2), 97–111 (2001).
[Crossref]

J. Opt. Soc. Am. (1)

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

J. Phys. E (1)

H. Hazebroek and A. Holscher, “Interferometric ellipsometry,” J. Phys. E 6(9), 822–826 (1973).
[Crossref]

Opt. Express (5)

Opt. Lett. (7)

Phys. Rev. Lett. (1)

I. Eom, S. Ahn, H. Rhee, and M. Cho, “Single-shot electronic optical activity interferometry: power and phase fluctuation-free measurement,” Phys. Rev. Lett. 108, 103901 (2012).

Thin Solid Films (1)

H. Huang and F. L. Terry., “Spectroscopic ellipsometry and reflectometry from gratings (Scatterometry) for critical dimension measurement and in situ, real-time process monitoring,” Thin Solid Films 455, 828–836 (2004).
[Crossref]

Other (2)

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987).

H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications (John Wiley, 2007).

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Figures (6)

Fig. 1
Fig. 1

Schematic of the Stokes vector measurement system based on polarization-sensitive spectral interferometry.

Fig. 2
Fig. 2

Interfered spectrum raw data captured by the TM channel in the dual-spectrum sensing module by varying (a) the spectral carrier frequency h (when α = ~0° and β = ~0°) and (b) the object tilt angle α and β (when h = 55 μm).

Fig. 3
Fig. 3

The systematic calibration function Γ(k,h,α,β) denoting the ratio between γTM(k,h,α,β) and γTE(k,h,α,β) by varying (a) the vertical position of the object h and (b) the object tilt angle α (when β = ~0°).

Fig. 4
Fig. 4

Complex object wave analysis in the complex plane: (a) EO_TM(k)EO_TM(k)* [red-colored arrow line] and EmO_TM(k)EmO_TM(k)* [blue-colored arrow line], and (b) EO_TM(k)EO_TE(k)* [red-colored] and EmO_TM(k)EmO_TE(k)* [blue-colored].

Fig. 5
Fig. 5

(a) |EO_TM (k)| and |EO_TE (k)|, and (b) [ϕTM_pattern(k) - ϕTM_non_pattern(k)] and [ϕTE_pattern(k) - ϕTE_non_pattern(k)] for the vertically aligned grating object. (c)|EO_TM (k)| and |EO_TE (k)|, and (d) [ϕTM_pattern(k) - ϕTM_non_pattern(k)] and [ϕTE_pattern(k) - ϕTE_non_pattern(k)]) for the horizontally aligned grating object.

Fig. 6
Fig. 6

(a) Normalized Stokes vector measurement results obtained by using Eq. (8), and (b) overlapped Stokes vector measurement results obtained by varying the object plane tilt to 0.01°.

Equations (8)

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I TM (k) = | E R_TM (k) | 2 + | E Ο_TM (k) | 2 +2 γ TM (k,h,α,β)| E R_TM (k) || E Ο_TM (k) |cos{ Φ TM (k,h,α,β)}
Φ TM (k,h,α,β) =2kh+ ϕ TM _ Obj anisotropy (k) ϕ TM _ R (k)+ ϕ TM _ Remaining optics (k,α,β)
S 0 (k)= E O_TM (k) E O_TM (k) * + E O_TE (k) E O_TE (k) * S 1 (k)= E O_TM (k) E O_TM (k) * E O_TE (k) E O_TE (k) * S 2 (k)= E O_TM (k) E O_TE (k) * + E O_TE (k) E O_TM (k) * S 3 (k)=i[ E O_TM (k) E O_TE (k) * E O_TE (k) E O_TM (k) * ]
I TM_mod (k)= I TM (k) | E R_TM (k) | 2 | E O_TM (k) | 2 2| E R_TM (k) || E O_TM (k) | = γ TM (k,h,α,β)cos{ Φ TM (k,h,α,β)} I TM_mod (k)= I TE (k) | E R_TE (k) | 2 | E O_TE (k) | 2 2| E R_TE (k) || E O_TE (k) | = γ TE (k,h,α,β)cos{ Φ TE (k,h,α,β)}
| E m O_TM (k) |= γ TM (k,h)| E O_TM (k) |= A TM (k,h) 2| E R _TM (k) | | E m O_TE (k) |= γ TE (k,h)| E C O_TE (k) |×Γ(k,h)= A TE (k,h) 2| E R _TE (k) | ×Γ(k,h)
Δ Φ TE (k,h)= Φ TM _ pattern (k,h) Φ TM _ non_ pattern (k,h) =2k( h 2 h 1 )+ Φ TM _ Obj anisotropy (k)+[ { ϕ TM_Remaining optics (k)} 2 { ϕ TM_Remaining optics (k)} 1 ] = ϕ TM _ Obj anisotropy (k)+ak+b Δ Φ TE (k,h)= Φ TE _ pattern (k,h) Φ TE _ non_ pattern (k,h) =2k( h 2 h 1 )+ ϕ TE _ Obj anisotropy (k)+[ { ϕ TE_Remaining optics (k)} 2 { ϕ TE_Remaining optics (k)} 1 ] = ϕ TE _ Objanisotropy (k)+ak+b
E m O_TM (k)=| E m O_TM (k) | e i[ ϕ TM_Obj anisotropy (k)+ak+b] = γ TM (k,h)| E O_TM (k) | e i[ ϕ TM_Obj anisotropy (k)+ak+b] E m O_TE (k)=| E m O_TE (k) | e i[ ϕ TE_Obj anisotropy (k)+ak+b] = γ TM (k,h)| E C O_TE (k) | e i[ ϕ TE_Obj anisotropy (k)+ak+b]
S 1 nor (k)= S 1 m (k)/ S 0 m (k)=[ E m O_TM (k) E m O_TM (k) * E m O_TE (k) E m O_TE (k) * ]/ I 0 (k) S 2 nor (k)= S 2 m (k)/ S 0 m (k)=[ E m O_TM (k) E m O_TE (k) * + E m O_TE (k) E m O_TM (k) * ]/ I 0 (k) S 3 nor (k)= S 3 m (k)/ S 0 m (k)=i[ E m O_TM (k) E m O_TE (k) * E m O_TE (k) E m O_TM (k) * ]/ I 0 (k)

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