Abstract

The design and construction of an ellipsometer based on a fixed-wavelength rotating-retarder Stokes polarimeter is described. Details are provided for an automated calibration scheme that provides two advantages for its operation. The first allows the phase of the lock-in amplifiers to be set based on the raw data, without a known calibration sample. The second illustrates that the relative amplitude of the acquired signals may also be calibrated in a similar manner. As an illustration, the refractive index and thickness of a glass cover slide are determined over a range of incident angles.

© 2012 Optical Society of America

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  1. A. Rothen, “The ellipsometer: an apparatus to measure the thickness of thin surface films,” Rev. Sci. Instrum. 16, 26–30 (1945).
    [CrossRef]
  2. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).
  3. H. G. Tompkins and E. A. Irene, Handbook of Ellipsometry (William Andrew, 2005).
  4. J. Humliček, “Polarized light and ellipsometry,” in Handbook of Ellipsometry (Springer, 2005), pp. 3–93.
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    [CrossRef]
  7. P. S. Hauge and F. H. Dill, “A rotating-compensator Fourier ellipsometer,” Opt. Commun. 14, 431–437 (1975).
    [CrossRef]
  8. D. E. Aspnes and P. S. Hauge, “Rotating-compensator/analyzer fixed-analyzer ellipsometer: analysis and comparison to other automatic ellipsometers,” J. Opt. Soc. Am. 66, 949–954 (1976).
    [CrossRef]
  9. D. E. Aspnes, “Optimizing precision of rotating-analyzer and rotating-compensator ellipsometers,” J. Opt. Soc. Am. A 21, 403–410 (2004).
    [CrossRef]
  10. M. Losurdo, M. Bergmair, G. Bruno, D. Cattelan, C. Cobet, A. Martino, K. Fleischer, Z. Dohcevic-Mitrovic, N. Esser, M. Galliet, R. Gajic, D. Hemzal, K. Hingerl, J. Humlicek, R. Ossikovski, Z. V. Popovic, and O. Saxl, “Spectroscopic ellipsometry and polarimetry for materials and systems analysis at the nanometer scale: state-of-the-art, potential, and perspectives,” J. Nanopart. Res. 11, 1521–1554 (2009).
    [CrossRef]
  11. G. C. Giakos, A. Medithe, S. Sumrain, S. Sukumar, L. Fraiwan, and A. Orozco, “Laser polarimetric imaging of surface defects of semiconductor wafers, microelectronics, and spacecraft structures,” IEEE Trans. Instrum. Meas. 55, 2126–2131 (2006).
    [CrossRef]
  12. D. K. Goyal and A. Subramanian, “In-situ protein adsorption study on biofunctionalized surfaces using spectroscopic ellipsometry,” Thin Solid Films 518, 2186–2193 (2010).
    [CrossRef]
  13. S. G. Thakurta, H. J. Viljoen, and A. Subramanian, “Evaluation of the real-time protein adsorption kinetics on albumin-binding surfaces by dynamic in situ spectroscopic ellipsometry,” Thin Solid Films 520, 2200–2207 (2012).
    [CrossRef]
  14. J. J. I. Ramos, S. Stahl, R. P. Richter, and S. E. Moya, “Water content and buildup of poly(diallyldimethylammonium chloride)/poly(sodium 4-styrenesulfonate) and poly(allylamine hydrochloride)/poly(sodium 4-styrenesulfonate) polyelectrolyte multilayers studied by an in situ combination of a quartz crystal microbalance with dissipation monitoring and spectroscopic ellipsometry,” Macromolecules 43, 9063–9070 (2010).
    [CrossRef]
  15. K. Buchner, N. Ehrhardt, B. P. Cahill, and C. Hoffmann, “Internal reflection ellipsometry for real-time monitoring of polyelectrolyte multilayer growth onto tantalum pentoxide,” Thin Solid Films 519, 6480–6485 (2011).
    [CrossRef]
  16. M. Kuwahara, R. Endo, K. Tsutsumi, F. Morikasa, T. Tsuroka, T. Fukaya, M. Suzuki, M. Susa, T. Endo, and T. Tadokoro, “Approach for measuring complex refractive index of molten Sb2Te3 by spectroscopic ellipsometry,” Appl. Phys. Lett. 100, 101910 (2012).
    [CrossRef]
  17. J.-F. Lin, J.-S. Wu, C.-H. Huang, T.-T. Liao, and C.-C. Chang, “The application of a rotating-wave-plate stokes polarimeter for measurement of the optical rotation angle,” Optik 122, 14–19 (2011).
    [CrossRef]
  18. J.-F. Lin, “Concurrent measurement of linear and circular birefringence using rotating-wave-plate stokes polarimeter,” Appl. Opt. 47, 4529–4539 (2008).
    [CrossRef]
  19. D. K. Hore, A. Natansohn, and P. Rochon, “Optical anisotropy as a probe of structural order by stokes polarimetry,” J. Phys. Chem. B 106, 9004–9012 (2002).
    [CrossRef]
  20. D. K. Hore, A. L. Natansohn, and P. L. Rochon, “The characterization of photoinduced chirality in a liquid-crystalline azo polymer on irradiation with circularly polarized light,” J. Phys. Chem. B 107, 2506–2518 (2003).
    [CrossRef]
  21. W. R. Hunter, “Effects of component imperfections on ellipsometer calibration,” J. Opt. Soc. Am. 63, 951–957 (1973).
    [CrossRef]
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    [CrossRef]
  23. S. F. Nee, “Error reductions for a serious compensator imperfection for null ellipsometry,” J. Opt. Soc. Am. A 8, 314–321 (1991).
    [CrossRef]
  24. P. S. Hauge, “Generalized rotating-compensator ellipsometry,” Surf. Sci. 56, 148–160 (1976).
    [CrossRef]
  25. R. Kleim, L. Kuntzler, and A. El Ghemmaz, “Systematic errors in rotating-compensator ellipsometry,” J. Opt. Soc. Am. 11, 2550–2559 (1994).
    [CrossRef]
  26. W. G. Oldeam, “Ellipsometry using a retardation plate as compensator,” J. Opt. Soc. Am. 57, 617–622 (1967).
    [CrossRef]
  27. C. Flueraru, S. Latoui, J. Besse, and P. Legendre, “Error analysis of a rotating quarter-wave plate Stokes polarimeter,” IEEE Trans. Instrum. Meas. 57, 731–735 (2008).
    [CrossRef]
  28. Y. W. Liu, G. A. Jones, Y. Peng, and T. H. Shen, “Generalized theory and application of Stokes parameter measurements made with a single photoelastic modulator,” J. Appl. Phys. 100, 063537 (2006).
    [CrossRef]
  29. E. Hecht and A. Zajac, Optics (Addison-Wesley, 1979).
  30. R. Byrd, P. Lu, and J. Nocedal, “A limited memory algorithm for bound constrained optimization,” SIAM J. Sci. Stat. Comput. 16, 1190–1208 (1995).
    [CrossRef]
  31. C. Zhu, R. Byrd, and J. Nocedal, “L-BFGS-B: algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization,” ACM Trans. Math. Softw. 23, 550–560 (1997).
    [CrossRef]
  32. K. C. Jena and D. K. Hore, “A simple transmission-based approach for determining the thickness of transparent films,” Am. J. Phys. 79, 256–260 (2011).
    [CrossRef]
  33. G. Bucher, Corning 0211, Tech. Rep. (Characterization Science and Services Directorate, Corning Inc., 2003).

2012

S. G. Thakurta, H. J. Viljoen, and A. Subramanian, “Evaluation of the real-time protein adsorption kinetics on albumin-binding surfaces by dynamic in situ spectroscopic ellipsometry,” Thin Solid Films 520, 2200–2207 (2012).
[CrossRef]

M. Kuwahara, R. Endo, K. Tsutsumi, F. Morikasa, T. Tsuroka, T. Fukaya, M. Suzuki, M. Susa, T. Endo, and T. Tadokoro, “Approach for measuring complex refractive index of molten Sb2Te3 by spectroscopic ellipsometry,” Appl. Phys. Lett. 100, 101910 (2012).
[CrossRef]

2011

J.-F. Lin, J.-S. Wu, C.-H. Huang, T.-T. Liao, and C.-C. Chang, “The application of a rotating-wave-plate stokes polarimeter for measurement of the optical rotation angle,” Optik 122, 14–19 (2011).
[CrossRef]

K. Buchner, N. Ehrhardt, B. P. Cahill, and C. Hoffmann, “Internal reflection ellipsometry for real-time monitoring of polyelectrolyte multilayer growth onto tantalum pentoxide,” Thin Solid Films 519, 6480–6485 (2011).
[CrossRef]

K. C. Jena and D. K. Hore, “A simple transmission-based approach for determining the thickness of transparent films,” Am. J. Phys. 79, 256–260 (2011).
[CrossRef]

2010

D. K. Goyal and A. Subramanian, “In-situ protein adsorption study on biofunctionalized surfaces using spectroscopic ellipsometry,” Thin Solid Films 518, 2186–2193 (2010).
[CrossRef]

J. J. I. Ramos, S. Stahl, R. P. Richter, and S. E. Moya, “Water content and buildup of poly(diallyldimethylammonium chloride)/poly(sodium 4-styrenesulfonate) and poly(allylamine hydrochloride)/poly(sodium 4-styrenesulfonate) polyelectrolyte multilayers studied by an in situ combination of a quartz crystal microbalance with dissipation monitoring and spectroscopic ellipsometry,” Macromolecules 43, 9063–9070 (2010).
[CrossRef]

2009

M. Losurdo, M. Bergmair, G. Bruno, D. Cattelan, C. Cobet, A. Martino, K. Fleischer, Z. Dohcevic-Mitrovic, N. Esser, M. Galliet, R. Gajic, D. Hemzal, K. Hingerl, J. Humlicek, R. Ossikovski, Z. V. Popovic, and O. Saxl, “Spectroscopic ellipsometry and polarimetry for materials and systems analysis at the nanometer scale: state-of-the-art, potential, and perspectives,” J. Nanopart. Res. 11, 1521–1554 (2009).
[CrossRef]

2008

C. Flueraru, S. Latoui, J. Besse, and P. Legendre, “Error analysis of a rotating quarter-wave plate Stokes polarimeter,” IEEE Trans. Instrum. Meas. 57, 731–735 (2008).
[CrossRef]

J.-F. Lin, “Concurrent measurement of linear and circular birefringence using rotating-wave-plate stokes polarimeter,” Appl. Opt. 47, 4529–4539 (2008).
[CrossRef]

2006

Y. W. Liu, G. A. Jones, Y. Peng, and T. H. Shen, “Generalized theory and application of Stokes parameter measurements made with a single photoelastic modulator,” J. Appl. Phys. 100, 063537 (2006).
[CrossRef]

G. C. Giakos, A. Medithe, S. Sumrain, S. Sukumar, L. Fraiwan, and A. Orozco, “Laser polarimetric imaging of surface defects of semiconductor wafers, microelectronics, and spacecraft structures,” IEEE Trans. Instrum. Meas. 55, 2126–2131 (2006).
[CrossRef]

2004

D. E. Aspnes, “Expanding horizons: new developments in ellipsometry and polarimetery,” Thin Solid Films 455–456, 3–13 (2004).
[CrossRef]

D. E. Aspnes, “Optimizing precision of rotating-analyzer and rotating-compensator ellipsometers,” J. Opt. Soc. Am. A 21, 403–410 (2004).
[CrossRef]

2003

D. K. Hore, A. L. Natansohn, and P. L. Rochon, “The characterization of photoinduced chirality in a liquid-crystalline azo polymer on irradiation with circularly polarized light,” J. Phys. Chem. B 107, 2506–2518 (2003).
[CrossRef]

2002

D. K. Hore, A. Natansohn, and P. Rochon, “Optical anisotropy as a probe of structural order by stokes polarimetry,” J. Phys. Chem. B 106, 9004–9012 (2002).
[CrossRef]

1997

C. Zhu, R. Byrd, and J. Nocedal, “L-BFGS-B: algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization,” ACM Trans. Math. Softw. 23, 550–560 (1997).
[CrossRef]

1995

R. Byrd, P. Lu, and J. Nocedal, “A limited memory algorithm for bound constrained optimization,” SIAM J. Sci. Stat. Comput. 16, 1190–1208 (1995).
[CrossRef]

1994

R. Kleim, L. Kuntzler, and A. El Ghemmaz, “Systematic errors in rotating-compensator ellipsometry,” J. Opt. Soc. Am. 11, 2550–2559 (1994).
[CrossRef]

1991

1976

1975

P. S. Hauge and F. H. Dill, “A rotating-compensator Fourier ellipsometer,” Opt. Commun. 14, 431–437 (1975).
[CrossRef]

1973

1970

1967

1945

A. Rothen, “The ellipsometer: an apparatus to measure the thickness of thin surface films,” Rev. Sci. Instrum. 16, 26–30 (1945).
[CrossRef]

Aspnes, D. E.

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

Bergmair, M.

M. Losurdo, M. Bergmair, G. Bruno, D. Cattelan, C. Cobet, A. Martino, K. Fleischer, Z. Dohcevic-Mitrovic, N. Esser, M. Galliet, R. Gajic, D. Hemzal, K. Hingerl, J. Humlicek, R. Ossikovski, Z. V. Popovic, and O. Saxl, “Spectroscopic ellipsometry and polarimetry for materials and systems analysis at the nanometer scale: state-of-the-art, potential, and perspectives,” J. Nanopart. Res. 11, 1521–1554 (2009).
[CrossRef]

Besse, J.

C. Flueraru, S. Latoui, J. Besse, and P. Legendre, “Error analysis of a rotating quarter-wave plate Stokes polarimeter,” IEEE Trans. Instrum. Meas. 57, 731–735 (2008).
[CrossRef]

Bruno, G.

M. Losurdo, M. Bergmair, G. Bruno, D. Cattelan, C. Cobet, A. Martino, K. Fleischer, Z. Dohcevic-Mitrovic, N. Esser, M. Galliet, R. Gajic, D. Hemzal, K. Hingerl, J. Humlicek, R. Ossikovski, Z. V. Popovic, and O. Saxl, “Spectroscopic ellipsometry and polarimetry for materials and systems analysis at the nanometer scale: state-of-the-art, potential, and perspectives,” J. Nanopart. Res. 11, 1521–1554 (2009).
[CrossRef]

Bucher, G.

G. Bucher, Corning 0211, Tech. Rep. (Characterization Science and Services Directorate, Corning Inc., 2003).

Buchner, K.

K. Buchner, N. Ehrhardt, B. P. Cahill, and C. Hoffmann, “Internal reflection ellipsometry for real-time monitoring of polyelectrolyte multilayer growth onto tantalum pentoxide,” Thin Solid Films 519, 6480–6485 (2011).
[CrossRef]

Byrd, R.

C. Zhu, R. Byrd, and J. Nocedal, “L-BFGS-B: algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization,” ACM Trans. Math. Softw. 23, 550–560 (1997).
[CrossRef]

R. Byrd, P. Lu, and J. Nocedal, “A limited memory algorithm for bound constrained optimization,” SIAM J. Sci. Stat. Comput. 16, 1190–1208 (1995).
[CrossRef]

Cahill, B. P.

K. Buchner, N. Ehrhardt, B. P. Cahill, and C. Hoffmann, “Internal reflection ellipsometry for real-time monitoring of polyelectrolyte multilayer growth onto tantalum pentoxide,” Thin Solid Films 519, 6480–6485 (2011).
[CrossRef]

Cattelan, D.

M. Losurdo, M. Bergmair, G. Bruno, D. Cattelan, C. Cobet, A. Martino, K. Fleischer, Z. Dohcevic-Mitrovic, N. Esser, M. Galliet, R. Gajic, D. Hemzal, K. Hingerl, J. Humlicek, R. Ossikovski, Z. V. Popovic, and O. Saxl, “Spectroscopic ellipsometry and polarimetry for materials and systems analysis at the nanometer scale: state-of-the-art, potential, and perspectives,” J. Nanopart. Res. 11, 1521–1554 (2009).
[CrossRef]

Chang, C.-C.

J.-F. Lin, J.-S. Wu, C.-H. Huang, T.-T. Liao, and C.-C. Chang, “The application of a rotating-wave-plate stokes polarimeter for measurement of the optical rotation angle,” Optik 122, 14–19 (2011).
[CrossRef]

Cobet, C.

M. Losurdo, M. Bergmair, G. Bruno, D. Cattelan, C. Cobet, A. Martino, K. Fleischer, Z. Dohcevic-Mitrovic, N. Esser, M. Galliet, R. Gajic, D. Hemzal, K. Hingerl, J. Humlicek, R. Ossikovski, Z. V. Popovic, and O. Saxl, “Spectroscopic ellipsometry and polarimetry for materials and systems analysis at the nanometer scale: state-of-the-art, potential, and perspectives,” J. Nanopart. Res. 11, 1521–1554 (2009).
[CrossRef]

Dill, F. H.

P. S. Hauge and F. H. Dill, “A rotating-compensator Fourier ellipsometer,” Opt. Commun. 14, 431–437 (1975).
[CrossRef]

Dohcevic-Mitrovic, Z.

M. Losurdo, M. Bergmair, G. Bruno, D. Cattelan, C. Cobet, A. Martino, K. Fleischer, Z. Dohcevic-Mitrovic, N. Esser, M. Galliet, R. Gajic, D. Hemzal, K. Hingerl, J. Humlicek, R. Ossikovski, Z. V. Popovic, and O. Saxl, “Spectroscopic ellipsometry and polarimetry for materials and systems analysis at the nanometer scale: state-of-the-art, potential, and perspectives,” J. Nanopart. Res. 11, 1521–1554 (2009).
[CrossRef]

Ehrhardt, N.

K. Buchner, N. Ehrhardt, B. P. Cahill, and C. Hoffmann, “Internal reflection ellipsometry for real-time monitoring of polyelectrolyte multilayer growth onto tantalum pentoxide,” Thin Solid Films 519, 6480–6485 (2011).
[CrossRef]

Endo, R.

M. Kuwahara, R. Endo, K. Tsutsumi, F. Morikasa, T. Tsuroka, T. Fukaya, M. Suzuki, M. Susa, T. Endo, and T. Tadokoro, “Approach for measuring complex refractive index of molten Sb2Te3 by spectroscopic ellipsometry,” Appl. Phys. Lett. 100, 101910 (2012).
[CrossRef]

Endo, T.

M. Kuwahara, R. Endo, K. Tsutsumi, F. Morikasa, T. Tsuroka, T. Fukaya, M. Suzuki, M. Susa, T. Endo, and T. Tadokoro, “Approach for measuring complex refractive index of molten Sb2Te3 by spectroscopic ellipsometry,” Appl. Phys. Lett. 100, 101910 (2012).
[CrossRef]

Esser, N.

M. Losurdo, M. Bergmair, G. Bruno, D. Cattelan, C. Cobet, A. Martino, K. Fleischer, Z. Dohcevic-Mitrovic, N. Esser, M. Galliet, R. Gajic, D. Hemzal, K. Hingerl, J. Humlicek, R. Ossikovski, Z. V. Popovic, and O. Saxl, “Spectroscopic ellipsometry and polarimetry for materials and systems analysis at the nanometer scale: state-of-the-art, potential, and perspectives,” J. Nanopart. Res. 11, 1521–1554 (2009).
[CrossRef]

Fleischer, K.

M. Losurdo, M. Bergmair, G. Bruno, D. Cattelan, C. Cobet, A. Martino, K. Fleischer, Z. Dohcevic-Mitrovic, N. Esser, M. Galliet, R. Gajic, D. Hemzal, K. Hingerl, J. Humlicek, R. Ossikovski, Z. V. Popovic, and O. Saxl, “Spectroscopic ellipsometry and polarimetry for materials and systems analysis at the nanometer scale: state-of-the-art, potential, and perspectives,” J. Nanopart. Res. 11, 1521–1554 (2009).
[CrossRef]

Flueraru, C.

C. Flueraru, S. Latoui, J. Besse, and P. Legendre, “Error analysis of a rotating quarter-wave plate Stokes polarimeter,” IEEE Trans. Instrum. Meas. 57, 731–735 (2008).
[CrossRef]

Fraiwan, L.

G. C. Giakos, A. Medithe, S. Sumrain, S. Sukumar, L. Fraiwan, and A. Orozco, “Laser polarimetric imaging of surface defects of semiconductor wafers, microelectronics, and spacecraft structures,” IEEE Trans. Instrum. Meas. 55, 2126–2131 (2006).
[CrossRef]

Fukaya, T.

M. Kuwahara, R. Endo, K. Tsutsumi, F. Morikasa, T. Tsuroka, T. Fukaya, M. Suzuki, M. Susa, T. Endo, and T. Tadokoro, “Approach for measuring complex refractive index of molten Sb2Te3 by spectroscopic ellipsometry,” Appl. Phys. Lett. 100, 101910 (2012).
[CrossRef]

Gajic, R.

M. Losurdo, M. Bergmair, G. Bruno, D. Cattelan, C. Cobet, A. Martino, K. Fleischer, Z. Dohcevic-Mitrovic, N. Esser, M. Galliet, R. Gajic, D. Hemzal, K. Hingerl, J. Humlicek, R. Ossikovski, Z. V. Popovic, and O. Saxl, “Spectroscopic ellipsometry and polarimetry for materials and systems analysis at the nanometer scale: state-of-the-art, potential, and perspectives,” J. Nanopart. Res. 11, 1521–1554 (2009).
[CrossRef]

Galliet, M.

M. Losurdo, M. Bergmair, G. Bruno, D. Cattelan, C. Cobet, A. Martino, K. Fleischer, Z. Dohcevic-Mitrovic, N. Esser, M. Galliet, R. Gajic, D. Hemzal, K. Hingerl, J. Humlicek, R. Ossikovski, Z. V. Popovic, and O. Saxl, “Spectroscopic ellipsometry and polarimetry for materials and systems analysis at the nanometer scale: state-of-the-art, potential, and perspectives,” J. Nanopart. Res. 11, 1521–1554 (2009).
[CrossRef]

Ghemmaz, A. El

R. Kleim, L. Kuntzler, and A. El Ghemmaz, “Systematic errors in rotating-compensator ellipsometry,” J. Opt. Soc. Am. 11, 2550–2559 (1994).
[CrossRef]

Giakos, G. C.

G. C. Giakos, A. Medithe, S. Sumrain, S. Sukumar, L. Fraiwan, and A. Orozco, “Laser polarimetric imaging of surface defects of semiconductor wafers, microelectronics, and spacecraft structures,” IEEE Trans. Instrum. Meas. 55, 2126–2131 (2006).
[CrossRef]

Goyal, D. K.

D. K. Goyal and A. Subramanian, “In-situ protein adsorption study on biofunctionalized surfaces using spectroscopic ellipsometry,” Thin Solid Films 518, 2186–2193 (2010).
[CrossRef]

Hauge, P. S.

D. E. Aspnes and P. S. Hauge, “Rotating-compensator/analyzer fixed-analyzer ellipsometer: analysis and comparison to other automatic ellipsometers,” J. Opt. Soc. Am. 66, 949–954 (1976).
[CrossRef]

P. S. Hauge, “Generalized rotating-compensator ellipsometry,” Surf. Sci. 56, 148–160 (1976).
[CrossRef]

P. S. Hauge and F. H. Dill, “A rotating-compensator Fourier ellipsometer,” Opt. Commun. 14, 431–437 (1975).
[CrossRef]

Hecht, E.

E. Hecht and A. Zajac, Optics (Addison-Wesley, 1979).

Hemzal, D.

M. Losurdo, M. Bergmair, G. Bruno, D. Cattelan, C. Cobet, A. Martino, K. Fleischer, Z. Dohcevic-Mitrovic, N. Esser, M. Galliet, R. Gajic, D. Hemzal, K. Hingerl, J. Humlicek, R. Ossikovski, Z. V. Popovic, and O. Saxl, “Spectroscopic ellipsometry and polarimetry for materials and systems analysis at the nanometer scale: state-of-the-art, potential, and perspectives,” J. Nanopart. Res. 11, 1521–1554 (2009).
[CrossRef]

Hingerl, K.

M. Losurdo, M. Bergmair, G. Bruno, D. Cattelan, C. Cobet, A. Martino, K. Fleischer, Z. Dohcevic-Mitrovic, N. Esser, M. Galliet, R. Gajic, D. Hemzal, K. Hingerl, J. Humlicek, R. Ossikovski, Z. V. Popovic, and O. Saxl, “Spectroscopic ellipsometry and polarimetry for materials and systems analysis at the nanometer scale: state-of-the-art, potential, and perspectives,” J. Nanopart. Res. 11, 1521–1554 (2009).
[CrossRef]

Hoffmann, C.

K. Buchner, N. Ehrhardt, B. P. Cahill, and C. Hoffmann, “Internal reflection ellipsometry for real-time monitoring of polyelectrolyte multilayer growth onto tantalum pentoxide,” Thin Solid Films 519, 6480–6485 (2011).
[CrossRef]

Hore, D. K.

K. C. Jena and D. K. Hore, “A simple transmission-based approach for determining the thickness of transparent films,” Am. J. Phys. 79, 256–260 (2011).
[CrossRef]

D. K. Hore, A. L. Natansohn, and P. L. Rochon, “The characterization of photoinduced chirality in a liquid-crystalline azo polymer on irradiation with circularly polarized light,” J. Phys. Chem. B 107, 2506–2518 (2003).
[CrossRef]

D. K. Hore, A. Natansohn, and P. Rochon, “Optical anisotropy as a probe of structural order by stokes polarimetry,” J. Phys. Chem. B 106, 9004–9012 (2002).
[CrossRef]

Huang, C.-H.

J.-F. Lin, J.-S. Wu, C.-H. Huang, T.-T. Liao, and C.-C. Chang, “The application of a rotating-wave-plate stokes polarimeter for measurement of the optical rotation angle,” Optik 122, 14–19 (2011).
[CrossRef]

Humlicek, J.

M. Losurdo, M. Bergmair, G. Bruno, D. Cattelan, C. Cobet, A. Martino, K. Fleischer, Z. Dohcevic-Mitrovic, N. Esser, M. Galliet, R. Gajic, D. Hemzal, K. Hingerl, J. Humlicek, R. Ossikovski, Z. V. Popovic, and O. Saxl, “Spectroscopic ellipsometry and polarimetry for materials and systems analysis at the nanometer scale: state-of-the-art, potential, and perspectives,” J. Nanopart. Res. 11, 1521–1554 (2009).
[CrossRef]

J. Humliček, “Polarized light and ellipsometry,” in Handbook of Ellipsometry (Springer, 2005), pp. 3–93.

Hunter, W. R.

Irene, E. A.

H. G. Tompkins and E. A. Irene, Handbook of Ellipsometry (William Andrew, 2005).

Jena, K. C.

K. C. Jena and D. K. Hore, “A simple transmission-based approach for determining the thickness of transparent films,” Am. J. Phys. 79, 256–260 (2011).
[CrossRef]

Jones, G. A.

Y. W. Liu, G. A. Jones, Y. Peng, and T. H. Shen, “Generalized theory and application of Stokes parameter measurements made with a single photoelastic modulator,” J. Appl. Phys. 100, 063537 (2006).
[CrossRef]

Kleim, R.

R. Kleim, L. Kuntzler, and A. El Ghemmaz, “Systematic errors in rotating-compensator ellipsometry,” J. Opt. Soc. Am. 11, 2550–2559 (1994).
[CrossRef]

Kuntzler, L.

R. Kleim, L. Kuntzler, and A. El Ghemmaz, “Systematic errors in rotating-compensator ellipsometry,” J. Opt. Soc. Am. 11, 2550–2559 (1994).
[CrossRef]

Kuwahara, M.

M. Kuwahara, R. Endo, K. Tsutsumi, F. Morikasa, T. Tsuroka, T. Fukaya, M. Suzuki, M. Susa, T. Endo, and T. Tadokoro, “Approach for measuring complex refractive index of molten Sb2Te3 by spectroscopic ellipsometry,” Appl. Phys. Lett. 100, 101910 (2012).
[CrossRef]

Latoui, S.

C. Flueraru, S. Latoui, J. Besse, and P. Legendre, “Error analysis of a rotating quarter-wave plate Stokes polarimeter,” IEEE Trans. Instrum. Meas. 57, 731–735 (2008).
[CrossRef]

Legendre, P.

C. Flueraru, S. Latoui, J. Besse, and P. Legendre, “Error analysis of a rotating quarter-wave plate Stokes polarimeter,” IEEE Trans. Instrum. Meas. 57, 731–735 (2008).
[CrossRef]

Liao, T.-T.

J.-F. Lin, J.-S. Wu, C.-H. Huang, T.-T. Liao, and C.-C. Chang, “The application of a rotating-wave-plate stokes polarimeter for measurement of the optical rotation angle,” Optik 122, 14–19 (2011).
[CrossRef]

Lin, J.-F.

J.-F. Lin, J.-S. Wu, C.-H. Huang, T.-T. Liao, and C.-C. Chang, “The application of a rotating-wave-plate stokes polarimeter for measurement of the optical rotation angle,” Optik 122, 14–19 (2011).
[CrossRef]

J.-F. Lin, “Concurrent measurement of linear and circular birefringence using rotating-wave-plate stokes polarimeter,” Appl. Opt. 47, 4529–4539 (2008).
[CrossRef]

Liu, Y. W.

Y. W. Liu, G. A. Jones, Y. Peng, and T. H. Shen, “Generalized theory and application of Stokes parameter measurements made with a single photoelastic modulator,” J. Appl. Phys. 100, 063537 (2006).
[CrossRef]

Losurdo, M.

M. Losurdo, M. Bergmair, G. Bruno, D. Cattelan, C. Cobet, A. Martino, K. Fleischer, Z. Dohcevic-Mitrovic, N. Esser, M. Galliet, R. Gajic, D. Hemzal, K. Hingerl, J. Humlicek, R. Ossikovski, Z. V. Popovic, and O. Saxl, “Spectroscopic ellipsometry and polarimetry for materials and systems analysis at the nanometer scale: state-of-the-art, potential, and perspectives,” J. Nanopart. Res. 11, 1521–1554 (2009).
[CrossRef]

Lu, P.

R. Byrd, P. Lu, and J. Nocedal, “A limited memory algorithm for bound constrained optimization,” SIAM J. Sci. Stat. Comput. 16, 1190–1208 (1995).
[CrossRef]

Martino, A.

M. Losurdo, M. Bergmair, G. Bruno, D. Cattelan, C. Cobet, A. Martino, K. Fleischer, Z. Dohcevic-Mitrovic, N. Esser, M. Galliet, R. Gajic, D. Hemzal, K. Hingerl, J. Humlicek, R. Ossikovski, Z. V. Popovic, and O. Saxl, “Spectroscopic ellipsometry and polarimetry for materials and systems analysis at the nanometer scale: state-of-the-art, potential, and perspectives,” J. Nanopart. Res. 11, 1521–1554 (2009).
[CrossRef]

McCrackin, F. L.

Medithe, A.

G. C. Giakos, A. Medithe, S. Sumrain, S. Sukumar, L. Fraiwan, and A. Orozco, “Laser polarimetric imaging of surface defects of semiconductor wafers, microelectronics, and spacecraft structures,” IEEE Trans. Instrum. Meas. 55, 2126–2131 (2006).
[CrossRef]

Morikasa, F.

M. Kuwahara, R. Endo, K. Tsutsumi, F. Morikasa, T. Tsuroka, T. Fukaya, M. Suzuki, M. Susa, T. Endo, and T. Tadokoro, “Approach for measuring complex refractive index of molten Sb2Te3 by spectroscopic ellipsometry,” Appl. Phys. Lett. 100, 101910 (2012).
[CrossRef]

Moya, S. E.

J. J. I. Ramos, S. Stahl, R. P. Richter, and S. E. Moya, “Water content and buildup of poly(diallyldimethylammonium chloride)/poly(sodium 4-styrenesulfonate) and poly(allylamine hydrochloride)/poly(sodium 4-styrenesulfonate) polyelectrolyte multilayers studied by an in situ combination of a quartz crystal microbalance with dissipation monitoring and spectroscopic ellipsometry,” Macromolecules 43, 9063–9070 (2010).
[CrossRef]

Natansohn, A.

D. K. Hore, A. Natansohn, and P. Rochon, “Optical anisotropy as a probe of structural order by stokes polarimetry,” J. Phys. Chem. B 106, 9004–9012 (2002).
[CrossRef]

Natansohn, A. L.

D. K. Hore, A. L. Natansohn, and P. L. Rochon, “The characterization of photoinduced chirality in a liquid-crystalline azo polymer on irradiation with circularly polarized light,” J. Phys. Chem. B 107, 2506–2518 (2003).
[CrossRef]

Nee, S. F.

Nocedal, J.

C. Zhu, R. Byrd, and J. Nocedal, “L-BFGS-B: algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization,” ACM Trans. Math. Softw. 23, 550–560 (1997).
[CrossRef]

R. Byrd, P. Lu, and J. Nocedal, “A limited memory algorithm for bound constrained optimization,” SIAM J. Sci. Stat. Comput. 16, 1190–1208 (1995).
[CrossRef]

Oldeam, W. G.

Orozco, A.

G. C. Giakos, A. Medithe, S. Sumrain, S. Sukumar, L. Fraiwan, and A. Orozco, “Laser polarimetric imaging of surface defects of semiconductor wafers, microelectronics, and spacecraft structures,” IEEE Trans. Instrum. Meas. 55, 2126–2131 (2006).
[CrossRef]

Ossikovski, R.

M. Losurdo, M. Bergmair, G. Bruno, D. Cattelan, C. Cobet, A. Martino, K. Fleischer, Z. Dohcevic-Mitrovic, N. Esser, M. Galliet, R. Gajic, D. Hemzal, K. Hingerl, J. Humlicek, R. Ossikovski, Z. V. Popovic, and O. Saxl, “Spectroscopic ellipsometry and polarimetry for materials and systems analysis at the nanometer scale: state-of-the-art, potential, and perspectives,” J. Nanopart. Res. 11, 1521–1554 (2009).
[CrossRef]

Peng, Y.

Y. W. Liu, G. A. Jones, Y. Peng, and T. H. Shen, “Generalized theory and application of Stokes parameter measurements made with a single photoelastic modulator,” J. Appl. Phys. 100, 063537 (2006).
[CrossRef]

Popovic, Z. V.

M. Losurdo, M. Bergmair, G. Bruno, D. Cattelan, C. Cobet, A. Martino, K. Fleischer, Z. Dohcevic-Mitrovic, N. Esser, M. Galliet, R. Gajic, D. Hemzal, K. Hingerl, J. Humlicek, R. Ossikovski, Z. V. Popovic, and O. Saxl, “Spectroscopic ellipsometry and polarimetry for materials and systems analysis at the nanometer scale: state-of-the-art, potential, and perspectives,” J. Nanopart. Res. 11, 1521–1554 (2009).
[CrossRef]

Ramos, J. J. I.

J. J. I. Ramos, S. Stahl, R. P. Richter, and S. E. Moya, “Water content and buildup of poly(diallyldimethylammonium chloride)/poly(sodium 4-styrenesulfonate) and poly(allylamine hydrochloride)/poly(sodium 4-styrenesulfonate) polyelectrolyte multilayers studied by an in situ combination of a quartz crystal microbalance with dissipation monitoring and spectroscopic ellipsometry,” Macromolecules 43, 9063–9070 (2010).
[CrossRef]

Richter, R. P.

J. J. I. Ramos, S. Stahl, R. P. Richter, and S. E. Moya, “Water content and buildup of poly(diallyldimethylammonium chloride)/poly(sodium 4-styrenesulfonate) and poly(allylamine hydrochloride)/poly(sodium 4-styrenesulfonate) polyelectrolyte multilayers studied by an in situ combination of a quartz crystal microbalance with dissipation monitoring and spectroscopic ellipsometry,” Macromolecules 43, 9063–9070 (2010).
[CrossRef]

Rochon, P.

D. K. Hore, A. Natansohn, and P. Rochon, “Optical anisotropy as a probe of structural order by stokes polarimetry,” J. Phys. Chem. B 106, 9004–9012 (2002).
[CrossRef]

Rochon, P. L.

D. K. Hore, A. L. Natansohn, and P. L. Rochon, “The characterization of photoinduced chirality in a liquid-crystalline azo polymer on irradiation with circularly polarized light,” J. Phys. Chem. B 107, 2506–2518 (2003).
[CrossRef]

Rothen, A.

A. Rothen, “The ellipsometer: an apparatus to measure the thickness of thin surface films,” Rev. Sci. Instrum. 16, 26–30 (1945).
[CrossRef]

Saxl, O.

M. Losurdo, M. Bergmair, G. Bruno, D. Cattelan, C. Cobet, A. Martino, K. Fleischer, Z. Dohcevic-Mitrovic, N. Esser, M. Galliet, R. Gajic, D. Hemzal, K. Hingerl, J. Humlicek, R. Ossikovski, Z. V. Popovic, and O. Saxl, “Spectroscopic ellipsometry and polarimetry for materials and systems analysis at the nanometer scale: state-of-the-art, potential, and perspectives,” J. Nanopart. Res. 11, 1521–1554 (2009).
[CrossRef]

Shen, T. H.

Y. W. Liu, G. A. Jones, Y. Peng, and T. H. Shen, “Generalized theory and application of Stokes parameter measurements made with a single photoelastic modulator,” J. Appl. Phys. 100, 063537 (2006).
[CrossRef]

Stahl, S.

J. J. I. Ramos, S. Stahl, R. P. Richter, and S. E. Moya, “Water content and buildup of poly(diallyldimethylammonium chloride)/poly(sodium 4-styrenesulfonate) and poly(allylamine hydrochloride)/poly(sodium 4-styrenesulfonate) polyelectrolyte multilayers studied by an in situ combination of a quartz crystal microbalance with dissipation monitoring and spectroscopic ellipsometry,” Macromolecules 43, 9063–9070 (2010).
[CrossRef]

Subramanian, A.

S. G. Thakurta, H. J. Viljoen, and A. Subramanian, “Evaluation of the real-time protein adsorption kinetics on albumin-binding surfaces by dynamic in situ spectroscopic ellipsometry,” Thin Solid Films 520, 2200–2207 (2012).
[CrossRef]

D. K. Goyal and A. Subramanian, “In-situ protein adsorption study on biofunctionalized surfaces using spectroscopic ellipsometry,” Thin Solid Films 518, 2186–2193 (2010).
[CrossRef]

Sukumar, S.

G. C. Giakos, A. Medithe, S. Sumrain, S. Sukumar, L. Fraiwan, and A. Orozco, “Laser polarimetric imaging of surface defects of semiconductor wafers, microelectronics, and spacecraft structures,” IEEE Trans. Instrum. Meas. 55, 2126–2131 (2006).
[CrossRef]

Sumrain, S.

G. C. Giakos, A. Medithe, S. Sumrain, S. Sukumar, L. Fraiwan, and A. Orozco, “Laser polarimetric imaging of surface defects of semiconductor wafers, microelectronics, and spacecraft structures,” IEEE Trans. Instrum. Meas. 55, 2126–2131 (2006).
[CrossRef]

Susa, M.

M. Kuwahara, R. Endo, K. Tsutsumi, F. Morikasa, T. Tsuroka, T. Fukaya, M. Suzuki, M. Susa, T. Endo, and T. Tadokoro, “Approach for measuring complex refractive index of molten Sb2Te3 by spectroscopic ellipsometry,” Appl. Phys. Lett. 100, 101910 (2012).
[CrossRef]

Suzuki, M.

M. Kuwahara, R. Endo, K. Tsutsumi, F. Morikasa, T. Tsuroka, T. Fukaya, M. Suzuki, M. Susa, T. Endo, and T. Tadokoro, “Approach for measuring complex refractive index of molten Sb2Te3 by spectroscopic ellipsometry,” Appl. Phys. Lett. 100, 101910 (2012).
[CrossRef]

Tadokoro, T.

M. Kuwahara, R. Endo, K. Tsutsumi, F. Morikasa, T. Tsuroka, T. Fukaya, M. Suzuki, M. Susa, T. Endo, and T. Tadokoro, “Approach for measuring complex refractive index of molten Sb2Te3 by spectroscopic ellipsometry,” Appl. Phys. Lett. 100, 101910 (2012).
[CrossRef]

Thakurta, S. G.

S. G. Thakurta, H. J. Viljoen, and A. Subramanian, “Evaluation of the real-time protein adsorption kinetics on albumin-binding surfaces by dynamic in situ spectroscopic ellipsometry,” Thin Solid Films 520, 2200–2207 (2012).
[CrossRef]

Tompkins, H. G.

H. G. Tompkins and E. A. Irene, Handbook of Ellipsometry (William Andrew, 2005).

H. G. Tompkins, A User’s Guide to Ellipsometry (Dover, 2006).

Tsuroka, T.

M. Kuwahara, R. Endo, K. Tsutsumi, F. Morikasa, T. Tsuroka, T. Fukaya, M. Suzuki, M. Susa, T. Endo, and T. Tadokoro, “Approach for measuring complex refractive index of molten Sb2Te3 by spectroscopic ellipsometry,” Appl. Phys. Lett. 100, 101910 (2012).
[CrossRef]

Tsutsumi, K.

M. Kuwahara, R. Endo, K. Tsutsumi, F. Morikasa, T. Tsuroka, T. Fukaya, M. Suzuki, M. Susa, T. Endo, and T. Tadokoro, “Approach for measuring complex refractive index of molten Sb2Te3 by spectroscopic ellipsometry,” Appl. Phys. Lett. 100, 101910 (2012).
[CrossRef]

Viljoen, H. J.

S. G. Thakurta, H. J. Viljoen, and A. Subramanian, “Evaluation of the real-time protein adsorption kinetics on albumin-binding surfaces by dynamic in situ spectroscopic ellipsometry,” Thin Solid Films 520, 2200–2207 (2012).
[CrossRef]

Wu, J.-S.

J.-F. Lin, J.-S. Wu, C.-H. Huang, T.-T. Liao, and C.-C. Chang, “The application of a rotating-wave-plate stokes polarimeter for measurement of the optical rotation angle,” Optik 122, 14–19 (2011).
[CrossRef]

Zajac, A.

E. Hecht and A. Zajac, Optics (Addison-Wesley, 1979).

Zhu, C.

C. Zhu, R. Byrd, and J. Nocedal, “L-BFGS-B: algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization,” ACM Trans. Math. Softw. 23, 550–560 (1997).
[CrossRef]

ACM Trans. Math. Softw.

C. Zhu, R. Byrd, and J. Nocedal, “L-BFGS-B: algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization,” ACM Trans. Math. Softw. 23, 550–560 (1997).
[CrossRef]

Am. J. Phys.

K. C. Jena and D. K. Hore, “A simple transmission-based approach for determining the thickness of transparent films,” Am. J. Phys. 79, 256–260 (2011).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

M. Kuwahara, R. Endo, K. Tsutsumi, F. Morikasa, T. Tsuroka, T. Fukaya, M. Suzuki, M. Susa, T. Endo, and T. Tadokoro, “Approach for measuring complex refractive index of molten Sb2Te3 by spectroscopic ellipsometry,” Appl. Phys. Lett. 100, 101910 (2012).
[CrossRef]

IEEE Trans. Instrum. Meas.

C. Flueraru, S. Latoui, J. Besse, and P. Legendre, “Error analysis of a rotating quarter-wave plate Stokes polarimeter,” IEEE Trans. Instrum. Meas. 57, 731–735 (2008).
[CrossRef]

G. C. Giakos, A. Medithe, S. Sumrain, S. Sukumar, L. Fraiwan, and A. Orozco, “Laser polarimetric imaging of surface defects of semiconductor wafers, microelectronics, and spacecraft structures,” IEEE Trans. Instrum. Meas. 55, 2126–2131 (2006).
[CrossRef]

J. Appl. Phys.

Y. W. Liu, G. A. Jones, Y. Peng, and T. H. Shen, “Generalized theory and application of Stokes parameter measurements made with a single photoelastic modulator,” J. Appl. Phys. 100, 063537 (2006).
[CrossRef]

J. Nanopart. Res.

M. Losurdo, M. Bergmair, G. Bruno, D. Cattelan, C. Cobet, A. Martino, K. Fleischer, Z. Dohcevic-Mitrovic, N. Esser, M. Galliet, R. Gajic, D. Hemzal, K. Hingerl, J. Humlicek, R. Ossikovski, Z. V. Popovic, and O. Saxl, “Spectroscopic ellipsometry and polarimetry for materials and systems analysis at the nanometer scale: state-of-the-art, potential, and perspectives,” J. Nanopart. Res. 11, 1521–1554 (2009).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Phys. Chem. B

D. K. Hore, A. Natansohn, and P. Rochon, “Optical anisotropy as a probe of structural order by stokes polarimetry,” J. Phys. Chem. B 106, 9004–9012 (2002).
[CrossRef]

D. K. Hore, A. L. Natansohn, and P. L. Rochon, “The characterization of photoinduced chirality in a liquid-crystalline azo polymer on irradiation with circularly polarized light,” J. Phys. Chem. B 107, 2506–2518 (2003).
[CrossRef]

Macromolecules

J. J. I. Ramos, S. Stahl, R. P. Richter, and S. E. Moya, “Water content and buildup of poly(diallyldimethylammonium chloride)/poly(sodium 4-styrenesulfonate) and poly(allylamine hydrochloride)/poly(sodium 4-styrenesulfonate) polyelectrolyte multilayers studied by an in situ combination of a quartz crystal microbalance with dissipation monitoring and spectroscopic ellipsometry,” Macromolecules 43, 9063–9070 (2010).
[CrossRef]

Opt. Commun.

P. S. Hauge and F. H. Dill, “A rotating-compensator Fourier ellipsometer,” Opt. Commun. 14, 431–437 (1975).
[CrossRef]

Optik

J.-F. Lin, J.-S. Wu, C.-H. Huang, T.-T. Liao, and C.-C. Chang, “The application of a rotating-wave-plate stokes polarimeter for measurement of the optical rotation angle,” Optik 122, 14–19 (2011).
[CrossRef]

Rev. Sci. Instrum.

A. Rothen, “The ellipsometer: an apparatus to measure the thickness of thin surface films,” Rev. Sci. Instrum. 16, 26–30 (1945).
[CrossRef]

SIAM J. Sci. Stat. Comput.

R. Byrd, P. Lu, and J. Nocedal, “A limited memory algorithm for bound constrained optimization,” SIAM J. Sci. Stat. Comput. 16, 1190–1208 (1995).
[CrossRef]

Surf. Sci.

P. S. Hauge, “Generalized rotating-compensator ellipsometry,” Surf. Sci. 56, 148–160 (1976).
[CrossRef]

Thin Solid Films

D. E. Aspnes, “Expanding horizons: new developments in ellipsometry and polarimetery,” Thin Solid Films 455–456, 3–13 (2004).
[CrossRef]

D. K. Goyal and A. Subramanian, “In-situ protein adsorption study on biofunctionalized surfaces using spectroscopic ellipsometry,” Thin Solid Films 518, 2186–2193 (2010).
[CrossRef]

S. G. Thakurta, H. J. Viljoen, and A. Subramanian, “Evaluation of the real-time protein adsorption kinetics on albumin-binding surfaces by dynamic in situ spectroscopic ellipsometry,” Thin Solid Films 520, 2200–2207 (2012).
[CrossRef]

K. Buchner, N. Ehrhardt, B. P. Cahill, and C. Hoffmann, “Internal reflection ellipsometry for real-time monitoring of polyelectrolyte multilayer growth onto tantalum pentoxide,” Thin Solid Films 519, 6480–6485 (2011).
[CrossRef]

Other

E. Hecht and A. Zajac, Optics (Addison-Wesley, 1979).

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

H. G. Tompkins and E. A. Irene, Handbook of Ellipsometry (William Andrew, 2005).

J. Humliček, “Polarized light and ellipsometry,” in Handbook of Ellipsometry (Springer, 2005), pp. 3–93.

H. G. Tompkins, A User’s Guide to Ellipsometry (Dover, 2006).

G. Bucher, Corning 0211, Tech. Rep. (Characterization Science and Services Directorate, Corning Inc., 2003).

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of the fixed-wavelength, variable-angle ellipsometer. The sample moves back and forth in order to accommodate the changing beam position as the angle of incidence is varied.

Fig. 2.
Fig. 2.

Calibration data prior to amplitude or phase correction. (a) IDC, (b) I4X dashed curve through circles and I4Y dashed curve through squares, and (c) I2X dashed curve through circles and I2Y dashed curve through squares. Data after phase correction, prior to amplitude correction, are also shown in panels (b) and (c) with solid curves through the data points. Again, circles are for the (now rephased) X components and squares are for the Y components. All data are represented by points. Curves are merely connecting the points, to help distinguish the data sets.

Fig. 3.
Fig. 3.

Final amplitude and phase-corrected calibration data result in the experimental Stokes vector elements (points), along with the modeled response (curves). s1 (circles), s2 (triangles), s3 (squares), and the degree of polarization (diamonds).

Fig. 4.
Fig. 4.

k-value determinations for amplitude correction. The determination of (a) kDC=0.2134mV1, (b) k2=1.0187mV1, and (c) k3=0.5687mV1, all relative to k1=1mV1, is based on the equality in Eq. (2) assuming no depolarization.

Fig. 5.
Fig. 5.

Normalized Stokes vectors as a function of the angle of incidence reflecting from a glass microscope cover slide, obtained for 60°<θi<70°. The θi axis has been broken to zoom in on the data in the ranges 60°<θi<62° and 68°<θi<70° in order to highlight the difference in amplitude of the observed interference fringes.

Equations (25)

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

s=[s0s1s2s3]=[ItotalI0I90I+45I45IrcpIlcp],
s02s12+s22+s32,
s=[s0s1s2s3],
s=A(ψ=0°)·W(δ=90°,ψ=2ωt)·s.
A(ψ=0°)=12[1100110000000000],
W(δ=90°,ψ=2ωt)=[10000cos22ψsin2ψcos2ψsin2ψ0sin2ψcos2ψsin22ψcos2ψ0sin2ψcos2ψ0],
s0=12s0+14s1+14s1cos2ψ+14s2sin2ψ12s3sinψ,
s0=2kDCIDC12k1I4X,
s1=k1I4X,
s2=k2I4Y,
s3=k3I2Y,
θ4ω=arctan[13i=0,90,180°I4Y(ψ=i)I4X(ψ=i)].
[I4XI4Y]=[cos(90°θ4ω)sin(90°θ4ω)sin(90°θ4ω)cos(90°θ4ω)][I4XorigI4Yorig].
θ2ω=arctan[I4Y(ψ=90°)I4X(ψ=90°)],
I2Y=I2Xorigcos(180°θ2ω)I2Yorigsin(180°θ2ω).
s12=s02s22s32=(2kDCIDC12k1I4X)2(k2I4Y)2(k3I2Y)2,
xi=xR+c(1tanθR1tanθi),
M=T(JJ*)A1,
T=[1001100101100ii0],
J=[Rp00Rs].
Rp=rp(na,ng,θi)+rp(ng,na,θt)e2iβ1+rp(na,ng,θi)rp(ng,na,θt)e2iβ,
Rs=rs(na,ng,θi)+rs(ng,na,θt)e2iβ1+rs(na,ng,θi)rs(ng,na,θt)e2iβ,
β=2πngdλcosθi
rp(n1,n2,θ)=n2cosθ1n1cosθ2n2cosθ1+n1cosθ2,
rs(n1,n2,θ)=n1cosθ1n2cosθ2n1cosθ1+n2cosθ2.

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