Abstract

This paper reviews the current status of instruments for measuring the full 4×1 Stokes vector S, which describes the state of polarization (SOP) of totally or partially polarized light, and the 4×4 Mueller matrix M, which determines how the SOP is transformed as light interacts with a material sample or an optical element or system. The principle of operation of each instrument is briefly explained by using the Stokes–Mueller calculus. The development of fast, automated, imaging, and spectroscopic instruments over the last 50 years has greatly expanded the range of applications of optical polarimetry and ellipsometry in almost every branch of science and technology. Current challenges and future directions of this important branch of optics are also discussed.

© 2016 Optical Society of America

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  136. Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011).
    [Crossref]
  137. F. Afshinmanesh, J. S. White, W. Cai, and M. L. Brongersma, “Measurement of the polarization state of light using an integrated plasmonic polarimeter,” Nanophotonics 1, 125–129 (2012).
    [Crossref]
  138. I. Mandel, J. N. Gollub, I. Bendoym, and D. T. Crouse, “Theory and design of a novel integrated polarimeter sensor utilizing a light sorting metamaterial grating,” IEEE Sens. J. 13, 618–625 (2013).
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  139. A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Plasmonic metagratings for simultaneous determination of Stokes parameters,” Optica 2, 716–723 (2015).
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  140. A. Shaltout, J. Liu, A. Kildishev, and V. Shalaev, “Photonic spin Hall effect in gap-plasmon metasurfaces for on-chip chiro-optical spectroscopy,” Optica 2, 860–863 (2015).
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  141. J. P. B. Mueller, K. Leosson, and F. Capasso, “Ultracompact metasurface in-line polarimeter,” Optica 3, 42–47 (2016).
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  142. T. Heinzl, B. Liesfeld, K.-U. Amthor, H. Schwoerer, R. Sauerbrey, and A. Wipf, “On the observation of vacuum birefringence,” Opt. Commun. 267, 318–321 (2006).
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  143. B. Marx, K. S. Schulze, I. Uschmann, T. Kämpfer, R. Lötzsch, O. Wehrhan, W. Wagner, C. Detlefs, T. Roth, J. Härtwig, E. Förster, T. Stöhlker, and G. G. Paulus, “High-precision x-ray polarimetry,” Phys. Rev. Lett. 110, 254801 (2013).
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  144. T. Hoffman, C. M. Herzinger, J. L. Tedesco, D. K. Gaskill, J. A. Woollam, and M. Schubert, “Terahertz ellipsometry and terahertz optical-Hall effect,” Thin Solid Films 519, 2593–2600 (2011).
    [Crossref]
  145. K. Wiesauer and C. Jördens, “Recent advances in birefringence studies at THz frequencies,” J. Infrared Millim. Terahertz Waves 34, 663–681 (2013).
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  146. B. N. Simon, S. Simon, N. Mukunda, F. Gori, M. Santarsiero, R. Borghi, and R. Simon, “A complete characterization of pre-Mueller and Mueller matrices in polarization optics,” J. Opt. Soc. Am. A 27, 188–199 (2010).
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  147. J. J. Gil, I. San José, and R. Ossikovski, “Serial-parallel decompositions of Mueller matrices,” J. Opt. Soc. Am. A 30, 32–50 (2013).
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  148. O. Arteaga, “Useful Mueller matrix symmetries for ellipsometry,” Thin Solid Films 571, 584–588 (2014).
    [Crossref]
  149. E. Muñoz-Pineda, K. Järrendahl, H. Arwin, and A. Mendoza-Galván, “Symmetries and relationships between elements of the Mueller matrix spectra of the beetle Cotinis mutabillis,” Thin Solid Films 571, 660–665 (2014).
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  150. A. F. Abouraddy and K. C. Toussaint, “Three-dimensional polarization control in microscopy,” Phys. Rev. Lett. 96, 153901 (2006).
    [Crossref]
  151. J. J. Gil, “Polarimetric characterization of light and media,” Eur. Phys. J. Appl. Phys. 40, 1–47 (2007).
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  152. P. Olk, T. Härtling, R. Kullock, and L. M. Eng, “Three-dimensional, arbitrary orientation of focal polarization,” Appl. Opt. 49, 4479–4482 (2010).
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  153. R. M. A. Azzam, “Three-dimensional polarization states of monochromatic light fields,” J. Opt. Soc. Am. A 28, 2279–2283 (2011).
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  154. C. R. Sheppard, “Jones and Stokes vectors for polarization in three dimensions,” Phys. Rev. A 90, 023809 (2014).
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2016 (4)

2015 (6)

2014 (6)

D. E. Aspnes, “Spectroscopic ellipsometry—past, present, and future,” Thin Solid Films 571, 334–344 (2014).
[Crossref]

T. W. H. Oates, T. Shaykhutdinov, T. Wagner, A. Furchner, and K. Hinrichs, “Mid-infrared gyrotropy in split-ring resonators measured by Mueller matrix ellipsometry,” Opt. Mater. Express 4, 2646–2655 (2014).
[Crossref]

D. Schmidt, “Characterization of highly anisotropic three-dimensionally nanostructured surfaces,” Thin Solid Films 571, 364–370 (2014).
[Crossref]

O. Arteaga, “Useful Mueller matrix symmetries for ellipsometry,” Thin Solid Films 571, 584–588 (2014).
[Crossref]

E. Muñoz-Pineda, K. Järrendahl, H. Arwin, and A. Mendoza-Galván, “Symmetries and relationships between elements of the Mueller matrix spectra of the beetle Cotinis mutabillis,” Thin Solid Films 571, 660–665 (2014).
[Crossref]

C. R. Sheppard, “Jones and Stokes vectors for polarization in three dimensions,” Phys. Rev. A 90, 023809 (2014).
[Crossref]

2013 (7)

J. J. Gil, I. San José, and R. Ossikovski, “Serial-parallel decompositions of Mueller matrices,” J. Opt. Soc. Am. A 30, 32–50 (2013).
[Crossref]

B. Marx, K. S. Schulze, I. Uschmann, T. Kämpfer, R. Lötzsch, O. Wehrhan, W. Wagner, C. Detlefs, T. Roth, J. Härtwig, E. Förster, T. Stöhlker, and G. G. Paulus, “High-precision x-ray polarimetry,” Phys. Rev. Lett. 110, 254801 (2013).
[Crossref]

K. Wiesauer and C. Jördens, “Recent advances in birefringence studies at THz frequencies,” J. Infrared Millim. Terahertz Waves 34, 663–681 (2013).
[Crossref]

I. Mandel, J. N. Gollub, I. Bendoym, and D. T. Crouse, “Theory and design of a novel integrated polarimeter sensor utilizing a light sorting metamaterial grating,” IEEE Sens. J. 13, 618–625 (2013).
[Crossref]

N. Hagen, K. Oka, and E. L. Dereniak, “Snapshot Mueller matrix spectropolarimeter: erratum,” Opt. Lett. 38, 1675 (2013).

G. W. Kattawar, “Genesis and evolution of polarization of light in the ocean [Invited],” Appl. Opt. 52, 940–948 (2013).
[Crossref]

P. C. Collins, G. Kyne, D. Lara, M. Redfern, A. Shearer, and B. Sheehan, “The Galway astronomical Stokes polarimeter: an all-Stokes optical polarimeter with ultra-high time resolution,” Exp. Astron. 36, 479–503 (2013).
[Crossref]

2012 (5)

2011 (7)

Ø. Svensen, J. J. Stamnes, M. Keldemo, L. M. S. Aas, S. R. Erga, and Ø. Frette, “Mueller matrix measurements of algae with different shape and size distributions,” Appl. Opt. 50, 5149–5157 (2011).
[Crossref]

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011).
[Crossref]

T. W. H. Oates, H. Wormeester, and H. Arwin, “Characterization of plasmonic effects in thin films and metamaterials using spectroscopic ellipsometry,” Prog. Surf. Sci. 86, 328–376 (2011).
[Crossref]

T. Hoffman, C. M. Herzinger, J. L. Tedesco, D. K. Gaskill, J. A. Woollam, and M. Schubert, “Terahertz ellipsometry and terahertz optical-Hall effect,” Thin Solid Films 519, 2593–2600 (2011).
[Crossref]

R. M. A. Azzam, “Three-dimensional polarization states of monochromatic light fields,” J. Opt. Soc. Am. A 28, 2279–2283 (2011).
[Crossref]

R. M. A. Azzam, “The intertwined history of ellipsometry and polarimetry,” Thin Solid Films 519, 2584–2588 (2011).
[Crossref]

N. Ghosh and I. A. Vitkin, “Tissue polarimetry: concepts, challenges, applications, and outlook,” J. Biomed. Opt. 16, 110801 (2011).
[Crossref]

2010 (2)

2009 (3)

E. DeHoog, H. Luo, K. Oka, E. Dereniak, and J. Schwiegerling, “Snapshot polarimeter fundus camera,” Appl. Opt. 48, 1663–1667 (2009).
[Crossref]

D. Baumann, M. G. Jackson, P. Adshead, A. Amblard, A. Ashoorioon, N. Bartolo, R. Bean, M. Beltrán, F. de Bernardis, S. Bird, X. Chen, D. J. H. Chung, L. Colombo, A. Cooray, P. Creminelli, S. Dodelson, J. Dunkley, C. Dvorkin, R. Easthher, F. Einelli, R. Fluager, M. P. Hertzberg, K. Jones-Smith, S. Kachru, K. Kadota, J. Khoury, W. H. Kinney, E. Komatsu, L. M. Krauss, A. Liddle, M. Ligouri, E. Lim, A. Linde, S. Matarres, H. Mathur, L. McAllister, A. Melchoirri, A. Nicolis, L. Pagano, H. V. Peiris, M. Peloso, L. Pogosian, E. Pierpaoli, A. Riotto, U. Seljak, L. Senatore, S. Shandera, E. Silverstein, T. Smith, P. Vaudrevange, L. Verde, B. Wandelt, D. Wands, S. Watson, M. Wyman, A. Yadav, W. Valkenburg, and M. Zaldxarriaga, “Probing inflation with CMB polarization,” AIP Conf. Proc. 1141, 10–120 (2009).
[Crossref]

T. Dittmar, A. Kreter, and A. von Keudell, and the TEXTOR Team, “Development of an in situ ellipsometer for deposition and erosion studies at the first wall of a tokamak,” Nucl. Fusion 49, 045004 (2009).
[Crossref]

2008 (3)

M. Ottaviani, K. Stamnes, J. Koskulics, H. Eide, S. R. Long, W. Su, and W. Wiscombe, “Light reflection from water waves: suitable setup for a polarimetric investigation under controlled laboratory conditions,” J. Atmos. Ocean. Technol. 25, 715–728 (2008).
[Crossref]

F. Stabo-Eeg, M. Kildemo, E. Garcia-Caurel, and M. Lindgren, “Design and characterization of achromatic 132° retarders in CaF2 and fused silica,” J. Mod. Opt. 55, 2203–2214 (2008).
[Crossref]

K. Twietmeyer and R. A. Chipman, “Optimization of Mueller-matrix polarimeters in the presence of error sources,” Opt. Express 16, 11589–11603 (2008).
[Crossref]

2007 (4)

2006 (6)

J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt. 45, 5453–5469 (2006).
[Crossref]

D. Lara and C. Dainty, “Axially resolved complete Mueller matrix confocal microscopy,” Appl. Opt. 45, 1917–1930 (2006).
[Crossref]

A. F. Abouraddy and K. C. Toussaint, “Three-dimensional polarization control in microscopy,” Phys. Rev. Lett. 96, 153901 (2006).
[Crossref]

T. Heinzl, B. Liesfeld, K.-U. Amthor, H. Schwoerer, R. Sauerbrey, and A. Wipf, “On the observation of vacuum birefringence,” Opt. Commun. 267, 318–321 (2006).
[Crossref]

T. Novikova, A. De Martino, S. B. Hatit, and B. Drévillon, “Application of Mueller polarimetry in conical diffraction for critical dimension measurements in microelectronics,” Appl. Opt. 45, 3688–3697 (2006).
[Crossref]

C. Chen, M. W. Horn, S. Pursel, C. Ross, and R. W. Collins, “The ultimate in real-time ellipsometry: multichannel Mueller matrix spectroscopy,” Thin Solid Films 253, 38–46 (2006).

2005 (1)

2004 (3)

2003 (3)

2002 (3)

2000 (5)

G. Cipparrone, G. Russo, C. Versace, G. Strangi, and V. Carbone, “Polarimetric study of the optically induced dynamical behavior in nematic liquid-crystal films,” Opt. Commun. 173, 1–10 (2000).
[Crossref]

P. S. Westbrook, T. A. Strasser, and T. Erdogan, “In-line polarimeter using blazed fiber gratings,” IEEE Photon. Technol. Lett. 12, 1352–1354 (2000).
[Crossref]

J. M. Bueno, “Polarimetry using liquid-crystal variable retarders: theory and calibration,” J. Opt. A 2, 216–222 (2000).
[Crossref]

D. S. Sabatke, M. R. Descour, E. L. Dereniak, W. C. Sweat, S. A. Kemme, and G. S. Phillips, “Optimization of retardance for a complete Stokes polarimeter,” Opt. Lett. 25, 802–804 (2000).
[Crossref]

R. M. A. Azzam, “Poincaré sphere representation of the fixed-polarizer rotating-retarder optical system,” J. Opt. Soc. Am. A 17, 2105–2107 (2000).
[Crossref]

1999 (2)

G. Strangi, C. Versace, N. Scaramuzza, D. E. Lucchetta, V. Carbone, and R. Bartolino, “Photopolarimetric characterization of the transition between two turbulent states in a nematic liquid-crystal film,” Phys. Rev. E 59, 5523–5527 (1999).
[Crossref]

E. Compain, S. Poirier, and B. Drevillon, “General and self-consistent method for the calibration of polarization modulators, polarimeters, and Mueller-matrix ellipsometers,” Appl. Opt. 38, 3490–3502 (1999).
[Crossref]

1998 (2)

1997 (3)

1996 (1)

1995 (2)

A. Bouzid, A. G. Abushagur, A. El-Sabae, and R. M. A. Azzam, “Fiber-optic four-detector polarimeter,” Opt. Commun. 118, 329–334 (1995).
[Crossref]

Y. Cui and R. M. A. Azzam, “Calibration and testing of a sixteen-beam grating-based division-of-amplitude photopolarimeter,” Rev. Sci. Instrum. 66, 5552–5558 (1995).
[Crossref]

1994 (2)

S. Krishnan and P. C. Nordine, “Mueller-matrix ellipsometry using the division-of-amplitude photopolarimeter,” Appl. Opt. 33, 4184–4192 (1994).
[Crossref]

D. A. Ramsey and K. C. Ludema, “The influence of roughness on film thickness measurements by Mueller matrix ellipsometry,” Rev. Sci. Instrum. 65, 2874–2881 (1994).
[Crossref]

1993 (2)

R. M. A. Azzam and K. A. Giardina, “Photopolarimeter based on planar grating diffraction,” J. Opt. Soc. Am. A 10, 1190–1196 (1993).
[Crossref]

R. M. A. Azzam, “Polarization Michelson interferometer as a global polarization state generator and for measurement of the coherence and spectral properties of quasi-monochromatic light,” Rev. Sci. Instrum. 64, 2834–2838 (1993).
[Crossref]

1992 (4)

1991 (1)

R. M. A. Azzam, K. A. Giardina, and A. G. Lopez, “Conventional and generalized Mueller-matrix ellipsometry using the four-detector photopolarimeter,” Opt. Eng. 30, 1583–1589 (1991).
[Crossref]

1990 (5)

R. M. A. Azzam, “Longitudinal polarization-dependent coupling of light from an optical fiber to a side-bonded planar proximity detector: application to integrated azimuthally distributed multi-detector photopolarimeters,” IEEE Photon. Technol. Lett. 2, 893–895 (1990).
[Crossref]

R. M. A. Azzam, “Instrument matrix of the four-detector photopolarimeter: physical meaning of its rows and columns and constraints on its elements,” J. Opt. Soc. Am. A 7, 87–91 (1990).
[Crossref]

J. Badoz, M. P. Silverman, and J. C. Canit, “Wave propagation through a medium with static and dynamic birefringence: theory of the photoelastic modulator,” J. Opt. Soc. Am. A 7, 672–682 (1990).
[Crossref]

R. N. Weinreb, A. W. Dreher, A. Coleman, H. Quigley, B. Shaw, and K. Reiter, “Histopathologic validation of Fourier-ellipsometry measurements of retinal nerve fiber layer thickness,” Arch. Ophthalmol. 108, 557–560 (1990).
[Crossref]

D. H. Goldstein and R. A. Chipman, “Error analysis of a Mueller matrix polarimeter,” J. Opt. Soc. Am. A 7, 693–700 (1990).
[Crossref]

1989 (1)

1988 (2)

R. M. A. Azzam, E. Masetti, I. M. Elminyawi, and F. B. Grosz, “Construction, calibration, and testing of a four-detector photopolarimeter,” Rev. Sci. Instrum. 59, 84–88 (1988).
[Crossref]

R. M. A. Azzam, I. M. Elminyawi, and A. M. El-Saba, “General analysis and optimization of the four-detector photopolarimeter,” J. Opt. Soc. Am. A 5, 681–689 (1988).
[Crossref]

1987 (1)

1986 (1)

1985 (2)

R. M. A. Azzam, “Arrangement of four photodetectors for measuring the state of polarization of light,” Opt. Lett. 10, 309–311 (1985).
[Crossref]

G. E. Jellison and D. H. Lowndes, “Time-resolved measurements of the optical properties of silicon during pulsed excimer irradiation,” Appl. Phys. Lett. 47, 718–721 (1985).
[Crossref]

1984 (1)

1983 (1)

1982 (1)

R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” J. Mod. Opt. 29, 685–689 (1982).

1980 (4)

1978 (3)

1977 (2)

1973 (1)

A. J. Hunt and D. R. Huffman, “A new polarization-modulated light scattering instrument,” Rev. Sci. Instrum. 44, 1753–1762 (1973).
[Crossref]

1971 (1)

1970 (1)

1969 (1)

1968 (1)

1957 (1)

1951 (1)

1948 (1)

H. Mueller, “The foundation of optics,” J. Opt. Soc. Am. 38, 661 (1948).

1925 (1)

1852 (1)

G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Cambridge Philos. Soc. 9, 399–416 (1852).

Aas, L. M. S.

Abouraddy, A. F.

A. F. Abouraddy and K. C. Toussaint, “Three-dimensional polarization control in microscopy,” Phys. Rev. Lett. 96, 153901 (2006).
[Crossref]

Abushagur, A. G.

A. Bouzid, A. G. Abushagur, A. El-Sabae, and R. M. A. Azzam, “Fiber-optic four-detector polarimeter,” Opt. Commun. 118, 329–334 (1995).
[Crossref]

Adshead, P.

D. Baumann, M. G. Jackson, P. Adshead, A. Amblard, A. Ashoorioon, N. Bartolo, R. Bean, M. Beltrán, F. de Bernardis, S. Bird, X. Chen, D. J. H. Chung, L. Colombo, A. Cooray, P. Creminelli, S. Dodelson, J. Dunkley, C. Dvorkin, R. Easthher, F. Einelli, R. Fluager, M. P. Hertzberg, K. Jones-Smith, S. Kachru, K. Kadota, J. Khoury, W. H. Kinney, E. Komatsu, L. M. Krauss, A. Liddle, M. Ligouri, E. Lim, A. Linde, S. Matarres, H. Mathur, L. McAllister, A. Melchoirri, A. Nicolis, L. Pagano, H. V. Peiris, M. Peloso, L. Pogosian, E. Pierpaoli, A. Riotto, U. Seljak, L. Senatore, S. Shandera, E. Silverstein, T. Smith, P. Vaudrevange, L. Verde, B. Wandelt, D. Wands, S. Watson, M. Wyman, A. Yadav, W. Valkenburg, and M. Zaldxarriaga, “Probing inflation with CMB polarization,” AIP Conf. Proc. 1141, 10–120 (2009).
[Crossref]

Afshinmanesh, F.

F. Afshinmanesh, J. S. White, W. Cai, and M. L. Brongersma, “Measurement of the polarization state of light using an integrated plasmonic polarimeter,” Nanophotonics 1, 125–129 (2012).
[Crossref]

Åkerlind, C.

Alcaraz, C.

Alhassen, F.

Alù, A.

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011).
[Crossref]

Amblard, A.

D. Baumann, M. G. Jackson, P. Adshead, A. Amblard, A. Ashoorioon, N. Bartolo, R. Bean, M. Beltrán, F. de Bernardis, S. Bird, X. Chen, D. J. H. Chung, L. Colombo, A. Cooray, P. Creminelli, S. Dodelson, J. Dunkley, C. Dvorkin, R. Easthher, F. Einelli, R. Fluager, M. P. Hertzberg, K. Jones-Smith, S. Kachru, K. Kadota, J. Khoury, W. H. Kinney, E. Komatsu, L. M. Krauss, A. Liddle, M. Ligouri, E. Lim, A. Linde, S. Matarres, H. Mathur, L. McAllister, A. Melchoirri, A. Nicolis, L. Pagano, H. V. Peiris, M. Peloso, L. Pogosian, E. Pierpaoli, A. Riotto, U. Seljak, L. Senatore, S. Shandera, E. Silverstein, T. Smith, P. Vaudrevange, L. Verde, B. Wandelt, D. Wands, S. Watson, M. Wyman, A. Yadav, W. Valkenburg, and M. Zaldxarriaga, “Probing inflation with CMB polarization,” AIP Conf. Proc. 1141, 10–120 (2009).
[Crossref]

Amthor, K.-U.

T. Heinzl, B. Liesfeld, K.-U. Amthor, H. Schwoerer, R. Sauerbrey, and A. Wipf, “On the observation of vacuum birefringence,” Opt. Commun. 267, 318–321 (2006).
[Crossref]

Arteaga, O.

Arwin, H.

C. Åkerlind, H. Arwin, T. Hallberg, J. Landin, J. Gustafsson, H. Kariis, and K. Järrendahl, “Scattering and polarization properties of the scarab beetle Cyphochilus insulanus cuticle,” Appl. Opt. 54, 6037–6045 (2015).
[Crossref]

E. Muñoz-Pineda, K. Järrendahl, H. Arwin, and A. Mendoza-Galván, “Symmetries and relationships between elements of the Mueller matrix spectra of the beetle Cotinis mutabillis,” Thin Solid Films 571, 660–665 (2014).
[Crossref]

T. W. H. Oates, H. Wormeester, and H. Arwin, “Characterization of plasmonic effects in thin films and metamaterials using spectroscopic ellipsometry,” Prog. Surf. Sci. 86, 328–376 (2011).
[Crossref]

Ashoorioon, A.

D. Baumann, M. G. Jackson, P. Adshead, A. Amblard, A. Ashoorioon, N. Bartolo, R. Bean, M. Beltrán, F. de Bernardis, S. Bird, X. Chen, D. J. H. Chung, L. Colombo, A. Cooray, P. Creminelli, S. Dodelson, J. Dunkley, C. Dvorkin, R. Easthher, F. Einelli, R. Fluager, M. P. Hertzberg, K. Jones-Smith, S. Kachru, K. Kadota, J. Khoury, W. H. Kinney, E. Komatsu, L. M. Krauss, A. Liddle, M. Ligouri, E. Lim, A. Linde, S. Matarres, H. Mathur, L. McAllister, A. Melchoirri, A. Nicolis, L. Pagano, H. V. Peiris, M. Peloso, L. Pogosian, E. Pierpaoli, A. Riotto, U. Seljak, L. Senatore, S. Shandera, E. Silverstein, T. Smith, P. Vaudrevange, L. Verde, B. Wandelt, D. Wands, S. Watson, M. Wyman, A. Yadav, W. Valkenburg, and M. Zaldxarriaga, “Probing inflation with CMB polarization,” AIP Conf. Proc. 1141, 10–120 (2009).
[Crossref]

Aspnes, D. E.

D. E. Aspnes, “Spectroscopic ellipsometry—past, present, and future,” Thin Solid Films 571, 334–344 (2014).
[Crossref]

D. E. Aspnes and J. Y. M. Law, “Ellipsometer and polarimeter with zero-order plate compensator,” U.S. patent6,181,421 (January 30, 2001).

Azzam, R. M. A.

R. M. A. Azzam, “The intertwined history of ellipsometry and polarimetry,” Thin Solid Films 519, 2584–2588 (2011).
[Crossref]

R. M. A. Azzam, “Three-dimensional polarization states of monochromatic light fields,” J. Opt. Soc. Am. A 28, 2279–2283 (2011).
[Crossref]

R. M. A. Azzam and F. F. Sudradjat, “Single-layer-coated beam splitters for the division-of-amplitude photopolarimeter,” Appl. Opt. 44, 190–196 (2005).
[Crossref]

S. Krishnan, S. Hampton, J. Rix, B. Taylor, and R. M. A. Azzam, “Spectral polarization measurement by use of the grating division-of-amplitude photopolarimeter,” Appl. Opt. 42, 1216–1227 (2003).
[Crossref]

R. M. A. Azzam and A. De, “Optimal beam splitters for the division-of-amplitude photopolarimeter,” J. Opt. Soc. Am. A 20, 955–958 (2003).
[Crossref]

R. M. A. Azzam, “Poincaré sphere representation of the fixed-polarizer rotating-retarder optical system,” J. Opt. Soc. Am. A 17, 2105–2107 (2000).
[Crossref]

J. Liu and R. M. A. Azzam, “Polarization properties of corner-cube retroreflectors: theory and experiment,” Appl. Opt. 36, 1553–1559 (1997).
[Crossref]

A. Bouzid, A. G. Abushagur, A. El-Sabae, and R. M. A. Azzam, “Fiber-optic four-detector polarimeter,” Opt. Commun. 118, 329–334 (1995).
[Crossref]

Y. Cui and R. M. A. Azzam, “Calibration and testing of a sixteen-beam grating-based division-of-amplitude photopolarimeter,” Rev. Sci. Instrum. 66, 5552–5558 (1995).
[Crossref]

R. M. A. Azzam, “Polarization Michelson interferometer as a global polarization state generator and for measurement of the coherence and spectral properties of quasi-monochromatic light,” Rev. Sci. Instrum. 64, 2834–2838 (1993).
[Crossref]

R. M. A. Azzam and K. A. Giardina, “Photopolarimeter based on planar grating diffraction,” J. Opt. Soc. Am. A 10, 1190–1196 (1993).
[Crossref]

R. M. A. Azzam, “Division-of-amplitude photopolarimeter based on conical diffraction from a metallic grating,” Appl. Opt. 31, 3574–3576 (1992).
[Crossref]

R. M. A. Azzam, K. A. Giardina, and A. G. Lopez, “Conventional and generalized Mueller-matrix ellipsometry using the four-detector photopolarimeter,” Opt. Eng. 30, 1583–1589 (1991).
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B. Marx, K. S. Schulze, I. Uschmann, T. Kämpfer, R. Lötzsch, O. Wehrhan, W. Wagner, C. Detlefs, T. Roth, J. Härtwig, E. Förster, T. Stöhlker, and G. G. Paulus, “High-precision x-ray polarimetry,” Phys. Rev. Lett. 110, 254801 (2013).
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Weinreb, R. N.

A. W. Dreher, K. Reiter, and R. N. Weinreb, “Spatially resolved birefringence of the retinal nerve fiber layer assessed with a retinal laser ellipsometer,” Appl. Opt. 31, 3730–3735 (1992).
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R. N. Weinreb, A. W. Dreher, A. Coleman, H. Quigley, B. Shaw, and K. Reiter, “Histopathologic validation of Fourier-ellipsometry measurements of retinal nerve fiber layer thickness,” Arch. Ophthalmol. 108, 557–560 (1990).
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Westbrook, P. S.

P. S. Westbrook, T. A. Strasser, and T. Erdogan, “In-line polarimeter using blazed fiber gratings,” IEEE Photon. Technol. Lett. 12, 1352–1354 (2000).
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Westphal, P.

White, J. S.

F. Afshinmanesh, J. S. White, W. Cai, and M. L. Brongersma, “Measurement of the polarization state of light using an integrated plasmonic polarimeter,” Nanophotonics 1, 125–129 (2012).
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Wicker, K.

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K. Wiesauer and C. Jördens, “Recent advances in birefringence studies at THz frequencies,” J. Infrared Millim. Terahertz Waves 34, 663–681 (2013).
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Wipf, A.

T. Heinzl, B. Liesfeld, K.-U. Amthor, H. Schwoerer, R. Sauerbrey, and A. Wipf, “On the observation of vacuum birefringence,” Opt. Commun. 267, 318–321 (2006).
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Wiscombe, W.

M. Ottaviani, K. Stamnes, J. Koskulics, H. Eide, S. R. Long, W. Su, and W. Wiscombe, “Light reflection from water waves: suitable setup for a polarimetric investigation under controlled laboratory conditions,” J. Atmos. Ocean. Technol. 25, 715–728 (2008).
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Woollam, J. A.

T. Hoffman, C. M. Herzinger, J. L. Tedesco, D. K. Gaskill, J. A. Woollam, and M. Schubert, “Terahertz ellipsometry and terahertz optical-Hall effect,” Thin Solid Films 519, 2593–2600 (2011).
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D. Baumann, M. G. Jackson, P. Adshead, A. Amblard, A. Ashoorioon, N. Bartolo, R. Bean, M. Beltrán, F. de Bernardis, S. Bird, X. Chen, D. J. H. Chung, L. Colombo, A. Cooray, P. Creminelli, S. Dodelson, J. Dunkley, C. Dvorkin, R. Easthher, F. Einelli, R. Fluager, M. P. Hertzberg, K. Jones-Smith, S. Kachru, K. Kadota, J. Khoury, W. H. Kinney, E. Komatsu, L. M. Krauss, A. Liddle, M. Ligouri, E. Lim, A. Linde, S. Matarres, H. Mathur, L. McAllister, A. Melchoirri, A. Nicolis, L. Pagano, H. V. Peiris, M. Peloso, L. Pogosian, E. Pierpaoli, A. Riotto, U. Seljak, L. Senatore, S. Shandera, E. Silverstein, T. Smith, P. Vaudrevange, L. Verde, B. Wandelt, D. Wands, S. Watson, M. Wyman, A. Yadav, W. Valkenburg, and M. Zaldxarriaga, “Probing inflation with CMB polarization,” AIP Conf. Proc. 1141, 10–120 (2009).
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Yadav, A.

D. Baumann, M. G. Jackson, P. Adshead, A. Amblard, A. Ashoorioon, N. Bartolo, R. Bean, M. Beltrán, F. de Bernardis, S. Bird, X. Chen, D. J. H. Chung, L. Colombo, A. Cooray, P. Creminelli, S. Dodelson, J. Dunkley, C. Dvorkin, R. Easthher, F. Einelli, R. Fluager, M. P. Hertzberg, K. Jones-Smith, S. Kachru, K. Kadota, J. Khoury, W. H. Kinney, E. Komatsu, L. M. Krauss, A. Liddle, M. Ligouri, E. Lim, A. Linde, S. Matarres, H. Mathur, L. McAllister, A. Melchoirri, A. Nicolis, L. Pagano, H. V. Peiris, M. Peloso, L. Pogosian, E. Pierpaoli, A. Riotto, U. Seljak, L. Senatore, S. Shandera, E. Silverstein, T. Smith, P. Vaudrevange, L. Verde, B. Wandelt, D. Wands, S. Watson, M. Wyman, A. Yadav, W. Valkenburg, and M. Zaldxarriaga, “Probing inflation with CMB polarization,” AIP Conf. Proc. 1141, 10–120 (2009).
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Zaldxarriaga, M.

D. Baumann, M. G. Jackson, P. Adshead, A. Amblard, A. Ashoorioon, N. Bartolo, R. Bean, M. Beltrán, F. de Bernardis, S. Bird, X. Chen, D. J. H. Chung, L. Colombo, A. Cooray, P. Creminelli, S. Dodelson, J. Dunkley, C. Dvorkin, R. Easthher, F. Einelli, R. Fluager, M. P. Hertzberg, K. Jones-Smith, S. Kachru, K. Kadota, J. Khoury, W. H. Kinney, E. Komatsu, L. M. Krauss, A. Liddle, M. Ligouri, E. Lim, A. Linde, S. Matarres, H. Mathur, L. McAllister, A. Melchoirri, A. Nicolis, L. Pagano, H. V. Peiris, M. Peloso, L. Pogosian, E. Pierpaoli, A. Riotto, U. Seljak, L. Senatore, S. Shandera, E. Silverstein, T. Smith, P. Vaudrevange, L. Verde, B. Wandelt, D. Wands, S. Watson, M. Wyman, A. Yadav, W. Valkenburg, and M. Zaldxarriaga, “Probing inflation with CMB polarization,” AIP Conf. Proc. 1141, 10–120 (2009).
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Zhao, Y.

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011).
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V. V. Tuchin, L. Wang, and D. A. Zimnyakov, Optical Polarization in Biomedical Applications (Springer, 2006).

AIP Conf. Proc. (1)

D. Baumann, M. G. Jackson, P. Adshead, A. Amblard, A. Ashoorioon, N. Bartolo, R. Bean, M. Beltrán, F. de Bernardis, S. Bird, X. Chen, D. J. H. Chung, L. Colombo, A. Cooray, P. Creminelli, S. Dodelson, J. Dunkley, C. Dvorkin, R. Easthher, F. Einelli, R. Fluager, M. P. Hertzberg, K. Jones-Smith, S. Kachru, K. Kadota, J. Khoury, W. H. Kinney, E. Komatsu, L. M. Krauss, A. Liddle, M. Ligouri, E. Lim, A. Linde, S. Matarres, H. Mathur, L. McAllister, A. Melchoirri, A. Nicolis, L. Pagano, H. V. Peiris, M. Peloso, L. Pogosian, E. Pierpaoli, A. Riotto, U. Seljak, L. Senatore, S. Shandera, E. Silverstein, T. Smith, P. Vaudrevange, L. Verde, B. Wandelt, D. Wands, S. Watson, M. Wyman, A. Yadav, W. Valkenburg, and M. Zaldxarriaga, “Probing inflation with CMB polarization,” AIP Conf. Proc. 1141, 10–120 (2009).
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Biomed. Opt. Express (1)

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IEEE Sens. J. (1)

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J. Atmos. Ocean. Technol. (1)

M. Ottaviani, K. Stamnes, J. Koskulics, H. Eide, S. R. Long, W. Su, and W. Wiscombe, “Light reflection from water waves: suitable setup for a polarimetric investigation under controlled laboratory conditions,” J. Atmos. Ocean. Technol. 25, 715–728 (2008).
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Nanophotonics (1)

F. Afshinmanesh, J. S. White, W. Cai, and M. L. Brongersma, “Measurement of the polarization state of light using an integrated plasmonic polarimeter,” Nanophotonics 1, 125–129 (2012).
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Nucl. Fusion (1)

T. Dittmar, A. Kreter, and A. von Keudell, and the TEXTOR Team, “Development of an in situ ellipsometer for deposition and erosion studies at the first wall of a tokamak,” Nucl. Fusion 49, 045004 (2009).
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Opt. Commun. (3)

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Opt. Mater. Express (1)

Opt. Photon. News (1)

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Optica (3)

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Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011).
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Figures (7)

Fig. 1.
Fig. 1. Polarization state generator. LS is a source of collimated unpolarized quasi-monochromatic light traveling in the z direction. LP is a linear polarizer with transmission-axis azimuth α , and QWR is a quarter-wave retarder with fast-axis azimuth β . The angles α and β are measured from the reference transverse x axis.
Fig. 2.
Fig. 2. PSG that consists of a collimated light source (LS), fixed linear polarizer (LP) with the transmission axis at α = 0 , first LR with retardance Δ 1 and fast-axis azimuth β 1 = 45 ° , and second LR with retardance Δ 2 and fast-axis azimuth β 2 = 0 .
Fig. 3.
Fig. 3. Division-of-amplitude photopolarimeter. The incident light beam i whose SOP is to be measured is divided into reflected ( r ) and transmitted ( t ) components by beam splitter BS. WP1 and WP2 are Wollaston prisms placed in the r and t beams, respectively, to generate four linearly polarized output beams that are intercepted by four linear photodetectors D n ( n = 0 , 1 , 2 , 3 ) to generate four output electrical signals i n ( n = 0 , 1 , 2 , 3 ) (after [72]).
Fig. 4.
Fig. 4. Grating-based division-of-amplitude photopolarimeter. S, light source; PSG, polarization state generator; BS, beam splitter; G, diffraction grating; D, reference detector; L, imaging lens; PDA, linear photodetector array; P m , array of sheet polarizing elements with fanned-out transmission-axis orientations; QWR, quarter-wave retarder (after [88]).
Fig. 5.
Fig. 5. Four-detector photopolarimeter consisting of four windowless planar Si photodetectors D n ( n = 0 , 1 , 2 , 3 ) , of which the first three are partially specularly reflective and the fourth is nearly totally absorbing. The Stokes vector S of incident light is determined by the four detector output electrical signals i n ( n = 0 , 1 , 2 , 3 ) (after [90]).
Fig. 6.
Fig. 6. Block diagram of a general single-channel Mueller-matrix polarimeter. LS, source of collimated quasi-monochromatic light; PO, polarizing optics; S, sample or system whose Mueller matrix M is to be measured; AO, polarization-analyzing optics; D, linear photodetector.
Fig. 7.
Fig. 7. Dual-rotating-retarder Mueller-matrix polarimeter. L, source of collimated quasi-monochromatic light; P , linear polarizer; C , first rotating QWR (or compensator); S, sample or system whose Mueller matrix M is to be measured; C , second rotating QWR; A , linear polarization analyzer; D, linear photodetector. The polarizer and analyzer P and A are set at fixed orientations, e.g., with their transmission axes parallel to the x axis. M is determined by Fourier analysis of the output signal of D (after [109]).

Equations (36)

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S = [ S 0 S 1 S 2 S 3 ] t ,
S 0 = I x + I y = I x + I y = I R C + I L C , S 1 = I x I y , S 2 = I x I y , S 3 = I R C I L C .
s⃗ = ( s 1 , s 2 , s 3 ) = ( S 1 / S 0 , S 2 / S 0 , S 3 / S 0 ) .
P = | s⃗ | = s 1 2 + s 2 2 + s 3 2 , 0 | s⃗ | 1 .
S = [ P S 0 , S 1 , S 2 , S 3 ] t + [ ( 1 P ) S 0 , 0 , 0 , 0 ] t .
θ = 1 2 arctan ( s 2 / s 1 ) .
ε = 1 2 arcsin ( s 3 / | s⃗ | ) .
S = S 0 [ 1 P cos ( 2 θ ) cos ( 2 ε ) P sin ( 2 θ ) cos ( 2 ε ) P sin ( 2 ε ) ] t .
S = MS .
M ( LP ) = τ 2 [ 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 ] .
M ( LR ) = τ [ 1 0 0 0 0 1 0 0 0 0 cos Δ sin Δ 0 0 sin Δ cos Δ ] ,
M new = R ( α ) MR ( α ) .
R ( α ) = [ 1 0 0 0 0 cos ( 2 α ) sin ( 2 α ) 0 0 sin ( 2 α ) cos ( 2 α ) 0 0 0 0 1 ] .
M cascade = M N M N 1 M 2 M 1 .
E = JE .
Δ = 2 π ( n e n o ) d / λ .
S = S 0 × [ 1 cos ( 2 β ) cos ( 2 β 2 α ) sin ( 2 β ) cos ( 2 β 2 α ) sin ( 2 β 2 α ) ] t .
[ s 1 1 2 cos ( 2 α ) ] 2 + [ s 2 1 2 sin ( 2 α ) ] 2 = 1 4 .
S = S 0 [ 1 cos Δ 1 sin Δ 1 sin Δ 2 sin Δ 1 cos Δ 2 ] t .
i = 1 2 K { S 0 + [ cos 2 ( Δ / 2 ) + sin 2 ( Δ / 2 ) cos ( 4 β ) ] S 1 + sin 2 ( Δ / 2 ) sin ( 4 β ) S 2 sin Δ sin ( 2 β ) S 3 } ,
i = 1 2 K { S 0 + 1 2 [ 1 + cos ( 4 β ) ] S 1 + 1 2 sin ( 4 β ) S 2 sin ( 2 β ) S 3 } .
Δ = 2 arcsin 5 / 6 = 131.810 °
β = 1 4 arccos ( 0.2 ± 0.4 3 ) = ± 15.118 ° , ± 51.693 ° .
i = 1 2 K [ S 0 + ( cos Δ 2 ) S 1 + ( sin Δ 1 sin Δ 2 ) S 2 ( cos Δ 1 sin Δ 2 ) S 3 ] .
Δ = Δ max sin ( ω t ) .
cos [ Δ max sin ( ω t ) ] = J 0 ( Δ max ) + n = 1 J 2 n ( Δ max ) cos ( 2 n ω t ) , sin [ Δ max sin ( ω t ) ] = 2 n = 1 J 2 n + 1 ( Δ max ) sin [ ( 2 n + 1 ) ω t ] ,
I = [ i 0 i 1 i 2 i 3 ] t ,
I = AS .
S = A 1 I .
det A = ( R T ) 2 sin ( 2 ψ r ) sin ( 2 ψ t ) [ cos ( 2 ψ r ) cos ( 2 ψ t ) ] sin ( Δ r Δ t ) .
R = T = 0.5 , ( ψ r , ψ t ) = ( 27.368 ° , 62.632 ° ) , Δ r Δ t = ± π / 2 .
i = c AMP .
i = c k , l = 0 3 μ k l m k l , μ k l = a k p l , k , l = 0 , 1 , 2 , 3 .
[ i ] = c [ A ] M [ P ] ,
M = ( 1 / c ) [ A ] 1 [ i ] [ P ] 1 .
i ( t ) = a 0 + n = 1 12 [ a n cos ( n ω f t ) + b n sin ( n ω f t ) ] ,

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