Abstract

We propose a new method for determining the Mueller matrix of an arbitrary optical element and verify it with three known optical elements. This method makes use of two universal SU(2) polarization gadgets to obtain the projection matrix directly from the experiment. It allows us to determine the Mueller matrix without precalibration of the setup, since the generated polarization states are fully determined by the azimuths of the wave plates. We calculate errors in determining the Mueller matrix and compare with other techniques.

© 2014 Optical Society of America

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References

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  1. S. Y. Lu and R. A. Chipman, “Interpretation of Mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A 13, 1106–1113 (1996).
    [CrossRef]
  2. S. Manhas, M. K. Swami, P. Buddhiwant, N. Ghosh, P. K. Gupta, and K. Singh, “Mueller matrix approach for determination of optical rotation in chiral turbid media in backscattering geometry,” Opt. Express 14, 190–202 (2006).
    [CrossRef]
  3. W. C. Kuo, N. K. Chou, C. Chou, C. M. Lai, H. J. Huang, S. S. Wang, and J. J. Shyu, “Polarization-sensitive optical coherence tomography for imaging human atherosclerosis,” Appl. Opt. 46, 2520–2527 (2007).
    [CrossRef]
  4. C. K. Hitzenberger, E. Götzinger, M. Sticker, M. Pircher, and A. F. Fercher, “Measurement and imaging of birefringence and optic axis orientation by phase resolved polarization sensitive optical coherence tomography,” Opt. Express 9, 780–790 (2001).
    [CrossRef]
  5. V. K. Jaiswal, R. P. Singh, and R. Simon, “Producing optical vortices through forked holographic grating: study of polarization,” J. Mod. Opt. 57, 2031–2038 (2010).
    [CrossRef]
  6. I. Moreno, A. Lizana, J. Campos, A. Márquez, C. Iemmi, and M. J. Yzuel, “Combined Mueller and Jones matrix method for the evaluation of the complex modulation in a liquid-crystal-on-silicon display,” Opt. Lett. 33, 627–629 (2008).
    [CrossRef]
  7. 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]
  8. J. Tinbergen, Astronomical Polarimetry (Cambridge University, 1996).
  9. K. J. Voss and E. S. Fry, “Measurement of the Mueller matrix for ocean water,” Appl. Opt. 23, 4427–4439 (1984).
    [CrossRef]
  10. R. Simon and N. Mukunda, “Minimal three-component SU(2) gadget for polarization optics,” Phys. Lett. A 143, 165–169 (1990).
    [CrossRef]
  11. V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. Schirripa Spagnolo, “The Simon–Mukunda polarization gadget,” Eur. J. Phys. 17, 279–284 (1996).
    [CrossRef]
  12. B. Neethi Simon, C. M. Chandrashekar, and S. Simon, “Hamilton’s turns as visual tool-kit for designing of single qubit unitary gates,” Phys. Rev. A 85, 022323 (2012).
    [CrossRef]
  13. M. Hayman and J. P. Thayer, “Lidar polarization measurements of PMCs,” J. Atmos. Sol. Terr. Phys. 73, 2110–2117 (2011).
    [CrossRef]
  14. M. Hayman and J. P. Thayer, “General description of polarization in lidar using Stokes vectors and polar decomposition of Mueller matrices,” J. Opt. Soc. Am. A 29, 400–409 (2012).
    [CrossRef]
  15. U. Schilling, J. V. Zanthier, and G. S. Agarwal, “Measuring arbitrary-order coherences: tomography of single-mode multiphoton polarization-entangled states,” Phys. Rev. A 81, 013826 (2010).
    [CrossRef]
  16. J. C. Loredo, O. Ortz, R. Weingärtner, and F. De Zela, “Measurement of Pancharatnam phase by robust interferometric and polarimetric methods,” Phys. Rev. A 80, 012113 (2009).
    [CrossRef]
  17. D. Layden, M. F. G. Wood, and I. A. Vitkin, “Optimum selection of input polarization states in determining the sample Mueller matrix: a dual photoelastic polarimeter approach,” Opt. Express 20, 20466–20481 (2012).
    [CrossRef]
  18. W. S. Bicke and W. M. Bailey, “Stokes vectors, Mueller matrices and polarized light scattering,” Am. J. Phys. 53, 468–478 (1985).
    [CrossRef]
  19. R. M. A. Azzam, “Photopolarimetric measurement of the Mueller matrix by Fourier analysis of a single detected signal,” Opt. Lett. 2, 148–150 (1978).
    [CrossRef]
  20. D. Goldstein, Polarized Light (Marcel Dekker, 2003).
  21. R. Simon, “The connection between Mueller and Jones matrices of polarization optics,” Opt. Commun. 42, 293–297 (1982).
    [CrossRef]
  22. E. S. Fry and G. W. Kattawar, “Relationships between elements of the Stokes matrix,” Appl. Opt. 20, 2811–2814 (1981).
    [CrossRef]
  23. H. H. Ku, “Notes on the use of propagation of error formulas,” J. Res. Natl. Bur. Standards C 70C, 263–273 (1966).
  24. A. C. Melissinos, Experiments in Modern Physics (Academic, 1966), Sec. 10.4, pp. 467–479.
  25. D. F. V. James, P. G. Kwait, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
    [CrossRef]
  26. D. H. Goldstein, “Mueller matrix dual-rotating retarder polarimeter,” Appl. Opt. 31, 6676–6683 (1992).
    [CrossRef]
  27. K. Dev and A. Asundi, “Mueller Stokes polarimetric characterization of transmissive liquid crystal spatial light modulator,” Opt. Lasers Eng. 50, 599–607 (2012).
    [CrossRef]
  28. J. M. Bueno, “Polarimetry using liquid-crystal variable retarders: theory and calibration,” J. Opt. A 2, 216–222 (2000).
    [CrossRef]
  29. J. S. Baba, J. R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Cote, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7, 341–349 (2002).
    [CrossRef]
  30. A. Ling, K. P. Soh, A. L. Linares, and C. Kurtsiefer, “Experimental polarization state tomography using optimal polarimeters,” Phys. Rev. A 74, 022309 (2006).
    [CrossRef]
  31. M. W. Mitchell, C. W. Ellenor, S. Schneider, and A. M. Steinberg, “Diagnosis, prescription, and prognosis of a Bell-state filter by quantum process tomography,” Phys. Rev. Lett. 91, 120402 (2003).
    [CrossRef]

2012

B. Neethi Simon, C. M. Chandrashekar, and S. Simon, “Hamilton’s turns as visual tool-kit for designing of single qubit unitary gates,” Phys. Rev. A 85, 022323 (2012).
[CrossRef]

K. Dev and A. Asundi, “Mueller Stokes polarimetric characterization of transmissive liquid crystal spatial light modulator,” Opt. Lasers Eng. 50, 599–607 (2012).
[CrossRef]

M. Hayman and J. P. Thayer, “General description of polarization in lidar using Stokes vectors and polar decomposition of Mueller matrices,” J. Opt. Soc. Am. A 29, 400–409 (2012).
[CrossRef]

D. Layden, M. F. G. Wood, and I. A. Vitkin, “Optimum selection of input polarization states in determining the sample Mueller matrix: a dual photoelastic polarimeter approach,” Opt. Express 20, 20466–20481 (2012).
[CrossRef]

2011

M. Hayman and J. P. Thayer, “Lidar polarization measurements of PMCs,” J. Atmos. Sol. Terr. Phys. 73, 2110–2117 (2011).
[CrossRef]

2010

U. Schilling, J. V. Zanthier, and G. S. Agarwal, “Measuring arbitrary-order coherences: tomography of single-mode multiphoton polarization-entangled states,” Phys. Rev. A 81, 013826 (2010).
[CrossRef]

V. K. Jaiswal, R. P. Singh, and R. Simon, “Producing optical vortices through forked holographic grating: study of polarization,” J. Mod. Opt. 57, 2031–2038 (2010).
[CrossRef]

2009

J. C. Loredo, O. Ortz, R. Weingärtner, and F. De Zela, “Measurement of Pancharatnam phase by robust interferometric and polarimetric methods,” Phys. Rev. A 80, 012113 (2009).
[CrossRef]

2008

2007

2006

2003

M. W. Mitchell, C. W. Ellenor, S. Schneider, and A. M. Steinberg, “Diagnosis, prescription, and prognosis of a Bell-state filter by quantum process tomography,” Phys. Rev. Lett. 91, 120402 (2003).
[CrossRef]

2002

J. S. Baba, J. R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Cote, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7, 341–349 (2002).
[CrossRef]

2001

2000

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

1996

S. Y. Lu and R. A. Chipman, “Interpretation of Mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A 13, 1106–1113 (1996).
[CrossRef]

V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. Schirripa Spagnolo, “The Simon–Mukunda polarization gadget,” Eur. J. Phys. 17, 279–284 (1996).
[CrossRef]

1992

1990

R. Simon and N. Mukunda, “Minimal three-component SU(2) gadget for polarization optics,” Phys. Lett. A 143, 165–169 (1990).
[CrossRef]

1985

W. S. Bicke and W. M. Bailey, “Stokes vectors, Mueller matrices and polarized light scattering,” Am. J. Phys. 53, 468–478 (1985).
[CrossRef]

1984

1982

R. Simon, “The connection between Mueller and Jones matrices of polarization optics,” Opt. Commun. 42, 293–297 (1982).
[CrossRef]

1981

1978

1966

H. H. Ku, “Notes on the use of propagation of error formulas,” J. Res. Natl. Bur. Standards C 70C, 263–273 (1966).

Agarwal, G. S.

U. Schilling, J. V. Zanthier, and G. S. Agarwal, “Measuring arbitrary-order coherences: tomography of single-mode multiphoton polarization-entangled states,” Phys. Rev. A 81, 013826 (2010).
[CrossRef]

Asundi, A.

K. Dev and A. Asundi, “Mueller Stokes polarimetric characterization of transmissive liquid crystal spatial light modulator,” Opt. Lasers Eng. 50, 599–607 (2012).
[CrossRef]

Azzam, R. M. A.

Baba, J. S.

J. S. Baba, J. R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Cote, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7, 341–349 (2002).
[CrossRef]

Bagini, V.

V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. Schirripa Spagnolo, “The Simon–Mukunda polarization gadget,” Eur. J. Phys. 17, 279–284 (1996).
[CrossRef]

Bailey, W. M.

W. S. Bicke and W. M. Bailey, “Stokes vectors, Mueller matrices and polarized light scattering,” Am. J. Phys. 53, 468–478 (1985).
[CrossRef]

Bicke, W. S.

W. S. Bicke and W. M. Bailey, “Stokes vectors, Mueller matrices and polarized light scattering,” Am. J. Phys. 53, 468–478 (1985).
[CrossRef]

Borghi, R.

V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. Schirripa Spagnolo, “The Simon–Mukunda polarization gadget,” Eur. J. Phys. 17, 279–284 (1996).
[CrossRef]

Buddhiwant, P.

Bueno, J. M.

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

Cameron, B. D.

J. S. Baba, J. R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Cote, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7, 341–349 (2002).
[CrossRef]

Campos, J.

Chandrashekar, C. M.

B. Neethi Simon, C. M. Chandrashekar, and S. Simon, “Hamilton’s turns as visual tool-kit for designing of single qubit unitary gates,” Phys. Rev. A 85, 022323 (2012).
[CrossRef]

Chipman, R. A.

Chou, C.

Chou, N. K.

Chung, J. R.

J. S. Baba, J. R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Cote, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7, 341–349 (2002).
[CrossRef]

Cote, G. L.

J. S. Baba, J. R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Cote, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7, 341–349 (2002).
[CrossRef]

De Martino, A.

De Zela, F.

J. C. Loredo, O. Ortz, R. Weingärtner, and F. De Zela, “Measurement of Pancharatnam phase by robust interferometric and polarimetric methods,” Phys. Rev. A 80, 012113 (2009).
[CrossRef]

DeLaughter, A. H.

J. S. Baba, J. R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Cote, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7, 341–349 (2002).
[CrossRef]

Dev, K.

K. Dev and A. Asundi, “Mueller Stokes polarimetric characterization of transmissive liquid crystal spatial light modulator,” Opt. Lasers Eng. 50, 599–607 (2012).
[CrossRef]

Drévillon, B.

Ellenor, C. W.

M. W. Mitchell, C. W. Ellenor, S. Schneider, and A. M. Steinberg, “Diagnosis, prescription, and prognosis of a Bell-state filter by quantum process tomography,” Phys. Rev. Lett. 91, 120402 (2003).
[CrossRef]

Fercher, A. F.

Frezza, F.

V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. Schirripa Spagnolo, “The Simon–Mukunda polarization gadget,” Eur. J. Phys. 17, 279–284 (1996).
[CrossRef]

Fry, E. S.

Ghosh, N.

Goldstein, D.

D. Goldstein, Polarized Light (Marcel Dekker, 2003).

Goldstein, D. H.

Gori, F.

V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. Schirripa Spagnolo, “The Simon–Mukunda polarization gadget,” Eur. J. Phys. 17, 279–284 (1996).
[CrossRef]

Götzinger, E.

Gupta, P. K.

Hatit, S. B.

Hayman, M.

Hitzenberger, C. K.

Huang, H. J.

Iemmi, C.

Jaiswal, V. K.

V. K. Jaiswal, R. P. Singh, and R. Simon, “Producing optical vortices through forked holographic grating: study of polarization,” J. Mod. Opt. 57, 2031–2038 (2010).
[CrossRef]

James, D. F. V.

D. F. V. James, P. G. Kwait, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
[CrossRef]

Kattawar, G. W.

Ku, H. H.

H. H. Ku, “Notes on the use of propagation of error formulas,” J. Res. Natl. Bur. Standards C 70C, 263–273 (1966).

Kuo, W. C.

Kurtsiefer, C.

A. Ling, K. P. Soh, A. L. Linares, and C. Kurtsiefer, “Experimental polarization state tomography using optimal polarimeters,” Phys. Rev. A 74, 022309 (2006).
[CrossRef]

Kwait, P. G.

D. F. V. James, P. G. Kwait, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
[CrossRef]

Lai, C. M.

Layden, D.

Linares, A. L.

A. Ling, K. P. Soh, A. L. Linares, and C. Kurtsiefer, “Experimental polarization state tomography using optimal polarimeters,” Phys. Rev. A 74, 022309 (2006).
[CrossRef]

Ling, A.

A. Ling, K. P. Soh, A. L. Linares, and C. Kurtsiefer, “Experimental polarization state tomography using optimal polarimeters,” Phys. Rev. A 74, 022309 (2006).
[CrossRef]

Lizana, A.

Loredo, J. C.

J. C. Loredo, O. Ortz, R. Weingärtner, and F. De Zela, “Measurement of Pancharatnam phase by robust interferometric and polarimetric methods,” Phys. Rev. A 80, 012113 (2009).
[CrossRef]

Lu, S. Y.

Manhas, S.

Márquez, A.

Melissinos, A. C.

A. C. Melissinos, Experiments in Modern Physics (Academic, 1966), Sec. 10.4, pp. 467–479.

Mitchell, M. W.

M. W. Mitchell, C. W. Ellenor, S. Schneider, and A. M. Steinberg, “Diagnosis, prescription, and prognosis of a Bell-state filter by quantum process tomography,” Phys. Rev. Lett. 91, 120402 (2003).
[CrossRef]

Moreno, I.

Mukunda, N.

R. Simon and N. Mukunda, “Minimal three-component SU(2) gadget for polarization optics,” Phys. Lett. A 143, 165–169 (1990).
[CrossRef]

Munro, W. J.

D. F. V. James, P. G. Kwait, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
[CrossRef]

Neethi Simon, B.

B. Neethi Simon, C. M. Chandrashekar, and S. Simon, “Hamilton’s turns as visual tool-kit for designing of single qubit unitary gates,” Phys. Rev. A 85, 022323 (2012).
[CrossRef]

Novikova, T.

Ortz, O.

J. C. Loredo, O. Ortz, R. Weingärtner, and F. De Zela, “Measurement of Pancharatnam phase by robust interferometric and polarimetric methods,” Phys. Rev. A 80, 012113 (2009).
[CrossRef]

Pircher, M.

Santarsiero, M.

V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. Schirripa Spagnolo, “The Simon–Mukunda polarization gadget,” Eur. J. Phys. 17, 279–284 (1996).
[CrossRef]

Schettini, G.

V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. Schirripa Spagnolo, “The Simon–Mukunda polarization gadget,” Eur. J. Phys. 17, 279–284 (1996).
[CrossRef]

Schilling, U.

U. Schilling, J. V. Zanthier, and G. S. Agarwal, “Measuring arbitrary-order coherences: tomography of single-mode multiphoton polarization-entangled states,” Phys. Rev. A 81, 013826 (2010).
[CrossRef]

Schirripa Spagnolo, G.

V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. Schirripa Spagnolo, “The Simon–Mukunda polarization gadget,” Eur. J. Phys. 17, 279–284 (1996).
[CrossRef]

Schneider, S.

M. W. Mitchell, C. W. Ellenor, S. Schneider, and A. M. Steinberg, “Diagnosis, prescription, and prognosis of a Bell-state filter by quantum process tomography,” Phys. Rev. Lett. 91, 120402 (2003).
[CrossRef]

Shyu, J. J.

Simon, R.

V. K. Jaiswal, R. P. Singh, and R. Simon, “Producing optical vortices through forked holographic grating: study of polarization,” J. Mod. Opt. 57, 2031–2038 (2010).
[CrossRef]

R. Simon and N. Mukunda, “Minimal three-component SU(2) gadget for polarization optics,” Phys. Lett. A 143, 165–169 (1990).
[CrossRef]

R. Simon, “The connection between Mueller and Jones matrices of polarization optics,” Opt. Commun. 42, 293–297 (1982).
[CrossRef]

Simon, S.

B. Neethi Simon, C. M. Chandrashekar, and S. Simon, “Hamilton’s turns as visual tool-kit for designing of single qubit unitary gates,” Phys. Rev. A 85, 022323 (2012).
[CrossRef]

Singh, K.

Singh, R. P.

V. K. Jaiswal, R. P. Singh, and R. Simon, “Producing optical vortices through forked holographic grating: study of polarization,” J. Mod. Opt. 57, 2031–2038 (2010).
[CrossRef]

Soh, K. P.

A. Ling, K. P. Soh, A. L. Linares, and C. Kurtsiefer, “Experimental polarization state tomography using optimal polarimeters,” Phys. Rev. A 74, 022309 (2006).
[CrossRef]

Steinberg, A. M.

M. W. Mitchell, C. W. Ellenor, S. Schneider, and A. M. Steinberg, “Diagnosis, prescription, and prognosis of a Bell-state filter by quantum process tomography,” Phys. Rev. Lett. 91, 120402 (2003).
[CrossRef]

Sticker, M.

Swami, M. K.

Thayer, J. P.

Tinbergen, J.

J. Tinbergen, Astronomical Polarimetry (Cambridge University, 1996).

Vitkin, I. A.

Voss, K. J.

Wang, S. S.

Weingärtner, R.

J. C. Loredo, O. Ortz, R. Weingärtner, and F. De Zela, “Measurement of Pancharatnam phase by robust interferometric and polarimetric methods,” Phys. Rev. A 80, 012113 (2009).
[CrossRef]

White, A. G.

D. F. V. James, P. G. Kwait, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
[CrossRef]

Wood, M. F. G.

Yzuel, M. J.

Zanthier, J. V.

U. Schilling, J. V. Zanthier, and G. S. Agarwal, “Measuring arbitrary-order coherences: tomography of single-mode multiphoton polarization-entangled states,” Phys. Rev. A 81, 013826 (2010).
[CrossRef]

Am. J. Phys.

W. S. Bicke and W. M. Bailey, “Stokes vectors, Mueller matrices and polarized light scattering,” Am. J. Phys. 53, 468–478 (1985).
[CrossRef]

Appl. Opt.

Eur. J. Phys.

V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. Schirripa Spagnolo, “The Simon–Mukunda polarization gadget,” Eur. J. Phys. 17, 279–284 (1996).
[CrossRef]

J. Atmos. Sol. Terr. Phys.

M. Hayman and J. P. Thayer, “Lidar polarization measurements of PMCs,” J. Atmos. Sol. Terr. Phys. 73, 2110–2117 (2011).
[CrossRef]

J. Biomed. Opt.

J. S. Baba, J. R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Cote, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7, 341–349 (2002).
[CrossRef]

J. Mod. Opt.

V. K. Jaiswal, R. P. Singh, and R. Simon, “Producing optical vortices through forked holographic grating: study of polarization,” J. Mod. Opt. 57, 2031–2038 (2010).
[CrossRef]

J. Opt. A

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

J. Opt. Soc. Am. A

J. Res. Natl. Bur. Standards C

H. H. Ku, “Notes on the use of propagation of error formulas,” J. Res. Natl. Bur. Standards C 70C, 263–273 (1966).

Opt. Commun.

R. Simon, “The connection between Mueller and Jones matrices of polarization optics,” Opt. Commun. 42, 293–297 (1982).
[CrossRef]

Opt. Express

Opt. Lasers Eng.

K. Dev and A. Asundi, “Mueller Stokes polarimetric characterization of transmissive liquid crystal spatial light modulator,” Opt. Lasers Eng. 50, 599–607 (2012).
[CrossRef]

Opt. Lett.

Phys. Lett. A

R. Simon and N. Mukunda, “Minimal three-component SU(2) gadget for polarization optics,” Phys. Lett. A 143, 165–169 (1990).
[CrossRef]

Phys. Rev. A

D. F. V. James, P. G. Kwait, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
[CrossRef]

A. Ling, K. P. Soh, A. L. Linares, and C. Kurtsiefer, “Experimental polarization state tomography using optimal polarimeters,” Phys. Rev. A 74, 022309 (2006).
[CrossRef]

U. Schilling, J. V. Zanthier, and G. S. Agarwal, “Measuring arbitrary-order coherences: tomography of single-mode multiphoton polarization-entangled states,” Phys. Rev. A 81, 013826 (2010).
[CrossRef]

J. C. Loredo, O. Ortz, R. Weingärtner, and F. De Zela, “Measurement of Pancharatnam phase by robust interferometric and polarimetric methods,” Phys. Rev. A 80, 012113 (2009).
[CrossRef]

B. Neethi Simon, C. M. Chandrashekar, and S. Simon, “Hamilton’s turns as visual tool-kit for designing of single qubit unitary gates,” Phys. Rev. A 85, 022323 (2012).
[CrossRef]

Phys. Rev. Lett.

M. W. Mitchell, C. W. Ellenor, S. Schneider, and A. M. Steinberg, “Diagnosis, prescription, and prognosis of a Bell-state filter by quantum process tomography,” Phys. Rev. Lett. 91, 120402 (2003).
[CrossRef]

Other

D. Goldstein, Polarized Light (Marcel Dekker, 2003).

J. Tinbergen, Astronomical Polarimetry (Cambridge University, 1996).

A. C. Melissinos, Experiments in Modern Physics (Academic, 1966), Sec. 10.4, pp. 467–479.

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Figures (2)

Fig. 1.
Fig. 1.

Geometrical representation of (a) the Euler angles and (b) the three chosen tetrahedrons on the Poincaré sphere.

Fig. 2.
Fig. 2.

Experimental setup for the determination of the Mueller matrix using two SM gadgets.

Tables (3)

Tables Icon

Table 1. Angles of Rotation for Wave Plates in SM Gadget 1 to Generate the Four Vertices of Three Tetrahedrons

Tables Icon

Table 2. Difference in the Frobenius Norms of Experimental and Theoretical Projection Matrices with Three Tetrahedronsa

Tables Icon

Table 3. Experimental and Theoretical Mueller Matrices for Free Space, Half-Wave Plate (HWP), and Quarter-Wave Plate (QWP)

Equations (27)

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

S˜=MS,
Ω=[S1S2S3S4],Ω˜=[S˜1S˜2S˜3S˜4].
Ω˜=MΩ.
Λij=12(Sj)TS˜i=12α=14SjαS˜iα,
Λ=12ΩTΩ˜=12ΩTMΩ,
M=2(ΩT)1ΛΩ1.
ı=14qi=ı=14ui=ı=14vi=0;
ı=14qiui=ı=14uivi=ı=14viqi=0;
ı=14qi2=ı=14ui2=ı=14vi2=43.
Ω(1)=[1.0001.0001.0001.0001.0000.3330.3330.3340.0000.9430.4720.4710.0000.0000.8160.816],
Ω(2)=[1.0001.0001.0001.0000.6800.4300.7300.3900.7010.7520.3920.3500.2140.5000.5600.852],
Ω(3)=[1.0001.0001.0001.0000.5800.5800.5800.5800.5760.5800.5760.5800.5800.5720.5720.580],
ΩF=trace(Ω*Ω),
cF=ΩF*Ω1F.
u(ξ,η,ζ)=Qπ4+ξ2Hπ4+ξ+ηζ4Qπ4ζ2,
(Qθ)1=Qπ2+θ,(Hθ)1=Hπ2+θand(Qθ)1=Qπ2+θ.
J=(ExEy),I=|Ex|2+|Ey|2.
Joutput=JP2JQ2JH2JQ2JsampleJQ1JH1JQ1JP1Jinput.
JR(ϕ,θ)=(eiϕ2cos2(θ)+eiϕ2sin2(θ)(eiϕ2eiϕ2)cos(θ)sin(θ)(eiϕ2eiϕ2)cos(θ)sin(θ)eiϕ2sin2(θ)+eiϕ2cos2(θ)),
Jp(θ)=(cos2(θ)cos(θ)sin(θ)cos(θ)sin(θ)sin2(θ)).
Nfree=[1.0000.0080.002i0.0100.000i0.999+0.013i0.008+0.002i0.0060.0130.004i0.011+0.001i0.010+0.000i0.013+0.004i0.0000.004+0.005i0.9990.013i0.0110.001i0.0040.005i1.006],NH=[1.0000.0000.005i0.003+0.002i1.0000.009i0.000+0.005i0.0030.009+0.008i0.000+0.000i0.0030.002i0.0090.008i0.0070.008+0.003i1.000+0.009i0.0000.000i0.0080.003i1.011],NQ=[1.0000.0050.003i0.003+0.004i0.001+0.999i0.005+0.003i0.0040.0000.000i0.004+0.002i0.0030.004i0.000+0.000i0.0020.007+0.009i0.0010.999i0.0040.002i0.0070.009i1.015].
N2=tr(N)·N,
tr(MMT)4m002.
Λij=I[JP(θP2)·JR(ϕRQ2,θQ2j)·JR(ϕRH2,θH2j)·JR(ϕRQ2,θQ2j)·O·JR(ϕRQ1,θQ1i)·JR(ϕRH1,θH1i)·JR(ϕRQ1,θQ1i)·JP(θP1)·L],
σΛij=allx(Λijx)2σx2,
ΔθP1=ΔθP2=±0.03°,ΔϕRH=ΔϕRQ=±1.26°,ΔθRi=ΔθRj=±0.04°,fori,j=1to3.
σM=[0.0070.0120.0120.0130.0120.0210.0210.0220.0120.0210.0190.0200.0130.0220.0200.026].

Metrics