Abstract

A spectroscopic Mueller matrix polarimeter with four photoelastic modulators (PEMs) and no moving parts is introduced. In the 4-PEM polarimeter, all the elements of the Mueller matrix are simultaneously determined from the analysis of the frequencies of the time-dependent intensity of the light beam.

© 2012 Optical Society of America

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References

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  1. B. Wang, E. Hinds, and E. Krivoy, “Basic optical properties of the photoelastic modulator part II: residual birefringence in the optical element,” Proc. SPIE 7461, 746110 (2009).
    [CrossRef]
  2. G. E. Jellison and F. A. Modine, “Two-modulator generalized ellipsometry: theory,” Appl. Opt. 36, 8190–8198 (1997).
    [CrossRef]
  3. G. E. Jellison and F. A. Modine, “Two-modulator generalized ellipsometry: experiment and calibration,” Appl. Opt. 36, 8184–8189 (1997).
    [CrossRef]
  4. G. E. Jellison and F. Modine, “Two modulator generalized ellipsometer for complete Mueller matrix measurement,” U.S. patent 5,956,147 (21 September, 1999).
  5. Jellison, J. D. Hunn, and C. M. Rouleau, “Normal-incidence generalized ellipsometry using the two-modulator generalized ellipsometry microscope,” Appl. Opt. 45, 5479–5488 (2006).
    [CrossRef]
  6. G. E. Jellison, C. O. Griffiths, D. E. Holcomb, and C. M. Rouleau, “Transmission two-modulator generalized ellipsometry measurements,” Appl. Opt. 41, 6555–6566 (2002).
    [CrossRef]
  7. O. Arteaga, Z. El-Hachemi, A. Canillas, and J. M. Ribó, “Transmission Mueller matrix ellipsometry of chirality switching phenomena,” Thin Solid Films 519, 2617–2623 (2011).
    [CrossRef]
  8. O. Arteaga, “Mueller matrix polarimetry of anisotropic chiral media,” Ph.D. thesis (University of Barcelona, 2010).
  9. L. Cross and D. Hore, “Dual-modulator broadband infrared Mueller matrix ellipsometry,” Appl. Opt. 51, 5100–5110 (2012).
    [CrossRef]
  10. R. C. Thompson, J. R. Bottiger, and E. S. Fry, “Measurement of polarized light interactions via the Mueller matrix,” Appl. Opt. 19, 1323–1332 (1980).
    [CrossRef]
  11. 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]
  12. G. E. Jellison and F. A. Modine, “Accurate calibration of a photoelastic modulator in polarization modulation ellipsometry,” Proc. SPIE 1166, 231–241 (1990).
  13. O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
    [CrossRef]
  14. G. E. Jellison, F. A. Modine, and C. Chen, “Calibration procedures for a two-modular generalized ellipsometer,” Proc. SPIE 3754, 150–160 (1999).
    [CrossRef]
  15. A. Zeng, L. Huang, Z. Dong, J. Hu, H. Huang, and X. Wang, “Calibration method for a photoelastic modulator with a peak retardation of less than a half-wavelength,” Appl. Opt. 46, 699–703 (2007).
    [CrossRef]
  16. O. Arteaga, J. Freudenthal, and B. Kahr, “Reckoning electromagnetic principles with polarimetric measurements of anisotropic optically active crystals,” J. Appl. Crystallogr. 45, 279–291 (2012).
    [CrossRef]
  17. Y. Velikhov, I. Pritula, I. Canina, M. Kolybayeva, V. Puzikov, and A. Levchenko, “Growth and properties of dyed KDP crystals,” Cryst. Res. Technol. 42, 27–33 (2007).
    [CrossRef]
  18. I. Pritula, V. Gayvoronsky, Y. Gromov, M. Kopylovsky, M. Kolybaeva, V. Puzikov, A. Kosinova, Y. Savvin, Y. Velikhov, and A. Levchenko, “Linear and nonlinear optical properties of dye-doped KDP crystals: Effect of thermal treatment,” Opt. Commun. 282, 1141–1147 (2009).
    [CrossRef]
  19. B. Kahr and R. W. Gurney, “Dyeing crystals,” Chem. Rev. 101, 893–952 (2001).
    [CrossRef]
  20. Y. Bing, D. Selassie, R. H. Paradise, C. Isborn, N. Kramer, M. Sadilek, W. Kaminsky, and B. Kahr, “Circular dichroism tensor of a triarylmethyl propeller in sodium chlorate crystals,” J. Am. Chem. Soc. 132, 7454–7465 (2010).
    [CrossRef]

2012 (2)

O. Arteaga, J. Freudenthal, and B. Kahr, “Reckoning electromagnetic principles with polarimetric measurements of anisotropic optically active crystals,” J. Appl. Crystallogr. 45, 279–291 (2012).
[CrossRef]

L. Cross and D. Hore, “Dual-modulator broadband infrared Mueller matrix ellipsometry,” Appl. Opt. 51, 5100–5110 (2012).
[CrossRef]

2011 (1)

O. Arteaga, Z. El-Hachemi, A. Canillas, and J. M. Ribó, “Transmission Mueller matrix ellipsometry of chirality switching phenomena,” Thin Solid Films 519, 2617–2623 (2011).
[CrossRef]

2010 (1)

Y. Bing, D. Selassie, R. H. Paradise, C. Isborn, N. Kramer, M. Sadilek, W. Kaminsky, and B. Kahr, “Circular dichroism tensor of a triarylmethyl propeller in sodium chlorate crystals,” J. Am. Chem. Soc. 132, 7454–7465 (2010).
[CrossRef]

2009 (2)

B. Wang, E. Hinds, and E. Krivoy, “Basic optical properties of the photoelastic modulator part II: residual birefringence in the optical element,” Proc. SPIE 7461, 746110 (2009).
[CrossRef]

I. Pritula, V. Gayvoronsky, Y. Gromov, M. Kopylovsky, M. Kolybaeva, V. Puzikov, A. Kosinova, Y. Savvin, Y. Velikhov, and A. Levchenko, “Linear and nonlinear optical properties of dye-doped KDP crystals: Effect of thermal treatment,” Opt. Commun. 282, 1141–1147 (2009).
[CrossRef]

2007 (2)

Y. Velikhov, I. Pritula, I. Canina, M. Kolybayeva, V. Puzikov, and A. Levchenko, “Growth and properties of dyed KDP crystals,” Cryst. Res. Technol. 42, 27–33 (2007).
[CrossRef]

A. Zeng, L. Huang, Z. Dong, J. Hu, H. Huang, and X. Wang, “Calibration method for a photoelastic modulator with a peak retardation of less than a half-wavelength,” Appl. Opt. 46, 699–703 (2007).
[CrossRef]

2006 (1)

2002 (1)

2001 (1)

B. Kahr and R. W. Gurney, “Dyeing crystals,” Chem. Rev. 101, 893–952 (2001).
[CrossRef]

1999 (1)

G. E. Jellison, F. A. Modine, and C. Chen, “Calibration procedures for a two-modular generalized ellipsometer,” Proc. SPIE 3754, 150–160 (1999).
[CrossRef]

1997 (2)

1990 (2)

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]

G. E. Jellison and F. A. Modine, “Accurate calibration of a photoelastic modulator in polarization modulation ellipsometry,” Proc. SPIE 1166, 231–241 (1990).

1989 (1)

O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
[CrossRef]

1980 (1)

Acher, O.

O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
[CrossRef]

Arteaga, O.

O. Arteaga, J. Freudenthal, and B. Kahr, “Reckoning electromagnetic principles with polarimetric measurements of anisotropic optically active crystals,” J. Appl. Crystallogr. 45, 279–291 (2012).
[CrossRef]

O. Arteaga, Z. El-Hachemi, A. Canillas, and J. M. Ribó, “Transmission Mueller matrix ellipsometry of chirality switching phenomena,” Thin Solid Films 519, 2617–2623 (2011).
[CrossRef]

O. Arteaga, “Mueller matrix polarimetry of anisotropic chiral media,” Ph.D. thesis (University of Barcelona, 2010).

Badoz, J.

Bigan, E.

O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
[CrossRef]

Bing, Y.

Y. Bing, D. Selassie, R. H. Paradise, C. Isborn, N. Kramer, M. Sadilek, W. Kaminsky, and B. Kahr, “Circular dichroism tensor of a triarylmethyl propeller in sodium chlorate crystals,” J. Am. Chem. Soc. 132, 7454–7465 (2010).
[CrossRef]

Bottiger, J. R.

Canillas, A.

O. Arteaga, Z. El-Hachemi, A. Canillas, and J. M. Ribó, “Transmission Mueller matrix ellipsometry of chirality switching phenomena,” Thin Solid Films 519, 2617–2623 (2011).
[CrossRef]

Canina, I.

Y. Velikhov, I. Pritula, I. Canina, M. Kolybayeva, V. Puzikov, and A. Levchenko, “Growth and properties of dyed KDP crystals,” Cryst. Res. Technol. 42, 27–33 (2007).
[CrossRef]

Canit, J. C.

Chen, C.

G. E. Jellison, F. A. Modine, and C. Chen, “Calibration procedures for a two-modular generalized ellipsometer,” Proc. SPIE 3754, 150–160 (1999).
[CrossRef]

Cross, L.

Dong, Z.

Drévillon, B.

O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
[CrossRef]

El-Hachemi, Z.

O. Arteaga, Z. El-Hachemi, A. Canillas, and J. M. Ribó, “Transmission Mueller matrix ellipsometry of chirality switching phenomena,” Thin Solid Films 519, 2617–2623 (2011).
[CrossRef]

Freudenthal, J.

O. Arteaga, J. Freudenthal, and B. Kahr, “Reckoning electromagnetic principles with polarimetric measurements of anisotropic optically active crystals,” J. Appl. Crystallogr. 45, 279–291 (2012).
[CrossRef]

Fry, E. S.

Gayvoronsky, V.

I. Pritula, V. Gayvoronsky, Y. Gromov, M. Kopylovsky, M. Kolybaeva, V. Puzikov, A. Kosinova, Y. Savvin, Y. Velikhov, and A. Levchenko, “Linear and nonlinear optical properties of dye-doped KDP crystals: Effect of thermal treatment,” Opt. Commun. 282, 1141–1147 (2009).
[CrossRef]

Griffiths, C. O.

Gromov, Y.

I. Pritula, V. Gayvoronsky, Y. Gromov, M. Kopylovsky, M. Kolybaeva, V. Puzikov, A. Kosinova, Y. Savvin, Y. Velikhov, and A. Levchenko, “Linear and nonlinear optical properties of dye-doped KDP crystals: Effect of thermal treatment,” Opt. Commun. 282, 1141–1147 (2009).
[CrossRef]

Gurney, R. W.

B. Kahr and R. W. Gurney, “Dyeing crystals,” Chem. Rev. 101, 893–952 (2001).
[CrossRef]

Hinds, E.

B. Wang, E. Hinds, and E. Krivoy, “Basic optical properties of the photoelastic modulator part II: residual birefringence in the optical element,” Proc. SPIE 7461, 746110 (2009).
[CrossRef]

Holcomb, D. E.

Hore, D.

Hu, J.

Huang, H.

Huang, L.

Hunn, J. D.

Isborn, C.

Y. Bing, D. Selassie, R. H. Paradise, C. Isborn, N. Kramer, M. Sadilek, W. Kaminsky, and B. Kahr, “Circular dichroism tensor of a triarylmethyl propeller in sodium chlorate crystals,” J. Am. Chem. Soc. 132, 7454–7465 (2010).
[CrossRef]

Jellison,

Jellison, G. E.

G. E. Jellison, C. O. Griffiths, D. E. Holcomb, and C. M. Rouleau, “Transmission two-modulator generalized ellipsometry measurements,” Appl. Opt. 41, 6555–6566 (2002).
[CrossRef]

G. E. Jellison, F. A. Modine, and C. Chen, “Calibration procedures for a two-modular generalized ellipsometer,” Proc. SPIE 3754, 150–160 (1999).
[CrossRef]

G. E. Jellison and F. A. Modine, “Two-modulator generalized ellipsometry: experiment and calibration,” Appl. Opt. 36, 8184–8189 (1997).
[CrossRef]

G. E. Jellison and F. A. Modine, “Two-modulator generalized ellipsometry: theory,” Appl. Opt. 36, 8190–8198 (1997).
[CrossRef]

G. E. Jellison and F. A. Modine, “Accurate calibration of a photoelastic modulator in polarization modulation ellipsometry,” Proc. SPIE 1166, 231–241 (1990).

G. E. Jellison and F. Modine, “Two modulator generalized ellipsometer for complete Mueller matrix measurement,” U.S. patent 5,956,147 (21 September, 1999).

Kahr, B.

O. Arteaga, J. Freudenthal, and B. Kahr, “Reckoning electromagnetic principles with polarimetric measurements of anisotropic optically active crystals,” J. Appl. Crystallogr. 45, 279–291 (2012).
[CrossRef]

Y. Bing, D. Selassie, R. H. Paradise, C. Isborn, N. Kramer, M. Sadilek, W. Kaminsky, and B. Kahr, “Circular dichroism tensor of a triarylmethyl propeller in sodium chlorate crystals,” J. Am. Chem. Soc. 132, 7454–7465 (2010).
[CrossRef]

B. Kahr and R. W. Gurney, “Dyeing crystals,” Chem. Rev. 101, 893–952 (2001).
[CrossRef]

Kaminsky, W.

Y. Bing, D. Selassie, R. H. Paradise, C. Isborn, N. Kramer, M. Sadilek, W. Kaminsky, and B. Kahr, “Circular dichroism tensor of a triarylmethyl propeller in sodium chlorate crystals,” J. Am. Chem. Soc. 132, 7454–7465 (2010).
[CrossRef]

Kolybaeva, M.

I. Pritula, V. Gayvoronsky, Y. Gromov, M. Kopylovsky, M. Kolybaeva, V. Puzikov, A. Kosinova, Y. Savvin, Y. Velikhov, and A. Levchenko, “Linear and nonlinear optical properties of dye-doped KDP crystals: Effect of thermal treatment,” Opt. Commun. 282, 1141–1147 (2009).
[CrossRef]

Kolybayeva, M.

Y. Velikhov, I. Pritula, I. Canina, M. Kolybayeva, V. Puzikov, and A. Levchenko, “Growth and properties of dyed KDP crystals,” Cryst. Res. Technol. 42, 27–33 (2007).
[CrossRef]

Kopylovsky, M.

I. Pritula, V. Gayvoronsky, Y. Gromov, M. Kopylovsky, M. Kolybaeva, V. Puzikov, A. Kosinova, Y. Savvin, Y. Velikhov, and A. Levchenko, “Linear and nonlinear optical properties of dye-doped KDP crystals: Effect of thermal treatment,” Opt. Commun. 282, 1141–1147 (2009).
[CrossRef]

Kosinova, A.

I. Pritula, V. Gayvoronsky, Y. Gromov, M. Kopylovsky, M. Kolybaeva, V. Puzikov, A. Kosinova, Y. Savvin, Y. Velikhov, and A. Levchenko, “Linear and nonlinear optical properties of dye-doped KDP crystals: Effect of thermal treatment,” Opt. Commun. 282, 1141–1147 (2009).
[CrossRef]

Kramer, N.

Y. Bing, D. Selassie, R. H. Paradise, C. Isborn, N. Kramer, M. Sadilek, W. Kaminsky, and B. Kahr, “Circular dichroism tensor of a triarylmethyl propeller in sodium chlorate crystals,” J. Am. Chem. Soc. 132, 7454–7465 (2010).
[CrossRef]

Krivoy, E.

B. Wang, E. Hinds, and E. Krivoy, “Basic optical properties of the photoelastic modulator part II: residual birefringence in the optical element,” Proc. SPIE 7461, 746110 (2009).
[CrossRef]

Levchenko, A.

I. Pritula, V. Gayvoronsky, Y. Gromov, M. Kopylovsky, M. Kolybaeva, V. Puzikov, A. Kosinova, Y. Savvin, Y. Velikhov, and A. Levchenko, “Linear and nonlinear optical properties of dye-doped KDP crystals: Effect of thermal treatment,” Opt. Commun. 282, 1141–1147 (2009).
[CrossRef]

Y. Velikhov, I. Pritula, I. Canina, M. Kolybayeva, V. Puzikov, and A. Levchenko, “Growth and properties of dyed KDP crystals,” Cryst. Res. Technol. 42, 27–33 (2007).
[CrossRef]

Modine, F.

G. E. Jellison and F. Modine, “Two modulator generalized ellipsometer for complete Mueller matrix measurement,” U.S. patent 5,956,147 (21 September, 1999).

Modine, F. A.

G. E. Jellison, F. A. Modine, and C. Chen, “Calibration procedures for a two-modular generalized ellipsometer,” Proc. SPIE 3754, 150–160 (1999).
[CrossRef]

G. E. Jellison and F. A. Modine, “Two-modulator generalized ellipsometry: experiment and calibration,” Appl. Opt. 36, 8184–8189 (1997).
[CrossRef]

G. E. Jellison and F. A. Modine, “Two-modulator generalized ellipsometry: theory,” Appl. Opt. 36, 8190–8198 (1997).
[CrossRef]

G. E. Jellison and F. A. Modine, “Accurate calibration of a photoelastic modulator in polarization modulation ellipsometry,” Proc. SPIE 1166, 231–241 (1990).

Paradise, R. H.

Y. Bing, D. Selassie, R. H. Paradise, C. Isborn, N. Kramer, M. Sadilek, W. Kaminsky, and B. Kahr, “Circular dichroism tensor of a triarylmethyl propeller in sodium chlorate crystals,” J. Am. Chem. Soc. 132, 7454–7465 (2010).
[CrossRef]

Pritula, I.

I. Pritula, V. Gayvoronsky, Y. Gromov, M. Kopylovsky, M. Kolybaeva, V. Puzikov, A. Kosinova, Y. Savvin, Y. Velikhov, and A. Levchenko, “Linear and nonlinear optical properties of dye-doped KDP crystals: Effect of thermal treatment,” Opt. Commun. 282, 1141–1147 (2009).
[CrossRef]

Y. Velikhov, I. Pritula, I. Canina, M. Kolybayeva, V. Puzikov, and A. Levchenko, “Growth and properties of dyed KDP crystals,” Cryst. Res. Technol. 42, 27–33 (2007).
[CrossRef]

Puzikov, V.

I. Pritula, V. Gayvoronsky, Y. Gromov, M. Kopylovsky, M. Kolybaeva, V. Puzikov, A. Kosinova, Y. Savvin, Y. Velikhov, and A. Levchenko, “Linear and nonlinear optical properties of dye-doped KDP crystals: Effect of thermal treatment,” Opt. Commun. 282, 1141–1147 (2009).
[CrossRef]

Y. Velikhov, I. Pritula, I. Canina, M. Kolybayeva, V. Puzikov, and A. Levchenko, “Growth and properties of dyed KDP crystals,” Cryst. Res. Technol. 42, 27–33 (2007).
[CrossRef]

Ribó, J. M.

O. Arteaga, Z. El-Hachemi, A. Canillas, and J. M. Ribó, “Transmission Mueller matrix ellipsometry of chirality switching phenomena,” Thin Solid Films 519, 2617–2623 (2011).
[CrossRef]

Rouleau, C. M.

Sadilek, M.

Y. Bing, D. Selassie, R. H. Paradise, C. Isborn, N. Kramer, M. Sadilek, W. Kaminsky, and B. Kahr, “Circular dichroism tensor of a triarylmethyl propeller in sodium chlorate crystals,” J. Am. Chem. Soc. 132, 7454–7465 (2010).
[CrossRef]

Savvin, Y.

I. Pritula, V. Gayvoronsky, Y. Gromov, M. Kopylovsky, M. Kolybaeva, V. Puzikov, A. Kosinova, Y. Savvin, Y. Velikhov, and A. Levchenko, “Linear and nonlinear optical properties of dye-doped KDP crystals: Effect of thermal treatment,” Opt. Commun. 282, 1141–1147 (2009).
[CrossRef]

Selassie, D.

Y. Bing, D. Selassie, R. H. Paradise, C. Isborn, N. Kramer, M. Sadilek, W. Kaminsky, and B. Kahr, “Circular dichroism tensor of a triarylmethyl propeller in sodium chlorate crystals,” J. Am. Chem. Soc. 132, 7454–7465 (2010).
[CrossRef]

Silverman, M. P.

Thompson, R. C.

Velikhov, Y.

I. Pritula, V. Gayvoronsky, Y. Gromov, M. Kopylovsky, M. Kolybaeva, V. Puzikov, A. Kosinova, Y. Savvin, Y. Velikhov, and A. Levchenko, “Linear and nonlinear optical properties of dye-doped KDP crystals: Effect of thermal treatment,” Opt. Commun. 282, 1141–1147 (2009).
[CrossRef]

Y. Velikhov, I. Pritula, I. Canina, M. Kolybayeva, V. Puzikov, and A. Levchenko, “Growth and properties of dyed KDP crystals,” Cryst. Res. Technol. 42, 27–33 (2007).
[CrossRef]

Wang, B.

B. Wang, E. Hinds, and E. Krivoy, “Basic optical properties of the photoelastic modulator part II: residual birefringence in the optical element,” Proc. SPIE 7461, 746110 (2009).
[CrossRef]

Wang, X.

Zeng, A.

Appl. Opt. (7)

Chem. Rev. (1)

B. Kahr and R. W. Gurney, “Dyeing crystals,” Chem. Rev. 101, 893–952 (2001).
[CrossRef]

Cryst. Res. Technol. (1)

Y. Velikhov, I. Pritula, I. Canina, M. Kolybayeva, V. Puzikov, and A. Levchenko, “Growth and properties of dyed KDP crystals,” Cryst. Res. Technol. 42, 27–33 (2007).
[CrossRef]

J. Am. Chem. Soc. (1)

Y. Bing, D. Selassie, R. H. Paradise, C. Isborn, N. Kramer, M. Sadilek, W. Kaminsky, and B. Kahr, “Circular dichroism tensor of a triarylmethyl propeller in sodium chlorate crystals,” J. Am. Chem. Soc. 132, 7454–7465 (2010).
[CrossRef]

J. Appl. Crystallogr. (1)

O. Arteaga, J. Freudenthal, and B. Kahr, “Reckoning electromagnetic principles with polarimetric measurements of anisotropic optically active crystals,” J. Appl. Crystallogr. 45, 279–291 (2012).
[CrossRef]

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

Opt. Commun. (1)

I. Pritula, V. Gayvoronsky, Y. Gromov, M. Kopylovsky, M. Kolybaeva, V. Puzikov, A. Kosinova, Y. Savvin, Y. Velikhov, and A. Levchenko, “Linear and nonlinear optical properties of dye-doped KDP crystals: Effect of thermal treatment,” Opt. Commun. 282, 1141–1147 (2009).
[CrossRef]

Proc. SPIE (3)

G. E. Jellison, F. A. Modine, and C. Chen, “Calibration procedures for a two-modular generalized ellipsometer,” Proc. SPIE 3754, 150–160 (1999).
[CrossRef]

G. E. Jellison and F. A. Modine, “Accurate calibration of a photoelastic modulator in polarization modulation ellipsometry,” Proc. SPIE 1166, 231–241 (1990).

B. Wang, E. Hinds, and E. Krivoy, “Basic optical properties of the photoelastic modulator part II: residual birefringence in the optical element,” Proc. SPIE 7461, 746110 (2009).
[CrossRef]

Rev. Sci. Instrum. (1)

O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
[CrossRef]

Thin Solid Films (1)

O. Arteaga, Z. El-Hachemi, A. Canillas, and J. M. Ribó, “Transmission Mueller matrix ellipsometry of chirality switching phenomena,” Thin Solid Films 519, 2617–2623 (2011).
[CrossRef]

Other (2)

O. Arteaga, “Mueller matrix polarimetry of anisotropic chiral media,” Ph.D. thesis (University of Barcelona, 2010).

G. E. Jellison and F. Modine, “Two modulator generalized ellipsometer for complete Mueller matrix measurement,” U.S. patent 5,956,147 (21 September, 1999).

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Figures (6)

Fig. 1.
Fig. 1.

Values of Bessel functions Jn of different orders as a function of the amplitude of modulation. The values at 2.4048 and 0.85 rad are compared.

Fig. 2.
Fig. 2.

The graphs on the left side show the first 15, 000 points (at 1μs/point) of the experimentally detected waveform in the straight-through configuration. In calibration I, A0=A1=A2=A3=2.4048, while for calibration II, A0=A3=2.4048 and A1=A2=0.85. The right side graphs show the fast Fourier transform power spectrum of the waveform.

Fig. 3.
Fig. 3.

Schematic diagram of the 4-PEM. Light travels from left to right. A, xenon arc lamp and monochromator; B, optical fiber; C, lenses; D, polarizer; E, PEM at 90°; F, PEM at 45°; G, sample and rotation stage; H, iris; I, detector.

Fig. 4.
Fig. 4.

Static retardations for each modulator or combination of modulators as a function of the wavelength. The solid curves indicate a fitting to a Cauchy dispersion relation.

Fig. 5.
Fig. 5.

Measured Mueller matrix for a multiorder 532 nm quarter-wave plate (Thorlabs) with the fast axis oriented at 64.75±0.05°.

Fig. 6.
Fig. 6.

Example of a spatially resolved Mueller matrix measured at 460 nm for a portion of a KH2PO4 crystal dyed with xylenol orange [18]. The scanning covers an area of 2.8mm×2.1mm. The numbers on the top of each matrix element indicate the scaling factor of each element.

Tables (1)

Tables Icon

Table 1. Frequency Components of the Fourier Analysis that is Used in the Measurement of the Mueller Matrix or in the Calibrationa

Equations (61)

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

Mm=[1000010000YδXδ00XδYδ],
Yδcos(δ),
Xδsin(δ).
δ(t)=Asin(ωt+ϕ)+δ0,
SPSG=I02R(θm1)Mm1R(θm1)R(θm0)Mm0R(θm0)R(θp0)Mp0R(θp0)[1000],
R(θx)=[10000CxSx00SxCx00001],
SPSG=I02[1Sm1[Y1δ(2εb02εb1Y0δ)+X0δX1δ]Cm1(Y0δ+4εb0εb1)Cm1[Y1δ(2εb02εb1Y0δ)+X0δX1δ]Sm1(Y0δ+4εb0εb1)X1δY1δX1δ(2εb02εb1Y0δ)].
SPSAT=[1000]R(θp1)Mp1R(θp1)R(θm3)Mm3R(θm3)R(θm2)Mm2R(θm2).
SPSAT=I02[1Sm2[Y2δ(2εb32εb2Y3δ)+X2δX3δ]Cm2(Y3δ+4εb2εb3)Cm2[Y2δ(2εb32εb2Y3δ)+X2δX3δ]Sm2(Y3δ+4εb2εb3)X3δY2δX2δ(2εb32εb2Y3δ)].
I(t)=SPSATMSPSG,
I=[m00m01m02m03m10m11m12m13m20m21m22m23m30m31m32m33]T[1Cm1Y0δSm1X0δX1δCm1X0δX1δSm1Y0δX0δY1δSm2X2δX3δCm2Y3δ(Cm1Y0δ+Sm1X0δX1δ)(Cm2Y3δSm2X2δX3δ)(Sm1Y0δCm1X0δX1δ)(Cm2Y3δSm2X2δX3δ)X0δY1δ(Cm2Y3δSm2X2δX3δ)Sm2Y3δCm2X2δX3δ(Cm1Y0δ+Sm1X0δX1δ)(Sm2Y3δ+Cm2X2δX3δ)(Sm1Y0δCm1X0δX1δ)(Sm2Y3δ+Cm2X2δX3δ)X0δY1δ(Sm2Y3δ+Cm2X2δX3δ)X3δY2δX3δY2δ(Cm1Y0δ+Sm1X0δX1δ)X3δY2δ(Sm1Y0δCm1X0δX1δ)X0δY1δX3δY2δ].
M=[1IX0X1IY0IX0Y1IX2X3IX0X1X2X3IY0X2X3IX0Y1X2X3IY3IX0X1Y3IY0Y3IX0Y1Y3IY2X3IX0X1Y2X3IY0Y2X3IX0Y1Y2X3],
Xδ=sin[Asin(ωt+ϕ)+δ]X+δY,
Yδ=cos[Asin(ωt+ϕ)+δ]YδX,
X=2k=1J2k1(A)sin[(2k1)(ωt+ϕ)],
Y=J0(A)+2k=1J2k(A)cos[2k(ωt+ϕ)].
X0X1=2J1(A0)J1(A1)[cos[(ω0ω1)t+ϕ0ϕ1]cos[(ω0+ω1)t+ϕ0+ϕ1]]+2J1(A0)J3(A1)[cos[(ω03ω1)t+ϕ03ϕ1]cos[(ω0+3ω1)t+ϕ0+3ϕ1]]+2J3(A0)J1(A1)[cos[(3ω0ω1)t+3ϕ0ϕ1]cos[(3ω0+ω1)t+3ϕ0+ϕ1]]+2J3(A0)J3(A1)[cos[3(ω0ω1)t+3(ϕ0ϕ1)]cos[3(ω0+ω1)t+3(ϕ0+ϕ1)]]+.
I(t)=Idc+2k=1IkRk[sin(Ωkt+Φk)],
IX0X1=sign[cos(ϕmϕ0+ϕ1)]BX0X12J1(A0)J1(A1),
IY0=sign[cos(ϕm+2ϕ0)]BY02J2(A0),
IX0Y1=sign[cos(ϕm+ϕ090°)]BX0Y12J1(A0)J0(A1),
IX2X3=sign[cos(ϕm+ϕ2+ϕ3180°)]BX2X32J1(A0)J0(A1),
IX0X1X2X3=sign[cos(ϕm+ϕ0+ϕ1ϕ2+ϕ3180°)]BX0X1X2X32J1(A0)J1(A1)J1(A2)J1(A3),
IY0X2X3=sign[cos(ϕm+2ϕ0+ϕ2+ϕ3180°)]BY0X2X32J2(A0)J1(A2)J1(A3),
IX0Y1X2X3=sign[cos(ϕm+ϕ0+ϕ2+ϕ3+90°)]BX0Y1X2X32J1(A0)J0(A1)J1(A2)J1(A3),
IY3=sign[cos(ϕm+ϕ3)]BY32J2(A3),
IX0X1Y3=sign[cos(ϕmϕ0+ϕ1+2ϕ3)]BX0X1Y32J1(A0)J1(A1)J2(A3),
IY0Y3=sign[cos(ϕm+2ϕ02ϕ3)]BY0Y32J2(A0)J2(A3),
IX0Y1Y3=sign[cos(ϕm+ϕ02ϕ390°)]BX0Y1Y32J1(A0)J0(A1)J2(A3),
IY2X3=sign[cos(ϕm+ϕ390°)]BY2X32J0(A2)J1(A3),
IX0X1Y2X3=sign[cos(ϕm+ϕ0+ϕ1+ϕ3+90°)]BX0X1Y2X32J1(A0)J1(A1)J0(A2)J1(A3),
IY0Y2X3=sign[cos(ϕm+2ϕ0ϕ3+90°)]BY0Y1X32J2(A0)J0(A2)J1(A3),
IX0Y1Y2X3=sign[cos(ϕm+ϕ0+ϕ3180°)]BX0Y1Y2X32J1(A0)J0(A1)J0(A2)J1(A3).
Bj,dc=1,Bj,X0X1=sin(δ0(jΔt))sin(δ1(jΔt)),Bj,Y0=cos(δ0(jΔt)),Bj,X0Y1=sin(δ0(jΔt))cos(δ0(jΔt)),[],Bj,X0Y1Y2X3=sin(δ0(jΔt))cos(δ1(jΔt))cos(δ2(jΔt))sin(δ3(jΔt)),
I=BTA,
A=(BBT)1BI=KBI,
I(t)=SPSATSPSG.
m22(Y0δY3δ)m22[Y0δY3δ+Y0δJ0(A3)+Y3δJ0(A0)+J0(A0)J0(A3)],
m33(X0δY1δY2δX3δ)m33X0δX3δ[Y1δY2δ+Y1δJ0(A2)+Y2δJ0(A1)+J0(A1)J0(A2)].
m22(Y0δY3δ)m22[Y0Y3X0Y3δ0X0Y3δ],
m33[X0δY1δY2δX3δ]m33[X0Y1Y2X3X0X1Y2X3δ1X0Y1X2X3δ2+],
m11[X0δX1δX2δX3δ]m11[X0X1X2X3X0X1Y2X3δ2X0Y1X2X3δ1+].
IY3=J0(A0),
IX0Y2X3=J0(A1),
IX0Y1Y3=J0(A2),
IY0=J0(A3),
IX0Y3=δ0,
IX0X1Y2X3=δ1δ2,
IX0Y1X2X3=δ1δ2,
IY0X3=δ3,
IY1X2X3=2εb0,
IY0X1Y2X3=2εb1,
IX0X1Y2Y3=2εb2,
IX0Y1X2=2εb3.
Vmi(λ)=KiAiλk=0αki/λ2k,
BX0X3=|IX0X3|2J1(A0)J1(A3)=2|m33|J0(A1)J0(A2)J1(A0)J1(A3),
BX0Y1X3=|IX0Y1X3|2J1(A0)J1(A3)J2(A1)=2|m33|J0(A2)J1(A0)J1(A3)J2(A1),
BX0Y2X3=|IX0Y2X3|2J1(A0)J1(A3)J2(A2)=2|m33|J0(A1)J1(A0)J1(A3)J2(A2).
RPEM1=BX0Y1X3BX0X3=J2(A1)J0(A1),
RPEM2=BX0Y2X3BX0X3=J2(A2)J0(A2).
Mmean=[10.00020.00020.00020.00010.99750.00020.00140.00020.00001.00220.00120.00000.00140.00041.0010],Mσ=[00.1380.0740.0070.2070.1570.2360.0320.0310.3440.2930.0360.0060.0350.0220.146]×103,

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