Abstract

The optical axes of achromatic waveplate retarders (AWR) may deform from ideal linear eigenpolarizations and be frequency-dependent owing to the imperfect design and fabrication. Such deformations result in the ellipticity error and the orientation error of an AWR away from the nominal values. In this paper, we address the measurement errors of Stokes parameters induced by deformation of optical axes of AWRs in roatatable retarder fixed polarizer (RRFP) Stokes polarimeters. A set of theoretical formulas is derived to reveal that such measurement errors actually depend on both retardance and angular orientations of the AWR in use, as well as the state of polarization (SOP) under test. We demonstrate that,by rotating the AWR to N (N≥5) uniformly spaced angles with the angle step of 180°/N or 360°/N, the measurement errors of Stokes parameters induced by the ellipticity error of the AWR can be suppressed compared with the result using any set of four specific angles, especially when the SOP under test is nearly circular. On the other hand, the measurement errors induced by the orientation error of the AWR have more complicated relationships with the angular orientations of the AWR: 1) when the SOP under test is nearly circular, above-mentioned N (N≥5) uniformly spaced angles also lead to much smaller measurement errors than any set of four specific angles; 2) when the SOP under test is nearly linear, N (N≥5) uniformly spaced angles result in smaller or larger measurement errors, depending on the SOP under test, compared with the usually-recommended sets of four specific angles. By theoretical calculations and numerical simulations, we can conclude that the RRFP Stokes polarimeters employing angle sets of N (N≥5) uniformly spaced angles, ( ± 90°, −54°, −18°, 18°, 54°) for instance, can effectively reduce the measurement errors of Stokes parameters induced by the optical axes deformation of the AWR.

© 2012 OSA

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2012

H. Dong, P. Shum, Y. D. Gong, and Q. Z. Sun, “Measurement errors induced by retardance deviation in a rotatable retarder fixed polarizer Stokes polarimeter,” Opt. Eng.51(3), 033001 (2012).
[CrossRef]

2009

2007

L. Giudicotti and M. Brombin, “Data analysis for a rotating quarter-wave, far-infrared Stokes polarimeter,” Appl. Opt.46(14), 2638–2648 (2007).
[CrossRef] [PubMed]

H. Ito, K. Suizu, T. Yamashita, A. Nawahara, and T. Sato, “Radom frequency accessible broad tunable terahertz-wave source using phase-matched 4-dimethylamino-N-methyl-4-stilbazolium Tosylate crystal,” J. Appl. Phys.93, 7321–7324 (2007).

2006

2004

A. Galtarossa and L. Palmieri, “Reflectometric measurements of polarization properties in optical-fiber links,” IEEE Trans. Instrum. Meas.53(1), 86–94 (2004).
[CrossRef]

2002

B. Boulbry, B. L. Jeune, F. Pellen, J. Cariou, and J. Lotrian, “Identification of error parameters and calibration of a double-crystal birefringent wave plate with a broadband spectral light source,” J. Phys. D Appl. Phys.35(20), 2508–2515 (2002).
[CrossRef]

2001

2000

1999

R. M. Jopson, L. E. Nelson, and H. Kogelnik, “Measurement of second-order polarization-mode dispersion vectors in optical fibers,” IEEE Photon. Technol. Lett.11(9), 1153–1155 (1999).
[CrossRef]

1996

1995

A. Ambirajan and D. C. Look., “Optimum angles for a polarimeter: part I,” Opt. Eng.34(6), 1651–1655 (1995).
[CrossRef]

Ambirajan, A.

A. Ambirajan and D. C. Look., “Optimum angles for a polarimeter: part I,” Opt. Eng.34(6), 1651–1655 (1995).
[CrossRef]

Boulbry, B.

B. Boulbry, B. L. Jeune, F. Pellen, J. Cariou, and J. Lotrian, “Identification of error parameters and calibration of a double-crystal birefringent wave plate with a broadband spectral light source,” J. Phys. D Appl. Phys.35(20), 2508–2515 (2002).
[CrossRef]

B. Boulbry, B. Bousquet, B. Le Jeune, Y. Guern, and J. Lotrian, “Polarization errors associated with zero-order achromatic quarter-wave plates in the whole visible spectral range,” Opt. Express9(5), 225–235 (2001).
[CrossRef] [PubMed]

Bousquet, B.

Brombin, M.

Cariou, J.

B. Boulbry, B. L. Jeune, F. Pellen, J. Cariou, and J. Lotrian, “Identification of error parameters and calibration of a double-crystal birefringent wave plate with a broadband spectral light source,” J. Phys. D Appl. Phys.35(20), 2508–2515 (2002).
[CrossRef]

Chipman, R. A.

Dereniak, E. L.

Descour, M. R.

Dong, H.

H. Dong, P. Shum, Y. D. Gong, and Q. Z. Sun, “Measurement errors induced by retardance deviation in a rotatable retarder fixed polarizer Stokes polarimeter,” Opt. Eng.51(3), 033001 (2012).
[CrossRef]

Gallot, G.

Galtarossa, A.

A. Galtarossa and L. Palmieri, “Reflectometric measurements of polarization properties in optical-fiber links,” IEEE Trans. Instrum. Meas.53(1), 86–94 (2004).
[CrossRef]

Giudicotti, L.

Gong, Y. D.

H. Dong, P. Shum, Y. D. Gong, and Q. Z. Sun, “Measurement errors induced by retardance deviation in a rotatable retarder fixed polarizer Stokes polarimeter,” Opt. Eng.51(3), 033001 (2012).
[CrossRef]

Goudail, F.

Guern, Y.

Ito, H.

H. Ito, K. Suizu, T. Yamashita, A. Nawahara, and T. Sato, “Radom frequency accessible broad tunable terahertz-wave source using phase-matched 4-dimethylamino-N-methyl-4-stilbazolium Tosylate crystal,” J. Appl. Phys.93, 7321–7324 (2007).

Jeune, B. L.

B. Boulbry, B. L. Jeune, F. Pellen, J. Cariou, and J. Lotrian, “Identification of error parameters and calibration of a double-crystal birefringent wave plate with a broadband spectral light source,” J. Phys. D Appl. Phys.35(20), 2508–2515 (2002).
[CrossRef]

Jopson, R. M.

R. M. Jopson, L. E. Nelson, and H. Kogelnik, “Measurement of second-order polarization-mode dispersion vectors in optical fibers,” IEEE Photon. Technol. Lett.11(9), 1153–1155 (1999).
[CrossRef]

Kemme, S. A.

Kogelnik, H.

R. M. Jopson, L. E. Nelson, and H. Kogelnik, “Measurement of second-order polarization-mode dispersion vectors in optical fibers,” IEEE Photon. Technol. Lett.11(9), 1153–1155 (1999).
[CrossRef]

Le Jeune, B.

Look, D. C.

A. Ambirajan and D. C. Look., “Optimum angles for a polarimeter: part I,” Opt. Eng.34(6), 1651–1655 (1995).
[CrossRef]

Lotrian, J.

B. Boulbry, B. L. Jeune, F. Pellen, J. Cariou, and J. Lotrian, “Identification of error parameters and calibration of a double-crystal birefringent wave plate with a broadband spectral light source,” J. Phys. D Appl. Phys.35(20), 2508–2515 (2002).
[CrossRef]

B. Boulbry, B. Bousquet, B. Le Jeune, Y. Guern, and J. Lotrian, “Polarization errors associated with zero-order achromatic quarter-wave plates in the whole visible spectral range,” Opt. Express9(5), 225–235 (2001).
[CrossRef] [PubMed]

Lu, S. Y.

Masson, J. B.

Nawahara, A.

H. Ito, K. Suizu, T. Yamashita, A. Nawahara, and T. Sato, “Radom frequency accessible broad tunable terahertz-wave source using phase-matched 4-dimethylamino-N-methyl-4-stilbazolium Tosylate crystal,” J. Appl. Phys.93, 7321–7324 (2007).

Nelson, L. E.

R. M. Jopson, L. E. Nelson, and H. Kogelnik, “Measurement of second-order polarization-mode dispersion vectors in optical fibers,” IEEE Photon. Technol. Lett.11(9), 1153–1155 (1999).
[CrossRef]

Palmieri, L.

A. Galtarossa and L. Palmieri, “Reflectometric measurements of polarization properties in optical-fiber links,” IEEE Trans. Instrum. Meas.53(1), 86–94 (2004).
[CrossRef]

Pellen, F.

B. Boulbry, B. L. Jeune, F. Pellen, J. Cariou, and J. Lotrian, “Identification of error parameters and calibration of a double-crystal birefringent wave plate with a broadband spectral light source,” J. Phys. D Appl. Phys.35(20), 2508–2515 (2002).
[CrossRef]

Phipps, G. S.

Sabatke, D. S.

Sato, T.

H. Ito, K. Suizu, T. Yamashita, A. Nawahara, and T. Sato, “Radom frequency accessible broad tunable terahertz-wave source using phase-matched 4-dimethylamino-N-methyl-4-stilbazolium Tosylate crystal,” J. Appl. Phys.93, 7321–7324 (2007).

Shum, P.

H. Dong, P. Shum, Y. D. Gong, and Q. Z. Sun, “Measurement errors induced by retardance deviation in a rotatable retarder fixed polarizer Stokes polarimeter,” Opt. Eng.51(3), 033001 (2012).
[CrossRef]

Suizu, K.

H. Ito, K. Suizu, T. Yamashita, A. Nawahara, and T. Sato, “Radom frequency accessible broad tunable terahertz-wave source using phase-matched 4-dimethylamino-N-methyl-4-stilbazolium Tosylate crystal,” J. Appl. Phys.93, 7321–7324 (2007).

Sun, Q. Z.

H. Dong, P. Shum, Y. D. Gong, and Q. Z. Sun, “Measurement errors induced by retardance deviation in a rotatable retarder fixed polarizer Stokes polarimeter,” Opt. Eng.51(3), 033001 (2012).
[CrossRef]

Sweatt, W. C.

Tyo, J. S.

Yamashita, T.

H. Ito, K. Suizu, T. Yamashita, A. Nawahara, and T. Sato, “Radom frequency accessible broad tunable terahertz-wave source using phase-matched 4-dimethylamino-N-methyl-4-stilbazolium Tosylate crystal,” J. Appl. Phys.93, 7321–7324 (2007).

Appl. Opt.

IEEE Photon. Technol. Lett.

R. M. Jopson, L. E. Nelson, and H. Kogelnik, “Measurement of second-order polarization-mode dispersion vectors in optical fibers,” IEEE Photon. Technol. Lett.11(9), 1153–1155 (1999).
[CrossRef]

IEEE Trans. Instrum. Meas.

A. Galtarossa and L. Palmieri, “Reflectometric measurements of polarization properties in optical-fiber links,” IEEE Trans. Instrum. Meas.53(1), 86–94 (2004).
[CrossRef]

J. Appl. Phys.

H. Ito, K. Suizu, T. Yamashita, A. Nawahara, and T. Sato, “Radom frequency accessible broad tunable terahertz-wave source using phase-matched 4-dimethylamino-N-methyl-4-stilbazolium Tosylate crystal,” J. Appl. Phys.93, 7321–7324 (2007).

J. Opt. Soc. Am. A

J. Phys. D Appl. Phys.

B. Boulbry, B. L. Jeune, F. Pellen, J. Cariou, and J. Lotrian, “Identification of error parameters and calibration of a double-crystal birefringent wave plate with a broadband spectral light source,” J. Phys. D Appl. Phys.35(20), 2508–2515 (2002).
[CrossRef]

Opt. Eng.

H. Dong, P. Shum, Y. D. Gong, and Q. Z. Sun, “Measurement errors induced by retardance deviation in a rotatable retarder fixed polarizer Stokes polarimeter,” Opt. Eng.51(3), 033001 (2012).
[CrossRef]

A. Ambirajan and D. C. Look., “Optimum angles for a polarimeter: part I,” Opt. Eng.34(6), 1651–1655 (1995).
[CrossRef]

Opt. Express

Opt. Lett.

Other

D. Goldstein, Polarized Light (Marcel Dekker, Inc., 2003), Chap. 27.

M. T. Heath, Scientific Computing: An Introductory Survey (McGraw-Hill Companies, 1997).

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Figures (8)

Fig. 1
Fig. 1

The structure of a RRFP Stokes polarimeter.

Fig. 2
Fig. 2

The ellipse to illustrate the fast axis (i.e. fast eigenpolarization) of an AWR.

Fig. 3
Fig. 3

Simulation and theoretical results of Δ s i ,i=0,1,2,3 induced by Δχ= 3 for the four angles (−51.7°, −15.1°, 15.1°, 51.7°). The SOP under simulation is ( 1,1/ 3 ,1/ 3 ,1/ 3 ) T .

Fig. 4
Fig. 4

Simulation and theoretical results of Δ s i ,i=0,1,2,3 induced by Δθ= 3 for the four angles (−51.7°, −15.1°, 15.1°, 51.7°). The SOP under simulation is ( 1,1/ 3 ,1/ 3 ,1/ 3 ) T .

Fig. 5
Fig. 5

Simulation and theoretical results of Δ s i ,i=0,1,2,3 induced by Δχ= 3 for the five uniformly spaced angles (−90°, −54°, −18°, 18°, 54°). The SOP under simulation is ( 1,1/ 3 ,1/ 3 ,1/ 3 ) T .

Fig. 6
Fig. 6

Simulation and theoretical results of Δ s i ,i=0,1,2,3 induced by Δθ= 3 for the five uniformly spaced angles (−90°, −54°, −18°, 18°, 54°). The SOP under simulation is ( 1,1/ 3 ,1/ 3 ,1/ 3 ) T .

Fig. 7
Fig. 7

Simulation results of Δ S χ (left) and Δ S θ (right) for the four angles (−51.7°, −15.1°, 15.1°, 51.7°) and the five uniformly spaced angles (−90°, −54°, −18°, 18°, 54°). The SOP under simulation is ( 1,1/ 3 ,1/ 3 ,1/ 3 ) T .

Fig. 8
Fig. 8

Simulation results of Δ S χ (left) and Δ S θ (right) for the four angles (−51.7°, −15.1°, 15.1°, 51.7°) and the five uniformly spaced angles (−90°, −54°, −18°, 18°, 54°). The SOP under simulation is ( 1,0,0,1 ) T .

Tables (1)

Tables Icon

Table 1 The Values of A i 4 ,i=1,2,3,4 for Different Retardances and Angle Sets

Equations (4)

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W 1 Δ W θ =2Δθ( 00( 1+cosδ )cot( δ/2 ) A 1 4 002cot( δ/2 ) A 2 4 020cot( δ/2 ) A 3 4 000cot( δ/2 ) A 4 4 )
W + Δ W θ =2Δθ( 00( 1+cosδ )cot( δ/2 ) A 1 N 002cot( δ/2 ) A 2 N 020cot( δ/2 ) A 3 N 000cot( δ/2 ) A 4 N )
W N T Δ W N,χ = W N1 T Δ W N1,χ + V N Δ V N,χ T
( V N Δ V N,χ T ) L =2Δχ V N V N T A L

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