Abstract

We present a new real-time Stokes parameter measurement technique using three polarized beam splitters without mechanical motion or electrical tuning. This system can analyze the polarization state of light at 30 kHz, limited only by the speed of the detector analog to digital converters. The optical system is also compact (52×30×25mm) because it consists only of small volume optical devices. We show that the system can measure arbitrary polarization states with an accuracy of better than 0.006 in the normalized Stokes parameters. We also demonstrate the ability to measure fast dynamic polarization states by analyzing the state produced by a fast rotating quarter-wave plate and the time-dependent stress induced in a PMMA block by hitting the block with a hammer.

© 2019 Optical Society of America

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References

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  1. D. H. Goldstein, Polarized Light, 3rd ed. (CRC Press, 2011).
  2. M. Tanaka, Y. Nakashima, H. Amamiya, M. Chujo, and Y. Otani, “Spectroscopic Stokes polarimeter with dual rotating retarder and analyzer for optical rotation measurement,” Proc. SPIE 7461, 74610O (2009).
    [Crossref]
  3. B. B. Wang, J. List, and R. R. Rockwell, “A Stokes polarimeter using two photoelastic modulators,” Proc. SPIE 4819, 1–9 (2002).
    [Crossref]
  4. J. P. Nathan and J. A. Shaw, “Dual-field imaging polarimeter using liquid crystal variable retarders,” Appl. Opt. 45, 5470–5478 (2006).
    [Crossref]
  5. R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” Opt. Acta 29, 685–689 (1982).
    [Crossref]
  6. R. M. A. Azzam, “Beam-splitters for the division-of-amplitude photopolarimeter,” Opt. Acta 32, 1407–1412 (1985).
    [Crossref]
  7. R. M. A. Azzam, “Arrangement of four photodetectors for measuring the state of polarization of light,” Opt. Lett. 10, 309–311 (1985).
    [Crossref]
  8. S. Kawabata, “Modified transmission type four-detector polarimeter,” Proc. SPIE 5524, 337–344 (2004).
    [Crossref]
  9. Axometrics, https://www.axometrics.com .

2009 (1)

M. Tanaka, Y. Nakashima, H. Amamiya, M. Chujo, and Y. Otani, “Spectroscopic Stokes polarimeter with dual rotating retarder and analyzer for optical rotation measurement,” Proc. SPIE 7461, 74610O (2009).
[Crossref]

2006 (1)

2004 (1)

S. Kawabata, “Modified transmission type four-detector polarimeter,” Proc. SPIE 5524, 337–344 (2004).
[Crossref]

2002 (1)

B. B. Wang, J. List, and R. R. Rockwell, “A Stokes polarimeter using two photoelastic modulators,” Proc. SPIE 4819, 1–9 (2002).
[Crossref]

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]

R. M. A. Azzam, “Beam-splitters for the division-of-amplitude photopolarimeter,” Opt. Acta 32, 1407–1412 (1985).
[Crossref]

1982 (1)

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

Amamiya, H.

M. Tanaka, Y. Nakashima, H. Amamiya, M. Chujo, and Y. Otani, “Spectroscopic Stokes polarimeter with dual rotating retarder and analyzer for optical rotation measurement,” Proc. SPIE 7461, 74610O (2009).
[Crossref]

Azzam, R. M. A.

R. M. A. Azzam, “Beam-splitters for the division-of-amplitude photopolarimeter,” Opt. Acta 32, 1407–1412 (1985).
[Crossref]

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

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

Chujo, M.

M. Tanaka, Y. Nakashima, H. Amamiya, M. Chujo, and Y. Otani, “Spectroscopic Stokes polarimeter with dual rotating retarder and analyzer for optical rotation measurement,” Proc. SPIE 7461, 74610O (2009).
[Crossref]

Goldstein, D. H.

D. H. Goldstein, Polarized Light, 3rd ed. (CRC Press, 2011).

Kawabata, S.

S. Kawabata, “Modified transmission type four-detector polarimeter,” Proc. SPIE 5524, 337–344 (2004).
[Crossref]

List, J.

B. B. Wang, J. List, and R. R. Rockwell, “A Stokes polarimeter using two photoelastic modulators,” Proc. SPIE 4819, 1–9 (2002).
[Crossref]

Nakashima, Y.

M. Tanaka, Y. Nakashima, H. Amamiya, M. Chujo, and Y. Otani, “Spectroscopic Stokes polarimeter with dual rotating retarder and analyzer for optical rotation measurement,” Proc. SPIE 7461, 74610O (2009).
[Crossref]

Nathan, J. P.

Otani, Y.

M. Tanaka, Y. Nakashima, H. Amamiya, M. Chujo, and Y. Otani, “Spectroscopic Stokes polarimeter with dual rotating retarder and analyzer for optical rotation measurement,” Proc. SPIE 7461, 74610O (2009).
[Crossref]

Rockwell, R. R.

B. B. Wang, J. List, and R. R. Rockwell, “A Stokes polarimeter using two photoelastic modulators,” Proc. SPIE 4819, 1–9 (2002).
[Crossref]

Shaw, J. A.

Tanaka, M.

M. Tanaka, Y. Nakashima, H. Amamiya, M. Chujo, and Y. Otani, “Spectroscopic Stokes polarimeter with dual rotating retarder and analyzer for optical rotation measurement,” Proc. SPIE 7461, 74610O (2009).
[Crossref]

Wang, B. B.

B. B. Wang, J. List, and R. R. Rockwell, “A Stokes polarimeter using two photoelastic modulators,” Proc. SPIE 4819, 1–9 (2002).
[Crossref]

Appl. Opt. (1)

Opt. Acta (2)

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

R. M. A. Azzam, “Beam-splitters for the division-of-amplitude photopolarimeter,” Opt. Acta 32, 1407–1412 (1985).
[Crossref]

Opt. Lett. (1)

Proc. SPIE (3)

M. Tanaka, Y. Nakashima, H. Amamiya, M. Chujo, and Y. Otani, “Spectroscopic Stokes polarimeter with dual rotating retarder and analyzer for optical rotation measurement,” Proc. SPIE 7461, 74610O (2009).
[Crossref]

B. B. Wang, J. List, and R. R. Rockwell, “A Stokes polarimeter using two photoelastic modulators,” Proc. SPIE 4819, 1–9 (2002).
[Crossref]

S. Kawabata, “Modified transmission type four-detector polarimeter,” Proc. SPIE 5524, 337–344 (2004).
[Crossref]

Other (2)

Axometrics, https://www.axometrics.com .

D. H. Goldstein, Polarized Light, 3rd ed. (CRC Press, 2011).

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Figures (9)

Fig. 1.
Fig. 1. Optical setup of Stokes polarimeter using 3WPPS.
Fig. 2.
Fig. 2. Concept for maintaining the input polarization while dividing the light into two beams.
Fig. 3.
Fig. 3. Optical setup for Stokes parameter measurement using a PBS and detector pair oriented at (a) 0° to split horizontal and vertical polarizations for measuring s1, (b) 45° to split the two states needed for measuring s2, and (c) 0° in combination with a QWP oriented at 45° for measuring s3.
Fig. 4.
Fig. 4. Measurements of beam splitter polarization properties by the Axoscan polarimeter. In (a)–(d), the black dashed curves indicate the values after the first beam splitter, while the red curves indicate the values after the combination of two beam splitters. Panels (e) and (f) show the residual values produced before each detector’s polarizing beam splitter, i.e., exiting the 3WPPS at points (1), (2), and (3), as shown.
Fig. 5.
Fig. 5. Simulation of the impact that the residual retardance and diattenuation of the 3WPPS will have on the measurement of the Stokes parameters at λ=633nm. Plus/minus ellipticity indicates right/left-handedness. The image gray scale indicates the error in the normalized Stokes parameters.
Fig. 6.
Fig. 6. Measurement setup.
Fig. 7.
Fig. 7. Measured normalized Stokes parameters of (a) a rotating analyzer and (c) a rotating QWP. The dashed curves indicate the known polarization state, while the squares indicate the measurements. (b) and (d) show differences between the measured and ideal normalized Stokes parameters. Filled dots show the measurements corrected using Eq. (5), while the open squares show the uncorrected measurements obtained directly from Eq. (4).
Fig. 8.
Fig. 8. Measured normalized Stokes parameters of the QWP rotated by the servomotor in 25 rps during (a) 250 ms, (b) 1 ms.
Fig. 9.
Fig. 9. Demonstration of high-speed measurement of the polarization state after passing through an acrylic block due to impact by a hammer. (a) Time-resolved Stokes parameters; (b) linear retardance δPMMA and azimuthal angle ϕ calculated by Eq. (6) using the Stokes parameters of (a); (c) principal stress difference Δσ calculated by Eq. (7) using the linear retardance of (b).

Equations (7)

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s˜1=I0°I90°I0°+I90°,s˜2=I45°I45°I45°+I45°,s˜3=IRCILCIRC+ILC,
gi=kiαikiβi.
g1=212+1·I0°I90°,g2=212+1·I45°I45°,g3=IRCILC.
s˜1=I0°g1I90°I0°+g1I90°,s˜2=I45°g2I45°I45°+g2I45°,s˜3=IRCg3ILCIRC+g3ILC.
s˜1=s˜1D(1)1s˜1D(1),s˜2=s˜2+D(2)s˜1s˜21s˜1D(1)δ(2)s˜3,s˜3=s˜3+D(3)s˜1s˜31s˜1D(1)+δ(3)s˜2.
ϕ=12tan1s2s1,δPMMA=tan1s12+s22s3.
Δσ=λ2πGdδPMMA.

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