Abstract

A new polarimeter for the simultaneous measurement of all Stokes parameters in a single shot is presented. It consists of only a gradient index (GRIN) lens, a polarizer, an imaging lens, and a CCD, without mechanical movements, electrical signal modulation, or the division of amplitude components. This design takes advantage of the continuous spatial distributions of birefringence value and the fast axis direction of a GRIN lens and derives the state of polarization (SOP) of the incident beam from the characteristic patterns on the CCD images. Tests show that this polarimeter is very accurate even with low-resolution images. It is versatile and adapts to light sources of different wavelengths. It is also very stable, robust, low cost, and simple to use.

© 2014 Optical Society of America

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References

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2013 (2)

2011 (1)

2010 (1)

2009 (3)

2007 (2)

I. Nishiyama, N. Yoshida, Y. Otani, and N. Umeda, Meas. Sci. Technol. 18, 1673 (2007).
[CrossRef]

V. Gruev, A. Ortu, N. Lazarus, J. V. Spiegel, and N. Engheta, Opt. Express 15, 4994 (2007).
[CrossRef]

2006 (1)

2003 (1)

2002 (1)

2000 (1)

1999 (1)

1996 (2)

1985 (1)

1982 (1)

R. M. A. Azzam, Opt. Acta 29, 685 (1982).
[CrossRef]

Alali, S.

Antonelli, M. R.

Azzam, R. M. A.

R. M. A. Azzam, Opt. Lett. 10, 309 (1985).
[CrossRef]

R. M. A. Azzam, Opt. Acta 29, 685 (1982).
[CrossRef]

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987).

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987).

Benali, A.

Campos, J.

Chen, X.

Chipman, R. A.

Dereniak, E. L.

Descour, M. R.

Drevillon, B.

Engheta, N.

Fernandez, E.

Gaurel, E. G.

Gayet, B.

Gilbert, J. A.

Gruev, V.

Karalidi, T.

Keller, C. U.

Kemme, S. A.

Kim, Y. K.

LaCasse, C. F.

Laude, B.

Lazarus, N.

Lizana, A.

Lu, S. Y.

Martino, A. D.

Mompart, J.

Moore, D. T.

Nishiyama, I.

I. Nishiyama, N. Yoshida, Y. Otani, and N. Umeda, Meas. Sci. Technol. 18, 1673 (2007).
[CrossRef]

Novikova, T.

Ortu, A.

Otani, Y.

T. Wakayama, Y. Otani, and T. Yoshizawa, Proc. SPIE 7461, 74610M (2009).
[CrossRef]

I. Nishiyama, N. Yoshida, Y. Otani, and N. Umeda, Meas. Sci. Technol. 18, 1673 (2007).
[CrossRef]

Peinado, A.

Phipps, G. S.

Pierangelo, A.

Ratliff, B. M.

Rouke, J. L.

Sabatke, D. S.

Snik, F.

Spiegel, J. V.

Su, W.

Sweatt, W. C.

Turpin, A.

Tyo, J. S.

Umeda, N.

I. Nishiyama, N. Yoshida, Y. Otani, and N. Umeda, Meas. Sci. Technol. 18, 1673 (2007).
[CrossRef]

Validire, P.

Vitkin, I. A.

Wakayama, T.

T. Wakayama, Y. Otani, and T. Yoshizawa, Proc. SPIE 7461, 74610M (2009).
[CrossRef]

Yan, L.

Yang, T.

Yao, X. S.

Yoshida, N.

I. Nishiyama, N. Yoshida, Y. Otani, and N. Umeda, Meas. Sci. Technol. 18, 1673 (2007).
[CrossRef]

Yoshizawa, T.

T. Wakayama, Y. Otani, and T. Yoshizawa, Proc. SPIE 7461, 74610M (2009).
[CrossRef]

Appl. Opt. (4)

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

Meas. Sci. Technol. (1)

I. Nishiyama, N. Yoshida, Y. Otani, and N. Umeda, Meas. Sci. Technol. 18, 1673 (2007).
[CrossRef]

Opt. Acta (1)

R. M. A. Azzam, Opt. Acta 29, 685 (1982).
[CrossRef]

Opt. Express (3)

Opt. Lett. (7)

Proc. SPIE (1)

T. Wakayama, Y. Otani, and T. Yoshizawa, Proc. SPIE 7461, 74610M (2009).
[CrossRef]

Other (2)

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987).

R. A. Chipman, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009, Vol. 1.

Supplementary Material (1)

» Media 1: AVI (20709 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

Optical layout of the polarization state generaator (PSG) and the GRIN lens polarimeter. The diameter of the GRIN lens is 1.4 mm and the pitch is 3/4. L1, collimating len;, L2, imaging lens; F, band pass filter; P1 and P2, polarizer; and Q, quarter wave plate. The CCD is placed at the imaging plane (AB) of the front surface of the GRIN lens (AB). In this Letter the incident rays are nearly parallel. Birefringence value increases along the radial direction, and the larger birefringence value is displayed with a darker orange color; thus, the red and the blue rays would experience larger linear retardance than the green rays.

Fig. 2.
Fig. 2.

Spatial distributions of linear retardance (a) and (c) and fast axis direction (b) and (d) of a GRIN lens 60 mm long, 1.4 mm in diameter, and 0.1 NA.

Fig. 3.
Fig. 3.

(a) Experimental images from the CCD corresponding to linearly polarized incident lights at 0° (H), 90° (V), 45° (P), and 135° (M), and the left (L) and right (R) hand circularly polarized lights. Note Fig. 3(a) HR are normalized pixel by pixel with the image for the unpolarized beam. (b) Retardance and fast axis profiles of the GRIN lens, some subregions with different retardance are plotted with different colors. The size of the images of (a) and (b) is 280×280pixels.

Fig. 4.
Fig. 4.

CNs of the 146 annular subregions ranging from 15° to 160°, and the mean angular accuracies of the 60 measurements for the 146 annular subregions.

Fig. 5.
Fig. 5.

Experimental (square marker, s1; circle marker, s2; triangle marker, s3) and calculated (red line, s1; green line, s2; blue line, s3) Stokes parameters corresponding to different incident SOPs, where in the PSG the polarizer is fixed and the wave plate is rotated 180° in 60 equal steps. The patterns on the CCD are recorded (see Media 1).

Equations (8)

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S=MP·MGRIN·S,
MP(1,:)=(pt+pe,(ptpe)cos2θP,(ptpe)sin2θP,0),
MP(1,:)=(pt,pt,0,0).
MGRINn(1,0,0,00,cos22θn+sin22θncosδn,0.5sin4θn(1cosδn),sin2θnsinδn0,0.5sin4θn(1cosδn),sin22θn+cos22θncosδn,cos2θnsinδn0,sin2θnsinδn,cos2θnsinδn,cosδn),
s0n=pts0+pt(cos22θn+sin22θncosδn)s1+0.5ptsin4θn(1cosδn)s2ptsin2θnsinδns3.
I=A·S,
I=(s01,s02,s03,,s0n)T.
S=Ap1·I.

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