Abstract

Polarization analyzers are an essential measuring tool to improve the characteristics of optical components and optimize them with respect to a useful application in optical networks. We describe an instrument of this kind, which consists of two crossed birefringent wedges and acts as a continuous structured polarizer for all the states of polarization of light. We analyze this device theoretically by using the Poincaré-sphere and the Jones-matrix method and verify our results in a number of experiments with quartz wedges and red filtered light. Different realizations of this instrument are discussed, and an application as a beam splitter for all the states of polarization is proposed.

© 2013 Optical Society of America

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References

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  1. W. Driscoll, Handbook of Optics (McGraw-Hill, 1978), pp. 10–15; pp. 16–26.
  2. E. Frins, B. Hils, H. Schmitzer, and W. Dultz, “Haidinger’s dichroskopische Lupe,” in Proceedings of the 108th Spring Meeting of the German Society of Applied Optics (Deutsche Gesellschaft für Angewandte Optik, 2007), www.dgao-proceedings.de .
  3. GrendelFish, “Sunstone” (2006), http://gfish.livejournal.com/175265.html .
  4. E. Frins, B. Hils, H. Schmitzer, and W. Dultz, “Radialpolarisatoren als Instrumente für optische Polarisationsmessungen,” in Proceedings of the 109th Spring Meeting of the German Society of Applied Optics (Deutsche Gesellschaft für Angewandte Optik, 2008), www.dgao-proceedings.de .
  5. M. Stalder and M. Schadt, “Linear polarized light with axial symmetry generated by liquid crystal polarization converters,” Opt. Lett. 211948–1950 (1996).
    [CrossRef]
  6. F. Woolley, “Handbook of Polarized Animation Materials” (Frank Woolley), pp. 1–110.
  7. Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings,” Opt. Lett. 27, 285–287 (2002).
    [CrossRef]
  8. M. Rothmayer, W. Dultz, E. Frins, Q. Zhan, D. Tierney, and H. Schmitzer, “Nonlinearity in the rotational dynamics of Haidinger’s brushes,” Appl. Opt. 46, 7244–7251 (2007).
    [CrossRef]
  9. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
    [CrossRef]
  10. Y. Zhao, Q. Zhan, Y. Zhang, and Y. Li, “Creation of a three-dimensional optical chain for controllable delivery,” Opt. Lett. 30, 848–850 (2005).
    [CrossRef]
  11. J. Ferrari, W. Dultz, H. Schmitzer, and E. Frins, “Achromatic wavefront forming with space-variant polarizers: application to phase singularities and light focusing,” Phys. Rev. A 76, 053815 (2007).
    [CrossRef]
  12. W. Wozniak and P. Kurzynowski, “Compact spatial polariscope for light polarization state analysis,” Opt. Express 16, 10471–10479 (2008).
    [CrossRef]
  13. J. Simmons and M. Guttmann, States, Waves and Photons (Addison-Wesley, 1970), p. 53.

2008 (1)

2007 (2)

M. Rothmayer, W. Dultz, E. Frins, Q. Zhan, D. Tierney, and H. Schmitzer, “Nonlinearity in the rotational dynamics of Haidinger’s brushes,” Appl. Opt. 46, 7244–7251 (2007).
[CrossRef]

J. Ferrari, W. Dultz, H. Schmitzer, and E. Frins, “Achromatic wavefront forming with space-variant polarizers: application to phase singularities and light focusing,” Phys. Rev. A 76, 053815 (2007).
[CrossRef]

2005 (1)

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

2002 (1)

1996 (1)

Biener, G.

Bomzon, Z.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Driscoll, W.

W. Driscoll, Handbook of Optics (McGraw-Hill, 1978), pp. 10–15; pp. 16–26.

Dultz, W.

M. Rothmayer, W. Dultz, E. Frins, Q. Zhan, D. Tierney, and H. Schmitzer, “Nonlinearity in the rotational dynamics of Haidinger’s brushes,” Appl. Opt. 46, 7244–7251 (2007).
[CrossRef]

J. Ferrari, W. Dultz, H. Schmitzer, and E. Frins, “Achromatic wavefront forming with space-variant polarizers: application to phase singularities and light focusing,” Phys. Rev. A 76, 053815 (2007).
[CrossRef]

E. Frins, B. Hils, H. Schmitzer, and W. Dultz, “Radialpolarisatoren als Instrumente für optische Polarisationsmessungen,” in Proceedings of the 109th Spring Meeting of the German Society of Applied Optics (Deutsche Gesellschaft für Angewandte Optik, 2008), www.dgao-proceedings.de .

E. Frins, B. Hils, H. Schmitzer, and W. Dultz, “Haidinger’s dichroskopische Lupe,” in Proceedings of the 108th Spring Meeting of the German Society of Applied Optics (Deutsche Gesellschaft für Angewandte Optik, 2007), www.dgao-proceedings.de .

Ferrari, J.

J. Ferrari, W. Dultz, H. Schmitzer, and E. Frins, “Achromatic wavefront forming with space-variant polarizers: application to phase singularities and light focusing,” Phys. Rev. A 76, 053815 (2007).
[CrossRef]

Frins, E.

M. Rothmayer, W. Dultz, E. Frins, Q. Zhan, D. Tierney, and H. Schmitzer, “Nonlinearity in the rotational dynamics of Haidinger’s brushes,” Appl. Opt. 46, 7244–7251 (2007).
[CrossRef]

J. Ferrari, W. Dultz, H. Schmitzer, and E. Frins, “Achromatic wavefront forming with space-variant polarizers: application to phase singularities and light focusing,” Phys. Rev. A 76, 053815 (2007).
[CrossRef]

E. Frins, B. Hils, H. Schmitzer, and W. Dultz, “Radialpolarisatoren als Instrumente für optische Polarisationsmessungen,” in Proceedings of the 109th Spring Meeting of the German Society of Applied Optics (Deutsche Gesellschaft für Angewandte Optik, 2008), www.dgao-proceedings.de .

E. Frins, B. Hils, H. Schmitzer, and W. Dultz, “Haidinger’s dichroskopische Lupe,” in Proceedings of the 108th Spring Meeting of the German Society of Applied Optics (Deutsche Gesellschaft für Angewandte Optik, 2007), www.dgao-proceedings.de .

Guttmann, M.

J. Simmons and M. Guttmann, States, Waves and Photons (Addison-Wesley, 1970), p. 53.

Hasman, E.

Hils, B.

E. Frins, B. Hils, H. Schmitzer, and W. Dultz, “Haidinger’s dichroskopische Lupe,” in Proceedings of the 108th Spring Meeting of the German Society of Applied Optics (Deutsche Gesellschaft für Angewandte Optik, 2007), www.dgao-proceedings.de .

E. Frins, B. Hils, H. Schmitzer, and W. Dultz, “Radialpolarisatoren als Instrumente für optische Polarisationsmessungen,” in Proceedings of the 109th Spring Meeting of the German Society of Applied Optics (Deutsche Gesellschaft für Angewandte Optik, 2008), www.dgao-proceedings.de .

Kleiner, V.

Kurzynowski, P.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Li, Y.

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Rothmayer, M.

Schadt, M.

Schmitzer, H.

M. Rothmayer, W. Dultz, E. Frins, Q. Zhan, D. Tierney, and H. Schmitzer, “Nonlinearity in the rotational dynamics of Haidinger’s brushes,” Appl. Opt. 46, 7244–7251 (2007).
[CrossRef]

J. Ferrari, W. Dultz, H. Schmitzer, and E. Frins, “Achromatic wavefront forming with space-variant polarizers: application to phase singularities and light focusing,” Phys. Rev. A 76, 053815 (2007).
[CrossRef]

E. Frins, B. Hils, H. Schmitzer, and W. Dultz, “Radialpolarisatoren als Instrumente für optische Polarisationsmessungen,” in Proceedings of the 109th Spring Meeting of the German Society of Applied Optics (Deutsche Gesellschaft für Angewandte Optik, 2008), www.dgao-proceedings.de .

E. Frins, B. Hils, H. Schmitzer, and W. Dultz, “Haidinger’s dichroskopische Lupe,” in Proceedings of the 108th Spring Meeting of the German Society of Applied Optics (Deutsche Gesellschaft für Angewandte Optik, 2007), www.dgao-proceedings.de .

Simmons, J.

J. Simmons and M. Guttmann, States, Waves and Photons (Addison-Wesley, 1970), p. 53.

Stalder, M.

Tierney, D.

Woolley, F.

F. Woolley, “Handbook of Polarized Animation Materials” (Frank Woolley), pp. 1–110.

Wozniak, W.

Zhan, Q.

Zhang, Y.

Zhao, Y.

Appl. Opt. (1)

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. A (1)

J. Ferrari, W. Dultz, H. Schmitzer, and E. Frins, “Achromatic wavefront forming with space-variant polarizers: application to phase singularities and light focusing,” Phys. Rev. A 76, 053815 (2007).
[CrossRef]

Phys. Rev. Lett. (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Other (6)

J. Simmons and M. Guttmann, States, Waves and Photons (Addison-Wesley, 1970), p. 53.

W. Driscoll, Handbook of Optics (McGraw-Hill, 1978), pp. 10–15; pp. 16–26.

E. Frins, B. Hils, H. Schmitzer, and W. Dultz, “Haidinger’s dichroskopische Lupe,” in Proceedings of the 108th Spring Meeting of the German Society of Applied Optics (Deutsche Gesellschaft für Angewandte Optik, 2007), www.dgao-proceedings.de .

GrendelFish, “Sunstone” (2006), http://gfish.livejournal.com/175265.html .

E. Frins, B. Hils, H. Schmitzer, and W. Dultz, “Radialpolarisatoren als Instrumente für optische Polarisationsmessungen,” in Proceedings of the 109th Spring Meeting of the German Society of Applied Optics (Deutsche Gesellschaft für Angewandte Optik, 2008), www.dgao-proceedings.de .

F. Woolley, “Handbook of Polarized Animation Materials” (Frank Woolley), pp. 1–110.

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Figures (5)

Fig. 1.
Fig. 1.

(a) Poincaré sphere and the path of polarization through wedge 1 with retardation Δ1 from the incident polarization |P0 to |P and through wedge 2 with Δ2 from |P to |V. The fast axis of the main part of wedge 2 has the orientation |45° or |135° (b) Light ellipse for left-handed elliptically polarized light.

Fig. 2.
Fig. 2.

Calculated polarization patterns on area A (showing our experimental area A inside the cutout) for several states of polarization of the light: |+45°, |+75°, and |R. The axes indicate the retardations Δ1 in the horizontal and Δ2 in the vertical directions in degrees. As in the experiment, Δ1 increases in the positive x direction, whereas Δ2 increases in the negative y direction.

Fig. 3.
Fig. 3.

Experiment with a polarization analyzer consisting of two quartz wedges, a linear polarizer, and a camera. The axes are chosen such that they form a right-hand system with the direction of the beam propagation. The arrows on the main part of the wedges indicate the orientations of the fast axes. Note that the second wedge is oriented at |+45° and the exit polarizer is horizontal.

Fig. 4.
Fig. 4.

Intensity patterns as seen on the active area for different incident polarizations: 1, linear horizontal |0°; 2, linear |15°; 3, linear |30°; 4, linear |45°; 5, linear |60°;6, linear |75°; 7, linear vertical |90°; and 8, linear |45°; 10 and 11, right |R and left |L circular. In panel 9 the incident polarization is linear |+45° and the exit polarizer linear |45°. Like Fig. 5, the schematic in panel 12 helps to identify the positions of the darks spots with the incoming polarization; the depicted area is adapted to the intensity patterns in panels 1–11.

Fig. 5.
Fig. 5.

Map of the locations of dark spots created by incoming polarization states on the area of the crossed birefringent wedges. R and L indicate where right and left circularly polarized light creates dark spots; ellipses of various orientations and ellipticities correspond to dark spots created by elliptically polarized light; double arrows at various angles correspond to linearly polarized light inclined at different angles with the horizontal x axis. The map encompasses a larger area than in our experiment in order to show the periodicity of the pattern. The scaling of the axes describes the retardations Δ1, Δ2 of the two wedges in degrees. The x, y directions indicate the axes of the laboratory system and of the light ellipses; see Fig. 1(b).

Equations (4)

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|P=cos(1/2(90°2ω))exp(iλ)|L+cos(1/2(90°+2ω))exp(+iλ)|R.
|Pt=(1000)(cosαsinαsinαcosα)(eiΔ2001)(cosαsinαsinαcosα)(eiΔ1001)|P0=((sin2α+eiΔ2cos2α)eiΔ1(eiΔ21)cosαsinα00)|P0,
|P0=12(cos(12(90°2ω))eiλ+cos(12(90°+2ω))eiλi{cos(12(90°2ω))eiλcos(12(90°+2ω))eiλ}).
λ(|P0)=1/2arctan(sinΔ1/cotΔ2);ω(|P0)=1/2arccos(cosΔ2/cos2λ(|P0)).

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