Abstract

We show that a device consisting of an optical rotator placed between two identically oriented quarter-wave plates always acts as a halfwave retarder for some pair of orthogonal elliptically polarized states that can be selected by linear adjustment of the optical rotation and orientation of the quarter-wave plates.

© 1997 Optical Society of America

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References

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  1. R. C. Jones, “A new calculus for the treatment of optical systems,” J. Opt. Soc. Am. 31, 500–503 (1941).
    [CrossRef]
  2. A. G. Fox, “An adjustable waveguide phase changer,” Proc. IRE 35, 1489–1498 (1947).
    [CrossRef]
  3. S. Pancharatnam, “Achromatic combinations of birefringent plates,” Proc. Indian Acad. Sci. A 41, 137–144 (1955).
  4. M. O. Freeman, T. A. Brown, D. M. Walba, “Quantized complex ferroelectric liquid crystal spatial light modulators,” Appl. Opt. 31, 3917–3929 (1992).
    [CrossRef] [PubMed]
  5. R. Bhandari, “Polarization of light and topological phases,” Phys. Reports 281, 1–64 (1997).
    [CrossRef]
  6. R. J. C. Spreeuw, M. W. Beijersbergen, J. P. Woerdman, “Optical ring cavities as tailored four-level systems: an application of the group U(2, 2),” Phys. Rev. A 45, 1213–1229 (1992).
    [CrossRef] [PubMed]
  7. K. Mattle, H. Weinfurter, P. G. Kwiat, A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656–4659 (1996).
    [CrossRef] [PubMed]
  8. R. Bhandari, “Synthesis of general polarization transformers—a geometric phase approach,” Phys. Lett. A 138, 469–473 (1989).
    [CrossRef]
  9. R. Bhandari, T. Dasgupta, “A spin-1/2 interferometer using light beams,” Phys. Lett. A 143, 170–175 (1990).
    [CrossRef]
  10. Y. Aharonov, J. Anandan, Phys. Rev. Lett. 58, 1593–1596 (1987).
  11. C. H. Bennett, “Quantum information and computing,” Phys. Today 48 (10), 24–30 (1995).
  12. G. S. Agarwal, “Geometric phase induced changes in the correlation properties of the entangled states,” Opt. Commun. 87, 193–195 (1992).
    [CrossRef]

1997 (1)

R. Bhandari, “Polarization of light and topological phases,” Phys. Reports 281, 1–64 (1997).
[CrossRef]

1996 (1)

K. Mattle, H. Weinfurter, P. G. Kwiat, A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656–4659 (1996).
[CrossRef] [PubMed]

1995 (1)

C. H. Bennett, “Quantum information and computing,” Phys. Today 48 (10), 24–30 (1995).

1992 (3)

G. S. Agarwal, “Geometric phase induced changes in the correlation properties of the entangled states,” Opt. Commun. 87, 193–195 (1992).
[CrossRef]

R. J. C. Spreeuw, M. W. Beijersbergen, J. P. Woerdman, “Optical ring cavities as tailored four-level systems: an application of the group U(2, 2),” Phys. Rev. A 45, 1213–1229 (1992).
[CrossRef] [PubMed]

M. O. Freeman, T. A. Brown, D. M. Walba, “Quantized complex ferroelectric liquid crystal spatial light modulators,” Appl. Opt. 31, 3917–3929 (1992).
[CrossRef] [PubMed]

1990 (1)

R. Bhandari, T. Dasgupta, “A spin-1/2 interferometer using light beams,” Phys. Lett. A 143, 170–175 (1990).
[CrossRef]

1989 (1)

R. Bhandari, “Synthesis of general polarization transformers—a geometric phase approach,” Phys. Lett. A 138, 469–473 (1989).
[CrossRef]

1987 (1)

Y. Aharonov, J. Anandan, Phys. Rev. Lett. 58, 1593–1596 (1987).

1955 (1)

S. Pancharatnam, “Achromatic combinations of birefringent plates,” Proc. Indian Acad. Sci. A 41, 137–144 (1955).

1947 (1)

A. G. Fox, “An adjustable waveguide phase changer,” Proc. IRE 35, 1489–1498 (1947).
[CrossRef]

1941 (1)

Agarwal, G. S.

G. S. Agarwal, “Geometric phase induced changes in the correlation properties of the entangled states,” Opt. Commun. 87, 193–195 (1992).
[CrossRef]

Aharonov, Y.

Y. Aharonov, J. Anandan, Phys. Rev. Lett. 58, 1593–1596 (1987).

Anandan, J.

Y. Aharonov, J. Anandan, Phys. Rev. Lett. 58, 1593–1596 (1987).

Beijersbergen, M. W.

R. J. C. Spreeuw, M. W. Beijersbergen, J. P. Woerdman, “Optical ring cavities as tailored four-level systems: an application of the group U(2, 2),” Phys. Rev. A 45, 1213–1229 (1992).
[CrossRef] [PubMed]

Bennett, C. H.

C. H. Bennett, “Quantum information and computing,” Phys. Today 48 (10), 24–30 (1995).

Bhandari, R.

R. Bhandari, “Polarization of light and topological phases,” Phys. Reports 281, 1–64 (1997).
[CrossRef]

R. Bhandari, T. Dasgupta, “A spin-1/2 interferometer using light beams,” Phys. Lett. A 143, 170–175 (1990).
[CrossRef]

R. Bhandari, “Synthesis of general polarization transformers—a geometric phase approach,” Phys. Lett. A 138, 469–473 (1989).
[CrossRef]

Brown, T. A.

Dasgupta, T.

R. Bhandari, T. Dasgupta, “A spin-1/2 interferometer using light beams,” Phys. Lett. A 143, 170–175 (1990).
[CrossRef]

Fox, A. G.

A. G. Fox, “An adjustable waveguide phase changer,” Proc. IRE 35, 1489–1498 (1947).
[CrossRef]

Freeman, M. O.

Jones, R. C.

Kwiat, P. G.

K. Mattle, H. Weinfurter, P. G. Kwiat, A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656–4659 (1996).
[CrossRef] [PubMed]

Mattle, K.

K. Mattle, H. Weinfurter, P. G. Kwiat, A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656–4659 (1996).
[CrossRef] [PubMed]

Pancharatnam, S.

S. Pancharatnam, “Achromatic combinations of birefringent plates,” Proc. Indian Acad. Sci. A 41, 137–144 (1955).

Spreeuw, R. J. C.

R. J. C. Spreeuw, M. W. Beijersbergen, J. P. Woerdman, “Optical ring cavities as tailored four-level systems: an application of the group U(2, 2),” Phys. Rev. A 45, 1213–1229 (1992).
[CrossRef] [PubMed]

Walba, D. M.

Weinfurter, H.

K. Mattle, H. Weinfurter, P. G. Kwiat, A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656–4659 (1996).
[CrossRef] [PubMed]

Woerdman, J. P.

R. J. C. Spreeuw, M. W. Beijersbergen, J. P. Woerdman, “Optical ring cavities as tailored four-level systems: an application of the group U(2, 2),” Phys. Rev. A 45, 1213–1229 (1992).
[CrossRef] [PubMed]

Zeilinger, A.

K. Mattle, H. Weinfurter, P. G. Kwiat, A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656–4659 (1996).
[CrossRef] [PubMed]

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

G. S. Agarwal, “Geometric phase induced changes in the correlation properties of the entangled states,” Opt. Commun. 87, 193–195 (1992).
[CrossRef]

Phys. Lett. A (2)

R. Bhandari, “Synthesis of general polarization transformers—a geometric phase approach,” Phys. Lett. A 138, 469–473 (1989).
[CrossRef]

R. Bhandari, T. Dasgupta, “A spin-1/2 interferometer using light beams,” Phys. Lett. A 143, 170–175 (1990).
[CrossRef]

Phys. Reports (1)

R. Bhandari, “Polarization of light and topological phases,” Phys. Reports 281, 1–64 (1997).
[CrossRef]

Phys. Rev. A (1)

R. J. C. Spreeuw, M. W. Beijersbergen, J. P. Woerdman, “Optical ring cavities as tailored four-level systems: an application of the group U(2, 2),” Phys. Rev. A 45, 1213–1229 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

K. Mattle, H. Weinfurter, P. G. Kwiat, A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656–4659 (1996).
[CrossRef] [PubMed]

Y. Aharonov, J. Anandan, Phys. Rev. Lett. 58, 1593–1596 (1987).

Phys. Today (1)

C. H. Bennett, “Quantum information and computing,” Phys. Today 48 (10), 24–30 (1995).

Proc. Indian Acad. Sci. A (1)

S. Pancharatnam, “Achromatic combinations of birefringent plates,” Proc. Indian Acad. Sci. A 41, 137–144 (1955).

Proc. IRE (1)

A. G. Fox, “An adjustable waveguide phase changer,” Proc. IRE 35, 1489–1498 (1947).
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

Action of the QRQ device on the elliptically polarized state M represented on the Poincaré sphere by the closed circuit consisting of arcs MH, HQV, and VM. R and L represent the right and left circularly polarized states, respectively, and the states on the equator of the sphere represent linearly polarized states. Point Q with azimuth 0° corresponds to linear polarization along the x direction, and a rotation of linear polarization through angle ϕ/2 in real space corresponds to a rotation through ϕ on the sphere.

Equations (10)

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

U=exp-iα/2σ·nˆ=cosα/2-isinα/2σ·nˆ,
σ1=0110, σ2=0-ii0, σ3=100-1,
σpσq=i r=13 pqrσr
W=-icos β cos ϕ σ1+cos β sin ϕσ2+sin βσ3.
Ψ+>=1>2>+2>1>/2,
Ψ->=1>2>-2>1>/2,
Φ+>=1>1>+2>2>/2,
Φ->=1>1>-2>2>/2,
Φ>=1>1>+exp-2iβ2>2>/2
Ψ>=1>2>+exp-2iβ2>1>/2,

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