Abstract

We report on the design, construction, and testing of a four-mirror reflective polarization rotator, proposed by Smith and Koch [J. Opt. Soc. Am. A 13, 2102 (1996)], that rotates by an angle ϕ the input linear polarization while preserving the input–output beam collinearity. We correct errors in the previous work that led to an incorrect design for a ϕ=π/2 rotator. This type of pure rotator is simple and inexpensive, and it is a direct application of the concept of the nonadiabatic geometric phase to polarization rotation. We also present measurements of the polarization rotation for the case of three metallic mirrors with antiparallel input and output beams, a test of geometric phase in polarization optics not done before.

© 1997 Optical Society of America

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References

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  1. J. Anandan, J. Christian, K. Wanelik, “Geometric phases in physics,” Am. J. Phys. 65, 180–185 (1997).
    [CrossRef]
  2. M. V. Berry, “Quantum phase factors accompanying adiabatic changes,” Proc. R. Soc. London Ser. A 392, 45–57 (1984).
    [CrossRef]
  3. R. Y. Chiao, Y.-S. Wu, “Manifestations of Berry’s topological phase for the photon,” Phys. Rev. Lett. 57, 933–936 (1986).
    [CrossRef] [PubMed]
  4. A. Tomita, R. Y. Chiao, “Observation of Berry’s topological phase by use of an optical fiber,” Phys. Rev. Lett. 57, 937–940 (1986).
    [CrossRef] [PubMed]
  5. M. Kitano, T. Yabuzaki, T. Ogawa, “Comment on ‘Observation of Berry’s topological phase by use of an optical fiber’,” Phys. Rev. Lett. 58, 523 (1987).
    [CrossRef]
  6. R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, H. Nathel, “Observation of a topological phase by means of a nonplanar Mach–Zehnder interferometer,” Phys. Rev. Lett. 60, 1214–1217 (1988).
    [CrossRef] [PubMed]
  7. H. Jiao, S. R. Wilkinson, R. Y. Chiao, H. Nathel, “Two topological phases in optics by means of a nonplanar Mach–Zender interferometer,” Phys. Rev. A 39, 3475–3486 (1989).
    [CrossRef] [PubMed]
  8. L. L. Smith, P. M. Koch, “Use of four mirrors to rotate linear polarization but preserve input–output collinearity,” J. Opt. Soc. Am. A 13, 2102–2105 (1996).
    [CrossRef]
  9. M. V. Berry, “Interpreting the anholonomy of coiled light,” Nature 326, 277–278 (1987).
    [CrossRef]
  10. L. H. Johnston, “Broadband polarization rotator for the infrared,” Appl. Opt. 16, 1082–1084 (1977).
    [PubMed]
  11. C. E. Greninger, “Reflective device for polarization rotation,” Appl. Opt. 27, 774–776 (1988).
    [CrossRef] [PubMed]
  12. F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957).
  13. G. Hass, L. Hadley, “Optical Properties of Metals,” in American Institute of Physics Handbook, D. E. Gray, ed. (McGraw-Hill, New York, 1982), Sec. 6, pp. 118–160.
  14. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).

1997 (1)

J. Anandan, J. Christian, K. Wanelik, “Geometric phases in physics,” Am. J. Phys. 65, 180–185 (1997).
[CrossRef]

1996 (1)

1989 (1)

H. Jiao, S. R. Wilkinson, R. Y. Chiao, H. Nathel, “Two topological phases in optics by means of a nonplanar Mach–Zender interferometer,” Phys. Rev. A 39, 3475–3486 (1989).
[CrossRef] [PubMed]

1988 (2)

C. E. Greninger, “Reflective device for polarization rotation,” Appl. Opt. 27, 774–776 (1988).
[CrossRef] [PubMed]

R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, H. Nathel, “Observation of a topological phase by means of a nonplanar Mach–Zehnder interferometer,” Phys. Rev. Lett. 60, 1214–1217 (1988).
[CrossRef] [PubMed]

1987 (2)

M. Kitano, T. Yabuzaki, T. Ogawa, “Comment on ‘Observation of Berry’s topological phase by use of an optical fiber’,” Phys. Rev. Lett. 58, 523 (1987).
[CrossRef]

M. V. Berry, “Interpreting the anholonomy of coiled light,” Nature 326, 277–278 (1987).
[CrossRef]

1986 (2)

R. Y. Chiao, Y.-S. Wu, “Manifestations of Berry’s topological phase for the photon,” Phys. Rev. Lett. 57, 933–936 (1986).
[CrossRef] [PubMed]

A. Tomita, R. Y. Chiao, “Observation of Berry’s topological phase by use of an optical fiber,” Phys. Rev. Lett. 57, 937–940 (1986).
[CrossRef] [PubMed]

1984 (1)

M. V. Berry, “Quantum phase factors accompanying adiabatic changes,” Proc. R. Soc. London Ser. A 392, 45–57 (1984).
[CrossRef]

1977 (1)

Anandan, J.

J. Anandan, J. Christian, K. Wanelik, “Geometric phases in physics,” Am. J. Phys. 65, 180–185 (1997).
[CrossRef]

Antaramian, A.

R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, H. Nathel, “Observation of a topological phase by means of a nonplanar Mach–Zehnder interferometer,” Phys. Rev. Lett. 60, 1214–1217 (1988).
[CrossRef] [PubMed]

Berry, M. V.

M. V. Berry, “Interpreting the anholonomy of coiled light,” Nature 326, 277–278 (1987).
[CrossRef]

M. V. Berry, “Quantum phase factors accompanying adiabatic changes,” Proc. R. Soc. London Ser. A 392, 45–57 (1984).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).

Chiao, R. Y.

H. Jiao, S. R. Wilkinson, R. Y. Chiao, H. Nathel, “Two topological phases in optics by means of a nonplanar Mach–Zender interferometer,” Phys. Rev. A 39, 3475–3486 (1989).
[CrossRef] [PubMed]

R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, H. Nathel, “Observation of a topological phase by means of a nonplanar Mach–Zehnder interferometer,” Phys. Rev. Lett. 60, 1214–1217 (1988).
[CrossRef] [PubMed]

R. Y. Chiao, Y.-S. Wu, “Manifestations of Berry’s topological phase for the photon,” Phys. Rev. Lett. 57, 933–936 (1986).
[CrossRef] [PubMed]

A. Tomita, R. Y. Chiao, “Observation of Berry’s topological phase by use of an optical fiber,” Phys. Rev. Lett. 57, 937–940 (1986).
[CrossRef] [PubMed]

Christian, J.

J. Anandan, J. Christian, K. Wanelik, “Geometric phases in physics,” Am. J. Phys. 65, 180–185 (1997).
[CrossRef]

Ganga, K. M.

R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, H. Nathel, “Observation of a topological phase by means of a nonplanar Mach–Zehnder interferometer,” Phys. Rev. Lett. 60, 1214–1217 (1988).
[CrossRef] [PubMed]

Greninger, C. E.

Hadley, L.

G. Hass, L. Hadley, “Optical Properties of Metals,” in American Institute of Physics Handbook, D. E. Gray, ed. (McGraw-Hill, New York, 1982), Sec. 6, pp. 118–160.

Hass, G.

G. Hass, L. Hadley, “Optical Properties of Metals,” in American Institute of Physics Handbook, D. E. Gray, ed. (McGraw-Hill, New York, 1982), Sec. 6, pp. 118–160.

Jenkins, F. A.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957).

Jiao, H.

H. Jiao, S. R. Wilkinson, R. Y. Chiao, H. Nathel, “Two topological phases in optics by means of a nonplanar Mach–Zender interferometer,” Phys. Rev. A 39, 3475–3486 (1989).
[CrossRef] [PubMed]

R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, H. Nathel, “Observation of a topological phase by means of a nonplanar Mach–Zehnder interferometer,” Phys. Rev. Lett. 60, 1214–1217 (1988).
[CrossRef] [PubMed]

Johnston, L. H.

Kitano, M.

M. Kitano, T. Yabuzaki, T. Ogawa, “Comment on ‘Observation of Berry’s topological phase by use of an optical fiber’,” Phys. Rev. Lett. 58, 523 (1987).
[CrossRef]

Koch, P. M.

Nathel, H.

H. Jiao, S. R. Wilkinson, R. Y. Chiao, H. Nathel, “Two topological phases in optics by means of a nonplanar Mach–Zender interferometer,” Phys. Rev. A 39, 3475–3486 (1989).
[CrossRef] [PubMed]

R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, H. Nathel, “Observation of a topological phase by means of a nonplanar Mach–Zehnder interferometer,” Phys. Rev. Lett. 60, 1214–1217 (1988).
[CrossRef] [PubMed]

Ogawa, T.

M. Kitano, T. Yabuzaki, T. Ogawa, “Comment on ‘Observation of Berry’s topological phase by use of an optical fiber’,” Phys. Rev. Lett. 58, 523 (1987).
[CrossRef]

Smith, L. L.

Tomita, A.

A. Tomita, R. Y. Chiao, “Observation of Berry’s topological phase by use of an optical fiber,” Phys. Rev. Lett. 57, 937–940 (1986).
[CrossRef] [PubMed]

Wanelik, K.

J. Anandan, J. Christian, K. Wanelik, “Geometric phases in physics,” Am. J. Phys. 65, 180–185 (1997).
[CrossRef]

White, H. E.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957).

Wilkinson, S. R.

H. Jiao, S. R. Wilkinson, R. Y. Chiao, H. Nathel, “Two topological phases in optics by means of a nonplanar Mach–Zender interferometer,” Phys. Rev. A 39, 3475–3486 (1989).
[CrossRef] [PubMed]

R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, H. Nathel, “Observation of a topological phase by means of a nonplanar Mach–Zehnder interferometer,” Phys. Rev. Lett. 60, 1214–1217 (1988).
[CrossRef] [PubMed]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).

Wu, Y.-S.

R. Y. Chiao, Y.-S. Wu, “Manifestations of Berry’s topological phase for the photon,” Phys. Rev. Lett. 57, 933–936 (1986).
[CrossRef] [PubMed]

Yabuzaki, T.

M. Kitano, T. Yabuzaki, T. Ogawa, “Comment on ‘Observation of Berry’s topological phase by use of an optical fiber’,” Phys. Rev. Lett. 58, 523 (1987).
[CrossRef]

Am. J. Phys. (1)

J. Anandan, J. Christian, K. Wanelik, “Geometric phases in physics,” Am. J. Phys. 65, 180–185 (1997).
[CrossRef]

Appl. Opt. (2)

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

Nature (1)

M. V. Berry, “Interpreting the anholonomy of coiled light,” Nature 326, 277–278 (1987).
[CrossRef]

Phys. Rev. A (1)

H. Jiao, S. R. Wilkinson, R. Y. Chiao, H. Nathel, “Two topological phases in optics by means of a nonplanar Mach–Zender interferometer,” Phys. Rev. A 39, 3475–3486 (1989).
[CrossRef] [PubMed]

Phys. Rev. Lett. (4)

R. Y. Chiao, Y.-S. Wu, “Manifestations of Berry’s topological phase for the photon,” Phys. Rev. Lett. 57, 933–936 (1986).
[CrossRef] [PubMed]

A. Tomita, R. Y. Chiao, “Observation of Berry’s topological phase by use of an optical fiber,” Phys. Rev. Lett. 57, 937–940 (1986).
[CrossRef] [PubMed]

M. Kitano, T. Yabuzaki, T. Ogawa, “Comment on ‘Observation of Berry’s topological phase by use of an optical fiber’,” Phys. Rev. Lett. 58, 523 (1987).
[CrossRef]

R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, H. Nathel, “Observation of a topological phase by means of a nonplanar Mach–Zehnder interferometer,” Phys. Rev. Lett. 60, 1214–1217 (1988).
[CrossRef] [PubMed]

Proc. R. Soc. London Ser. A (1)

M. V. Berry, “Quantum phase factors accompanying adiabatic changes,” Proc. R. Soc. London Ser. A 392, 45–57 (1984).
[CrossRef]

Other (3)

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957).

G. Hass, L. Hadley, “Optical Properties of Metals,” in American Institute of Physics Handbook, D. E. Gray, ed. (McGraw-Hill, New York, 1982), Sec. 6, pp. 118–160.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).

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Figures (3)

Fig. 1
Fig. 1

Arrangement of vectors (photon spin) for our four-mirror, reflective polarization rotator design (see text).

Fig. 2
Fig. 2

Trajectory of the light as it goes through the rotator. Also shown are the propagation vectors k, whose photon-spin space geometry is given by Fig. 1. For the case with θ˜3=120° and φ˜3=35.26°, the relative dimensions are a:b:c=1:1:1.414.

Fig. 3
Fig. 3

Measurements of the polarization rotation angle ϕ for the three-metallic-mirror case as a function of the solid angle Ω described by the spin of the photon in its closed and discrete trajectory. The two data sets shown correspond to two different values of the azimuth angle of the input polarization of the light (see text): ψ3=90° (squares) and ψ3=-74.2° (circles). The solid line is the expected polarization rotation angle.

Equations (5)

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k0=|r2-r1||r4-r1|k1+|r3-r2||r4-r1|k2+|r4-r3||r4-r1|k3=k4,
θ1=θ3<π/2
π/2<ϕ1=-φ3<π.
Ωk˜0,k˜1,k˜2,k˜3=2Ωk˜0,k˜2,k˜3,
Ωk˜0,k˜2,k˜3(θ˜3,φ˜3)=π/4.

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