Abstract

Few experiments have been reported for the observation of Berry’s phase for the photon. This may be due to the difficulty of configuring suitable experiments. We start by repeating previous work on the observation of the optical activity of a helically wound fiber coil in the transmissive mode, but then we go on to demonstrate that when the light is reflected back through the same coil from a mirrored surface, it cancels this optical activity. We also report on a new experimental configuration in which a helical fiber coil is built into the loop of a Sagnac interferometer. The changes in Berry’s phase acquired by the two counterpropagating beams can be varied by stretching the coil with the result that fringes are produced at the output. One of the major benefits of this experimental setup is that it enables observations of Berry’s phase to be made for light in any state of polarization.

© 2000 Optical Society of America

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References

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  1. M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. London, Ser. A 392, 45–57 (1984).
    [CrossRef]
  2. R. Y. Chiao and Y. S. Wu, “Manifestations of Berry’s topological phase for the photon,” Phys. Rev. Lett. 57, 933–936 (1986).
    [CrossRef] [PubMed]
  3. A. Tomita and R. Y. Chiao, “Observation of Berry’s topological phase by use of an optical fiber,” Phys. Rev. Lett. 57, 937–940 (1986).
    [CrossRef] [PubMed]
  4. E. M. Frins and W. Dultz, “Direct observation of Berry’s topological phase by using an optical fiber ring interferometer,” Opt. Commun. 136, 354–356 (1997).
    [CrossRef]
  5. A. V. Dooghin, N. D. Kundikova, V. S. Liberman, and B. Ya. Zel’dovich, “Optical Magnus effect,” Phys. Rev. A 45, 8204–8208 (1992).
    [CrossRef] [PubMed]
  6. M. V. Berry, “Interpreting the anholonomy of coiled light,” Nature 326, 277–278 (1987).
    [CrossRef]
  7. N. I. Petrov, “Evolution of Berry’s phase in a graded index medium,” Phys. Lett. A 234, 239–250 (1997).
    [CrossRef]
  8. O. J. Kwon, H. T. Lee, S. B. Lee, and S. S. Choi, “Observation of a topological phase in a noncyclic case by use of a half-turn optical fiber,” Opt. Lett. 16, 223–225 (1997).
    [CrossRef]
  9. J. N. Ross, “The rotation of the polarization in low birefringence monomode optical fibres due to geometric effects,” Opt. Quantum Electron. 16, 455–461 (1984).
    [CrossRef]
  10. J. Tromp and F. A. Dahlen, “The Berry phase of a slowly varying waveguide,” Proc. R. Soc. London, Ser. A 437, 329–342 (1984).
    [CrossRef]
  11. S. G. Lipson, “Berry’s phase in optical interferometry: a simple derivation,” Opt. Lett. 15, 154–155 (1990).
    [CrossRef] [PubMed]
  12. M. Kitano, T. Yabuzaki, and T. Ogawa, “Comment on observation of Berry’s topological phase by use of an optical fiber,” Phys. Rev. Lett. 58, 523 (1987).
    [CrossRef]
  13. R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, and H. Nathel, “Observation of a topological phase by means of a nonplanar Mach–Zehnder interferometer,” Phys. Rev. Lett. 60, 1214–1217 (1988).
    [CrossRef] [PubMed]
  14. P. G. Kwiat and R. Y. Chiao, “Observation of a nonclassical Berry’s phase for the photon,” Phys. Rev. Lett. 66, 588–591 (1991).
    [CrossRef] [PubMed]
  15. J. Christian and A. Shimony, “Non-cyclic geometric phases in a proposed two-photon interferometric experiment,” J. Phys. A: Math. Gen. 26, 5551–5567 (1993).
    [CrossRef]
  16. R. Y. Chiao, C. K. Hong, P. G. Kwiat, H. Nathel, and W. A. Vareka, “Optical manifestations of Berry’s topological phase: classical and quantum aspects,” in Coherence and Quantum Optics VI, J. H. Eberly, L. Mandel, and E. Wolf, eds. (Plenum, New York, 1990), pp. 155–160.
  17. S. Pancharatnam, “Generalized theory of interference, and its applications,” Proc. Indian Acad. Sci., Sect. A 44, 247–262 (1956).
  18. J. Samuel and R. Bhandari, “General setting for Berry’s phase,” Phys. Rev. Lett. 60, 2339–2342 (1988).
    [CrossRef] [PubMed]
  19. R. Bhandari and J. Samuel, “Observation of topological phase by use of a laser interferometer,” Phys. Rev. Lett. 60, 1211–1213 (1988).
    [CrossRef] [PubMed]
  20. T. H. Chyba, L. J. Wang, L. Mandel, and R. Simon, “Measurement of the Pancharatnam phase for a light beam,” Opt. Lett. 13, 562–564 (1988).
    [CrossRef] [PubMed]
  21. M. Martinelli and P. Vavassori, “A geometric (Pancharatnam) phase approach to the polarization and phase control in the coherent optics circuits,” Opt. Commun. 80, 166–176 (1990).
    [CrossRef]
  22. P. Hariharan and P. E. Ciddor, “An achromatic phase-shifter operating on the geometric phase,” Opt. Commun. 110, 13–17 (1994).
    [CrossRef]
  23. F. Wassmann and A. Ankiewicz, “Berry’s phase analysis of polarization rotation in helicoidal fibers,” Appl. Opt. 37, 3902–3911 (1998).
    [CrossRef]

1998 (1)

1997 (3)

E. M. Frins and W. Dultz, “Direct observation of Berry’s topological phase by using an optical fiber ring interferometer,” Opt. Commun. 136, 354–356 (1997).
[CrossRef]

N. I. Petrov, “Evolution of Berry’s phase in a graded index medium,” Phys. Lett. A 234, 239–250 (1997).
[CrossRef]

O. J. Kwon, H. T. Lee, S. B. Lee, and S. S. Choi, “Observation of a topological phase in a noncyclic case by use of a half-turn optical fiber,” Opt. Lett. 16, 223–225 (1997).
[CrossRef]

1994 (1)

P. Hariharan and P. E. Ciddor, “An achromatic phase-shifter operating on the geometric phase,” Opt. Commun. 110, 13–17 (1994).
[CrossRef]

1993 (1)

J. Christian and A. Shimony, “Non-cyclic geometric phases in a proposed two-photon interferometric experiment,” J. Phys. A: Math. Gen. 26, 5551–5567 (1993).
[CrossRef]

1992 (1)

A. V. Dooghin, N. D. Kundikova, V. S. Liberman, and B. Ya. Zel’dovich, “Optical Magnus effect,” Phys. Rev. A 45, 8204–8208 (1992).
[CrossRef] [PubMed]

1991 (1)

P. G. Kwiat and R. Y. Chiao, “Observation of a nonclassical Berry’s phase for the photon,” Phys. Rev. Lett. 66, 588–591 (1991).
[CrossRef] [PubMed]

1990 (2)

M. Martinelli and P. Vavassori, “A geometric (Pancharatnam) phase approach to the polarization and phase control in the coherent optics circuits,” Opt. Commun. 80, 166–176 (1990).
[CrossRef]

S. G. Lipson, “Berry’s phase in optical interferometry: a simple derivation,” Opt. Lett. 15, 154–155 (1990).
[CrossRef] [PubMed]

1988 (4)

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

J. Samuel and R. Bhandari, “General setting for Berry’s phase,” Phys. Rev. Lett. 60, 2339–2342 (1988).
[CrossRef] [PubMed]

R. Bhandari and J. Samuel, “Observation of topological phase by use of a laser interferometer,” Phys. Rev. Lett. 60, 1211–1213 (1988).
[CrossRef] [PubMed]

T. H. Chyba, L. J. Wang, L. Mandel, and R. Simon, “Measurement of the Pancharatnam phase for a light beam,” Opt. Lett. 13, 562–564 (1988).
[CrossRef] [PubMed]

1987 (2)

M. Kitano, T. Yabuzaki, and 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 and Y. S. Wu, “Manifestations of Berry’s topological phase for the photon,” Phys. Rev. Lett. 57, 933–936 (1986).
[CrossRef] [PubMed]

A. Tomita and 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 (3)

J. N. Ross, “The rotation of the polarization in low birefringence monomode optical fibres due to geometric effects,” Opt. Quantum Electron. 16, 455–461 (1984).
[CrossRef]

J. Tromp and F. A. Dahlen, “The Berry phase of a slowly varying waveguide,” Proc. R. Soc. London, Ser. A 437, 329–342 (1984).
[CrossRef]

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

1956 (1)

S. Pancharatnam, “Generalized theory of interference, and its applications,” Proc. Indian Acad. Sci., Sect. A 44, 247–262 (1956).

Ankiewicz, A.

Antaramian, A.

R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, and 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, “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. London, Ser. A 392, 45–57 (1984).
[CrossRef]

Bhandari, R.

J. Samuel and R. Bhandari, “General setting for Berry’s phase,” Phys. Rev. Lett. 60, 2339–2342 (1988).
[CrossRef] [PubMed]

R. Bhandari and J. Samuel, “Observation of topological phase by use of a laser interferometer,” Phys. Rev. Lett. 60, 1211–1213 (1988).
[CrossRef] [PubMed]

Chiao, R. Y.

P. G. Kwiat and R. Y. Chiao, “Observation of a nonclassical Berry’s phase for the photon,” Phys. Rev. Lett. 66, 588–591 (1991).
[CrossRef] [PubMed]

R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, and 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 and Y. S. Wu, “Manifestations of Berry’s topological phase for the photon,” Phys. Rev. Lett. 57, 933–936 (1986).
[CrossRef] [PubMed]

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

Choi, S. S.

Christian, J.

J. Christian and A. Shimony, “Non-cyclic geometric phases in a proposed two-photon interferometric experiment,” J. Phys. A: Math. Gen. 26, 5551–5567 (1993).
[CrossRef]

Chyba, T. H.

Ciddor, P. E.

P. Hariharan and P. E. Ciddor, “An achromatic phase-shifter operating on the geometric phase,” Opt. Commun. 110, 13–17 (1994).
[CrossRef]

Dahlen, F. A.

J. Tromp and F. A. Dahlen, “The Berry phase of a slowly varying waveguide,” Proc. R. Soc. London, Ser. A 437, 329–342 (1984).
[CrossRef]

Dooghin, A. V.

A. V. Dooghin, N. D. Kundikova, V. S. Liberman, and B. Ya. Zel’dovich, “Optical Magnus effect,” Phys. Rev. A 45, 8204–8208 (1992).
[CrossRef] [PubMed]

Dultz, W.

E. M. Frins and W. Dultz, “Direct observation of Berry’s topological phase by using an optical fiber ring interferometer,” Opt. Commun. 136, 354–356 (1997).
[CrossRef]

Frins, E. M.

E. M. Frins and W. Dultz, “Direct observation of Berry’s topological phase by using an optical fiber ring interferometer,” Opt. Commun. 136, 354–356 (1997).
[CrossRef]

Ganga, K. M.

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

Hariharan, P.

P. Hariharan and P. E. Ciddor, “An achromatic phase-shifter operating on the geometric phase,” Opt. Commun. 110, 13–17 (1994).
[CrossRef]

Jiao, H.

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

Kitano, M.

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

Kundikova, N. D.

A. V. Dooghin, N. D. Kundikova, V. S. Liberman, and B. Ya. Zel’dovich, “Optical Magnus effect,” Phys. Rev. A 45, 8204–8208 (1992).
[CrossRef] [PubMed]

Kwiat, P. G.

P. G. Kwiat and R. Y. Chiao, “Observation of a nonclassical Berry’s phase for the photon,” Phys. Rev. Lett. 66, 588–591 (1991).
[CrossRef] [PubMed]

Kwon, O. J.

Lee, H. T.

Lee, S. B.

Liberman, V. S.

A. V. Dooghin, N. D. Kundikova, V. S. Liberman, and B. Ya. Zel’dovich, “Optical Magnus effect,” Phys. Rev. A 45, 8204–8208 (1992).
[CrossRef] [PubMed]

Lipson, S. G.

Mandel, L.

Martinelli, M.

M. Martinelli and P. Vavassori, “A geometric (Pancharatnam) phase approach to the polarization and phase control in the coherent optics circuits,” Opt. Commun. 80, 166–176 (1990).
[CrossRef]

Nathel, H.

R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, and 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, and T. Ogawa, “Comment on observation of Berry’s topological phase by use of an optical fiber,” Phys. Rev. Lett. 58, 523 (1987).
[CrossRef]

Pancharatnam, S.

S. Pancharatnam, “Generalized theory of interference, and its applications,” Proc. Indian Acad. Sci., Sect. A 44, 247–262 (1956).

Petrov, N. I.

N. I. Petrov, “Evolution of Berry’s phase in a graded index medium,” Phys. Lett. A 234, 239–250 (1997).
[CrossRef]

Ross, J. N.

J. N. Ross, “The rotation of the polarization in low birefringence monomode optical fibres due to geometric effects,” Opt. Quantum Electron. 16, 455–461 (1984).
[CrossRef]

Samuel, J.

J. Samuel and R. Bhandari, “General setting for Berry’s phase,” Phys. Rev. Lett. 60, 2339–2342 (1988).
[CrossRef] [PubMed]

R. Bhandari and J. Samuel, “Observation of topological phase by use of a laser interferometer,” Phys. Rev. Lett. 60, 1211–1213 (1988).
[CrossRef] [PubMed]

Shimony, A.

J. Christian and A. Shimony, “Non-cyclic geometric phases in a proposed two-photon interferometric experiment,” J. Phys. A: Math. Gen. 26, 5551–5567 (1993).
[CrossRef]

Simon, R.

Tomita, A.

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

Tromp, J.

J. Tromp and F. A. Dahlen, “The Berry phase of a slowly varying waveguide,” Proc. R. Soc. London, Ser. A 437, 329–342 (1984).
[CrossRef]

Vavassori, P.

M. Martinelli and P. Vavassori, “A geometric (Pancharatnam) phase approach to the polarization and phase control in the coherent optics circuits,” Opt. Commun. 80, 166–176 (1990).
[CrossRef]

Wang, L. J.

Wassmann, F.

Wilkinson, S. R.

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

Wu, Y. S.

R. Y. Chiao and 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, and T. Ogawa, “Comment on observation of Berry’s topological phase by use of an optical fiber,” Phys. Rev. Lett. 58, 523 (1987).
[CrossRef]

Zel’dovich, B. Ya.

A. V. Dooghin, N. D. Kundikova, V. S. Liberman, and B. Ya. Zel’dovich, “Optical Magnus effect,” Phys. Rev. A 45, 8204–8208 (1992).
[CrossRef] [PubMed]

Appl. Opt. (1)

J. Phys. A: Math. Gen. (1)

J. Christian and A. Shimony, “Non-cyclic geometric phases in a proposed two-photon interferometric experiment,” J. Phys. A: Math. Gen. 26, 5551–5567 (1993).
[CrossRef]

Nature (1)

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

Opt. Commun. (3)

E. M. Frins and W. Dultz, “Direct observation of Berry’s topological phase by using an optical fiber ring interferometer,” Opt. Commun. 136, 354–356 (1997).
[CrossRef]

M. Martinelli and P. Vavassori, “A geometric (Pancharatnam) phase approach to the polarization and phase control in the coherent optics circuits,” Opt. Commun. 80, 166–176 (1990).
[CrossRef]

P. Hariharan and P. E. Ciddor, “An achromatic phase-shifter operating on the geometric phase,” Opt. Commun. 110, 13–17 (1994).
[CrossRef]

Opt. Lett. (3)

Opt. Quantum Electron. (1)

J. N. Ross, “The rotation of the polarization in low birefringence monomode optical fibres due to geometric effects,” Opt. Quantum Electron. 16, 455–461 (1984).
[CrossRef]

Phys. Lett. A (1)

N. I. Petrov, “Evolution of Berry’s phase in a graded index medium,” Phys. Lett. A 234, 239–250 (1997).
[CrossRef]

Phys. Rev. A (1)

A. V. Dooghin, N. D. Kundikova, V. S. Liberman, and B. Ya. Zel’dovich, “Optical Magnus effect,” Phys. Rev. A 45, 8204–8208 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (7)

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

A. Tomita and 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, and 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, and H. Nathel, “Observation of a topological phase by means of a nonplanar Mach–Zehnder interferometer,” Phys. Rev. Lett. 60, 1214–1217 (1988).
[CrossRef] [PubMed]

P. G. Kwiat and R. Y. Chiao, “Observation of a nonclassical Berry’s phase for the photon,” Phys. Rev. Lett. 66, 588–591 (1991).
[CrossRef] [PubMed]

J. Samuel and R. Bhandari, “General setting for Berry’s phase,” Phys. Rev. Lett. 60, 2339–2342 (1988).
[CrossRef] [PubMed]

R. Bhandari and J. Samuel, “Observation of topological phase by use of a laser interferometer,” Phys. Rev. Lett. 60, 1211–1213 (1988).
[CrossRef] [PubMed]

Proc. Indian Acad. Sci., Sect. A (1)

S. Pancharatnam, “Generalized theory of interference, and its applications,” Proc. Indian Acad. Sci., Sect. A 44, 247–262 (1956).

Proc. R. Soc. London, Ser. A (2)

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

J. Tromp and F. A. Dahlen, “The Berry phase of a slowly varying waveguide,” Proc. R. Soc. London, Ser. A 437, 329–342 (1984).
[CrossRef]

Other (1)

R. Y. Chiao, C. K. Hong, P. G. Kwiat, H. Nathel, and W. A. Vareka, “Optical manifestations of Berry’s topological phase: classical and quantum aspects,” in Coherence and Quantum Optics VI, J. H. Eberly, L. Mandel, and E. Wolf, eds. (Plenum, New York, 1990), pp. 155–160.

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Figures (10)

Fig. 1
Fig. 1

Basic apparatus to show the rotation of light in a helical coil.

Fig. 2
Fig. 2

Momentum space. The solid angle enclosed by the curve representing the optical path in momentum space gives a measure of Berry’s phase.

Fig. 3
Fig. 3

Variation of rotation of the plane of polarization as a function of displacement in experiment 1.

Fig. 4
Fig. 4

Optical activity of light reflected back into the helix.

Fig. 5
Fig. 5

Sagnac interferometer configured to study Berry’s phase of linearly polarized light.

Fig. 6
Fig. 6

Fringes observed with linearly polarized light.

Fig. 7
Fig. 7

Poincare sphere. A2 and B2 are the states of polarization of the two interfering beams.

Fig. 8
Fig. 8

Sagnac interferometer configured to observe Berry’s phase of elliptically polarized light.

Fig. 9
Fig. 9

Variation of output power as a function of Berry’s phase for three representative states of polarization (SOP’s).

Fig. 10
Fig. 10

Comparison of observed and theoretically generated curves for both direct and reflected (return) ports.

Equations (13)

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

γ=-σΩ=-2πσ(1-cos θ),
a1|Lexp(iγ-iγ)+a2|Rexp(-iγ+iγ)
=a1|L+a2|R.
I=I1+I2+2I1I2 cos 12c cos δ,
I=I1/2[1+cos(c/2)]=I1/2(1+cos 2γ).
ID=I1/2(1-cos 2γ).
|A=|B=(1/2){a1|R+a2|L}.
|A2=(1/2){a1|Lexp(-iγ)+a2|Rexp(iγ)}.
|B2=(1/2){a1|Lexp(iγ)+a2|Rexp(-iγ)},
|A2+|B2=(1/2){a1|R[exp(iγ)+e(iγ)]+a2|L[exp(-iγ)+exp(-iγ)]},
|A2+|B2={a1|L+a2|L}cos γ=|Ccos γ.
I=IIN/2(1+cos 2γ),
ID=IIN/2(1-cos 2γ).

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