Abstract

When an electromagnetic wave propagates around a circuit that is closed in k space, the value of Berry's topological phase can be deduced by solving Maxwell's equations in a rotating frame of reference.

© 1990 Optical Society of America

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References

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  1. M. V. Berry, Proc. R. Soc. London Ser. A 392, 45 (1984).
    [Crossref]
  2. J. H. Hannay, J. Phys. A 18, 221 (1985);M. V. Berry, Sci. Am. 259(6), 46 (1988).
    [Crossref]
  3. M. Kugler, S. Shtrikman, Phys. Rev. D 37, 934 (1988).
    [Crossref]
  4. R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, H. Nathel, Phys. Rev. Lett. 60, 1214 (1988).
    [Crossref] [PubMed]
  5. A. Tomita, R. Y. Chiao, Phys. Rev. Lett. 57, 937 (1986).
    [Crossref] [PubMed]
  6. Y. Aharonov, J. Ananden, Phys. Rev. Lett. 58, 1593 (1987).
    [Crossref] [PubMed]
  7. H. Jiao, S. R. Wilkinson, R. Y. Chaio, H. Nathel, Phys. Rev. A 39, 3475 (1989).
    [Crossref] [PubMed]
  8. M. V. Berry, Nature 326, 277 (1987).
    [Crossref]
  9. R. Y. Chiao, Y.-S. Wu, Phys. Rev. Lett. 57, 933 (1986).
    [Crossref] [PubMed]
  10. F. D. M. Haldane, Opt. Lett. 11, 730 (1986);J. N. Ross, Opt. Quantum Electron. 16, 445 (1984).
    [Crossref] [PubMed]
  11. In terms of the notation of Refs. 8 and 10, α = dn/dt × n, and in terms of the notation of Ref. 3, α = τ.
  12. The guiding mechanism can be conveniently introduced as a refractive-index profile n(x, y). This defines the propagation modes, but since n(x, y) is invariant in the rotating frame, it does not affect the results that follow.

1989 (1)

H. Jiao, S. R. Wilkinson, R. Y. Chaio, H. Nathel, Phys. Rev. A 39, 3475 (1989).
[Crossref] [PubMed]

1988 (2)

M. Kugler, S. Shtrikman, Phys. Rev. D 37, 934 (1988).
[Crossref]

R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, H. Nathel, Phys. Rev. Lett. 60, 1214 (1988).
[Crossref] [PubMed]

1987 (2)

M. V. Berry, Nature 326, 277 (1987).
[Crossref]

Y. Aharonov, J. Ananden, Phys. Rev. Lett. 58, 1593 (1987).
[Crossref] [PubMed]

1986 (3)

R. Y. Chiao, Y.-S. Wu, Phys. Rev. Lett. 57, 933 (1986).
[Crossref] [PubMed]

F. D. M. Haldane, Opt. Lett. 11, 730 (1986);J. N. Ross, Opt. Quantum Electron. 16, 445 (1984).
[Crossref] [PubMed]

A. Tomita, R. Y. Chiao, Phys. Rev. Lett. 57, 937 (1986).
[Crossref] [PubMed]

1985 (1)

J. H. Hannay, J. Phys. A 18, 221 (1985);M. V. Berry, Sci. Am. 259(6), 46 (1988).
[Crossref]

1984 (1)

M. V. Berry, Proc. R. Soc. London Ser. A 392, 45 (1984).
[Crossref]

Aharonov, Y.

Y. Aharonov, J. Ananden, Phys. Rev. Lett. 58, 1593 (1987).
[Crossref] [PubMed]

Ananden, J.

Y. Aharonov, J. Ananden, Phys. Rev. Lett. 58, 1593 (1987).
[Crossref] [PubMed]

Antaramian, A.

R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, H. Nathel, Phys. Rev. Lett. 60, 1214 (1988).
[Crossref] [PubMed]

Berry, M. V.

M. V. Berry, Nature 326, 277 (1987).
[Crossref]

M. V. Berry, Proc. R. Soc. London Ser. A 392, 45 (1984).
[Crossref]

Chaio, R. Y.

H. Jiao, S. R. Wilkinson, R. Y. Chaio, H. Nathel, Phys. Rev. A 39, 3475 (1989).
[Crossref] [PubMed]

Chiao, R. Y.

R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, H. Nathel, Phys. Rev. Lett. 60, 1214 (1988).
[Crossref] [PubMed]

A. Tomita, R. Y. Chiao, Phys. Rev. Lett. 57, 937 (1986).
[Crossref] [PubMed]

R. Y. Chiao, Y.-S. Wu, Phys. Rev. Lett. 57, 933 (1986).
[Crossref] [PubMed]

Ganga, K. M.

R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, H. Nathel, Phys. Rev. Lett. 60, 1214 (1988).
[Crossref] [PubMed]

Haldane, F. D. M.

Hannay, J. H.

J. H. Hannay, J. Phys. A 18, 221 (1985);M. V. Berry, Sci. Am. 259(6), 46 (1988).
[Crossref]

Jiao, H.

H. Jiao, S. R. Wilkinson, R. Y. Chaio, H. Nathel, Phys. Rev. A 39, 3475 (1989).
[Crossref] [PubMed]

R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, H. Nathel, Phys. Rev. Lett. 60, 1214 (1988).
[Crossref] [PubMed]

Kugler, M.

M. Kugler, S. Shtrikman, Phys. Rev. D 37, 934 (1988).
[Crossref]

Nathel, H.

H. Jiao, S. R. Wilkinson, R. Y. Chaio, H. Nathel, Phys. Rev. A 39, 3475 (1989).
[Crossref] [PubMed]

R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, H. Nathel, Phys. Rev. Lett. 60, 1214 (1988).
[Crossref] [PubMed]

Shtrikman, S.

M. Kugler, S. Shtrikman, Phys. Rev. D 37, 934 (1988).
[Crossref]

Tomita, A.

A. Tomita, R. Y. Chiao, Phys. Rev. Lett. 57, 937 (1986).
[Crossref] [PubMed]

Wilkinson, S. R.

H. Jiao, S. R. Wilkinson, R. Y. Chaio, H. Nathel, Phys. Rev. A 39, 3475 (1989).
[Crossref] [PubMed]

R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, H. Nathel, Phys. Rev. Lett. 60, 1214 (1988).
[Crossref] [PubMed]

Wu, Y.-S.

R. Y. Chiao, Y.-S. Wu, Phys. Rev. Lett. 57, 933 (1986).
[Crossref] [PubMed]

J. Phys. A (1)

J. H. Hannay, J. Phys. A 18, 221 (1985);M. V. Berry, Sci. Am. 259(6), 46 (1988).
[Crossref]

Nature (1)

M. V. Berry, Nature 326, 277 (1987).
[Crossref]

Opt. Lett. (1)

Phys. Rev. A (1)

H. Jiao, S. R. Wilkinson, R. Y. Chaio, H. Nathel, Phys. Rev. A 39, 3475 (1989).
[Crossref] [PubMed]

Phys. Rev. D (1)

M. Kugler, S. Shtrikman, Phys. Rev. D 37, 934 (1988).
[Crossref]

Phys. Rev. Lett. (4)

R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, H. Nathel, Phys. Rev. Lett. 60, 1214 (1988).
[Crossref] [PubMed]

A. Tomita, R. Y. Chiao, Phys. Rev. Lett. 57, 937 (1986).
[Crossref] [PubMed]

Y. Aharonov, J. Ananden, Phys. Rev. Lett. 58, 1593 (1987).
[Crossref] [PubMed]

R. Y. Chiao, Y.-S. Wu, Phys. Rev. Lett. 57, 933 (1986).
[Crossref] [PubMed]

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

M. V. Berry, Proc. R. Soc. London Ser. A 392, 45 (1984).
[Crossref]

Other (2)

In terms of the notation of Refs. 8 and 10, α = dn/dt × n, and in terms of the notation of Ref. 3, α = τ.

The guiding mechanism can be conveniently introduced as a refractive-index profile n(x, y). This defines the propagation modes, but since n(x, y) is invariant in the rotating frame, it does not affect the results that follow.

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Equations (10)

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B = 0 , E = 0 , × E = B t , c 2 × B = E t .
× E = B t α × B , c 2 × B = E t + α × E .
2 E t 2 α × E t = c 2 2 E
ω ± = c k ± α z 2 .
γ = 0 T α z d t .
γ = 2 π cos θ ,
Ω = 2 π ( 1 cos θ ) = γ + 2 π .
α ( t ) = d ϕ d t i + d θ d t ( i × z ) ,
γ = 0 T d ϕ d t ( i × z ) d t = 0 2 π cos θ ( ϕ ) d ϕ .
γ = Ω .

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