Abstract

It is shown that, similar to resonant enhancement of linear phase, birefringent phase, and chirality/optical activity by a ring resonator (RR), Berry’s phase, or the geometrical phase, can be amplified by repeatedly passing light through a Berry’s phase-generating element placed in a RR. Small-signal amplification of Berry’s phase is equal to the resonator finesse F. This amplification can be exploited when Berry’s phase is used for performing quantum computation or in fiber-optic and other sensors.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. Yeh, Optical Waves in Layered Media (Wiley, 1988), Chaps. 4 and 7.
  2. J. E. Heebner and R. Boyd, Opt. Lett. 24, 847 (1999).
    [CrossRef]
  3. B. E. Little and S. T. Chu, IEEE Photon. Technol. Lett. 12, 401 (2000).
    [CrossRef]
  4. A. Melloni, F. Morichetti, and M. Martinelli, Opt. Lett. 29, 2785 (2004).
    [CrossRef] [PubMed]
  5. I. Golub and E. Simova, Opt. Lett. 30, 87 (2005).
    [CrossRef] [PubMed]
  6. I. Golub, Opt. Lett. 31, 507 (2006).
    [CrossRef] [PubMed]
  7. M. V. Berry, Proc. R. Soc. London Ser. A 392, 45 (1984).
    [CrossRef]
  8. J. A. Jones, V. Vedral, A. Ekert, and G. Castagnoli, Nature 403, 869 (2000).
    [CrossRef] [PubMed]
  9. L.-M. Duan, J. I. Cirac, and P. Zoller, Science 292, 1695 (2001).
    [CrossRef] [PubMed]
  10. F. Wassmann and A. Ankiewicz, Appl. Opt. 37, 3902 (1998).
    [CrossRef]
  11. M. Kuzyk, J. Opt. Soc. Am. B 19, 2346 (2002).
    [CrossRef]
  12. A. Tomita and R. Y. Chiao, Phys. Rev. Lett. 57, 937 (1986).
    [CrossRef] [PubMed]
  13. E. M. Frins and W. Dultz, Opt. Commun. 136, 354 (1997).
    [CrossRef]
  14. P. Senthilkumaran, G. Thursby, and B. Culshaw, Opt. Lett. 25, 533 (2000).
    [CrossRef]
  15. R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, and H. Nathel, Phys. Rev. Lett. 60, 1214 (1988).
    [CrossRef] [PubMed]
  16. P. Senthilkumaran, G. Thursby, and B. Culshaw, J. Opt. Soc. Am. B 17, 1914 (2000).
    [CrossRef]
  17. P. Senthilkumaran, J. Opt. Soc. Am. B 22, 505 (2005).
    [CrossRef]

2006

2005

2004

2002

2001

L.-M. Duan, J. I. Cirac, and P. Zoller, Science 292, 1695 (2001).
[CrossRef] [PubMed]

2000

B. E. Little and S. T. Chu, IEEE Photon. Technol. Lett. 12, 401 (2000).
[CrossRef]

P. Senthilkumaran, G. Thursby, and B. Culshaw, Opt. Lett. 25, 533 (2000).
[CrossRef]

J. A. Jones, V. Vedral, A. Ekert, and G. Castagnoli, Nature 403, 869 (2000).
[CrossRef] [PubMed]

P. Senthilkumaran, G. Thursby, and B. Culshaw, J. Opt. Soc. Am. B 17, 1914 (2000).
[CrossRef]

1999

1998

1997

E. M. Frins and W. Dultz, Opt. Commun. 136, 354 (1997).
[CrossRef]

1988

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

1986

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

1984

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

Ankiewicz, A.

Antaramian, A.

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

Berry, M. V.

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

Boyd, R.

Castagnoli, G.

J. A. Jones, V. Vedral, A. Ekert, and G. Castagnoli, Nature 403, 869 (2000).
[CrossRef] [PubMed]

Chiao, R. Y.

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

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

Chu, S. T.

B. E. Little and S. T. Chu, IEEE Photon. Technol. Lett. 12, 401 (2000).
[CrossRef]

Cirac, J. I.

L.-M. Duan, J. I. Cirac, and P. Zoller, Science 292, 1695 (2001).
[CrossRef] [PubMed]

Culshaw, B.

Duan, L.-M.

L.-M. Duan, J. I. Cirac, and P. Zoller, Science 292, 1695 (2001).
[CrossRef] [PubMed]

Dultz, W.

E. M. Frins and W. Dultz, Opt. Commun. 136, 354 (1997).
[CrossRef]

Ekert, A.

J. A. Jones, V. Vedral, A. Ekert, and G. Castagnoli, Nature 403, 869 (2000).
[CrossRef] [PubMed]

Frins, E. M.

E. M. Frins and W. Dultz, Opt. Commun. 136, 354 (1997).
[CrossRef]

Ganga, K. M.

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

Golub, I.

Heebner, J. E.

Jiao, H.

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

Jones, J. A.

J. A. Jones, V. Vedral, A. Ekert, and G. Castagnoli, Nature 403, 869 (2000).
[CrossRef] [PubMed]

Kuzyk, M.

Little, B. E.

B. E. Little and S. T. Chu, IEEE Photon. Technol. Lett. 12, 401 (2000).
[CrossRef]

Martinelli, M.

Melloni, A.

Morichetti, F.

Nathel, H.

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

Senthilkumaran, P.

Simova, E.

Thursby, G.

Tomita, A.

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

Vedral, V.

J. A. Jones, V. Vedral, A. Ekert, and G. Castagnoli, Nature 403, 869 (2000).
[CrossRef] [PubMed]

Wassmann, F.

Wilkinson, S. R.

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

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, 1988), Chaps. 4 and 7.

Zoller, P.

L.-M. Duan, J. I. Cirac, and P. Zoller, Science 292, 1695 (2001).
[CrossRef] [PubMed]

Appl. Opt.

IEEE Photon. Technol. Lett.

B. E. Little and S. T. Chu, IEEE Photon. Technol. Lett. 12, 401 (2000).
[CrossRef]

J. Opt. Soc. Am. B

Nature

J. A. Jones, V. Vedral, A. Ekert, and G. Castagnoli, Nature 403, 869 (2000).
[CrossRef] [PubMed]

Opt. Commun.

E. M. Frins and W. Dultz, Opt. Commun. 136, 354 (1997).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

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

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

Proc. R. Soc. London Ser. A

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

Science

L.-M. Duan, J. I. Cirac, and P. Zoller, Science 292, 1695 (2001).
[CrossRef] [PubMed]

Other

P. Yeh, Optical Waves in Layered Media (Wiley, 1988), Chaps. 4 and 7.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Configuration of a ring resonator with a phase-changing element for amplification of the phase transferred to the beam by the PCE.

Fig. 2
Fig. 2

(a) Accumulation of Berry’s phase by multiple helically wound fiber stretches. (b) Amplification of Berry’s phase by placing a fiber helix in a RR.

Fig. 3
Fig. 3

Berry’s phase (dashed curve) and the amplification factor (solid curve) at the output of an r = 0.9 RR as a function of the single-pass Berry’s phase.

Equations (5)

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

E out = r + ( 1 r 2 ) ( exp i φ + r exp 2 i φ + ) = r + e i φ 1 r e i φ = exp i φ out .
φ out = 2 tan 1 ( 1 + r 1 r tan φ 2 ) .
E out = r + ( 1 r 2 ) ( exp i φ B exp i φ + r exp 2 i φ B exp 2 i φ + ) = r + e i φ B e i φ 1 r e i φ B e i φ = exp i φ Bout exp i φ out .
φ Bout = 2 tan 1 ( 1 + r 1 r tan φ B 2 ) ,
E out = r + α e i φ B e i φ 1 α e i φ B e i φ .

Metrics