Abstract

The spin profile of a fiber is usually optimized to reduce transmission impairments caused by polarization-mode dispersion (PMD). In this paper, we show that fiber-optic-based plug-and-play quantum-key distribution systems using polarization modulation and fibers with a spin profile optimal for PMD may suffer from a large Faraday rotation induced by the geomagnetic field. We show that, for periodic spin patterns of small periods, the Faraday rotation is minimum when no spin is applied to the fiber.

© 2008 Optical Society of America

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References

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  1. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).
    [CrossRef]
  2. A. Mecozzi, C. Antonelli, and M. Brodsky, “Theory of the effect of geomagnetic field on plug-and-play schemes for fiber-based quantum key distribution systems,” submitted to Opt. Lett.
  3. A. Galtarossa, P. Griggio, L. Palmieri, and A. Pizzinat, Opt. Lett. 28, 1639 (2003).
    [CrossRef] [PubMed]
  4. J. P. Gordon and H. Kogelnik, Proc. Natl. Acad. Sci. U.S.A. 97, 4541 (2000).
    [CrossRef] [PubMed]
  5. A. H. Rose, S. M. Etzel, and C. M. Wang, J. Lightwave Technol. 15, 803 (1997).
    [CrossRef]
  6. M. Brodsky, A. A. Sirenko, A. Zavriyev, and A. Trifonov, in Proceedings of the Optical Fiber Communications Conference (Optical Society of America, 2006), paper PDP6.
  7. P. K. A. Wai and C. Menyuk, J. Lightwave Technol. 14, 148 (1996).
    [CrossRef]
  8. A. Galtarossa, P. Griggio, A. Pizzinat, and L. Palmieri, Opt. Lett. 27, 692 (2002).
    [CrossRef]

2006

M. Brodsky, A. A. Sirenko, A. Zavriyev, and A. Trifonov, in Proceedings of the Optical Fiber Communications Conference (Optical Society of America, 2006), paper PDP6.

2003

2002

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

A. Galtarossa, P. Griggio, A. Pizzinat, and L. Palmieri, Opt. Lett. 27, 692 (2002).
[CrossRef]

2000

J. P. Gordon and H. Kogelnik, Proc. Natl. Acad. Sci. U.S.A. 97, 4541 (2000).
[CrossRef] [PubMed]

1997

A. H. Rose, S. M. Etzel, and C. M. Wang, J. Lightwave Technol. 15, 803 (1997).
[CrossRef]

1996

P. K. A. Wai and C. Menyuk, J. Lightwave Technol. 14, 148 (1996).
[CrossRef]

Antonelli, C.

A. Mecozzi, C. Antonelli, and M. Brodsky, “Theory of the effect of geomagnetic field on plug-and-play schemes for fiber-based quantum key distribution systems,” submitted to Opt. Lett.

Brodsky, M.

M. Brodsky, A. A. Sirenko, A. Zavriyev, and A. Trifonov, in Proceedings of the Optical Fiber Communications Conference (Optical Society of America, 2006), paper PDP6.

A. Mecozzi, C. Antonelli, and M. Brodsky, “Theory of the effect of geomagnetic field on plug-and-play schemes for fiber-based quantum key distribution systems,” submitted to Opt. Lett.

Etzel, S. M.

A. H. Rose, S. M. Etzel, and C. M. Wang, J. Lightwave Technol. 15, 803 (1997).
[CrossRef]

Galtarossa, A.

Gisin, N.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

Gordon, J. P.

J. P. Gordon and H. Kogelnik, Proc. Natl. Acad. Sci. U.S.A. 97, 4541 (2000).
[CrossRef] [PubMed]

Griggio, P.

Kogelnik, H.

J. P. Gordon and H. Kogelnik, Proc. Natl. Acad. Sci. U.S.A. 97, 4541 (2000).
[CrossRef] [PubMed]

Mecozzi, A.

A. Mecozzi, C. Antonelli, and M. Brodsky, “Theory of the effect of geomagnetic field on plug-and-play schemes for fiber-based quantum key distribution systems,” submitted to Opt. Lett.

Menyuk, C.

P. K. A. Wai and C. Menyuk, J. Lightwave Technol. 14, 148 (1996).
[CrossRef]

Palmieri, L.

Pizzinat, A.

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

Rose, A. H.

A. H. Rose, S. M. Etzel, and C. M. Wang, J. Lightwave Technol. 15, 803 (1997).
[CrossRef]

Sirenko, A. A.

M. Brodsky, A. A. Sirenko, A. Zavriyev, and A. Trifonov, in Proceedings of the Optical Fiber Communications Conference (Optical Society of America, 2006), paper PDP6.

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

Trifonov, A.

M. Brodsky, A. A. Sirenko, A. Zavriyev, and A. Trifonov, in Proceedings of the Optical Fiber Communications Conference (Optical Society of America, 2006), paper PDP6.

Wai, P. K. A.

P. K. A. Wai and C. Menyuk, J. Lightwave Technol. 14, 148 (1996).
[CrossRef]

Wang, C. M.

A. H. Rose, S. M. Etzel, and C. M. Wang, J. Lightwave Technol. 15, 803 (1997).
[CrossRef]

Zavriyev, A.

M. Brodsky, A. A. Sirenko, A. Zavriyev, and A. Trifonov, in Proceedings of the Optical Fiber Communications Conference (Optical Society of America, 2006), paper PDP6.

Zbinden, H.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

J. Lightwave Technol.

A. H. Rose, S. M. Etzel, and C. M. Wang, J. Lightwave Technol. 15, 803 (1997).
[CrossRef]

P. K. A. Wai and C. Menyuk, J. Lightwave Technol. 14, 148 (1996).
[CrossRef]

Opt. Lett.

Proc. Natl. Acad. Sci. U.S.A.

J. P. Gordon and H. Kogelnik, Proc. Natl. Acad. Sci. U.S.A. 97, 4541 (2000).
[CrossRef] [PubMed]

Rev. Mod. Phys.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

Other

A. Mecozzi, C. Antonelli, and M. Brodsky, “Theory of the effect of geomagnetic field on plug-and-play schemes for fiber-based quantum key distribution systems,” submitted to Opt. Lett.

M. Brodsky, A. A. Sirenko, A. Zavriyev, and A. Trifonov, in Proceedings of the Optical Fiber Communications Conference (Optical Society of America, 2006), paper PDP6.

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Figures (1)

Fig. 1
Fig. 1

rms angle θ F , rms = θ F 2 plotted versus the spin amplitude A 0 . The solid curve corresponds to the asymptotic approximation Eq. (15); the dotted curve, overlapping with the other in the scale of the plot, is the exact asymptotic result. The squares are the result of a Monte Carlo simulation. The dashed curve is the rms DGD.

Equations (17)

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d s ̂ d z = [ β 0 ( z ) + β F ( z ) ] × s ̂ ,
s ̂ out = R FM exp ( θ F × ) s ̂ in ,
θ F = 2 0 L R 0 ( z ) β F d z ,
β 0 ( z + u ) β 0 ( z ) = β 0 2 C ( u , z ) ,
C ( z z , z ) = cos { 2 [ A ( z ) A ( z ) ] } c ( z z ) ,
θ F 2 ( z ) = 8 β F 2 0 z d z 0 z z d u R ( u , z ) ,
d R ( u , z ) d u = β 0 2 0 u d u C ( u u , u + z ) R ( u , z ) ,
X ( u , z ) = n exp ( i k n z ) X n ( u ) ,
L [ θ F 2 ( z ) ] = 8 β F 2 s 2 [ R ̃ 0 ( s ) + s n 0 R ̃ n ( s ) s i n k 1 ] .
d R m ( u ) d u = β 0 2 n 0 u d u C n ( u u ) exp ( i k n u ) R m n ( u ) .
[ s + i m k 1 + β 0 2 C 0 ( s + i m k 1 ) ] R ̃ m ( s + i m k 1 ) = δ m , 0 β 0 2 h m C ̃ m h ( s + i m k 1 ) R ̃ h ( s + i h k 1 ) ,
R ̃ 0 ( s ) 1 s + β 0 2 C ̃ 0 ( s ) .
L [ θ F 2 ( z ) ] 8 β F 2 R ̃ 0 ( 0 ) s 2 .
L [ θ F 2 ( z ) ] 8 β F 2 s 2 [ s + β 0 2 C ̃ 0 ( s ) ] .
θ F 2 8 β F 2 L β 0 2 C ̃ 0 ( 0 ) ,
c m , h = 1 exp ( Z L F ) Z 0 Z d u 0 Z d z C ( u , z ) exp [ i m k 1 u i ( m h ) k 1 z ] .
c m , h = 1 exp ( Z L F ) Z 0 Z d z 0 Z d z C Z ( z z , z ) exp ( i m k 1 z + i h k 1 z ) ,

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