Abstract

We consider the counterpropagating interaction of a signal and a pump beam in a spun fiber and in a randomly birefringent fiber, the latter being relevant to optical telecommunication systems. On the basis of a geometrical anal ysis of the Hamiltonian singularities of the system, we provide a complete understanding of the phenomenon of polarization attraction in these two systems, which allows to achieve a control of the polarization state of the signal beam by adjusting the polarization of the pump. In spun fibers, all polarization states of the signal beam are attracted toward a specific line of polarization states on the Poincaré sphere, whose characteristics are determined by the polarization state of the injected backward pump. In randomly birefringent telecommunication fibers, we show that an unpolarized signal beam can be repolarized into any particular polarization state, without loss of energy.

© 2011 Optical Society of America

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  1. E. Heebner, R. S. Bennink, R. W. Boyd, and R. A. Fisher, Opt. Lett. 25, 257 (2000).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  5. S. Pitois, J. Fatome, and G. Millot, Opt. Express 16, 6646(2008).
    [CrossRef] [PubMed]
  6. E. Assémat, S. Lagrange, A. Picozzi, H. R. Jauslin, and D. Sugny, Opt. Lett. 35, 2025 (2010).
    [CrossRef] [PubMed]
  7. V. V. Kozlov and S. Wabnitz, Opt. Lett. 35, 3949 (2010).
    [CrossRef] [PubMed]
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  9. V. V. Kozlov, J. Nuno, and S. Wabnitz, J. Opt. Soc. Am. B 28, 100 (2011).
    [CrossRef]
  10. D. Sugny, A. Picozzi, S. Lagrange, and H. R. Jauslin, Phys. Rev. Lett. 103, 034102 (2009).
    [CrossRef] [PubMed]
  11. S. Lagrange, D. Sugny, A. Picozzi, and H. R. Jauslin, Phys. Rev. E 81, 016202 (2010).
    [CrossRef]
  12. R. H. Cushman and L. Bates, Global Aspects of Classical Integrable Systems (Birkhauser, 1997).
    [CrossRef]
  13. D. Sugny, P. Mardesic, M. Pelletier, J. Jebrane, and H. R. Jauslin, J. Math. Phys. 49, 042701 (2008).
    [CrossRef]
  14. E. Assémat, A. Picozzi, H. R. Jauslin, and D. Sugny, Optical Polarization Control: A Pedagogical Approach to New Hamiltonian Tools, in preparation (2011).

2011 (1)

2010 (4)

2009 (1)

D. Sugny, A. Picozzi, S. Lagrange, and H. R. Jauslin, Phys. Rev. Lett. 103, 034102 (2009).
[CrossRef] [PubMed]

2008 (3)

2005 (1)

S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, Europhys. Lett. 70, 88 (2005).
[CrossRef]

2000 (1)

1998 (1)

S. Pitois, G. Millot, and S. Wabnitz, Phys. Rev. Lett. 81, 1409(1998).
[CrossRef]

Assémat, E.

E. Assémat, S. Lagrange, A. Picozzi, H. R. Jauslin, and D. Sugny, Opt. Lett. 35, 2025 (2010).
[CrossRef] [PubMed]

E. Assémat, A. Picozzi, H. R. Jauslin, and D. Sugny, Optical Polarization Control: A Pedagogical Approach to New Hamiltonian Tools, in preparation (2011).

Bates, L.

R. H. Cushman and L. Bates, Global Aspects of Classical Integrable Systems (Birkhauser, 1997).
[CrossRef]

Bennink, R. S.

Boyd, R. W.

Cushman, R. H.

R. H. Cushman and L. Bates, Global Aspects of Classical Integrable Systems (Birkhauser, 1997).
[CrossRef]

Fatome, J.

Fisher, R. A.

Haelterman, M.

S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, Europhys. Lett. 70, 88 (2005).
[CrossRef]

Heebner, E.

Jauslin, H. R.

S. Lagrange, D. Sugny, A. Picozzi, and H. R. Jauslin, Phys. Rev. E 81, 016202 (2010).
[CrossRef]

E. Assémat, S. Lagrange, A. Picozzi, H. R. Jauslin, and D. Sugny, Opt. Lett. 35, 2025 (2010).
[CrossRef] [PubMed]

D. Sugny, A. Picozzi, S. Lagrange, and H. R. Jauslin, Phys. Rev. Lett. 103, 034102 (2009).
[CrossRef] [PubMed]

D. Sugny, P. Mardesic, M. Pelletier, J. Jebrane, and H. R. Jauslin, J. Math. Phys. 49, 042701 (2008).
[CrossRef]

S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, Europhys. Lett. 70, 88 (2005).
[CrossRef]

E. Assémat, A. Picozzi, H. R. Jauslin, and D. Sugny, Optical Polarization Control: A Pedagogical Approach to New Hamiltonian Tools, in preparation (2011).

Jebrane, J.

D. Sugny, P. Mardesic, M. Pelletier, J. Jebrane, and H. R. Jauslin, J. Math. Phys. 49, 042701 (2008).
[CrossRef]

Kozlov, V. V.

Lagrange, S.

S. Lagrange, D. Sugny, A. Picozzi, and H. R. Jauslin, Phys. Rev. E 81, 016202 (2010).
[CrossRef]

E. Assémat, S. Lagrange, A. Picozzi, H. R. Jauslin, and D. Sugny, Opt. Lett. 35, 2025 (2010).
[CrossRef] [PubMed]

D. Sugny, A. Picozzi, S. Lagrange, and H. R. Jauslin, Phys. Rev. Lett. 103, 034102 (2009).
[CrossRef] [PubMed]

Mardesic, P.

D. Sugny, P. Mardesic, M. Pelletier, J. Jebrane, and H. R. Jauslin, J. Math. Phys. 49, 042701 (2008).
[CrossRef]

Millot, G.

J. Fatome, S. Pitois, P. Morin, and G. Millot, Opt. Express 18, 15311 (2010).
[CrossRef] [PubMed]

S. Pitois, J. Fatome, and G. Millot, Opt. Express 16, 6646(2008).
[CrossRef] [PubMed]

S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, Europhys. Lett. 70, 88 (2005).
[CrossRef]

S. Pitois, G. Millot, and S. Wabnitz, Phys. Rev. Lett. 81, 1409(1998).
[CrossRef]

Morin, P.

Nuno, J.

Pelletier, M.

D. Sugny, P. Mardesic, M. Pelletier, J. Jebrane, and H. R. Jauslin, J. Math. Phys. 49, 042701 (2008).
[CrossRef]

Picozzi, A.

S. Lagrange, D. Sugny, A. Picozzi, and H. R. Jauslin, Phys. Rev. E 81, 016202 (2010).
[CrossRef]

E. Assémat, S. Lagrange, A. Picozzi, H. R. Jauslin, and D. Sugny, Opt. Lett. 35, 2025 (2010).
[CrossRef] [PubMed]

D. Sugny, A. Picozzi, S. Lagrange, and H. R. Jauslin, Phys. Rev. Lett. 103, 034102 (2009).
[CrossRef] [PubMed]

A. Picozzi, Opt. Express 16, 17171 (2008).
[CrossRef] [PubMed]

S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, Europhys. Lett. 70, 88 (2005).
[CrossRef]

E. Assémat, A. Picozzi, H. R. Jauslin, and D. Sugny, Optical Polarization Control: A Pedagogical Approach to New Hamiltonian Tools, in preparation (2011).

Pitois, S.

J. Fatome, S. Pitois, P. Morin, and G. Millot, Opt. Express 18, 15311 (2010).
[CrossRef] [PubMed]

S. Pitois, J. Fatome, and G. Millot, Opt. Express 16, 6646(2008).
[CrossRef] [PubMed]

S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, Europhys. Lett. 70, 88 (2005).
[CrossRef]

S. Pitois, G. Millot, and S. Wabnitz, Phys. Rev. Lett. 81, 1409(1998).
[CrossRef]

Sugny, D.

S. Lagrange, D. Sugny, A. Picozzi, and H. R. Jauslin, Phys. Rev. E 81, 016202 (2010).
[CrossRef]

E. Assémat, S. Lagrange, A. Picozzi, H. R. Jauslin, and D. Sugny, Opt. Lett. 35, 2025 (2010).
[CrossRef] [PubMed]

D. Sugny, A. Picozzi, S. Lagrange, and H. R. Jauslin, Phys. Rev. Lett. 103, 034102 (2009).
[CrossRef] [PubMed]

D. Sugny, P. Mardesic, M. Pelletier, J. Jebrane, and H. R. Jauslin, J. Math. Phys. 49, 042701 (2008).
[CrossRef]

E. Assémat, A. Picozzi, H. R. Jauslin, and D. Sugny, Optical Polarization Control: A Pedagogical Approach to New Hamiltonian Tools, in preparation (2011).

Wabnitz, S.

Europhys. Lett. (1)

S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, Europhys. Lett. 70, 88 (2005).
[CrossRef]

J. Math. Phys. (1)

D. Sugny, P. Mardesic, M. Pelletier, J. Jebrane, and H. R. Jauslin, J. Math. Phys. 49, 042701 (2008).
[CrossRef]

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

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. E (1)

S. Lagrange, D. Sugny, A. Picozzi, and H. R. Jauslin, Phys. Rev. E 81, 016202 (2010).
[CrossRef]

Phys. Rev. Lett. (2)

D. Sugny, A. Picozzi, S. Lagrange, and H. R. Jauslin, Phys. Rev. Lett. 103, 034102 (2009).
[CrossRef] [PubMed]

S. Pitois, G. Millot, and S. Wabnitz, Phys. Rev. Lett. 81, 1409(1998).
[CrossRef]

Other (2)

E. Assémat, A. Picozzi, H. R. Jauslin, and D. Sugny, Optical Polarization Control: A Pedagogical Approach to New Hamiltonian Tools, in preparation (2011).

R. H. Cushman and L. Bates, Global Aspects of Classical Integrable Systems (Birkhauser, 1997).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Energy momentum diagram ( H , K ) for the HBSF with (a) ϕ = π / 4 and (b) ϕ = 0 . The (a) singular (red) line and the (b) singular (red) point, play the role of attractors for the space–time dynamics (1). The dark crosses locate the positions of the stationary states obtained by solving numerically the space–time Eq. (1) for different initial conditions of the signal ( L = 5 , J ( L ) = ( 0 , 1 , 0 ) ). Note that, according to Eq. (4), the positions of the crosses satisfy | K | 1 . Each point of the singular red line in (a) is associated to a bitorus, while the singular red point at K = 0 in (b) corresponds to a sphere of singular points (see the text).

Fig. 2
Fig. 2

Polarization attraction toward a continuous line of polarization states for the HSBF: Numerical simulations of the spatiotemporal Eq. (1) on the Poincaré sphere [ ϕ = π / 4 for (a) and ϕ = π / 5 for (b)]. The green and red dots denote respectively the initial ( S ( 0 ) ) and final ( S ( L ) ) SOPs of the signal. The yellow dot denotes the fixed pump SOP: (a)  J ( L ) = ( 0 , 1 , 0 ) , (b)  J ( L ) = ( 0.7 , 0.7 , 0 ) for L = 5 . The blue line is calculated analytically from our method.

Fig. 3
Fig. 3

Same as Figs. 1, 2 but for the RBF. The polarization attraction is due to the presence of a sphere of singular points (a). All signal SOPs are attracted (up to a sign change) toward the pump SOP [ S 1 ( L ) = J 1 ( L ) , S 2 ( L ) = J 2 ( L ) , S 3 ( L ) = J 3 ( L ) ], as confirmed by the numerical simulations (b) with [ L = 20 , J ( L ) = ( 0.7 , 0.7 , 0 ) ].

Equations (4)

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{ S t + S z = S ( I S ) + S ( J J ) J t J z = J ( I J ) + J ( J S ) ,
H = cos 2 ϕ ( S 2 J 2 S 1 J 1 + 2 S 3 J 3 ) 2 sin 2 ϕ cos 2 ϕ 2 ( S 3 2 + J 3 2 ) .
H = cos 2 ϕ ( K 2 1 ) sin 2 ϕ 2 K 2 .
{ S 1 = ± | K | 1 K 2 S 2 = ε ( 1 K 2 ) S 3 = K ,

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