Abstract

We consider the counterpropagating interaction of a signal and a pump beam in an isotropic optical fiber. On the basis of recently developed mathematical techniques, we show that an arbitrary state of polarization of the signal beam can be converted into any other desired state of polarization. On the other hand, an unpolarized signal beam may be repolarized into two specific states of polarization, without loss of energy. Both processes of repolarization and polarization conversion may be controlled by adjusting the polarization state of the backward pump.

© 2010 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]
  2. A. Picozzi, Opt. Express 16, 17171 (2008).
    [CrossRef] [PubMed]
  3. S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, Europhys. Lett. 70, 88 (2005).
    [CrossRef]
  4. S. Pitois, J. Fatome, and G. Millot, Opt. Express 16, 6646 (2008).
    [CrossRef] [PubMed]
  5. D. Sugny, A. Picozzi, S. Lagrange, and H. R. Jauslin, Phys. Rev. Lett. 103, 034102 (2009).
    [CrossRef] [PubMed]
  6. S. Lagrange, D. Sugny, A. Picozzi, and H. R. Jauslin, Phys. Rev. E 81, 016202 (2010).
    [CrossRef]
  7. R. H. Cushman and L. Bates, Global Aspects of Classical Integrable Systems (Birkhauser, 1997).
    [CrossRef]
  8. D. Sugny, P. Mardesic, M. Pelletier, J. Jebrane, and H. R. Jauslin, J. Math. Phys. 49, 042701 (2008).
    [CrossRef]
  9. D. David, D. D. Holm, and M. V. Tratnik, Phys. Rep. 187, 281 (1990).
    [CrossRef]
  10. D. J. Gauthier, M. S. Malcuit, and R. Boyd, Phys. Rev. Lett. 61, 1827 (1988).
    [CrossRef] [PubMed]
  11. M. V. Tratnik and J. E. Sipe, Phys. Rev. A 35, 2976 (1987).
    [CrossRef] [PubMed]
  12. S. Trillo and S. Wabnitz, Phys. Rev. A 36, 3881 (1987).
    [CrossRef] [PubMed]
  13. S. Pitois, G. Millot, and S. Wabnitz, Phys. Rev. Lett. 81, 1409 (1998).
    [CrossRef]
  14. S. Wabnitz, Opt. Lett. 34, 908 (2009).
    [CrossRef] [PubMed]

2010 (1)

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

2009 (2)

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

S. Wabnitz, Opt. Lett. 34, 908 (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]

1990 (1)

D. David, D. D. Holm, and M. V. Tratnik, Phys. Rep. 187, 281 (1990).
[CrossRef]

1988 (1)

D. J. Gauthier, M. S. Malcuit, and R. Boyd, Phys. Rev. Lett. 61, 1827 (1988).
[CrossRef] [PubMed]

1987 (2)

M. V. Tratnik and J. E. Sipe, Phys. Rev. A 35, 2976 (1987).
[CrossRef] [PubMed]

S. Trillo and S. Wabnitz, Phys. Rev. A 36, 3881 (1987).
[CrossRef] [PubMed]

Bates, L.

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

Bennink, R. S.

Boyd, R.

D. J. Gauthier, M. S. Malcuit, and R. Boyd, Phys. Rev. Lett. 61, 1827 (1988).
[CrossRef] [PubMed]

Boyd, R. W.

Cushman, R. H.

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

David, D.

D. David, D. D. Holm, and M. V. Tratnik, Phys. Rep. 187, 281 (1990).
[CrossRef]

Fatome, J.

Fisher, R. A.

Gauthier, D. J.

D. J. Gauthier, M. S. Malcuit, and R. Boyd, Phys. Rev. Lett. 61, 1827 (1988).
[CrossRef] [PubMed]

Haelterman, M.

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

Heebner, E.

Holm, D. D.

D. David, D. D. Holm, and M. V. Tratnik, Phys. Rep. 187, 281 (1990).
[CrossRef]

Jauslin, H. R.

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

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]

Jebrane, J.

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

Lagrange, S.

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

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

Malcuit, M. S.

D. J. Gauthier, M. S. Malcuit, and R. Boyd, Phys. Rev. Lett. 61, 1827 (1988).
[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.

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]

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]

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]

Pitois, S.

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]

Sipe, J. E.

M. V. Tratnik and J. E. Sipe, Phys. Rev. A 35, 2976 (1987).
[CrossRef] [PubMed]

Sugny, D.

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

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]

Tratnik, M. V.

D. David, D. D. Holm, and M. V. Tratnik, Phys. Rep. 187, 281 (1990).
[CrossRef]

M. V. Tratnik and J. E. Sipe, Phys. Rev. A 35, 2976 (1987).
[CrossRef] [PubMed]

Trillo, S.

S. Trillo and S. Wabnitz, Phys. Rev. A 36, 3881 (1987).
[CrossRef] [PubMed]

Wabnitz, S.

S. Wabnitz, Opt. Lett. 34, 908 (2009).
[CrossRef] [PubMed]

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

S. Trillo and S. Wabnitz, Phys. Rev. A 36, 3881 (1987).
[CrossRef] [PubMed]

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]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rep. (1)

D. David, D. D. Holm, and M. V. Tratnik, Phys. Rep. 187, 281 (1990).
[CrossRef]

Phys. Rev. A (2)

M. V. Tratnik and J. E. Sipe, Phys. Rev. A 35, 2976 (1987).
[CrossRef] [PubMed]

S. Trillo and S. Wabnitz, Phys. Rev. A 36, 3881 (1987).
[CrossRef] [PubMed]

Phys. Rev. E (1)

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

Phys. Rev. Lett. (3)

D. J. Gauthier, M. S. Malcuit, and R. Boyd, Phys. Rev. Lett. 61, 1827 (1988).
[CrossRef] [PubMed]

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 (1)

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

(a) Schematic representation of the attraction process for an elliptic polarization of the pump (circle, J 2 ( L ) = e ). Regardless of its initial polarization S ( 0 ) , the signal beam is attracted toward two specific states of polarization A ± , whose ellipticity is fixed by the pump, e. The points A ± are represented by stars and their basins of attraction are displayed by the upper and lower hemispheres. (b) Illustration of the results of the numerical simulations of the spatiotemporal Eqs. (1, 2) in the plane ( S 1 , S 3 ) defined by S 2 = e (see text). At the scale of the plot, the numerical results (stars) coincide with the theoretical positions of A ± . [Parameters are S 0 = J 0 , J 2 ( L ) = e = 0.2 J 0 , J 1 ( L ) = 0.5 J 0 , L = 5 L 0 , and L 0 = v / ( γ J 0 ) ].

Fig. 2
Fig. 2

Stationary solutions S 2 ( z ) obtained by solving numerically the spatiotemporal Eqs. (1, 2): the signal ellipticity is attracted to the pump ellipticity S 2 ( L ) = J 2 ( L ) . If S 2 ( z = 0 ) > e ( S 2 ( z = 0 ) < e ), the signal passes through the north (south) pole and is attracted to A + ( A ). The corresponding trajectories on the doubly pinched tori are schematically represented. Parameters are the same as in Fig. 1.

Fig. 3
Fig. 3

Stationary solutions S 2 ( z ) and J 2 ( z ) obtained by solving numerically the spatiotemporal Eqs. (1, 2) when the signal and pump beams have different powers ( S 0 = 1.3 J 0 ). The two attraction points A ± no longer exhibit the same ellipticity, so that the signal ellipticity may be switched to S 2 ( L ) = e + Δ (i.e., A + ) or S 2 ( L ) = e Δ (i.e., A ). The upper (lower) curves refer to S 2 ( 0 ) = 0.05455 × S 0 ( S 2 ( 0 ) = 0.05452 × S 0 ), for a fixed pump polarization ( J 2 = 0.2 J 0 , J 1 = 0.1 J 0 ).

Equations (9)

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S t + v S z = [ S × J S + 2 S × J J ] ,
J t v J z = [ J × J J + 2 J × J S ] ,
H = γ v [ 2 ( S 1 J 1 + S 3 J 3 ) ( S 2 2 + J 2 2 ) 2 / 2 ] .
H = γ v [ 2 ( S 0 2 S 2 2 ) 1 / 2 ( J 0 2 J 2 2 ) 1 / 2 cos ( ϕ S ϕ P ) ( S 2 2 + J 2 2 ) / 2 ] ,
K = S 2 J 2 .
K = ± ( S 0 J 0 ) ,
H = γ 2 v ( S 0 2 + J 0 2 ) .
2 ( S 0 2 e 2 ) cos ( ϕ S ϕ P ) e 2 = S 0 2 .
cos ϕ 0 = ( e 2 K e S 0 J 0 ) / [ 2 ( S 0 2 e 2 ) 1 / 2 ( J 0 2 ( K e ) 2 ) 1 / 2 ] .

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