Abstract

We theoretically demonstrate in a nonlinear optical fiber system with a narrowband Raman gain that pulse walk-off between the pump and the Raman Stokes waves can be fully compensated for by Raman slow light, leading to group-velocity matching between the interacting waves, greater useful interaction length, and thereby enhanced Raman amplification efficiency. Limitations due to Kerr effect are further discussed.

© 2008 Optical Society of America

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References

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  1. G. P. Agrawal, in Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).
  2. R. H. Stolen and A. M. Johnson, IEEE J. Quantum Electron. 22, 2154 (1986).
    [CrossRef]
  3. R. Osborne, J. Opt. Soc. Am. B 6, 1726 (1989).
    [CrossRef]
  4. K. Lee and N. M. Lawandy, Appl. Phys. Lett. 78, 703 (2001).
    [CrossRef]
  5. J. E. Sharping, Y. Okawachi, and A. L. Gaeta, Opt. Express 13, 6092 (2005).
    [CrossRef] [PubMed]
  6. G. Fanjoux, J. Michaud, H. Maillotte, and T. Sylvestre, Phys. Rev. Lett. 100, 013908 (2008).
    [CrossRef] [PubMed]
  7. S. Lebrun, P. Delaye, R. Frey, and G. Roosen, Opt. Lett. 32, 337 (2003).
    [CrossRef]
  8. R. W. Boyd, in Nonlinear Optics (Academic, 1992), p. 371.
  9. N. Bloembergen and Y. R. Shen, Phys. Rev. Lett. 12, 504 (1964).
    [CrossRef]
  10. M. N. Islam, C. D. Poole, and J. P. Gordon, Opt. Lett. 14, 1011 (1989).
    [CrossRef] [PubMed]
  11. P. L. Baldeck, R. R. Alfano, and G. P. Agrawal, Appl. Phys. Lett. 52, 1939 (1988).
    [CrossRef]
  12. T. Sylvestre, H. Maillotte, E. Lantz, and D. Gindre, J. Nonlinear Opt. Phys. Mater. 6, 313 (1997).
    [CrossRef]
  13. D. Dahan, A. Bilenca, and G. Eisenstein, Opt. Lett. 28, 34 (2003).
    [CrossRef]

2008 (1)

G. Fanjoux, J. Michaud, H. Maillotte, and T. Sylvestre, Phys. Rev. Lett. 100, 013908 (2008).
[CrossRef] [PubMed]

2005 (1)

2003 (2)

2001 (2)

G. P. Agrawal, in Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

K. Lee and N. M. Lawandy, Appl. Phys. Lett. 78, 703 (2001).
[CrossRef]

1997 (1)

T. Sylvestre, H. Maillotte, E. Lantz, and D. Gindre, J. Nonlinear Opt. Phys. Mater. 6, 313 (1997).
[CrossRef]

1992 (1)

R. W. Boyd, in Nonlinear Optics (Academic, 1992), p. 371.

1989 (2)

1988 (1)

P. L. Baldeck, R. R. Alfano, and G. P. Agrawal, Appl. Phys. Lett. 52, 1939 (1988).
[CrossRef]

1986 (1)

R. H. Stolen and A. M. Johnson, IEEE J. Quantum Electron. 22, 2154 (1986).
[CrossRef]

1964 (1)

N. Bloembergen and Y. R. Shen, Phys. Rev. Lett. 12, 504 (1964).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, in Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

P. L. Baldeck, R. R. Alfano, and G. P. Agrawal, Appl. Phys. Lett. 52, 1939 (1988).
[CrossRef]

Alfano, R. R.

P. L. Baldeck, R. R. Alfano, and G. P. Agrawal, Appl. Phys. Lett. 52, 1939 (1988).
[CrossRef]

Baldeck, P. L.

P. L. Baldeck, R. R. Alfano, and G. P. Agrawal, Appl. Phys. Lett. 52, 1939 (1988).
[CrossRef]

Bilenca, A.

Bloembergen, N.

N. Bloembergen and Y. R. Shen, Phys. Rev. Lett. 12, 504 (1964).
[CrossRef]

Boyd, R. W.

R. W. Boyd, in Nonlinear Optics (Academic, 1992), p. 371.

Dahan, D.

Delaye, P.

Eisenstein, G.

Fanjoux, G.

G. Fanjoux, J. Michaud, H. Maillotte, and T. Sylvestre, Phys. Rev. Lett. 100, 013908 (2008).
[CrossRef] [PubMed]

Frey, R.

Gaeta, A. L.

Gindre, D.

T. Sylvestre, H. Maillotte, E. Lantz, and D. Gindre, J. Nonlinear Opt. Phys. Mater. 6, 313 (1997).
[CrossRef]

Gordon, J. P.

Islam, M. N.

Johnson, A. M.

R. H. Stolen and A. M. Johnson, IEEE J. Quantum Electron. 22, 2154 (1986).
[CrossRef]

Lantz, E.

T. Sylvestre, H. Maillotte, E. Lantz, and D. Gindre, J. Nonlinear Opt. Phys. Mater. 6, 313 (1997).
[CrossRef]

Lawandy, N. M.

K. Lee and N. M. Lawandy, Appl. Phys. Lett. 78, 703 (2001).
[CrossRef]

Lebrun, S.

Lee, K.

K. Lee and N. M. Lawandy, Appl. Phys. Lett. 78, 703 (2001).
[CrossRef]

Maillotte, H.

G. Fanjoux, J. Michaud, H. Maillotte, and T. Sylvestre, Phys. Rev. Lett. 100, 013908 (2008).
[CrossRef] [PubMed]

T. Sylvestre, H. Maillotte, E. Lantz, and D. Gindre, J. Nonlinear Opt. Phys. Mater. 6, 313 (1997).
[CrossRef]

Michaud, J.

G. Fanjoux, J. Michaud, H. Maillotte, and T. Sylvestre, Phys. Rev. Lett. 100, 013908 (2008).
[CrossRef] [PubMed]

Okawachi, Y.

Osborne, R.

Poole, C. D.

Roosen, G.

Sharping, J. E.

Shen, Y. R.

N. Bloembergen and Y. R. Shen, Phys. Rev. Lett. 12, 504 (1964).
[CrossRef]

Stolen, R. H.

R. H. Stolen and A. M. Johnson, IEEE J. Quantum Electron. 22, 2154 (1986).
[CrossRef]

Sylvestre, T.

G. Fanjoux, J. Michaud, H. Maillotte, and T. Sylvestre, Phys. Rev. Lett. 100, 013908 (2008).
[CrossRef] [PubMed]

T. Sylvestre, H. Maillotte, E. Lantz, and D. Gindre, J. Nonlinear Opt. Phys. Mater. 6, 313 (1997).
[CrossRef]

Appl. Phys. Lett. (2)

K. Lee and N. M. Lawandy, Appl. Phys. Lett. 78, 703 (2001).
[CrossRef]

P. L. Baldeck, R. R. Alfano, and G. P. Agrawal, Appl. Phys. Lett. 52, 1939 (1988).
[CrossRef]

IEEE J. Quantum Electron. (1)

R. H. Stolen and A. M. Johnson, IEEE J. Quantum Electron. 22, 2154 (1986).
[CrossRef]

J. Nonlinear Opt. Phys. Mater. (1)

T. Sylvestre, H. Maillotte, E. Lantz, and D. Gindre, J. Nonlinear Opt. Phys. Mater. 6, 313 (1997).
[CrossRef]

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

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. Lett. (2)

G. Fanjoux, J. Michaud, H. Maillotte, and T. Sylvestre, Phys. Rev. Lett. 100, 013908 (2008).
[CrossRef] [PubMed]

N. Bloembergen and Y. R. Shen, Phys. Rev. Lett. 12, 504 (1964).
[CrossRef]

Other (2)

R. W. Boyd, in Nonlinear Optics (Academic, 1992), p. 371.

G. P. Agrawal, in Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

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Figures (3)

Fig. 1
Fig. 1

Pulse profiles after 3 m of propagation length for the pump pulse (dotted curve, intensity × 1 ) and for the Stokes signal pulse in the linear dispersive regime (dashed curve, × 5.10 8 ), and in the walk-off compensation regime (solid curve, × 200 ), respectively. The dashed-dotted curve indicates the anti-Stokes pulse ( × 3 × 10 8 ) . The parameters are ( Ω R 2 π ) = 20 THz , ( Δ Ω R 2 π ) = 15 GHz , g R = 23.2 × 10 11 m W 1 , β 2 = 4.24 × 10 25 s 2 m 1 , and γ = 4.134 m 1 W 1 at the pump wavelength of 532 nm .

Fig. 2
Fig. 2

Raman gain per unit length (squares, right axis) and optical delay (circles, left axis) in function of the group-velocity dispersion.

Fig. 3
Fig. 3

Pulse walk-off (left, solid curve) and signal frequency shift (right, dashed curve) versus the propagation length in the walk-off compensation regime. Parameters are the same as in Fig. 1 and without the Kerr effect (dashed-dotted straight line). Inset, normalized intensity spectra of the Raman Stokes signal at the input (solid curve), and the output (dotted curve). The Raman gain curve is also drawn in gray.

Equations (4)

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Δ t L = L ( 1 v g p 1 v g s ) = L Ω R β 2 ,
Δ t N L = L ( 1 v g p 1 v g s ) = g R P L Δ Ω R A eff ,
P cr = β 2 Ω R Δ Ω R A eff g R .
A z + i 2 β 2 2 A t 2 = i γ A 2 A + i γ A 0 R ( t ) A ( z ; t t ) 2 d t ,

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