Abstract

We theoretically investigate slow light via stimulated Raman scattering, paying special attention to the picosecond regime where chromatic dispersion and cross-phase modulation must be considered. In addition to the control of the Raman pulse walk-off, we demonstrate that the cross-phase-modulation-induced frequency chirp can also be all-optically tuned via Raman slow light. We further demonstrate that this new implication is a consequence of the fact that the group velocity is significantly more affected than the phase velocity in slow-light media.

© 2009 Optical Society of America

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References

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  1. R. W. Boyd and D. J. Gauthier, in Progress in Optics, E.Wolf, ed. (Elsevier, 2002), Vol. 43, Chap. 6, p. 495.
    [CrossRef]
  2. L. Thévenaz, Nat. Photonics , 2, 474 (2008).
    [CrossRef]
  3. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
    [CrossRef] [PubMed]
  4. K. Y. Song, M. G. Herráez, and L. Thévenaz, Opt. Express 13, 82 (2005).
    [CrossRef] [PubMed]
  5. J. E. Sharping, Y. Okawachi, and A. L. Gaeta, Opt. Express 13, 6092 (2005).
    [CrossRef] [PubMed]
  6. D. Dahan and G. Eisenstein, Opt. Express 13, 6234 (2005).
    [CrossRef] [PubMed]
  7. S. Lebrun, P. Delaye, R. Frey, and G. Rosen, Opt. Lett. 32, 337 (2003).
    [CrossRef]
  8. G. Fanjoux and T. Sylvestre, Opt. Lett. 33, 2506 (2008).
    [CrossRef] [PubMed]
  9. G. Fanjoux, J. Michaud, H. Maillotte, and T. Sylvestre, Phys. Rev. Lett. 100, 013908 (2008).
    [CrossRef] [PubMed]
  10. P. L. Baldeck, R. R. Alfano, and G. P. Agrawal, Appl. Phys. Lett. 52, 1939 (1988).
    [CrossRef]
  11. G. P. Agrawal, in Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

2008 (3)

L. Thévenaz, Nat. Photonics , 2, 474 (2008).
[CrossRef]

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

G. Fanjoux and T. Sylvestre, Opt. Lett. 33, 2506 (2008).
[CrossRef] [PubMed]

2005 (4)

2003 (1)

1988 (1)

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

Agrawal, G. P.

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

G. P. Agrawal, in Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

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]

Bigelow, M. S.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Boyd, R. W.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

R. W. Boyd and D. J. Gauthier, in Progress in Optics, E.Wolf, ed. (Elsevier, 2002), Vol. 43, Chap. 6, p. 495.
[CrossRef]

Dahan, D.

Delaye, P.

Eisenstein, G.

Fanjoux, G.

G. Fanjoux and T. Sylvestre, Opt. Lett. 33, 2506 (2008).
[CrossRef] [PubMed]

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

Frey, R.

Gaeta, A. L.

J. E. Sharping, Y. Okawachi, and A. L. Gaeta, Opt. Express 13, 6092 (2005).
[CrossRef] [PubMed]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Gauthier, D. J.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

R. W. Boyd and D. J. Gauthier, in Progress in Optics, E.Wolf, ed. (Elsevier, 2002), Vol. 43, Chap. 6, p. 495.
[CrossRef]

Herráez, M. G.

Lebrun, S.

Maillotte, H.

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

Michaud, J.

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

Okawachi, Y.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

J. E. Sharping, Y. Okawachi, and A. L. Gaeta, Opt. Express 13, 6092 (2005).
[CrossRef] [PubMed]

Rosen, G.

Schweinsberg, A.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Sharping, J. E.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

J. E. Sharping, Y. Okawachi, and A. L. Gaeta, Opt. Express 13, 6092 (2005).
[CrossRef] [PubMed]

Song, K. Y.

Sylvestre, T.

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

G. Fanjoux and T. Sylvestre, Opt. Lett. 33, 2506 (2008).
[CrossRef] [PubMed]

Thévenaz, L.

Zhu, Z.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

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

Nat. Photonics (1)

L. Thévenaz, Nat. Photonics , 2, 474 (2008).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. Lett. (2)

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

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

Other (2)

G. P. Agrawal, in Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

R. W. Boyd and D. J. Gauthier, in Progress in Optics, E.Wolf, ed. (Elsevier, 2002), Vol. 43, Chap. 6, p. 495.
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Pulse walk-off (left, dashed) and XPM-induced frequency chirp (right, solid) as a function of the pump power P. Thin curve, standard theory without slow light, Eq. (2). Gray curve, analytical results with slow light [Eq. (4)]. Black curve, NLSE numerical results.

Fig. 2
Fig. 2

Frequency chirp δ ν ( τ ) (left, dotted curve) and pump and signal pulses profiles (dashed and solid normalized curves, respectively). The parameters are T 0 = 250 ps , γ = 4.134 m 1 . W 1 , L w = 4.69 m , L = 2 m , ( Ω R 2 π ) = 20 THz , ( Δ Ω R 2 π ) = 15 GHz , A eff = 10 μ m 2 , β 2 = 4.24 × 10 25 s 2 m 1 , and g R = 23.2 × 10 11 m W 1 at the pump wavelength of 532 nm . (a) Without slow light for P = P c r , similar to Eq. (1). (b) Zero walk-off for P = P c r = 0.285 W . (c) Zero frequency shift for P = 0.17 W . The insets show the signal spectrum at the medium’s input (dotted curves) and output (solid curves), respectively, and the Raman gain (dashed curves).

Equations (4)

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δ ν ( τ ) = γ P L w π T 0 [ exp ( τ 2 ) exp ( ( τ δ w ) 2 ) ] ,
δ ν ( 0 ) = γ P L w π T 0 [ 1 exp ( δ w 2 ) ] .
δ ν ( δ SL ) = γ P L w π T 0 × [ exp ( δ SL 2 ) exp ( ( δ SL δ w ) 2 ) ] .
δ ν ( δ w ) = γ P L w π T 0 [ exp ( δ w 2 ) 1 ] ,

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