Abstract

We demonstrate that a short pulse with spectrum in the range of normal group velocity dispersion can experience periodic reflections on a refractive index maximum created by a co-propagating with it soliton, providing the latter is continuously decelerated by the intrapulse Raman scattering. After each reflection the intensity profile and phase of the pulse are almost perfectly reconstructed, while its frequency is stepwise converted. This phenomenon has direct analogy with the effect of ’quantum bouncing’ known for cold atoms.

© 2007 Optical Society of America

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References

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  1. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001), 3rd ed.
  2. A. Gorbach and D.V. Skryabin, "Light trapping in gravity-like potentials and expansion of supercontinuum spectra in photonic crystal fibers," Nature-Photonics 1 (2007); http://xxx.lanl.gov/abs/0706.1187>.
  3. A. Gorbach and D. V. Skryabin. "Theory of radiation trapping by the accelerating solitons in optical fibers," Phys. Rev. A (to be published); http://xxx.lanl.gov/abs/0707.1598>.
  4. P. Beaud, W. Hodel, B. Zysset, and H. P. Weber. "Ultrashort pulse-propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber," IEEE J. Quantum Electron. 23, 1938-1946 (1987).
    [CrossRef]
  5. N. Nishizawa and T. Goto. "Experimental analysis of ultrashort pulse propagation in optical fibers around zerodispersion region using cross-correlation frequency resolved optical gating," Opt. Express 8, 328-334 (2001).
    [CrossRef] [PubMed]
  6. A. V. Gorbach, D. V. Skryabin, J. M. Stone, and J. C. Knight. "Four-wave mixing of solitons with radiation and quasi-nondispersive wave packets at the short-wavelength edge of a supercontinuum," Opt. Express 14, 9854- 9863 (2006).
    [CrossRef] [PubMed]
  7. J. Gea-Banacloche, "A quantum bouncing ball," Am. J. Phys. 67, 776 (1999).
    [CrossRef]
  8. C. V. Saba, P. A. Barton, M. G. Boshier, I. G. Hughes, P. Rosenbusch, B. E. Sauer, and E. A. Hinds, "Reconstruction of a cold atom cloud by magnetic focusing," Phys. Rev. Lett. 82, 468-471 (1999).
    [CrossRef]
  9. K. Bongs, S. Burger, G. Birkl, K. Sengstock, W. Ertmer, K. Rzazewski, A. Sanpera, and M. Lewenstein, "Coherent evolution of bouncing Bose-Einstein condensates," Phys. Rev. Lett. 83, 3577-3580 (1999).
    [CrossRef]
  10. K. J. Blow, N. J. Doran, and D. Wood, "Suppression of the soliton self-frequency shift by bandwidth-limited amplification," J. Opt. Soc. Am B 5, 1301-1304 (1988).
    [CrossRef]
  11. L. Gagnon and P. A. Belanger, "Soliton self-frequency shift versus Galilean-like symmetry," Opt. Lett. 15, 466- 468 (1990).
    [CrossRef] [PubMed]
  12. I. S. Averbukh and N. F. Perelman, "Dynamics of wave-packets from highly excited atomic and molecular-states," Usp. Fiz. Nauk 161, 41-81 (1991).
    [CrossRef]
  13. D. V. Skryabin and A. V. Yulin, "Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers," Phys. Rev. E 72, 016619 (2005).
    [CrossRef]

2006 (1)

2005 (1)

D. V. Skryabin and A. V. Yulin, "Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers," Phys. Rev. E 72, 016619 (2005).
[CrossRef]

2001 (1)

1999 (3)

J. Gea-Banacloche, "A quantum bouncing ball," Am. J. Phys. 67, 776 (1999).
[CrossRef]

C. V. Saba, P. A. Barton, M. G. Boshier, I. G. Hughes, P. Rosenbusch, B. E. Sauer, and E. A. Hinds, "Reconstruction of a cold atom cloud by magnetic focusing," Phys. Rev. Lett. 82, 468-471 (1999).
[CrossRef]

K. Bongs, S. Burger, G. Birkl, K. Sengstock, W. Ertmer, K. Rzazewski, A. Sanpera, and M. Lewenstein, "Coherent evolution of bouncing Bose-Einstein condensates," Phys. Rev. Lett. 83, 3577-3580 (1999).
[CrossRef]

1991 (1)

I. S. Averbukh and N. F. Perelman, "Dynamics of wave-packets from highly excited atomic and molecular-states," Usp. Fiz. Nauk 161, 41-81 (1991).
[CrossRef]

1990 (1)

1988 (1)

K. J. Blow, N. J. Doran, and D. Wood, "Suppression of the soliton self-frequency shift by bandwidth-limited amplification," J. Opt. Soc. Am B 5, 1301-1304 (1988).
[CrossRef]

1987 (1)

P. Beaud, W. Hodel, B. Zysset, and H. P. Weber. "Ultrashort pulse-propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber," IEEE J. Quantum Electron. 23, 1938-1946 (1987).
[CrossRef]

Am. J. Phys. (1)

J. Gea-Banacloche, "A quantum bouncing ball," Am. J. Phys. 67, 776 (1999).
[CrossRef]

IEEE J. Quantum Electron. (1)

P. Beaud, W. Hodel, B. Zysset, and H. P. Weber. "Ultrashort pulse-propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber," IEEE J. Quantum Electron. 23, 1938-1946 (1987).
[CrossRef]

J. Opt. Soc. Am B (1)

K. J. Blow, N. J. Doran, and D. Wood, "Suppression of the soliton self-frequency shift by bandwidth-limited amplification," J. Opt. Soc. Am B 5, 1301-1304 (1988).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. A (1)

A. Gorbach and D. V. Skryabin. "Theory of radiation trapping by the accelerating solitons in optical fibers," Phys. Rev. A (to be published); http://xxx.lanl.gov/abs/0707.1598>.

Phys. Rev. E (1)

D. V. Skryabin and A. V. Yulin, "Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers," Phys. Rev. E 72, 016619 (2005).
[CrossRef]

Phys. Rev. Lett. (2)

C. V. Saba, P. A. Barton, M. G. Boshier, I. G. Hughes, P. Rosenbusch, B. E. Sauer, and E. A. Hinds, "Reconstruction of a cold atom cloud by magnetic focusing," Phys. Rev. Lett. 82, 468-471 (1999).
[CrossRef]

K. Bongs, S. Burger, G. Birkl, K. Sengstock, W. Ertmer, K. Rzazewski, A. Sanpera, and M. Lewenstein, "Coherent evolution of bouncing Bose-Einstein condensates," Phys. Rev. Lett. 83, 3577-3580 (1999).
[CrossRef]

Usp. Fiz. Nauk (1)

I. S. Averbukh and N. F. Perelman, "Dynamics of wave-packets from highly excited atomic and molecular-states," Usp. Fiz. Nauk 161, 41-81 (1991).
[CrossRef]

Other (2)

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

A. Gorbach and D.V. Skryabin, "Light trapping in gravity-like potentials and expansion of supercontinuum spectra in photonic crystal fibers," Nature-Photonics 1 (2007); http://xxx.lanl.gov/abs/0706.1187>.

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Figures (4)

Fig. 1.
Fig. 1.

Solid (dashed) line corresponds to the soliton induced refractive index change (effective potential V(Vb )) in the accelerating frame of reference: q = 100, d 2 = -1/2. Initial localized pulse is detuned by L from the minimum at ξ 0. After reflection from the soliton, the pulse is reconstructed at the initial position, but its frequency is shifted by Δ. Ltr is the time delay such, that the linear potential equals the soliton peak.

Fig. 2.
Fig. 2.

Numerical propagation of the gaussian pulse (8) with a = 1 and different displacements: L = 2 and L = 5. Model parameters are the same as in Fig. 1. (a) Expansion coefficients cn of the gaussian. Filled circles correspond to L = 2, open squares to L = 5. (b) time-domain evolution within Eqs. (1) for L = 2. A 1 (dashed red lines) is initialized with the soliton (3), q = 100. Full blue lines show A 2. (c), (d) time-domain evolution of ∣A 22 along the fiber calculated using linearized Eq. (5) for L = 2 and L = 5, respectively.; (e), (f) deviation from the initial pulse D(z), calculated using the expansion in Eq. (7).

Fig. 3.
Fig. 3.

Spectral evolution within the linearized Eq. (5), (a), and coupled Eqs. (1), (b) and (c). Initial delay of the gaussian pulse is L = 2 for (a) and (b) and L = 5 for (c). Initial amplitude is a = 1.

Fig. 4.
Fig. 4.

Temporal (a) and spectal (b) evolution of the radiation bouncing on the soliton calculated using Eqs. (1) and transformedinto the ξ coordinate system The plots show (a) the intensity ofthe totalfield A 1 exp[ik 1 z - 1 t] + A 2 exp[ik 2 z - 1 t] and (b) its spectrum with δ 2 = -δ 1 = 20. Initial pulse ampltude a = 5 is larger than in the previous cases in Figs. 2,3. Other parameters are the same as in Fig. 2(b).

Equations (8)

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i z A 1,2 + d 1,2 x 2 A 1,2 = [ A 1,2 2 + 2 A 2,1 2 ] A 1,2 + TA 1,2 x [ A 1 2 + A 2 2 ] ,
A 1 ( s ) = ψ 0 ( ξ ) exp [ i ξgz 2 d 1 i g 2 z 3 12 d 1 + iqz ] ,
ψ 0 = 2 q sech ( q d 1 ξ ) , ξ = x gz 2 2 , g = 32 Tq 2 15 .
A 2 = φ ( z , ξ ) exp [ i ξgz 2 d z i g 2 z 2 12 d 2 ] .
i z φ d 2 ξ 2 φ + V ( ξ ) φ = 0 ,
V ( ξ ) = 2 ψ 0 2 T ξ ψ 0 2 + 2 d 2 .
φ ( z , ξ ) n c n y n ( ξ ) exp ( n z ) .
φ ( ξ , z = 0 ) = a exp [ ( ξ ξ 0 L ) 2 w 2 ] .

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