Abstract

It is shown that the dispersion-managed nonlinear pulse solutions can be viewed as nonlinear Bloch waves with a periodic scattering potential that is set up self-consistently by the wave itself. The pulses are shown to be chirp-free at the center of each dispersion segment. The essential physical mechanism is explained by the interaction of the m=0 and the m=2 Hermite–Gaussian components of the pulse.

© 1999 Optical Society of America

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References

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  1. M. Suzuki, N. Edagawa, I. Morita, S. Yamamoto, and S. Akiba, “Soliton-based return-to-zero transmission over transoceanic distances by periodic dispersion compensation,” J. Opt. Soc. Am. B 14, 2953–2959 (1997).
    [CrossRef]
  2. J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, “Stable soliton-like propagation in dispersion-managed systems with net anomalous, zero and normal dispersion,” Electron. Lett. 23, 1726–1727 (1997).
    [CrossRef]
  3. G. M. Carter, J. M. Jacob, C. R. Menyuk, E. A. Golovchenko, and A. N. Pilipetskii, “Timing-jitter reduction for a dispersion-managed soliton system,” Opt. Lett. 22, 513–515 (1997).
    [CrossRef] [PubMed]
  4. Y. Kodama, S. Kumar, and A. Maruta, “Chirped nonlinear pulse propagation in a dispersion-compensated system,” Opt. Lett. 22, 1689–1691 (1997).
    [CrossRef]
  5. V. S. Grigoryan and C. R. Menyuk, “Dispersion-managed solitons at normal average dispersion,” Opt. Lett. 23, 609–611 (1998).
    [CrossRef]
  6. S. K. Turitsyn, T. Schafer, and K. Mezentsev, “Self-similar core and oscillatory tails of a path-averaged chirped dispersion-managed optical pulse,” Opt. Lett. 23, 1351–1353 (1998).
    [CrossRef]
  7. T. I. Lakoba and D. J. Kaup, “Shape of stationary pulse in strong dispersion management regime,” Electron. Lett. 34, 1124–1126 (1998).
    [CrossRef]
  8. S. M. J. Kelly, “Characteristic sideband instability of periodically amplified average solitons,” Electron. Lett. 28, 806–807 (1992).
    [CrossRef]
  9. H. Poincaré, Les méthodes nouvelles de la mécanique céleste (Gauthier-Villars, Paris, 1892), Vol. 3.
  10. N. Minorsky, Nonlinear Oscillations (Van Nostrand, Princeton, N.J., 1992), Chap. 10.

1998 (3)

1997 (4)

1992 (1)

S. M. J. Kelly, “Characteristic sideband instability of periodically amplified average solitons,” Electron. Lett. 28, 806–807 (1992).
[CrossRef]

Akiba, S.

Carter, G. M.

Doran, N. J.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, “Stable soliton-like propagation in dispersion-managed systems with net anomalous, zero and normal dispersion,” Electron. Lett. 23, 1726–1727 (1997).
[CrossRef]

Edagawa, N.

Forysiak, W.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, “Stable soliton-like propagation in dispersion-managed systems with net anomalous, zero and normal dispersion,” Electron. Lett. 23, 1726–1727 (1997).
[CrossRef]

Golovchenko, E. A.

Grigoryan, V. S.

Jacob, J. M.

Kaup, D. J.

T. I. Lakoba and D. J. Kaup, “Shape of stationary pulse in strong dispersion management regime,” Electron. Lett. 34, 1124–1126 (1998).
[CrossRef]

Kelly, S. M. J.

S. M. J. Kelly, “Characteristic sideband instability of periodically amplified average solitons,” Electron. Lett. 28, 806–807 (1992).
[CrossRef]

Knox, F. M.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, “Stable soliton-like propagation in dispersion-managed systems with net anomalous, zero and normal dispersion,” Electron. Lett. 23, 1726–1727 (1997).
[CrossRef]

Kodama, Y.

Kumar, S.

Lakoba, T. I.

T. I. Lakoba and D. J. Kaup, “Shape of stationary pulse in strong dispersion management regime,” Electron. Lett. 34, 1124–1126 (1998).
[CrossRef]

Maruta, A.

Menyuk, C. R.

Mezentsev, K.

Morita, I.

Nijhof, J. H. B.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, “Stable soliton-like propagation in dispersion-managed systems with net anomalous, zero and normal dispersion,” Electron. Lett. 23, 1726–1727 (1997).
[CrossRef]

Pilipetskii, A. N.

Schafer, T.

Suzuki, M.

Turitsyn, S. K.

Yamamoto, S.

Electron. Lett. (3)

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, “Stable soliton-like propagation in dispersion-managed systems with net anomalous, zero and normal dispersion,” Electron. Lett. 23, 1726–1727 (1997).
[CrossRef]

T. I. Lakoba and D. J. Kaup, “Shape of stationary pulse in strong dispersion management regime,” Electron. Lett. 34, 1124–1126 (1998).
[CrossRef]

S. M. J. Kelly, “Characteristic sideband instability of periodically amplified average solitons,” Electron. Lett. 28, 806–807 (1992).
[CrossRef]

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

Opt. Lett. (4)

Other (2)

H. Poincaré, Les méthodes nouvelles de la mécanique céleste (Gauthier-Villars, Paris, 1892), Vol. 3.

N. Minorsky, Nonlinear Oscillations (Van Nostrand, Princeton, N.J., 1992), Chap. 10.

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Figures (7)

Fig. 1
Fig. 1

Dispersion map.

Fig. 2
Fig. 2

Normalized pulse intensity profile |(δ/Δk)1/2τ0u|2 on a log scale from the numerical simulation compared with the Bloch wave constructed from modes m=0 and m=2, at the centers of the positively and negatively dispersive segments where k-=-5.1 ps2/km, k+=4.9 ps2/km, L=100 km, and FWHM=20 ps.

Fig. 3
Fig. 3

Same as Fig. 2, with modes m=0, 2, 4.

Fig. 4
Fig. 4

Autocorrelation functions of the Bloch wave of Fig. 2 compared with Gaussian and hyperbolic secant profile pulses with the same FWHM.

Fig. 5
Fig. 5

Same as Fig. 2, except that |k-|=|k+|=11 ps2/km.

Fig. 6
Fig. 6

Same as Fig. 5, with m=0, 2, 4.

Fig. 7
Fig. 7

(a) Energy for a fixed pulse width as a function of dispersion imbalance; (b) maximum swing in the magnitude of second-order Hermite–Gaussian.

Equations (11)

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uz=jk(z)22t2u-jδ|u|2u.
ψm(±)(t, z)=jb±z+jb1/2Hmtτ±×exp-jt2±z+jbexp[±jmϕ(z)],
τ±2=τo±21+z2b2;b=τo±2|kΔk|;θ=tan-1zb,
nan-(L/2)ψn-(t, L/2)=mam+(-L/2)ψm+(t, -L/2).
am+(-L/2)=nan-(L/2)dt×ψm+*(-L/2)ψn-(L/2)dt|ψm+(-L/2)|2.
u(t, z)=m-evenam(±)(z)ψm(±)(t, z)
ddzam(±)(z)=-jδp,q,r-evencmpqr(±)(z)ap(±)*(z)aq(±)(z)ar(±)(z),
cmpqr(±)(z)=dtψm(±)*(t, z)ψp(±)*(t, z)ψq(±)(t, z)
×ψr(±)(t, z)dt|ψm(±)(t, z)|2
=exp[±j(q+r-m-p)ϕ(z)][1+(z/b)2]1/2dxHm(x)
×Hp(x)Hq(x)Hr(x)dx|Hm(x)|2.

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