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

1997

1992

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.

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

Opt. Lett.

Other

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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