Abstract

Applying variational methods, we derive a reduced system of equations from the nonlocal equation that governs the average dynamics in dispersion-managed systems. These equations, which apply for any type of return-to-zero pulse, describe the stroboscopic evolution of the pulse parameters and bypass the fast variations inside each dispersion map. In the limit of large map strength we integrate the equations to obtain explicitly formulas for the parameters of a chirped return-to-zero pulse as well as the amount of post-transmission compensation needed to restore the initial pulse width.

© 2001 Optical Society of America

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  7. M. Matsumoto and H. A. Haus, IEEE Photon. Technol. Lett. 9, 785–787 (1997).
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  8. V. S. Grigoryan, T. Yu, E. A. Golovchenko, C. R. Menyuk, and A. N. Pilipetskii, Opt. Lett. 22, 1609–1611 (1997).
    [CrossRef]
  9. S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, Opt. Commun. 151, 117–135 (1997).
    [CrossRef]
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  13. A. Berntson, N. J. Doran, W. Forysiak, and J. H. Nijhof, Opt. Lett. 23, 900–902 (1998).
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  15. D. E. Pelinovsky, Phys. Rev. E 62, 4283–4293 (2000).
    [CrossRef]
  16. P.-A. Bélanger and N. Bélanger, Opt. Commun. 117, 56–60 (1995).
    [CrossRef]
  17. T.-S. Wang, W. L. Kath, and S. G. Evangelides, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper ThQ4.
  18. S. K. Turitsyn, T. Schäfer, and V. K. Mezentsev, IEEE Photon. Technol. Lett. 11, 203–205 (1999).
    [CrossRef]
  19. V. E. Zakharov and S. V. Manakov, JETP Lett. 70, 578–582 (1999).
    [CrossRef]

2001

2000

V. Cautaerts, A. Maruta, and Y. Kodama, Chaos 10, 515–528 (2000).
[CrossRef]

D. E. Pelinovsky, Phys. Rev. E 62, 4283–4293 (2000).
[CrossRef]

1999

S. K. Turitsyn, T. Schäfer, and V. K. Mezentsev, IEEE Photon. Technol. Lett. 11, 203–205 (1999).
[CrossRef]

V. E. Zakharov and S. V. Manakov, JETP Lett. 70, 578–582 (1999).
[CrossRef]

1998

1997

M. Matsumoto and H. A. Haus, IEEE Photon. Technol. Lett. 9, 785–787 (1997).
[CrossRef]

V. S. Grigoryan, T. Yu, E. A. Golovchenko, C. R. Menyuk, and A. N. Pilipetskii, Opt. Lett. 22, 1609–1611 (1997).
[CrossRef]

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, Opt. Commun. 151, 117–135 (1997).
[CrossRef]

1996

I. R. Gabitov and S. K. Turitsyn, Opt. Lett. 21, 327–329 (1996).
[CrossRef]

I. R. Gabitov and S. K. Turitsyn, JETP Lett. 63, 861–866 (1996).
[CrossRef]

1995

P.-A. Bélanger and N. Bélanger, Opt. Commun. 117, 56–60 (1995).
[CrossRef]

Ablowitz, M. J.

Bélanger, N.

P.-A. Bélanger and N. Bélanger, Opt. Commun. 117, 56–60 (1995).
[CrossRef]

Bélanger, P.-A.

P.-A. Bélanger and N. Bélanger, Opt. Commun. 117, 56–60 (1995).
[CrossRef]

Berntson, A.

Biondini, G.

Cautaerts, V.

V. Cautaerts, A. Maruta, and Y. Kodama, Chaos 10, 515–528 (2000).
[CrossRef]

Doran, N. J.

Evangelides, S. G.

J. N. Kutz, P. Holmes, S. G. Evangelides, and J. P. Gordon, J. Opt. Soc. Am. B 15, 87–96 (1998).
[CrossRef]

T.-S. Wang, W. L. Kath, and S. G. Evangelides, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper ThQ4.

Forysiak, W.

Gabitov, I.

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, Opt. Commun. 151, 117–135 (1997).
[CrossRef]

Gabitov, I. R.

I. R. Gabitov and S. K. Turitsyn, Opt. Lett. 21, 327–329 (1996).
[CrossRef]

I. R. Gabitov and S. K. Turitsyn, JETP Lett. 63, 861–866 (1996).
[CrossRef]

Georges, T.

Golovchenko, E. A.

Gordon, J. P.

Grigoryan, V. S.

Haus, H. A.

M. Matsumoto and H. A. Haus, IEEE Photon. Technol. Lett. 9, 785–787 (1997).
[CrossRef]

Hirooka, T.

Holmes, P.

Kath, W. L.

T.-S. Wang, W. L. Kath, and S. G. Evangelides, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper ThQ4.

Kaup, D. J.

T. I. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, Opt. Commun. 149, 366–375 (1998).
[CrossRef]

Kodama, Y.

V. Cautaerts, A. Maruta, and Y. Kodama, Chaos 10, 515–528 (2000).
[CrossRef]

T. Okamawari, A. Maruta, and Y. Kodama, Opt. Lett. 22, 694–696 (1998).
[CrossRef]

Kutz, J. N.

Laedke, E. W.

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, Opt. Commun. 151, 117–135 (1997).
[CrossRef]

Lakoba, T. I.

T. I. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, Opt. Commun. 149, 366–375 (1998).
[CrossRef]

Malomed, B. A.

T. I. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, Opt. Commun. 149, 366–375 (1998).
[CrossRef]

Manakov, S. V.

V. E. Zakharov and S. V. Manakov, JETP Lett. 70, 578–582 (1999).
[CrossRef]

Maruta, A.

V. Cautaerts, A. Maruta, and Y. Kodama, Chaos 10, 515–528 (2000).
[CrossRef]

T. Okamawari, A. Maruta, and Y. Kodama, Opt. Lett. 22, 694–696 (1998).
[CrossRef]

Matsumoto, M.

M. Matsumoto and H. A. Haus, IEEE Photon. Technol. Lett. 9, 785–787 (1997).
[CrossRef]

Menyuk, C. R.

Mezentsev, V. K.

S. K. Turitsyn, T. Schäfer, and V. K. Mezentsev, IEEE Photon. Technol. Lett. 11, 203–205 (1999).
[CrossRef]

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, Opt. Commun. 151, 117–135 (1997).
[CrossRef]

Musher, S. L.

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, Opt. Commun. 151, 117–135 (1997).
[CrossRef]

Nijhof, J. H.

Okamawari, T.

Olson, E. S.

Pelinovsky, D. E.

D. E. Pelinovsky, Phys. Rev. E 62, 4283–4293 (2000).
[CrossRef]

Pilipetskii, A. N.

Schäfer, T.

S. K. Turitsyn, T. Schäfer, and V. K. Mezentsev, IEEE Photon. Technol. Lett. 11, 203–205 (1999).
[CrossRef]

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, Opt. Commun. 151, 117–135 (1997).
[CrossRef]

Shapiro, E. G.

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, Opt. Commun. 151, 117–135 (1997).
[CrossRef]

Spatschek, K. H.

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, Opt. Commun. 151, 117–135 (1997).
[CrossRef]

Turitsyn, S. K.

S. K. Turitsyn, T. Schäfer, and V. K. Mezentsev, IEEE Photon. Technol. Lett. 11, 203–205 (1999).
[CrossRef]

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, Opt. Commun. 151, 117–135 (1997).
[CrossRef]

I. R. Gabitov and S. K. Turitsyn, JETP Lett. 63, 861–866 (1996).
[CrossRef]

I. R. Gabitov and S. K. Turitsyn, Opt. Lett. 21, 327–329 (1996).
[CrossRef]

Wang, T.-S.

T.-S. Wang, W. L. Kath, and S. G. Evangelides, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper ThQ4.

Yang, J.

T. I. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, Opt. Commun. 149, 366–375 (1998).
[CrossRef]

Yu, T.

Zakharov, V. E.

V. E. Zakharov and S. V. Manakov, JETP Lett. 70, 578–582 (1999).
[CrossRef]

Chaos

V. Cautaerts, A. Maruta, and Y. Kodama, Chaos 10, 515–528 (2000).
[CrossRef]

IEEE Photon. Technol. Lett.

M. Matsumoto and H. A. Haus, IEEE Photon. Technol. Lett. 9, 785–787 (1997).
[CrossRef]

S. K. Turitsyn, T. Schäfer, and V. K. Mezentsev, IEEE Photon. Technol. Lett. 11, 203–205 (1999).
[CrossRef]

J. Opt. Soc. Am. B

JETP Lett.

I. R. Gabitov and S. K. Turitsyn, JETP Lett. 63, 861–866 (1996).
[CrossRef]

V. E. Zakharov and S. V. Manakov, JETP Lett. 70, 578–582 (1999).
[CrossRef]

Opt. Commun.

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, Opt. Commun. 151, 117–135 (1997).
[CrossRef]

T. I. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, Opt. Commun. 149, 366–375 (1998).
[CrossRef]

P.-A. Bélanger and N. Bélanger, Opt. Commun. 117, 56–60 (1995).
[CrossRef]

Opt. Lett.

Phys. Rev. E

D. E. Pelinovsky, Phys. Rev. E 62, 4283–4293 (2000).
[CrossRef]

Other

T.-S. Wang, W. L. Kath, and S. G. Evangelides, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper ThQ4.

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Figures (2)

Fig. 1
Fig. 1

Evolution of the pulse parameters for a Gaussian input with d=0.1, s=20, τ0=1, and E=2. Dashed curves, Eqs.  (9); solid curves, numerical simulations of the NLS equation with gz=1; dotted–dashed curves, NLS equation with one EDFA per map. [The spectral width for gz=1 is indistinguishable from the analytical curve.]

Fig. 2
Fig. 2

Chirp compensation needed at z=10 as left, a function of τ0 with s=20 and right, a function of s with τ0=1 for d=0 and E=2. Solid curves, Eqs.  (10); triangles, numerical results, gz=1; circles, numerical results, one EDFA per map.

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

iuz+1/2dzutt+gzu2u=0.
iU^z-1/2dω2U^+dωdωU^ω+ω,z×U^ω+ω,zU^*ω+ω+ω,zrωω=0,
H=ddωω2U^ω,z2-dωdωdωU^*ω,z×U^ω+ω,zU^ω+ω,zU^*ω+ω+ω,zrωω.
U^ω,z=Azexp-κ2z-2ibzω2/4+iϕz/2,
κ=e0κ4I1,
b=d+e0κ3I0-κ2I2,
ϕ=e0κ5I0-κ2I2,
I0a,b=gza2+Cz+b21/2,
I1a,b=-I0a,bb,I2a,b=-I0a,ba,
I0a,b=12slnb+s+a2+b+s21/2b-s+a2+b-s21/2.
I01/sln2s/a+a2-2b2/4s2+O1/s5,
I1b/s3+O1/s5,I21/as+O1/s3.
κz=τ0,
bz=d+c2z,
ϕz=c0z,
c0=e0τ0/s5ln4s/τ02-2,
c2=e0τ03/sln4s/τ02-2.

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