Abstract

We describe the breathing dynamics of the self-similar core and the oscillating tails of a dispersion-managed (DM) soliton. The path-averaged propagation equation governing the shape of the DM soliton in an arbitrary dispersion map is derived. The developed theory correctly predicts the locations of the dips in the tails of the DM soliton. A general solution of the propagation equation is presented in terms of chirped Gauss–Hermite orthogonal functions.

© 1998 Optical Society of America

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References

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  1. I. P. Kaminow and T. L. Koch, Optical Communications IIIa (Academic, San Diego, Calif., 1997).
  2. M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
    [CrossRef]
  3. N. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
    [CrossRef]
  4. H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
    [CrossRef]
  5. I. Gabitov and S. K. Turitsyn, Opt. Lett. 21, 327 (1996); JETP Lett. 63, 862 (1996).
    [CrossRef]
  6. J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
    [CrossRef]
  7. M. Matsumoto and H. A. Haus, IEEE Photon. Technol. Lett. 9, 785 (1997).
    [CrossRef]
  8. T. Georges, J. Opt. Soc. Am. B 15, 1553 (1998).
    [CrossRef]
  9. S. Kumar and A. Hasegawa, Opt. Lett. 22, 372 (1997).
    [CrossRef] [PubMed]
  10. E. Shapiro and S. K. Turitsyn, Opt. Lett. 22, 1544 (1997); Phys. Rev. E 56, R4951 (1997).
    [CrossRef]
  11. A. Hasegawa, Y. Kodama, and A. Maruta, Opt. Fiber Technol. 3, 197 (1997).
    [CrossRef]
  12. T. Yu, E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, Opt. Lett. 22, 793 (1997); V. S. Grigoryan and C. R. Menyuk, Opt. Lett. 23, 609 (1998).
    [CrossRef] [PubMed]
  13. S. K. Turitsyn, JETP Lett. 65, 845 (1997).
    [CrossRef]
  14. P. Lazaridis, G. Debarge, and P. Gallion, Opt. Lett. 22, 685 (1997).
    [CrossRef] [PubMed]

1998 (1)

1997 (8)

1996 (2)

N. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
[CrossRef]

I. Gabitov and S. K. Turitsyn, Opt. Lett. 21, 327 (1996); JETP Lett. 63, 862 (1996).
[CrossRef]

1995 (2)

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
[CrossRef]

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
[CrossRef]

Akiba, S.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
[CrossRef]

Bennion, I.

N. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
[CrossRef]

Blow, K. J.

N. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
[CrossRef]

Debarge, G.

Doran, N. J.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
[CrossRef]

N. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
[CrossRef]

Edagawa, N.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
[CrossRef]

Forysiak, W.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
[CrossRef]

Gabitov, I.

Gallion, P.

Georges, T.

Golovchenko, E. A.

Hasegawa, A.

S. Kumar and A. Hasegawa, Opt. Lett. 22, 372 (1997).
[CrossRef] [PubMed]

A. Hasegawa, Y. Kodama, and A. Maruta, Opt. Fiber Technol. 3, 197 (1997).
[CrossRef]

Haus, H. A.

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

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
[CrossRef]

Ippen, E. P.

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
[CrossRef]

Kaminow, I. P.

I. P. Kaminow and T. L. Koch, Optical Communications IIIa (Academic, San Diego, Calif., 1997).

Knox, F. M.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
[CrossRef]

N. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
[CrossRef]

Koch, T. L.

I. P. Kaminow and T. L. Koch, Optical Communications IIIa (Academic, San Diego, Calif., 1997).

Kodama, Y.

A. Hasegawa, Y. Kodama, and A. Maruta, Opt. Fiber Technol. 3, 197 (1997).
[CrossRef]

Kumar, S.

Lazaridis, P.

Maruta, A.

A. Hasegawa, Y. Kodama, and A. Maruta, Opt. Fiber Technol. 3, 197 (1997).
[CrossRef]

Matsumoto, M.

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

Menyuk, C. R.

Morita, I.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
[CrossRef]

Nelson, L. E.

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
[CrossRef]

Nijhof, J. H. B.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
[CrossRef]

Pilipetskii, A. N.

Shapiro, E.

Smith, N.

N. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
[CrossRef]

Suzuki, M.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
[CrossRef]

Taga, H.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
[CrossRef]

Tamura, K.

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
[CrossRef]

Turitsyn, S. K.

Yamamoto, S.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
[CrossRef]

Yu, T.

Electron. Lett. (3)

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
[CrossRef]

N. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
[CrossRef]

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
[CrossRef]

IEEE J. Quantum Electron. (1)

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

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

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

JETP Lett. (1)

S. K. Turitsyn, JETP Lett. 65, 845 (1997).
[CrossRef]

Opt. Fiber Technol. (1)

A. Hasegawa, Y. Kodama, and A. Maruta, Opt. Fiber Technol. 3, 197 (1997).
[CrossRef]

Opt. Lett. (5)

Other (1)

I. P. Kaminow and T. L. Koch, Optical Communications IIIa (Academic, San Diego, Calif., 1997).

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Figures (3)

Fig. 1
Fig. 1

Evolution of T, M, and R over one compensation period for the dispersion map dz=±d+d, with d=5 and d=0.15. The lossless model (in which the amplification distance is much shorter than the compensation period) is considered.

Fig. 2
Fig. 2

Comparison of the two-mode approximation n=0,4 with the true shape of the DM soliton. Left inset, dependence of the coefficients Bnz2 in the expansion of the DM soliton on n taken at z=0. Right inset, dynamics over one period of the first four nonzero coefficients Bn2.

Fig. 3
Fig. 3

Evolution over one compensation period of the DM soliton shown on normal (left) and logarithmic (right) scales. In the leading order the dynamics is self-similar (left) and is given by Eqs.  (3). In the right-hand plot it can be seen that dips appear at the beginning (end) and in the middle of the periodic cell.

Equations (8)

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

iAz+dzAtt+czA2A=0.
At,z=N expiMzTzt2Qx,zTz,  x=tTz.
dTdz=4dzM, dMdz=dzT3-czN2T2.
iQz+dT2Qxx-x2Q+βzQ2Q+x2Q=0,βz=czN2T.
idBndz+dT2λnBn+βzm exp2in-mRz×Sn,mBm+βzm,l,k exp2in+k-m-lRz×BmBlBk*Vm,l,k,n=0.
idUndz+dT2λnUn+mβzexp2in-mRz×Sn,mUm+m,l,kβzexp2in+k-m-lRz×UmUlUk*Vm,l,k,n=0.
Az,t2=ETzexp-t2/T2zπ+2NETz×m=1m=f0f2mF2mcos4mRz-Θ2m.
Az,ω2=ETzexp-ω2T21+4M2T2π1+4M2zT2z1/2+2 NTE1+4M2T21/2m=1m=f0ξf2mξF2m×cos4mRz-Θ˜2m.

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