Abstract

Approximate analytical expressions for quasi-steady-state pulse parameters of stretched pulses in dispersion-managed fibers are derived. The analysis uses the same approach as that developed for the analysis of stretched-pulse fiber ring lasers but with improved calculation of nonlinearity-induced pulse chirping by means of an approximate variational method. The energy-enhancement factor of the stretched pulse is derived, showing reasonable agreement with numerical results.

© 1997 Optical Society of America

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  1. K. Tamura, E. P. Ippen, H. A. Haus, and L. E. Nelson, Opt. Lett. 18, 1080 (1993).
    [CrossRef]
  2. H. Kubota and M. Nakazawa, Opt. Commun. 87, 15 (1991).
    [CrossRef]
  3. N. Edagawa, I. Morita, M. Suzuki, S. Yamamoto, H. Taga, and S. Akiba, in 21st European Conference on Optical Communication (IEEE, Piscataway, N.J., 1995), paper Th.A.3.5.
  4. M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
    [CrossRef]
  5. J. M. Jacob, E. A. Golovchenko, A. N. Pilipetskii, G. M. Carter, and C. R. Menyuk, IEEE Photon. Technol. Lett. 9, 130 (1997).
    [CrossRef]
  6. N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
    [CrossRef]
  7. M. Nakazawa, H. Kubota, A. Sahara, and K. Tamura, IEEE Photon. Technol. Lett. 8, 1088 (1996).
    [CrossRef]
  8. H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
    [CrossRef]
  9. D. Anderson, Phys. Rev. A 27, 3135 (1983).
    [CrossRef]
  10. I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Opt. Commun. 134, 317 (1997).
    [CrossRef]
  11. B. A. Malomed, Opt. Commun. 136, 313 (1997).
    [CrossRef]
  12. M. Matsumoto and H. A. Haus, IEEE Photon. Technol. Lett. 9, 785 (1997).
    [CrossRef]
  13. Y. Kodama and A. Kasegawa, Opt. Lett. 17, 31 (1992).
    [CrossRef] [PubMed]
  14. N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, Opt. Lett. 21, 1981 (1996).
    [CrossRef] [PubMed]

1997 (4)

J. M. Jacob, E. A. Golovchenko, A. N. Pilipetskii, G. M. Carter, and C. R. Menyuk, IEEE Photon. Technol. Lett. 9, 130 (1997).
[CrossRef]

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Opt. Commun. 134, 317 (1997).
[CrossRef]

B. A. Malomed, Opt. Commun. 136, 313 (1997).
[CrossRef]

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

1996 (3)

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

M. Nakazawa, H. Kubota, A. Sahara, and K. Tamura, IEEE Photon. Technol. Lett. 8, 1088 (1996).
[CrossRef]

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, Opt. Lett. 21, 1981 (1996).
[CrossRef] [PubMed]

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]

1993 (1)

1992 (1)

1991 (1)

H. Kubota and M. Nakazawa, Opt. Commun. 87, 15 (1991).
[CrossRef]

1983 (1)

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[CrossRef]

Akiba, S.

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

N. Edagawa, I. Morita, M. Suzuki, S. Yamamoto, H. Taga, and S. Akiba, in 21st European Conference on Optical Communication (IEEE, Piscataway, N.J., 1995), paper Th.A.3.5.

Anderson, D.

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[CrossRef]

Bennion, I.

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

Blow, K. J.

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

Carter, G. M.

J. M. Jacob, E. A. Golovchenko, A. N. Pilipetskii, G. M. Carter, and C. R. Menyuk, IEEE Photon. Technol. Lett. 9, 130 (1997).
[CrossRef]

Doran, N. J.

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

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, Opt. Lett. 21, 1981 (1996).
[CrossRef] [PubMed]

Edagawa, N.

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

N. Edagawa, I. Morita, M. Suzuki, S. Yamamoto, H. Taga, and S. Akiba, in 21st European Conference on Optical Communication (IEEE, Piscataway, N.J., 1995), paper Th.A.3.5.

Forysiak, W.

Gabitov, I.

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Opt. Commun. 134, 317 (1997).
[CrossRef]

Golovchenko, E. A.

J. M. Jacob, E. A. Golovchenko, A. N. Pilipetskii, G. M. Carter, and C. R. Menyuk, IEEE Photon. Technol. Lett. 9, 130 (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]

K. Tamura, E. P. Ippen, H. A. Haus, and L. E. Nelson, Opt. Lett. 18, 1080 (1993).
[CrossRef]

Ippen, E. P.

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

K. Tamura, E. P. Ippen, H. A. Haus, and L. E. Nelson, Opt. Lett. 18, 1080 (1993).
[CrossRef]

Jacob, J. M.

J. M. Jacob, E. A. Golovchenko, A. N. Pilipetskii, G. M. Carter, and C. R. Menyuk, IEEE Photon. Technol. Lett. 9, 130 (1997).
[CrossRef]

Kasegawa, A.

Knox, F. M.

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, Opt. Lett. 21, 1981 (1996).
[CrossRef] [PubMed]

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

Kodama, Y.

Kubota, H.

M. Nakazawa, H. Kubota, A. Sahara, and K. Tamura, IEEE Photon. Technol. Lett. 8, 1088 (1996).
[CrossRef]

H. Kubota and M. Nakazawa, Opt. Commun. 87, 15 (1991).
[CrossRef]

Malomed, B. A.

B. A. Malomed, Opt. Commun. 136, 313 (1997).
[CrossRef]

Matsumoto, M.

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

Menyuk, C. R.

J. M. Jacob, E. A. Golovchenko, A. N. Pilipetskii, G. M. Carter, and C. R. Menyuk, IEEE Photon. Technol. Lett. 9, 130 (1997).
[CrossRef]

Morita, I.

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

N. Edagawa, I. Morita, M. Suzuki, S. Yamamoto, H. Taga, and S. Akiba, in 21st European Conference on Optical Communication (IEEE, Piscataway, N.J., 1995), paper Th.A.3.5.

Nakazawa, M.

M. Nakazawa, H. Kubota, A. Sahara, and K. Tamura, IEEE Photon. Technol. Lett. 8, 1088 (1996).
[CrossRef]

H. Kubota and M. Nakazawa, Opt. Commun. 87, 15 (1991).
[CrossRef]

Nelson, L. E.

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

K. Tamura, E. P. Ippen, H. A. Haus, and L. E. Nelson, Opt. Lett. 18, 1080 (1993).
[CrossRef]

Pilipetskii, A. N.

J. M. Jacob, E. A. Golovchenko, A. N. Pilipetskii, G. M. Carter, and C. R. Menyuk, IEEE Photon. Technol. Lett. 9, 130 (1997).
[CrossRef]

Sahara, A.

M. Nakazawa, H. Kubota, A. Sahara, and K. Tamura, IEEE Photon. Technol. Lett. 8, 1088 (1996).
[CrossRef]

Shapiro, E. G.

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Opt. Commun. 134, 317 (1997).
[CrossRef]

Smith, N. J.

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, Opt. Lett. 21, 1981 (1996).
[CrossRef] [PubMed]

N. J. 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]

N. Edagawa, I. Morita, M. Suzuki, S. Yamamoto, H. Taga, and S. Akiba, in 21st European Conference on Optical Communication (IEEE, Piscataway, N.J., 1995), paper Th.A.3.5.

Taga, H.

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

N. Edagawa, I. Morita, M. Suzuki, S. Yamamoto, H. Taga, and S. Akiba, in 21st European Conference on Optical Communication (IEEE, Piscataway, N.J., 1995), paper Th.A.3.5.

Tamura, K.

M. Nakazawa, H. Kubota, A. Sahara, and K. Tamura, IEEE Photon. Technol. Lett. 8, 1088 (1996).
[CrossRef]

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

K. Tamura, E. P. Ippen, H. A. Haus, and L. E. Nelson, Opt. Lett. 18, 1080 (1993).
[CrossRef]

Turitsyn, S. K.

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Opt. Commun. 134, 317 (1997).
[CrossRef]

Yamamoto, S.

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

N. Edagawa, I. Morita, M. Suzuki, S. Yamamoto, H. Taga, and S. Akiba, in 21st European Conference on Optical Communication (IEEE, Piscataway, N.J., 1995), paper Th.A.3.5.

Electron. Lett. (2)

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

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
[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. (3)

M. Nakazawa, H. Kubota, A. Sahara, and K. Tamura, IEEE Photon. Technol. Lett. 8, 1088 (1996).
[CrossRef]

J. M. Jacob, E. A. Golovchenko, A. N. Pilipetskii, G. M. Carter, and C. R. Menyuk, IEEE Photon. Technol. Lett. 9, 130 (1997).
[CrossRef]

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

Opt. Commun. (3)

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Opt. Commun. 134, 317 (1997).
[CrossRef]

B. A. Malomed, Opt. Commun. 136, 313 (1997).
[CrossRef]

H. Kubota and M. Nakazawa, Opt. Commun. 87, 15 (1991).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (1)

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[CrossRef]

Other (1)

N. Edagawa, I. Morita, M. Suzuki, S. Yamamoto, H. Taga, and S. Akiba, in 21st European Conference on Optical Communication (IEEE, Piscataway, N.J., 1995), paper Th.A.3.5.

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Figures (4)

Fig. 1
Fig. 1

Nonlinearity-induced phase shift in one period of dispersion variation with D=1.5, d=0, L=1.5, τ0=0.7, and a=0. Solid curves, numerical simulation of the nonlinear Schrödinger equation in one period; dotted curves, numerical integration of Eq.  (2) with Eq.  (3); dashed curves, parabolic phase shift calculated by the variational method.

Fig. 2
Fig. 2

Nonlinearity-induced chirping in one period versus DL/τ02. Solid curve, approximate analytical expression  (7); dashed curves, numerical solution of Eq.  (4); dotted curve, ϕ2 evaluated from the power-series expansion of Eq.  (2) in t.

Fig. 3
Fig. 3

Pulse energy versus DL. Solid curves, theoretical expression (11); dashed curves, empirical expression  (12); circles, numerical results with d=0.02 and L=1.5.

Fig. 4
Fig. 4

Variations of pulse width with distance in the presence of filtering with (a) β=0.01 and (b) β=0.015. Other parameters are D=1, d=0.02, L=1.5, and g=0.01. Solid curves, theoretical curves constructed from Gaussian solution (3) with pulse parameters calculated with Eqs.  (8)–(10); dashed curves, numerical results. Midpoints in anomalous-dispersion segments are located at Z=210+3n (n is an integer).

Equations (13)

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

ikq=id2d2qdt2+iϕ2Lq+gq+βd2qdt2,
ϕ=oneperioduz, t2 dz,
uz, t=A01+iz-aD/τ021/2×exp-t22τ0211+iz-aD/τ02
dτ/dz=2Dτb,
dbdz=-E022τ3+D2τ4-2Db2,
vz, t=Azexp-t22τ2z+ibzt2+iθz,
db˜dz=-E022τL3-4DbLb˜
ϕ2=-b˜2L-b˜0=A022Dsinh-1L/2-aD/τ021+L/2-a2D2/τ04+sinh-1L/2+aD/τ021+L/2+a2D2/τ04.
τ0=β/2g,
a=d2/4+β21/2-d/2/2gD,
A02=22gLasinh-1L/2-aD/τ021+L/2-a2D2/τ04+sinh-1L/2+aD/τ021+L/2+a2D2/τ04-1.
E=πτ0A02=π2DLdτ031+DL/2τ022sinh-1DL/2τ02.
E=2 ln1+2dln 2τ01+αDL2τ02 ln 22

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