Abstract

Pulse propagation in optical fibers is considered after including the effects of chromatic dispersion and nonlinearity. To estimate the extent of pulse broadening, an analytic expression for the pulse width is obtained under certain simplifying assumptions. Its range of validity is discussed by comparing the analytical prediction with the numerically calculated pulse width. Results are presented for 1.55-μm optical pulses propagating in conventional as well as in dispersion-shifted fibers. Our results show that for relatively wide pulses the nonlinearity broadens the pulse considerably over the linear case, thereby reducing the bandwidth of optical communication systems. For sufficiently short pulses we have found that the nonlinearity can give rise to pulses narrower than the linear case at the zero-dispersion wavelength.

© 1986 Optical Society of America

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  1. W. J. Tomlinson, R. H. Stolen, and C. V. Shank, “Compression of optical pulses chirped by self-phase modulation in fibers,” J. Opt. Soc. Am. B 1, 139–149 (1984).
    [CrossRef]
  2. C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, “Compression of femtosecond optical pulses,” Appl. Phys. Lett. 40, 761–763 (1982).
    [CrossRef]
  3. B. Nikolous and D. Grischkowsky, “12 × pulse compression using optical fibers,” Appl. Phys. Lett. 43, 1–2 (1983).
    [CrossRef]
  4. L. F. Mollenauer, R. H. Stolen, J. P. Gordon, and W. J. Tomlinson, “Extreme picosecond pulse narrowing by means of soliton effect in single-mode optical fibers,” Opt. Lett. 8, 289–291 (1983).
    [CrossRef] [PubMed]
  5. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observations of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
    [CrossRef]
  6. A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers, I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
    [CrossRef]
  7. V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62–69 (1971).
  8. J. Satsuma and N. Yajima, “Initial value problems of one-dimensional self-modulation of nonlinear waves in dispersive media,” Prog. Theor. Phys. Suppl. 55, 284–306 (1974).
    [CrossRef]
  9. K. J. Blow, N. J. Doran, and E. Cummins, “Nonlinear limits on bandwidth at the minimum dispersion in optical fibers,” Opt. Commun. 48, 181–184 (1983).
    [CrossRef]
  10. V. A. Vysloukh, “Propagation of pulses in optical fibers in the region of dispersion minimum. Role of nonlinearity and higher-order dispersion,” Sov. J. Quantum Electron 13, 1113–1114 (1983).
    [CrossRef]
  11. A. Owyoung, R. W. Hellwarth, and N. George, “Intensity-induced changes in optical polarizations in glasses,” Phys. Rev. B 5, 628–633 (1972).
    [CrossRef]
  12. R. H. Stolen and C. Lin, “Self-phase modulation in silica optical fibers,” Phys. Rev. A 17, 1448–1453 (1978).
    [CrossRef]
  13. N. Tzoar and M. Jain, “Self-phase modulation in long-geometry optical waveguides,” Phys. Rev. A 23, 1266–1269 (1981).
    [CrossRef]
  14. D. Anderson and M. Lisak, “Nonlinear asymmetric self-phase modulation and self-steepening of pulses in long optical waveguides,” Phys. Rev. A 27, 1393–1398 (1983).
    [CrossRef]
  15. F. DeMartini, C. H. Townes, T. K. Gustafson, and P. L. Kelley, “Self-steepening of light pulses,” Phys. Rev. 164, 312–322 (1967).
    [CrossRef]
  16. M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1981).
    [CrossRef]
  17. W. Eckhaus and A. Van Harten, The Inverse Scattering Transform and the Theory of Solitons: An Introduction (North-Holland, Amsterdam, 1981).
  18. K. J. Blow and N. J. Doran, “Bandwidth limits of nonlinear (soliton) optical communication systems,” Electron. Lett. 19, 429–430 (1983).
    [CrossRef]
  19. D. Marcuse, “Pulse distortion in single-mode fibers,” Appl. Opt. 19, 1653–1660 (1980).
    [CrossRef] [PubMed]
  20. M. Miyagi and S. Nishida, “Pulse spreading in a single-mode fiber due to third-order dispersion,” Appl. Opt. 18, 678–682 (1979).
    [CrossRef] [PubMed]
  21. D. Gloge, “Effect of chromatic dispersion on pulses of arbitrary coherence,” Electron. Lett. 15, 685–686 (1979).
    [CrossRef]
  22. H. G. Unger, “Optical pulse distortion in glass fibers at the wavelength of minimum dispersion,” Kurzbericht 31, 518–519 (1977).
  23. D. Anderson and J. H. Askne, “Wave packets in strongly dispersive media,” Proc. IEEE 62, 1518–1523 (1974).
    [CrossRef]
  24. M. J. Bennett, “Dispersion characteristics of monomode optical fiber systems,” Proc. Inst. Electr. Eng. H 130, 309–314 (1983).
  25. R. A. Fisher and W. K. Bischel, “Numerical studies of the interplay between self-phase modulation and dispersion for intense plane-wave laser pulses,” J. Appl. Phys. 46, 4921–4934 (1975).
    [CrossRef]
  26. E. A. Sziklas and A. E. Siegman, “Mode calculations in unstable resonators with flowing saturable gain: fast Fourier transform method,” Appl. Opt. 14, 1874–1889 (1975).
    [CrossRef] [PubMed]
  27. M. D. Feit and J. A. Fleck, “Light propagation in graded-index optical fibers,” Appl. Opt. 17, 3990–3998 (1978).
    [CrossRef] [PubMed]
  28. M. Lax, J. H. Batteh, and G. P. Agrawal, “Channeling of intense electromagnetic beams,” J. Appl. Phys. 52, 109–125 (1981).
    [CrossRef]
  29. D. Yevick and B. Hermansson, “Soliton analysis with the propagating beam method,” Opt. Commun. 47, 101–106 (1983).
    [CrossRef]
  30. G. P. Agrawal, “Fast-Fourier transform based beam-propagation model for stripe-geometry semiconductor lasers: inclusion of axial effects,” J. Appl. Phys. 56, 3100–3109 (1984).
    [CrossRef]
  31. D. Marcuse and J. Stone, “Experimental comparison of the bandwidths of standard and dispersion-shifted fibers near their ‘zero-dispersion’ wavelengths,” Opt. Lett. 10, 163, 165 (1985).
    [CrossRef] [PubMed]
  32. B. J. Ainslie, K. J. Beales, C. R. Day, and J. D. Rush, “Interplay of design parameters and fabrication conditions on the performance of monomode fibers made by MCVD,” IEEE J. Quantum Electron. QE-17, 854–857 (1981).
    [CrossRef]
  33. U. C. Paek, G. E. Peterson, and A. Carnevale, “Dispersionless single-mode lightguides with index profiles,” Bell. Syst. Tech. J. 60, 583–598 (1981).
    [CrossRef]
  34. B. J. Ainslie, K. J. Beales, D. M. Cooper, C. R. Day, and J. D. Rush, “Monomode fiber with ultra-low-loss and minimum dispersion at 1.55 μ m,” Electron. Lett. 18, 842–843 (1982).
    [CrossRef]
  35. L. G. Cohen, W. L. Mammel, and S. J. Jang, “Low-loss quadruple-clad single-mode lightguides with dispersion below 2 ps/km-nm over the 1.28 μ m wavelength range,” Electron. Lett. 18, 1023–1024 (1982).
    [CrossRef]

1985 (1)

1984 (2)

G. P. Agrawal, “Fast-Fourier transform based beam-propagation model for stripe-geometry semiconductor lasers: inclusion of axial effects,” J. Appl. Phys. 56, 3100–3109 (1984).
[CrossRef]

W. J. Tomlinson, R. H. Stolen, and C. V. Shank, “Compression of optical pulses chirped by self-phase modulation in fibers,” J. Opt. Soc. Am. B 1, 139–149 (1984).
[CrossRef]

1983 (8)

K. J. Blow, N. J. Doran, and E. Cummins, “Nonlinear limits on bandwidth at the minimum dispersion in optical fibers,” Opt. Commun. 48, 181–184 (1983).
[CrossRef]

V. A. Vysloukh, “Propagation of pulses in optical fibers in the region of dispersion minimum. Role of nonlinearity and higher-order dispersion,” Sov. J. Quantum Electron 13, 1113–1114 (1983).
[CrossRef]

B. Nikolous and D. Grischkowsky, “12 × pulse compression using optical fibers,” Appl. Phys. Lett. 43, 1–2 (1983).
[CrossRef]

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, and W. J. Tomlinson, “Extreme picosecond pulse narrowing by means of soliton effect in single-mode optical fibers,” Opt. Lett. 8, 289–291 (1983).
[CrossRef] [PubMed]

D. Anderson and M. Lisak, “Nonlinear asymmetric self-phase modulation and self-steepening of pulses in long optical waveguides,” Phys. Rev. A 27, 1393–1398 (1983).
[CrossRef]

K. J. Blow and N. J. Doran, “Bandwidth limits of nonlinear (soliton) optical communication systems,” Electron. Lett. 19, 429–430 (1983).
[CrossRef]

D. Yevick and B. Hermansson, “Soliton analysis with the propagating beam method,” Opt. Commun. 47, 101–106 (1983).
[CrossRef]

M. J. Bennett, “Dispersion characteristics of monomode optical fiber systems,” Proc. Inst. Electr. Eng. H 130, 309–314 (1983).

1982 (3)

B. J. Ainslie, K. J. Beales, D. M. Cooper, C. R. Day, and J. D. Rush, “Monomode fiber with ultra-low-loss and minimum dispersion at 1.55 μ m,” Electron. Lett. 18, 842–843 (1982).
[CrossRef]

L. G. Cohen, W. L. Mammel, and S. J. Jang, “Low-loss quadruple-clad single-mode lightguides with dispersion below 2 ps/km-nm over the 1.28 μ m wavelength range,” Electron. Lett. 18, 1023–1024 (1982).
[CrossRef]

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, “Compression of femtosecond optical pulses,” Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

1981 (4)

N. Tzoar and M. Jain, “Self-phase modulation in long-geometry optical waveguides,” Phys. Rev. A 23, 1266–1269 (1981).
[CrossRef]

M. Lax, J. H. Batteh, and G. P. Agrawal, “Channeling of intense electromagnetic beams,” J. Appl. Phys. 52, 109–125 (1981).
[CrossRef]

B. J. Ainslie, K. J. Beales, C. R. Day, and J. D. Rush, “Interplay of design parameters and fabrication conditions on the performance of monomode fibers made by MCVD,” IEEE J. Quantum Electron. QE-17, 854–857 (1981).
[CrossRef]

U. C. Paek, G. E. Peterson, and A. Carnevale, “Dispersionless single-mode lightguides with index profiles,” Bell. Syst. Tech. J. 60, 583–598 (1981).
[CrossRef]

1980 (2)

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observations of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

D. Marcuse, “Pulse distortion in single-mode fibers,” Appl. Opt. 19, 1653–1660 (1980).
[CrossRef] [PubMed]

1979 (2)

M. Miyagi and S. Nishida, “Pulse spreading in a single-mode fiber due to third-order dispersion,” Appl. Opt. 18, 678–682 (1979).
[CrossRef] [PubMed]

D. Gloge, “Effect of chromatic dispersion on pulses of arbitrary coherence,” Electron. Lett. 15, 685–686 (1979).
[CrossRef]

1978 (2)

R. H. Stolen and C. Lin, “Self-phase modulation in silica optical fibers,” Phys. Rev. A 17, 1448–1453 (1978).
[CrossRef]

M. D. Feit and J. A. Fleck, “Light propagation in graded-index optical fibers,” Appl. Opt. 17, 3990–3998 (1978).
[CrossRef] [PubMed]

1977 (1)

H. G. Unger, “Optical pulse distortion in glass fibers at the wavelength of minimum dispersion,” Kurzbericht 31, 518–519 (1977).

1975 (2)

R. A. Fisher and W. K. Bischel, “Numerical studies of the interplay between self-phase modulation and dispersion for intense plane-wave laser pulses,” J. Appl. Phys. 46, 4921–4934 (1975).
[CrossRef]

E. A. Sziklas and A. E. Siegman, “Mode calculations in unstable resonators with flowing saturable gain: fast Fourier transform method,” Appl. Opt. 14, 1874–1889 (1975).
[CrossRef] [PubMed]

1974 (2)

D. Anderson and J. H. Askne, “Wave packets in strongly dispersive media,” Proc. IEEE 62, 1518–1523 (1974).
[CrossRef]

J. Satsuma and N. Yajima, “Initial value problems of one-dimensional self-modulation of nonlinear waves in dispersive media,” Prog. Theor. Phys. Suppl. 55, 284–306 (1974).
[CrossRef]

1973 (1)

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers, I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

1972 (1)

A. Owyoung, R. W. Hellwarth, and N. George, “Intensity-induced changes in optical polarizations in glasses,” Phys. Rev. B 5, 628–633 (1972).
[CrossRef]

1971 (1)

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62–69 (1971).

1967 (1)

F. DeMartini, C. H. Townes, T. K. Gustafson, and P. L. Kelley, “Self-steepening of light pulses,” Phys. Rev. 164, 312–322 (1967).
[CrossRef]

Ablowitz, M. J.

M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1981).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, “Fast-Fourier transform based beam-propagation model for stripe-geometry semiconductor lasers: inclusion of axial effects,” J. Appl. Phys. 56, 3100–3109 (1984).
[CrossRef]

M. Lax, J. H. Batteh, and G. P. Agrawal, “Channeling of intense electromagnetic beams,” J. Appl. Phys. 52, 109–125 (1981).
[CrossRef]

Ainslie, B. J.

B. J. Ainslie, K. J. Beales, D. M. Cooper, C. R. Day, and J. D. Rush, “Monomode fiber with ultra-low-loss and minimum dispersion at 1.55 μ m,” Electron. Lett. 18, 842–843 (1982).
[CrossRef]

B. J. Ainslie, K. J. Beales, C. R. Day, and J. D. Rush, “Interplay of design parameters and fabrication conditions on the performance of monomode fibers made by MCVD,” IEEE J. Quantum Electron. QE-17, 854–857 (1981).
[CrossRef]

Anderson, D.

D. Anderson and M. Lisak, “Nonlinear asymmetric self-phase modulation and self-steepening of pulses in long optical waveguides,” Phys. Rev. A 27, 1393–1398 (1983).
[CrossRef]

D. Anderson and J. H. Askne, “Wave packets in strongly dispersive media,” Proc. IEEE 62, 1518–1523 (1974).
[CrossRef]

Askne, J. H.

D. Anderson and J. H. Askne, “Wave packets in strongly dispersive media,” Proc. IEEE 62, 1518–1523 (1974).
[CrossRef]

Batteh, J. H.

M. Lax, J. H. Batteh, and G. P. Agrawal, “Channeling of intense electromagnetic beams,” J. Appl. Phys. 52, 109–125 (1981).
[CrossRef]

Beales, K. J.

B. J. Ainslie, K. J. Beales, D. M. Cooper, C. R. Day, and J. D. Rush, “Monomode fiber with ultra-low-loss and minimum dispersion at 1.55 μ m,” Electron. Lett. 18, 842–843 (1982).
[CrossRef]

B. J. Ainslie, K. J. Beales, C. R. Day, and J. D. Rush, “Interplay of design parameters and fabrication conditions on the performance of monomode fibers made by MCVD,” IEEE J. Quantum Electron. QE-17, 854–857 (1981).
[CrossRef]

Bennett, M. J.

M. J. Bennett, “Dispersion characteristics of monomode optical fiber systems,” Proc. Inst. Electr. Eng. H 130, 309–314 (1983).

Bischel, W. K.

R. A. Fisher and W. K. Bischel, “Numerical studies of the interplay between self-phase modulation and dispersion for intense plane-wave laser pulses,” J. Appl. Phys. 46, 4921–4934 (1975).
[CrossRef]

Blow, K. J.

K. J. Blow and N. J. Doran, “Bandwidth limits of nonlinear (soliton) optical communication systems,” Electron. Lett. 19, 429–430 (1983).
[CrossRef]

K. J. Blow, N. J. Doran, and E. Cummins, “Nonlinear limits on bandwidth at the minimum dispersion in optical fibers,” Opt. Commun. 48, 181–184 (1983).
[CrossRef]

Carnevale, A.

U. C. Paek, G. E. Peterson, and A. Carnevale, “Dispersionless single-mode lightguides with index profiles,” Bell. Syst. Tech. J. 60, 583–598 (1981).
[CrossRef]

Cohen, L. G.

L. G. Cohen, W. L. Mammel, and S. J. Jang, “Low-loss quadruple-clad single-mode lightguides with dispersion below 2 ps/km-nm over the 1.28 μ m wavelength range,” Electron. Lett. 18, 1023–1024 (1982).
[CrossRef]

Cooper, D. M.

B. J. Ainslie, K. J. Beales, D. M. Cooper, C. R. Day, and J. D. Rush, “Monomode fiber with ultra-low-loss and minimum dispersion at 1.55 μ m,” Electron. Lett. 18, 842–843 (1982).
[CrossRef]

Cummins, E.

K. J. Blow, N. J. Doran, and E. Cummins, “Nonlinear limits on bandwidth at the minimum dispersion in optical fibers,” Opt. Commun. 48, 181–184 (1983).
[CrossRef]

Day, C. R.

B. J. Ainslie, K. J. Beales, D. M. Cooper, C. R. Day, and J. D. Rush, “Monomode fiber with ultra-low-loss and minimum dispersion at 1.55 μ m,” Electron. Lett. 18, 842–843 (1982).
[CrossRef]

B. J. Ainslie, K. J. Beales, C. R. Day, and J. D. Rush, “Interplay of design parameters and fabrication conditions on the performance of monomode fibers made by MCVD,” IEEE J. Quantum Electron. QE-17, 854–857 (1981).
[CrossRef]

DeMartini, F.

F. DeMartini, C. H. Townes, T. K. Gustafson, and P. L. Kelley, “Self-steepening of light pulses,” Phys. Rev. 164, 312–322 (1967).
[CrossRef]

Doran, N. J.

K. J. Blow and N. J. Doran, “Bandwidth limits of nonlinear (soliton) optical communication systems,” Electron. Lett. 19, 429–430 (1983).
[CrossRef]

K. J. Blow, N. J. Doran, and E. Cummins, “Nonlinear limits on bandwidth at the minimum dispersion in optical fibers,” Opt. Commun. 48, 181–184 (1983).
[CrossRef]

Eckhaus, W.

W. Eckhaus and A. Van Harten, The Inverse Scattering Transform and the Theory of Solitons: An Introduction (North-Holland, Amsterdam, 1981).

Feit, M. D.

Fisher, R. A.

R. A. Fisher and W. K. Bischel, “Numerical studies of the interplay between self-phase modulation and dispersion for intense plane-wave laser pulses,” J. Appl. Phys. 46, 4921–4934 (1975).
[CrossRef]

Fleck, J. A.

Fork, R. L.

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, “Compression of femtosecond optical pulses,” Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

George, N.

A. Owyoung, R. W. Hellwarth, and N. George, “Intensity-induced changes in optical polarizations in glasses,” Phys. Rev. B 5, 628–633 (1972).
[CrossRef]

Gloge, D.

D. Gloge, “Effect of chromatic dispersion on pulses of arbitrary coherence,” Electron. Lett. 15, 685–686 (1979).
[CrossRef]

Gordon, J. P.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, and W. J. Tomlinson, “Extreme picosecond pulse narrowing by means of soliton effect in single-mode optical fibers,” Opt. Lett. 8, 289–291 (1983).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observations of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

Grischkowsky, D.

B. Nikolous and D. Grischkowsky, “12 × pulse compression using optical fibers,” Appl. Phys. Lett. 43, 1–2 (1983).
[CrossRef]

Gustafson, T. K.

F. DeMartini, C. H. Townes, T. K. Gustafson, and P. L. Kelley, “Self-steepening of light pulses,” Phys. Rev. 164, 312–322 (1967).
[CrossRef]

Hasegawa, A.

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers, I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

Hellwarth, R. W.

A. Owyoung, R. W. Hellwarth, and N. George, “Intensity-induced changes in optical polarizations in glasses,” Phys. Rev. B 5, 628–633 (1972).
[CrossRef]

Hermansson, B.

D. Yevick and B. Hermansson, “Soliton analysis with the propagating beam method,” Opt. Commun. 47, 101–106 (1983).
[CrossRef]

Jain, M.

N. Tzoar and M. Jain, “Self-phase modulation in long-geometry optical waveguides,” Phys. Rev. A 23, 1266–1269 (1981).
[CrossRef]

Jang, S. J.

L. G. Cohen, W. L. Mammel, and S. J. Jang, “Low-loss quadruple-clad single-mode lightguides with dispersion below 2 ps/km-nm over the 1.28 μ m wavelength range,” Electron. Lett. 18, 1023–1024 (1982).
[CrossRef]

Kelley, P. L.

F. DeMartini, C. H. Townes, T. K. Gustafson, and P. L. Kelley, “Self-steepening of light pulses,” Phys. Rev. 164, 312–322 (1967).
[CrossRef]

Lax, M.

M. Lax, J. H. Batteh, and G. P. Agrawal, “Channeling of intense electromagnetic beams,” J. Appl. Phys. 52, 109–125 (1981).
[CrossRef]

Lin, C.

R. H. Stolen and C. Lin, “Self-phase modulation in silica optical fibers,” Phys. Rev. A 17, 1448–1453 (1978).
[CrossRef]

Lisak, M.

D. Anderson and M. Lisak, “Nonlinear asymmetric self-phase modulation and self-steepening of pulses in long optical waveguides,” Phys. Rev. A 27, 1393–1398 (1983).
[CrossRef]

Mammel, W. L.

L. G. Cohen, W. L. Mammel, and S. J. Jang, “Low-loss quadruple-clad single-mode lightguides with dispersion below 2 ps/km-nm over the 1.28 μ m wavelength range,” Electron. Lett. 18, 1023–1024 (1982).
[CrossRef]

Marcuse, D.

Miyagi, M.

Mollenauer, L. F.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, and W. J. Tomlinson, “Extreme picosecond pulse narrowing by means of soliton effect in single-mode optical fibers,” Opt. Lett. 8, 289–291 (1983).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observations of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

Nikolous, B.

B. Nikolous and D. Grischkowsky, “12 × pulse compression using optical fibers,” Appl. Phys. Lett. 43, 1–2 (1983).
[CrossRef]

Nishida, S.

Owyoung, A.

A. Owyoung, R. W. Hellwarth, and N. George, “Intensity-induced changes in optical polarizations in glasses,” Phys. Rev. B 5, 628–633 (1972).
[CrossRef]

Paek, U. C.

U. C. Paek, G. E. Peterson, and A. Carnevale, “Dispersionless single-mode lightguides with index profiles,” Bell. Syst. Tech. J. 60, 583–598 (1981).
[CrossRef]

Peterson, G. E.

U. C. Paek, G. E. Peterson, and A. Carnevale, “Dispersionless single-mode lightguides with index profiles,” Bell. Syst. Tech. J. 60, 583–598 (1981).
[CrossRef]

Rush, J. D.

B. J. Ainslie, K. J. Beales, D. M. Cooper, C. R. Day, and J. D. Rush, “Monomode fiber with ultra-low-loss and minimum dispersion at 1.55 μ m,” Electron. Lett. 18, 842–843 (1982).
[CrossRef]

B. J. Ainslie, K. J. Beales, C. R. Day, and J. D. Rush, “Interplay of design parameters and fabrication conditions on the performance of monomode fibers made by MCVD,” IEEE J. Quantum Electron. QE-17, 854–857 (1981).
[CrossRef]

Satsuma, J.

J. Satsuma and N. Yajima, “Initial value problems of one-dimensional self-modulation of nonlinear waves in dispersive media,” Prog. Theor. Phys. Suppl. 55, 284–306 (1974).
[CrossRef]

Segur, H.

M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1981).
[CrossRef]

Shabat, A. B.

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62–69 (1971).

Shank, C. V.

W. J. Tomlinson, R. H. Stolen, and C. V. Shank, “Compression of optical pulses chirped by self-phase modulation in fibers,” J. Opt. Soc. Am. B 1, 139–149 (1984).
[CrossRef]

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, “Compression of femtosecond optical pulses,” Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

Siegman, A. E.

Stolen, R. H.

W. J. Tomlinson, R. H. Stolen, and C. V. Shank, “Compression of optical pulses chirped by self-phase modulation in fibers,” J. Opt. Soc. Am. B 1, 139–149 (1984).
[CrossRef]

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, and W. J. Tomlinson, “Extreme picosecond pulse narrowing by means of soliton effect in single-mode optical fibers,” Opt. Lett. 8, 289–291 (1983).
[CrossRef] [PubMed]

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, “Compression of femtosecond optical pulses,” Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observations of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

R. H. Stolen and C. Lin, “Self-phase modulation in silica optical fibers,” Phys. Rev. A 17, 1448–1453 (1978).
[CrossRef]

Stone, J.

Sziklas, E. A.

Tappert, F.

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers, I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

Tomlinson, W. J.

Townes, C. H.

F. DeMartini, C. H. Townes, T. K. Gustafson, and P. L. Kelley, “Self-steepening of light pulses,” Phys. Rev. 164, 312–322 (1967).
[CrossRef]

Tzoar, N.

N. Tzoar and M. Jain, “Self-phase modulation in long-geometry optical waveguides,” Phys. Rev. A 23, 1266–1269 (1981).
[CrossRef]

Unger, H. G.

H. G. Unger, “Optical pulse distortion in glass fibers at the wavelength of minimum dispersion,” Kurzbericht 31, 518–519 (1977).

Van Harten, A.

W. Eckhaus and A. Van Harten, The Inverse Scattering Transform and the Theory of Solitons: An Introduction (North-Holland, Amsterdam, 1981).

Vysloukh, V. A.

V. A. Vysloukh, “Propagation of pulses in optical fibers in the region of dispersion minimum. Role of nonlinearity and higher-order dispersion,” Sov. J. Quantum Electron 13, 1113–1114 (1983).
[CrossRef]

Yajima, N.

J. Satsuma and N. Yajima, “Initial value problems of one-dimensional self-modulation of nonlinear waves in dispersive media,” Prog. Theor. Phys. Suppl. 55, 284–306 (1974).
[CrossRef]

Yen, R.

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, “Compression of femtosecond optical pulses,” Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

Yevick, D.

D. Yevick and B. Hermansson, “Soliton analysis with the propagating beam method,” Opt. Commun. 47, 101–106 (1983).
[CrossRef]

Zakharov, V. E.

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62–69 (1971).

Appl. Opt. (4)

Appl. Phys. Lett. (3)

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, “Compression of femtosecond optical pulses,” Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

B. Nikolous and D. Grischkowsky, “12 × pulse compression using optical fibers,” Appl. Phys. Lett. 43, 1–2 (1983).
[CrossRef]

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers, I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

Bell. Syst. Tech. J. (1)

U. C. Paek, G. E. Peterson, and A. Carnevale, “Dispersionless single-mode lightguides with index profiles,” Bell. Syst. Tech. J. 60, 583–598 (1981).
[CrossRef]

Electron. Lett. (4)

B. J. Ainslie, K. J. Beales, D. M. Cooper, C. R. Day, and J. D. Rush, “Monomode fiber with ultra-low-loss and minimum dispersion at 1.55 μ m,” Electron. Lett. 18, 842–843 (1982).
[CrossRef]

L. G. Cohen, W. L. Mammel, and S. J. Jang, “Low-loss quadruple-clad single-mode lightguides with dispersion below 2 ps/km-nm over the 1.28 μ m wavelength range,” Electron. Lett. 18, 1023–1024 (1982).
[CrossRef]

D. Gloge, “Effect of chromatic dispersion on pulses of arbitrary coherence,” Electron. Lett. 15, 685–686 (1979).
[CrossRef]

K. J. Blow and N. J. Doran, “Bandwidth limits of nonlinear (soliton) optical communication systems,” Electron. Lett. 19, 429–430 (1983).
[CrossRef]

IEEE J. Quantum Electron. (1)

B. J. Ainslie, K. J. Beales, C. R. Day, and J. D. Rush, “Interplay of design parameters and fabrication conditions on the performance of monomode fibers made by MCVD,” IEEE J. Quantum Electron. QE-17, 854–857 (1981).
[CrossRef]

J. Appl. Phys. (3)

R. A. Fisher and W. K. Bischel, “Numerical studies of the interplay between self-phase modulation and dispersion for intense plane-wave laser pulses,” J. Appl. Phys. 46, 4921–4934 (1975).
[CrossRef]

G. P. Agrawal, “Fast-Fourier transform based beam-propagation model for stripe-geometry semiconductor lasers: inclusion of axial effects,” J. Appl. Phys. 56, 3100–3109 (1984).
[CrossRef]

M. Lax, J. H. Batteh, and G. P. Agrawal, “Channeling of intense electromagnetic beams,” J. Appl. Phys. 52, 109–125 (1981).
[CrossRef]

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

Kurzbericht (1)

H. G. Unger, “Optical pulse distortion in glass fibers at the wavelength of minimum dispersion,” Kurzbericht 31, 518–519 (1977).

Opt. Commun. (2)

D. Yevick and B. Hermansson, “Soliton analysis with the propagating beam method,” Opt. Commun. 47, 101–106 (1983).
[CrossRef]

K. J. Blow, N. J. Doran, and E. Cummins, “Nonlinear limits on bandwidth at the minimum dispersion in optical fibers,” Opt. Commun. 48, 181–184 (1983).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. (1)

F. DeMartini, C. H. Townes, T. K. Gustafson, and P. L. Kelley, “Self-steepening of light pulses,” Phys. Rev. 164, 312–322 (1967).
[CrossRef]

Phys. Rev. A (3)

R. H. Stolen and C. Lin, “Self-phase modulation in silica optical fibers,” Phys. Rev. A 17, 1448–1453 (1978).
[CrossRef]

N. Tzoar and M. Jain, “Self-phase modulation in long-geometry optical waveguides,” Phys. Rev. A 23, 1266–1269 (1981).
[CrossRef]

D. Anderson and M. Lisak, “Nonlinear asymmetric self-phase modulation and self-steepening of pulses in long optical waveguides,” Phys. Rev. A 27, 1393–1398 (1983).
[CrossRef]

Phys. Rev. B (1)

A. Owyoung, R. W. Hellwarth, and N. George, “Intensity-induced changes in optical polarizations in glasses,” Phys. Rev. B 5, 628–633 (1972).
[CrossRef]

Phys. Rev. Lett. (1)

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observations of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

Proc. IEEE (1)

D. Anderson and J. H. Askne, “Wave packets in strongly dispersive media,” Proc. IEEE 62, 1518–1523 (1974).
[CrossRef]

Proc. Inst. Electr. Eng. H (1)

M. J. Bennett, “Dispersion characteristics of monomode optical fiber systems,” Proc. Inst. Electr. Eng. H 130, 309–314 (1983).

Prog. Theor. Phys. Suppl. (1)

J. Satsuma and N. Yajima, “Initial value problems of one-dimensional self-modulation of nonlinear waves in dispersive media,” Prog. Theor. Phys. Suppl. 55, 284–306 (1974).
[CrossRef]

Sov. J. Quantum Electron (1)

V. A. Vysloukh, “Propagation of pulses in optical fibers in the region of dispersion minimum. Role of nonlinearity and higher-order dispersion,” Sov. J. Quantum Electron 13, 1113–1114 (1983).
[CrossRef]

Sov. Phys. JETP (1)

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62–69 (1971).

Other (2)

M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1981).
[CrossRef]

W. Eckhaus and A. Van Harten, The Inverse Scattering Transform and the Theory of Solitons: An Introduction (North-Holland, Amsterdam, 1981).

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Figures (3)

Fig. 1
Fig. 1

Variation of the pulse-broadening factor K with fiber length for the case of β(2) = −20 psec2/km and β(3) = 0. Initial half-widths are σ = 5 psec and σ = 50 psec.

Fig. 2
Fig. 2

Variation of the pulse-broadening factor K with fiber length for the case of β(2) = 0 and β(3) = 0.1 psec3/km. Three values of the initial half-widths are considered. For the case of σ = 50 fsec, the LIN and ANAL curves coincide.

Fig. 3
Fig. 3

Same as in Fig. 2 except for the initial half-width σ that now takes a value of 5 psec.

Tables (1)

Tables Icon

Table 1 Comparison of Pulse Broadening for Numerical, Analytical, and Linear Cases when β(2) = −20 psec2/km and β(3) = 0

Equations (46)

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2 E z 2 - 1 c 2 2 D t 2 = 0 ,
D [ n 2 ( ω ) + 2 n 0 n 2 E 2 ] E ,
2 E z 2 - n 2 ( ω ) c 2 2 E t 2 = 2 n 0 n 2 c 2 2 t 2 ( E 2 E ) .
n 2 ( ω ) c 2 2 E t 2 = - [ β ( i t ) ] 2 E ,
β ( ω ) = ω n ( ω ) / c
β ( ω ) β 0 + β ( 1 ) ( ω - ω 0 ) + ½ β ( 2 ) ( ω - ω 0 ) 2 + β ( 3 ) ( ω - ω 0 ) 3 .
E ( z , t ) = A ( z , t ) exp [ - i ( ω 0 t - β 0 z ) ] ,
A / z β 0 A ,             A / t ω 0 A .
τ = t - β ( 1 ) z ,
i A z + i γ A - 1 2 β ( 2 ) 2 A τ 2 - i 6 β ( 3 ) 3 A τ 3 + n 2 ω 0 c A 2 A + 2 i n 2 c τ ( A 2 A ) = 0.
i A z + i γ A - 1 2 β ( 2 ) 2 A τ 2 + n 2 ω 0 c A 2 A = 0.
i A z + i γ A - i 6 β ( 3 ) 3 A τ 3 + n 2 ω 0 c A 2 A = 0.
A ( 0 , τ ) = A 0 f ( τ ) ,
A eff ( 0 , τ ) = A 0 f ( τ ) exp ( i ϕ eff ) ,
A z = - γ A + i ω 0 c n 2 A 2 A .
ϕ ( z , τ ) = n 2 ω 0 c 0 z I ( ξ , τ ) d ξ ,
I ( ξ , τ ) = A 0 2 f 2 ( τ ) exp ( - 2 γ ξ ) .
ϕ m = n 2 ω 0 c A 0 2 ( 1 - e - γ z 2 γ ) .
A ( z , τ ) = A 0 e - γ z F - 1 [ g ( ω ) ] = A 0 e - γ z h ( τ ) ,
g ( ω ) = exp [ i θ ( ω ) ] F { f ( τ ) exp [ i ϕ m f 2 ( τ ) ] } .
θ ( ω ) = [ ½ β ( 2 ) ω 2 + β ( 3 ) ω 3 ] z .
Δ τ = τ 2 - τ 2 ,
τ n = τ n A ( z , τ ) 2 d τ A ( z , τ ) 2 d τ .
τ n = τ n h ( τ ) 2 d τ ,
τ n = lim ω 0 ( i ω ) n F [ h ( τ ) 2 ] .
F [ h ( τ ) 2 ] = g ( ω - ω ) g * ( ω ) d ω
τ n = ( - i ) n g ( n ) ( ω ) g * ( ω ) d ω ,
g ( 1 ) ( ω ) = i ( ω + θ ω ) g ( ω ) .
τ n = ( ω + θ ω ) n g ( ω ) 2 d ω .
g ( 1 ) ( ω ) 2 d ω = τ 2 f ( τ ) 2 d τ ,
ω g ( ω ) 2 d ω = [ 1 + 2 i ϕ m f ( τ ) ] f ( 1 ) ( τ ) f * ( τ ) d τ .
f ( τ ) = 1 σ 2 π exp ( - τ 2 / 2 σ 2 ) ,
Δ τ 0 = σ / 2 .
K = Δ τ Δ τ 0 = [ 1 + 2 ϕ m d eff + ( 1 + 4 3 3 ϕ m 2 ) d eff 2 ] 1 / 2 ,
d eff = β ( 2 ) z / σ 2
K = Δ τ Δ τ 0 = { 1 + [ 1 + 8 3 ϕ m 2 + ( 24 25 5 - 8 27 ) ϕ m 4 ] d eff 2 } 1 / 2 ,
d eff = β ( 3 ) z / 2 σ 3 .
K = ( 1 + d eff ) 1 / 2 ,
A z = ( D + N ) A ,
A ( z + 2 δ , τ ) { e δ D exp [ z z + 2 δ N ( z ) d z ] e δ D } A ( z , τ ) .
A ( z + δ , τ ) = { F - 1 exp [ δ D ( i μ ) ] F } A ( z , τ ) ,
z z + 2 δ N ( z ) d z δ [ N ( z ) + N ( z + 2 δ ) ] .
P ( z ) = A ( z , τ ) 2 d τ
P ( z ) = A 0 2 exp ( - 2 γ z ) .
N D 2 n 2 ω 0 A 0 2 c β ( 2 ) σ 2 .
N D 6 n 2 ω 0 A 0 2 c β ( 3 ) σ 3 .

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