Abstract

The collapse and soliton regimes for pulse generation and compression in laser systems employing passive mode locking by Kerr-effect or additive-pulse mode locking are examined. Using a phenomenological laser model introduced by Haus [J. Appl. Phys. 46, 3049 (1975)] for homogeneously broadened systems, we have found three distinct regimes of pulse generation. We attempt to satisfy both the condition of pulse generation from noise and the stability requirement, considering the generation of a train of quasi-stable localized pulses in the parameter region where a single soliton is unstable.

© 1995 Optical Society of America

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References

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  1. H. A. Haus, J. Appl. Phys. 46, 3049 (1975).
    [CrossRef]
  2. E. P. Ippen, H. A. Haus, L. Y. Liu, J. Opt. Soc. Am. B 6, 1736 (1989).
    [CrossRef]
  3. O. E. Martinez, R. L. Fork, J. P. Gordon, J. Opt. Soc. Am. B 2, 753 (1985); K. J. Blow, D. Wood, J. Opt. Soc. Am. B 5, 629 (1988); P. A. Belanger, J. Opt. Soc. Am. B 8, 2077 (1991).
    [CrossRef]
  4. H. A. Haus, J. P. Fujimoto, E. P. Ippen, J. Opt. Soc. Am. B 8, 2068 (1991); IEEE J. Quantum Electron. 28, 2086 (1992); J. D. Moores, Opt. Commun. 96, 65 (1993).
    [CrossRef]
  5. C. J. Chen, P. K. A. Wai, C. R. Menyuk, Opt. Lett. 19, 198 (1994); L. F. Mollenauer, R. H. Stolen, Opt. Lett. 9, 13 (1984); J. Mark, L. Y. Liu, K. L. Hall, H. A. Haus, E. P. Ippen, Opt. Lett. 14, 48 (1989).
    [CrossRef] [PubMed]
  6. K. Stewartson, L. Hocking, J. Stuart, J. Fluid Mech. 51, 705 (1972).
    [CrossRef]
  7. S. K. Turitsyn, Phys. Rev. A 47, R27 (1993).
    [CrossRef] [PubMed]
  8. H. Nakatsuka, D. Grishkovsky, A. C. Balant, Phys. Rev. Lett. 47, 910 (1981).
    [CrossRef]
  9. L. F. Mollenauer, R. H. Stolen, J. P. Gordon, W. J. Tomlinson, Opt. Lett. 8, 289 (1983).
    [CrossRef] [PubMed]
  10. A. B. Aceves, C. De Angelis, A. M. Rubenchik, S. K. Turitsyn, Opt. Lett. 19, 329 (1994)Proceedings of European Quantum Electronics Conference ’94 (Institute of Electrical and Electronics Engineers, New York, 1994), p. 272.
    [CrossRef] [PubMed]
  11. L. M. Hocking, K. Stewartson, Proc. R. Soc. London Ser. A 326, 289 (1972); N. R. Pereira, L. Stenflo, Phys. Fluids 20, 1733 (1977); P. A. Belanger, L. Gagnon, C. Pare, Opt. Lett. 14, 943 (1989).
    [CrossRef] [PubMed]
  12. W. Schoepf, L. Kramer, Phys. Rev. Lett. 66, 2316 (1991); J. A. Powell, P. K. Jakobsen, Physica D 64, 132 (1993).
    [CrossRef]
  13. E. Kaplan, E. A. Kuznetsov, V. Steinberg, Phys. Rev. E 28, 237 (1994).

1994 (3)

1993 (1)

S. K. Turitsyn, Phys. Rev. A 47, R27 (1993).
[CrossRef] [PubMed]

1991 (2)

1989 (1)

1985 (1)

1983 (1)

1981 (1)

H. Nakatsuka, D. Grishkovsky, A. C. Balant, Phys. Rev. Lett. 47, 910 (1981).
[CrossRef]

1975 (1)

H. A. Haus, J. Appl. Phys. 46, 3049 (1975).
[CrossRef]

1972 (2)

K. Stewartson, L. Hocking, J. Stuart, J. Fluid Mech. 51, 705 (1972).
[CrossRef]

L. M. Hocking, K. Stewartson, Proc. R. Soc. London Ser. A 326, 289 (1972); N. R. Pereira, L. Stenflo, Phys. Fluids 20, 1733 (1977); P. A. Belanger, L. Gagnon, C. Pare, Opt. Lett. 14, 943 (1989).
[CrossRef] [PubMed]

Aceves, A. B.

Balant, A. C.

H. Nakatsuka, D. Grishkovsky, A. C. Balant, Phys. Rev. Lett. 47, 910 (1981).
[CrossRef]

Chen, C. J.

De Angelis, C.

Fork, R. L.

Fujimoto, J. P.

Gordon, J. P.

Grishkovsky, D.

H. Nakatsuka, D. Grishkovsky, A. C. Balant, Phys. Rev. Lett. 47, 910 (1981).
[CrossRef]

Haus, H. A.

Hocking, L.

K. Stewartson, L. Hocking, J. Stuart, J. Fluid Mech. 51, 705 (1972).
[CrossRef]

Hocking, L. M.

L. M. Hocking, K. Stewartson, Proc. R. Soc. London Ser. A 326, 289 (1972); N. R. Pereira, L. Stenflo, Phys. Fluids 20, 1733 (1977); P. A. Belanger, L. Gagnon, C. Pare, Opt. Lett. 14, 943 (1989).
[CrossRef] [PubMed]

Ippen, E. P.

Kaplan, E.

E. Kaplan, E. A. Kuznetsov, V. Steinberg, Phys. Rev. E 28, 237 (1994).

Kramer, L.

W. Schoepf, L. Kramer, Phys. Rev. Lett. 66, 2316 (1991); J. A. Powell, P. K. Jakobsen, Physica D 64, 132 (1993).
[CrossRef]

Kuznetsov, E. A.

E. Kaplan, E. A. Kuznetsov, V. Steinberg, Phys. Rev. E 28, 237 (1994).

Liu, L. Y.

Martinez, O. E.

Menyuk, C. R.

Mollenauer, L. F.

Nakatsuka, H.

H. Nakatsuka, D. Grishkovsky, A. C. Balant, Phys. Rev. Lett. 47, 910 (1981).
[CrossRef]

Rubenchik, A. M.

Schoepf, W.

W. Schoepf, L. Kramer, Phys. Rev. Lett. 66, 2316 (1991); J. A. Powell, P. K. Jakobsen, Physica D 64, 132 (1993).
[CrossRef]

Steinberg, V.

E. Kaplan, E. A. Kuznetsov, V. Steinberg, Phys. Rev. E 28, 237 (1994).

Stewartson, K.

L. M. Hocking, K. Stewartson, Proc. R. Soc. London Ser. A 326, 289 (1972); N. R. Pereira, L. Stenflo, Phys. Fluids 20, 1733 (1977); P. A. Belanger, L. Gagnon, C. Pare, Opt. Lett. 14, 943 (1989).
[CrossRef] [PubMed]

K. Stewartson, L. Hocking, J. Stuart, J. Fluid Mech. 51, 705 (1972).
[CrossRef]

Stolen, R. H.

Stuart, J.

K. Stewartson, L. Hocking, J. Stuart, J. Fluid Mech. 51, 705 (1972).
[CrossRef]

Tomlinson, W. J.

Turitsyn, S. K.

Wai, P. K. A.

J. Appl. Phys. (1)

H. A. Haus, J. Appl. Phys. 46, 3049 (1975).
[CrossRef]

J. Fluid Mech. (1)

K. Stewartson, L. Hocking, J. Stuart, J. Fluid Mech. 51, 705 (1972).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Lett. (3)

Phys. Rev. A (1)

S. K. Turitsyn, Phys. Rev. A 47, R27 (1993).
[CrossRef] [PubMed]

Phys. Rev. E (1)

E. Kaplan, E. A. Kuznetsov, V. Steinberg, Phys. Rev. E 28, 237 (1994).

Phys. Rev. Lett. (2)

W. Schoepf, L. Kramer, Phys. Rev. Lett. 66, 2316 (1991); J. A. Powell, P. K. Jakobsen, Physica D 64, 132 (1993).
[CrossRef]

H. Nakatsuka, D. Grishkovsky, A. C. Balant, Phys. Rev. Lett. 47, 910 (1981).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

L. M. Hocking, K. Stewartson, Proc. R. Soc. London Ser. A 326, 289 (1972); N. R. Pereira, L. Stenflo, Phys. Fluids 20, 1733 (1977); P. A. Belanger, L. Gagnon, C. Pare, Opt. Lett. 14, 943 (1989).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Evolution of the shell with inhomogeneous perturbation. The initial distribution is A(0, t) = 0.5 + cos 2πt/T, T = 2π/2.1. The upper curve illustrates a blowup of the shell ( = 0), and the lower curve demonstrates collapse arrest for = 0.001.

Fig. 2
Fig. 2

Different regimes of a pulse generation on the plane (C1, C2). Crosses under the solid curve correspond to the collapse regime and squares to the formation of a train of quasi-stable solitons. The solid line bounds the region where solitons [Eq. (3)] are present.

Fig. 3
Fig. 3

Pulse compression by the collapse mechanism. The dashed curve shows initial Gaussian pulse; the solid curve shows the output signal after collapse of the initial pulse.

Equations (3)

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a z = - i θ a - i D 2 a t 2 - i δ a 2 a + ( g - l ) a + 1 L f Ω f 2 2 a t 2 + γ a 2 a .
A Z = - σ A + ( 1 + i C 1 ) 2 A T 2 + ( 1 + i C 2 ) A 2 A ,
A ( Z , T ) = A 0 sech ( T / T 0 ) × exp [ i β Z + i γ ln cosh ( T / T 0 ) ] ,

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