Abstract

A number of examples have recently been found in which stable, highly compressed pulses are produced in fibers on much shorter length scales than those present initially. These systems involve energy flow among different nonlinear waves. We present numerical model calculations that exhibit this compression when energy is pumped into the nonlinear wave. These models are simple enough to provide some understanding of the underlying generic behavior. We also present a theory of these results that relates the length scale of the pulse to the evolution of the energy.

© 1987 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. J. Blow, N. J. Doran, D. Wood, Opt. Lett. 12, 202 (1987).
    [Crossref] [PubMed]
  2. A. S. Govveia-Neto, A. S. L. Gomes, J. R. Taylor, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1987), paper MH1.
  3. V. A. Vysloukh, V. N. Serkin, JETP Lett. 38, 199 (1984).
  4. L. F. Mollenauer, R. H. Stolen, Opt. Lett. 9, 13 (1984).
    [Crossref] [PubMed]
  5. K. J. Blow, D. Wood, IEEE J. Quantum Electron. 22, 1109 (1986).
    [Crossref]
  6. R. G. Smith, Appl. Opt. 11, 2489 (1972).
    [Crossref] [PubMed]
  7. E. M. Dianov, Z. S. Nikonova, A. M. Prokhorov, V. N. Serkin, Sov. Phys. Dokl. 30, 689 (1986).
  8. J. P. Gordon, Opt. Lett. 11, 662 (1986).
    [Crossref] [PubMed]
  9. J. Satsuma, N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
    [Crossref]
  10. V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).
  11. D. R. Nicholson, M. V. Goldman, Phys. Fluids 19, 1621 (1976).
    [Crossref]
  12. N. J. Doran, K. J. Blow, IEEE J. Quantum Electron. 19, 1883 (1983).
    [Crossref]

1987 (1)

1986 (3)

K. J. Blow, D. Wood, IEEE J. Quantum Electron. 22, 1109 (1986).
[Crossref]

E. M. Dianov, Z. S. Nikonova, A. M. Prokhorov, V. N. Serkin, Sov. Phys. Dokl. 30, 689 (1986).

J. P. Gordon, Opt. Lett. 11, 662 (1986).
[Crossref] [PubMed]

1984 (2)

V. A. Vysloukh, V. N. Serkin, JETP Lett. 38, 199 (1984).

L. F. Mollenauer, R. H. Stolen, Opt. Lett. 9, 13 (1984).
[Crossref] [PubMed]

1983 (1)

N. J. Doran, K. J. Blow, IEEE J. Quantum Electron. 19, 1883 (1983).
[Crossref]

1976 (1)

D. R. Nicholson, M. V. Goldman, Phys. Fluids 19, 1621 (1976).
[Crossref]

1974 (1)

J. Satsuma, N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
[Crossref]

1972 (2)

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

R. G. Smith, Appl. Opt. 11, 2489 (1972).
[Crossref] [PubMed]

Blow, K. J.

K. J. Blow, N. J. Doran, D. Wood, Opt. Lett. 12, 202 (1987).
[Crossref] [PubMed]

K. J. Blow, D. Wood, IEEE J. Quantum Electron. 22, 1109 (1986).
[Crossref]

N. J. Doran, K. J. Blow, IEEE J. Quantum Electron. 19, 1883 (1983).
[Crossref]

Dianov, E. M.

E. M. Dianov, Z. S. Nikonova, A. M. Prokhorov, V. N. Serkin, Sov. Phys. Dokl. 30, 689 (1986).

Doran, N. J.

K. J. Blow, N. J. Doran, D. Wood, Opt. Lett. 12, 202 (1987).
[Crossref] [PubMed]

N. J. Doran, K. J. Blow, IEEE J. Quantum Electron. 19, 1883 (1983).
[Crossref]

Goldman, M. V.

D. R. Nicholson, M. V. Goldman, Phys. Fluids 19, 1621 (1976).
[Crossref]

Gomes, A. S. L.

A. S. Govveia-Neto, A. S. L. Gomes, J. R. Taylor, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1987), paper MH1.

Gordon, J. P.

Govveia-Neto, A. S.

A. S. Govveia-Neto, A. S. L. Gomes, J. R. Taylor, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1987), paper MH1.

Mollenauer, L. F.

Nicholson, D. R.

D. R. Nicholson, M. V. Goldman, Phys. Fluids 19, 1621 (1976).
[Crossref]

Nikonova, Z. S.

E. M. Dianov, Z. S. Nikonova, A. M. Prokhorov, V. N. Serkin, Sov. Phys. Dokl. 30, 689 (1986).

Prokhorov, A. M.

E. M. Dianov, Z. S. Nikonova, A. M. Prokhorov, V. N. Serkin, Sov. Phys. Dokl. 30, 689 (1986).

Satsuma, J.

J. Satsuma, N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
[Crossref]

Serkin, V. N.

E. M. Dianov, Z. S. Nikonova, A. M. Prokhorov, V. N. Serkin, Sov. Phys. Dokl. 30, 689 (1986).

V. A. Vysloukh, V. N. Serkin, JETP Lett. 38, 199 (1984).

Shabat, A. B.

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Smith, R. G.

Stolen, R. H.

Taylor, J. R.

A. S. Govveia-Neto, A. S. L. Gomes, J. R. Taylor, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1987), paper MH1.

Vysloukh, V. A.

V. A. Vysloukh, V. N. Serkin, JETP Lett. 38, 199 (1984).

Wood, D.

K. J. Blow, N. J. Doran, D. Wood, Opt. Lett. 12, 202 (1987).
[Crossref] [PubMed]

K. J. Blow, D. Wood, IEEE J. Quantum Electron. 22, 1109 (1986).
[Crossref]

Yajima, N.

J. Satsuma, N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
[Crossref]

Zakharov, V. E.

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Appl. Opt. (1)

IEEE J. Quantum Electron. (2)

K. J. Blow, D. Wood, IEEE J. Quantum Electron. 22, 1109 (1986).
[Crossref]

N. J. Doran, K. J. Blow, IEEE J. Quantum Electron. 19, 1883 (1983).
[Crossref]

JETP Lett. (1)

V. A. Vysloukh, V. N. Serkin, JETP Lett. 38, 199 (1984).

Opt. Lett. (3)

Phys. Fluids (1)

D. R. Nicholson, M. V. Goldman, Phys. Fluids 19, 1621 (1976).
[Crossref]

Prog. Theor. Phys. Suppl. (1)

J. Satsuma, N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
[Crossref]

Sov. Phys. Dokl. (1)

E. M. Dianov, Z. S. Nikonova, A. M. Prokhorov, V. N. Serkin, Sov. Phys. Dokl. 30, 689 (1986).

Sov. Phys. JETP (1)

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Other (1)

A. S. Govveia-Neto, A. S. L. Gomes, J. R. Taylor, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1987), paper MH1.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Perspective plot of the compression of an initial single-soliton sech(t) pulse in the NLS with gain for Γ = 0.2.

Fig. 2
Fig. 2

Fraction of energy, F, in the eigenvalues of the Zakharov–Shabat scattering problem, for calculations from an initial single soliton with Γ = 0.2 (largest eigenvalue) and Γ = 1.0 (largest two eigenvalues).

Fig. 3
Fig. 3

Perspective plot of the compression of an initial four-soliton, 4 sech(t) pulse with Γ = 0.2 and α = 0.001 in the perturbed NLS with gain and third-order dispersion.

Fig. 4
Fig. 4

Comparisons between the numerical solutions of the full wave equation [Eq. (3)] (unbroken curve) and the analytic solutions of the adiabatic evolution equation [Eq. (6)] (dashed curve). log10W(z)/W(0), where W(z) is the FWHM pulse width, plotted against Γz from an initial sech(t) pulse with Γ = 0.2, μ = 0.0 and Γ = 0.2, μ = 0.01.

Equations (6)

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

i u z = ½ u tt + i α u ttt + u 2 u * .
u ( t , z ; β ) = β exp ( i 2 β 2 z ) sech ( β t ) ,
i u z = ½ u tt + i α u ttt + u 2 u * + i Γ u + i μ u tt .
d E s d z = 2 Γ 0 E s 2 μ | t u s ( z , t ; β ) | 2 d t .
d f ( β ) d z = 2 Γ 0 f ( β ) 2 μ g ( β ) ,
d β d z = 2 Γ 0 β 2 μ 3 β 3 .

Metrics