Abstract

The effect of weak two-photon absorption on soliton propagation is investigated. It is found that fundamental solitons evolve adiabatically; expressions describing their broadening and attenuation are given. Higher-order solitons break up into two diverging fundamental solitons for a wide range of parameters.

© 1990 Optical Society of America

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References

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  1. V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).
  2. A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142, (1973), Appl. Phys. Lett. 23, 171 (1973).
    [CrossRef]
  3. L. F. Mollenauer, K. Smith, Opt. Lett. 13, 675 (1988).
    [CrossRef] [PubMed]
  4. K. J. Blow, N. J. Doran, B. K. Nayar, Opt. Lett. 14, 754 (1989).
    [CrossRef] [PubMed]
  5. M. N. Islam, Opt. Lett. 14, 1257 (1989).
    [CrossRef] [PubMed]
  6. A. Barthelemy, S. Maneuf, C. Froehly, Opt. Commun. 55, 201 (1985); S. Maneuf, R. Desailly, C. Froehly, Opt. Commun. 65, 193 (1988); S. Maneuf, F. Reynaud, Opt. Commun. 66, 325 (1988).
    [CrossRef]
  7. J. S. Aitchison, A. M. Weiner, Y. Silberberg, M. K. Oliver, J. L. Jackel, D. E. Leaird, E. M. Vogel, P. W. E. Smith, Opt. Lett. 15, 471 (1990).
    [CrossRef] [PubMed]
  8. R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 675 (1964).
    [CrossRef]
  9. V. Mizrahi, K. W. DeLong, G. I. Stegeman, M. A. Saifi, M. J. Andrejco, Opt. Lett. 14, 1140 (1989).
    [CrossRef] [PubMed]
  10. S. J. Aitchison, M. K. Oliver, E. Kapon, E. Colas, P. W. E. Smith, Appl. Phys. Lett. 56, 1305 (1990).
    [CrossRef]
  11. See, for example, M. D. Feit, J. A. Fleck, Appl. Opt. 7, 3990 (1978).
    [CrossRef]
  12. J. Satsuma, N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
    [CrossRef]

1990 (2)

1989 (3)

1988 (1)

1985 (1)

A. Barthelemy, S. Maneuf, C. Froehly, Opt. Commun. 55, 201 (1985); S. Maneuf, R. Desailly, C. Froehly, Opt. Commun. 65, 193 (1988); S. Maneuf, F. Reynaud, Opt. Commun. 66, 325 (1988).
[CrossRef]

1978 (1)

See, for example, M. D. Feit, J. A. Fleck, Appl. Opt. 7, 3990 (1978).
[CrossRef]

1974 (1)

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

1973 (1)

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142, (1973), Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

1972 (1)

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

1964 (1)

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 675 (1964).
[CrossRef]

Aitchison, J. S.

Aitchison, S. J.

S. J. Aitchison, M. K. Oliver, E. Kapon, E. Colas, P. W. E. Smith, Appl. Phys. Lett. 56, 1305 (1990).
[CrossRef]

Andrejco, M. J.

Barthelemy, A.

A. Barthelemy, S. Maneuf, C. Froehly, Opt. Commun. 55, 201 (1985); S. Maneuf, R. Desailly, C. Froehly, Opt. Commun. 65, 193 (1988); S. Maneuf, F. Reynaud, Opt. Commun. 66, 325 (1988).
[CrossRef]

Blow, K. J.

Chiao, R. Y.

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 675 (1964).
[CrossRef]

Colas, E.

S. J. Aitchison, M. K. Oliver, E. Kapon, E. Colas, P. W. E. Smith, Appl. Phys. Lett. 56, 1305 (1990).
[CrossRef]

DeLong, K. W.

Doran, N. J.

Feit, M. D.

See, for example, M. D. Feit, J. A. Fleck, Appl. Opt. 7, 3990 (1978).
[CrossRef]

Fleck, J. A.

See, for example, M. D. Feit, J. A. Fleck, Appl. Opt. 7, 3990 (1978).
[CrossRef]

Froehly, C.

A. Barthelemy, S. Maneuf, C. Froehly, Opt. Commun. 55, 201 (1985); S. Maneuf, R. Desailly, C. Froehly, Opt. Commun. 65, 193 (1988); S. Maneuf, F. Reynaud, Opt. Commun. 66, 325 (1988).
[CrossRef]

Garmire, E.

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 675 (1964).
[CrossRef]

Hasegawa, A.

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142, (1973), Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

Islam, M. N.

Jackel, J. L.

Kapon, E.

S. J. Aitchison, M. K. Oliver, E. Kapon, E. Colas, P. W. E. Smith, Appl. Phys. Lett. 56, 1305 (1990).
[CrossRef]

Leaird, D. E.

Maneuf, S.

A. Barthelemy, S. Maneuf, C. Froehly, Opt. Commun. 55, 201 (1985); S. Maneuf, R. Desailly, C. Froehly, Opt. Commun. 65, 193 (1988); S. Maneuf, F. Reynaud, Opt. Commun. 66, 325 (1988).
[CrossRef]

Mizrahi, V.

Mollenauer, L. F.

Nayar, B. K.

Oliver, M. K.

Saifi, M. A.

Satsuma, J.

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

Shabat, A. B.

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

Silberberg, Y.

Smith, K.

Smith, P. W. E.

Stegeman, G. I.

Tappert, F.

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142, (1973), Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

Townes, C. H.

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 675 (1964).
[CrossRef]

Vogel, E. M.

Weiner, A. M.

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)

See, for example, M. D. Feit, J. A. Fleck, Appl. Opt. 7, 3990 (1978).
[CrossRef]

Appl. Phys. Lett. (2)

S. J. Aitchison, M. K. Oliver, E. Kapon, E. Colas, P. W. E. Smith, Appl. Phys. Lett. 56, 1305 (1990).
[CrossRef]

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142, (1973), Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

Opt. Commun. (1)

A. Barthelemy, S. Maneuf, C. Froehly, Opt. Commun. 55, 201 (1985); S. Maneuf, R. Desailly, C. Froehly, Opt. Commun. 65, 193 (1988); S. Maneuf, F. Reynaud, Opt. Commun. 66, 325 (1988).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. Lett. (1)

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 675 (1964).
[CrossRef]

Prog. Theor. Phys. Suppl. (1)

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

Sov. Phys. JETP (1)

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

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Figures (3)

Fig. 1
Fig. 1

Evolution of the soliton amplitude, energy, and width along a medium with K = 0.01. The dashed curves are from a numerical simulation of Eq. (1), and the solid curves are from Eqs. (4). The distance is given in units of soliton periods z0 = π/2.

Fig. 2
Fig. 2

Evolving intensity profile along z for an initial beam with A(0) = 2.45 and TPA coefficients of (A) 0, (B) 0.01, (C) 0.02, and (D) 0.05. The profiles are shown at equal intervals, and the total length is z = 3.2z0. A small transverse velocity has been added for easy visualization.

Fig. 3
Fig. 3

Intensity profiles at z = 6.4z0 for a launched sech(s) pulse along z with increasing amplitudes for K = 0.01 and K = 0.02. The peak intensity of the launched pulse is marked at the center.

Equations (6)

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i d u d z + 1 2 d 2 u d s 2 + ( 1 + iK ) | u | 2 u = 0 ,
K = β 2 k n 2 .
d d z | u | 2 d s = 2 K | u | 4 d s .
A 2 ( z ) = A 2 ( 0 ) 1 + 8 3 K A 2 ( 0 ) z ,
W 2 ( z ) = W 2 ( 0 ) + 8 3 Kz ,
P 2 ( z ) = P 2 ( 0 ) 1 + 2 3 K P 2 ( 0 ) z .

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