Abstract

We show that an optical pulse can propagate undistorted as a bright solitary wave in the normal dispersion regime when it couples through cross-phase modulation to a dark pulse in the anomalous dispersion regime.

© 1988 Optical Society of America

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References

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  1. A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973); A. Hasegawa, Opt. Lett. 8, 650 (1983).
    [CrossRef] [PubMed]
  2. L. F. Mollenauer, R. H. Stolen, Laser Focus 18, 193 (1982).
  3. N. J. Doran, D. Wood, J. Opt. Soc. Am. B 4, 1843 (1987).
    [CrossRef]
  4. S. Trillo, S. Wabnitz, E. M. Wright, G. I. Stegeman, Opt. Lett. 13, 672 (1988).
    [CrossRef] [PubMed]
  5. K. Tai, A. Hasegawa, A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
    [CrossRef] [PubMed]
  6. G. P. Agrawal, Phys. Rev. Lett. 59, 880 (1987).
    [CrossRef] [PubMed]
  7. D. Schadt, B. Jaskorzynska, Electron. Lett. 23, 1090 (1987).
    [CrossRef]
  8. A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
    [CrossRef]
  9. D. Krokel, N. J. Halas, G. Giuliani, D. Grischkowsky, Phys. Rev. Lett. 60, 29 (1988).
    [CrossRef] [PubMed]
  10. A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurson, E. M. Kirschener, D. E. Leaird, W. J. Tomlinson, in Technical Digest of the Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), p. 513.
  11. P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, A. Barthelemy, Opt. Commun. 62, 374 (1987).
    [CrossRef]
  12. In terms of the soliton units used for the computations, the distance z0 = π/2 is the period of multisoliton solutions (N > 1) to the nonlinear Schrödinger equation; see, e.g., L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
    [CrossRef]

1988 (2)

S. Trillo, S. Wabnitz, E. M. Wright, G. I. Stegeman, Opt. Lett. 13, 672 (1988).
[CrossRef] [PubMed]

D. Krokel, N. J. Halas, G. Giuliani, D. Grischkowsky, Phys. Rev. Lett. 60, 29 (1988).
[CrossRef] [PubMed]

1987 (4)

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, A. Barthelemy, Opt. Commun. 62, 374 (1987).
[CrossRef]

G. P. Agrawal, Phys. Rev. Lett. 59, 880 (1987).
[CrossRef] [PubMed]

D. Schadt, B. Jaskorzynska, Electron. Lett. 23, 1090 (1987).
[CrossRef]

N. J. Doran, D. Wood, J. Opt. Soc. Am. B 4, 1843 (1987).
[CrossRef]

1986 (1)

K. Tai, A. Hasegawa, A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

1982 (1)

L. F. Mollenauer, R. H. Stolen, Laser Focus 18, 193 (1982).

1980 (1)

In terms of the soliton units used for the computations, the distance z0 = π/2 is the period of multisoliton solutions (N > 1) to the nonlinear Schrödinger equation; see, e.g., L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

1973 (2)

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

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973); A. Hasegawa, Opt. Lett. 8, 650 (1983).
[CrossRef] [PubMed]

Agrawal, G. P.

G. P. Agrawal, Phys. Rev. Lett. 59, 880 (1987).
[CrossRef] [PubMed]

Barthelemy, A.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, A. Barthelemy, Opt. Commun. 62, 374 (1987).
[CrossRef]

Doran, N. J.

Emplit, P.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, A. Barthelemy, Opt. Commun. 62, 374 (1987).
[CrossRef]

Froehly, C.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, A. Barthelemy, Opt. Commun. 62, 374 (1987).
[CrossRef]

Giuliani, G.

D. Krokel, N. J. Halas, G. Giuliani, D. Grischkowsky, Phys. Rev. Lett. 60, 29 (1988).
[CrossRef] [PubMed]

Gordon, J. P.

In terms of the soliton units used for the computations, the distance z0 = π/2 is the period of multisoliton solutions (N > 1) to the nonlinear Schrödinger equation; see, e.g., L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Grischkowsky, D.

D. Krokel, N. J. Halas, G. Giuliani, D. Grischkowsky, Phys. Rev. Lett. 60, 29 (1988).
[CrossRef] [PubMed]

Halas, N. J.

D. Krokel, N. J. Halas, G. Giuliani, D. Grischkowsky, Phys. Rev. Lett. 60, 29 (1988).
[CrossRef] [PubMed]

Hamaide, J. P.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, A. Barthelemy, Opt. Commun. 62, 374 (1987).
[CrossRef]

Hasegawa, A.

K. Tai, A. Hasegawa, A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

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

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973); A. Hasegawa, Opt. Lett. 8, 650 (1983).
[CrossRef] [PubMed]

Hawkins, R. J.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurson, E. M. Kirschener, D. E. Leaird, W. J. Tomlinson, in Technical Digest of the Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), p. 513.

Heritage, J. P.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurson, E. M. Kirschener, D. E. Leaird, W. J. Tomlinson, in Technical Digest of the Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), p. 513.

Jaskorzynska, B.

D. Schadt, B. Jaskorzynska, Electron. Lett. 23, 1090 (1987).
[CrossRef]

Kirschener, E. M.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurson, E. M. Kirschener, D. E. Leaird, W. J. Tomlinson, in Technical Digest of the Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), p. 513.

Krokel, D.

D. Krokel, N. J. Halas, G. Giuliani, D. Grischkowsky, Phys. Rev. Lett. 60, 29 (1988).
[CrossRef] [PubMed]

Leaird, D. E.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurson, E. M. Kirschener, D. E. Leaird, W. J. Tomlinson, in Technical Digest of the Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), p. 513.

Mollenauer, L. F.

L. F. Mollenauer, R. H. Stolen, Laser Focus 18, 193 (1982).

In terms of the soliton units used for the computations, the distance z0 = π/2 is the period of multisoliton solutions (N > 1) to the nonlinear Schrödinger equation; see, e.g., L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Reynaud, F.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, A. Barthelemy, Opt. Commun. 62, 374 (1987).
[CrossRef]

Schadt, D.

D. Schadt, B. Jaskorzynska, Electron. Lett. 23, 1090 (1987).
[CrossRef]

Stegeman, G. I.

Stolen, R. H.

L. F. Mollenauer, R. H. Stolen, Laser Focus 18, 193 (1982).

In terms of the soliton units used for the computations, the distance z0 = π/2 is the period of multisoliton solutions (N > 1) to the nonlinear Schrödinger equation; see, e.g., L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Tai, K.

K. Tai, A. Hasegawa, A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

Tappert, F.

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

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973); A. Hasegawa, Opt. Lett. 8, 650 (1983).
[CrossRef] [PubMed]

Thurson, R. N.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurson, E. M. Kirschener, D. E. Leaird, W. J. Tomlinson, in Technical Digest of the Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), p. 513.

Tomita, A.

K. Tai, A. Hasegawa, A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

Tomlinson, W. J.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurson, E. M. Kirschener, D. E. Leaird, W. J. Tomlinson, in Technical Digest of the Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), p. 513.

Trillo, S.

Wabnitz, S.

Weiner, A. M.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurson, E. M. Kirschener, D. E. Leaird, W. J. Tomlinson, in Technical Digest of the Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), p. 513.

Wood, D.

Wright, E. M.

Appl. Phys. Lett. (2)

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973); A. Hasegawa, Opt. Lett. 8, 650 (1983).
[CrossRef] [PubMed]

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

Electron. Lett. (1)

D. Schadt, B. Jaskorzynska, Electron. Lett. 23, 1090 (1987).
[CrossRef]

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

Laser Focus (1)

L. F. Mollenauer, R. H. Stolen, Laser Focus 18, 193 (1982).

Opt. Commun. (1)

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, A. Barthelemy, Opt. Commun. 62, 374 (1987).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (4)

K. Tai, A. Hasegawa, A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

G. P. Agrawal, Phys. Rev. Lett. 59, 880 (1987).
[CrossRef] [PubMed]

D. Krokel, N. J. Halas, G. Giuliani, D. Grischkowsky, Phys. Rev. Lett. 60, 29 (1988).
[CrossRef] [PubMed]

In terms of the soliton units used for the computations, the distance z0 = π/2 is the period of multisoliton solutions (N > 1) to the nonlinear Schrödinger equation; see, e.g., L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Other (1)

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurson, E. M. Kirschener, D. E. Leaird, W. J. Tomlinson, in Technical Digest of the Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), p. 513.

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Figures (4)

Fig. 1
Fig. 1

Propagation of dark and bright pulses in the anomalous and normal group-velocity dispersion regimes (a) without CPM and (b) with CPM.

Fig. 2
Fig. 2

Comparison of the input pulse (peak intensity = 1) with the propagated pulse (in the normal dispersion regime) after a distance z = 10 from Fig. 1(b).

Fig. 3
Fig. 3

(a) Propagation of an initially Gaussian pulse of unitary amplitude and a variance t0 = 5 in the anomalous dispersion regime, coupled by CPM to a longer pulse (b) in the normal dispersion regime.

Fig. 4
Fig. 4

Comparison of the input Gaussian pulse and the propagated waveform after a distance (a) z = 5.5 and (b) z = 9 from Fig. 3(a).

Equations (4)

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i ( u / z ) + ( β 1 / 2 ) 2 u / t 2 + R 1 ( u 2 + 2 v 2 ) u = 0 , i ( v / z ) - ( β 2 / 2 ) 2 v / t 2 + R 2 ( v 2 + 2 u 2 ) v = 0 ,
u ( z , t ) = U tanh [ C ( t - z / V ) ] exp [ i ( K 1 z - Ω 1 t ) ] , v ( z , t ) = V sech [ C ( t - z / V ) ] exp [ i ( K 2 z - Ω 2 t ) ] ,
U 2 = ( 2 R 1 β 2 + R 2 β 1 ) C 2 / ( 3 R 1 R 2 ) , V 2 = ( 2 R 2 β 1 + R 1 β 2 ) C 2 / ( 3 R 1 R 2 ) , K 1 = R 1 U 2 - β 1 Ω 1 2 / 2 ,             K 2 = β 2 ( Ω 2 2 - C 2 ) / 2 , V - 1 = - β 1 Ω 1 = β 2 Ω 2 .
u ( z = 0 , t ) = Q ( t ) tanh ( t ) , v ( z = 0 , t ) = sech ( t ) ,

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