Abstract

We experimentally demonstrate the generation of a periodic array of dark spatial solitons from two plane waves propagating at some angle in the regime of adiabatic amplification in a Kerr-like medium. The importance of amplification for the generation of clean dark solitons is shown. The combined action of nonlinearity, diffraction, and amplification leads to the reshaping of the input signal into an array of dark solitons with flat phase fronts in the bright background region.

© 1994 Optical Society of America

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  1. V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62–69 (1972); “Interactions between solitons in a stable medium,” Sov. Phys. JETP 37, 823–828 (1973).
  2. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
    [CrossRef]
  3. A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
    [CrossRef] [PubMed]
  4. D. R. Anderson, D. E. Hooton, G. A. Swartzlander, and A. E. Kaplan, “Direct measurement of the transverse velocity of dark spatial solitons,” Opt. Lett. 15, 783–785 (1990).
    [CrossRef]
  5. G. A. Swartzlander, D. R. Anderson, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583–1586 (1991).
    [CrossRef] [PubMed]
  6. G. A. Swartzlander and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2506 (1992).
    [CrossRef] [PubMed]
  7. S. R. Skinner, G. R. Allan, D. R. Anderson, and A. L. Smirl, “Dark spatial soliton propagation in bulk ZnSe,” IEEE J. Quantum Electron. 27, 2211–2219 (1991).
    [CrossRef]
  8. J. S. Aitchison, Y. Silberberg, A. M. Weiner, D. E. Leaird, M. K. Oliver, J. L. Jaeckel, E. M. Vogel, and P. W. E. Smith, “Spatial optical solitons in planar glass waveguides,” J. Opt. Soc. Am. B 8, 1290–1297 (1991).
    [CrossRef]
  9. A. Barthelemy, S. Maneuf, and C. Froehly, “Propagation soliton et autoconfinement de faisceaus laser par nonlinearite de Kerr,” Opt. Commun. 55, 201–206 (1985); M. Shalaby and A. J. Barthelemy, “Observation of the self-guided propagation of a dark and bright soliton pair in a focusing nonlinear medium,” IEEE J. Quantum Electron. 28, 2736–2741 (1992).
    [CrossRef]
  10. P. V. Mamyshev, S. V. Chernikov, and E. M. Dianov, “Generation of fundamental soliton trains for high-bit-rate optical fiber communication lines,” IEEE J. Quantum Electron. 27, 2347–2355 (1991).
    [CrossRef]
  11. E. M. Dianov, P. V. Mamyshev, A. M. Prokhorov, and S. V. Chernikov, “Generation of a train of fundamental solitons at a high repetition rate in optical fibers,” Opt. Lett. 14, 1008–1010 (1989).
    [CrossRef] [PubMed]
  12. P. V. Mamyshev, “Generation and compression of femtosecond solitons in optical fibers,” in Optical Solitons—Theory and Experiment, J. R. Taylor, ed. (Cambridge U. Press, Cambridge, 1992), Chap. 8, pp. 266–313.
    [CrossRef]
  13. S. V. Chernikov, P. V. Mamyshev, E. M. Dianov, D. J. Richardson, R. I. Laming, and D. N. Payne, “Cw soliton train generation in the repetition rate range 70–90 GHz using a dispersion decreasing fiber,” Sov. Lightwave Commun. 2, 161–169 (1992).
  14. J. R. Thompson and R. Roy, “Nonlinear dynamics of multiple four-wave mixing process in a single-mode fiber,” Phys. Rev. A 43, 4987–4996 (1991).
    [CrossRef] [PubMed]
  15. C. S. West and T. A. Kennedy, “Optical multi-wave mixing: dark soliton wave trains and quasi-periodic dynamics,” Phys. Rev. A 47, 1252–1262 (1993).
    [CrossRef] [PubMed]
  16. P. V. Mamyshev, P. Wigley, J. Wilson, and G. I. Stegeman, “Restoration of dual-frequency signals with nonlinear propagation in fibers with positive group velocity dispersion,” Appl. Phys. Lett. (to be published).
  17. N. Akhmediev and A. Ankiewicz, “First order exact solitons of the nonlinear Schrödinger equation in the normal dispersion regime,” Phys. Rev. A 47, 3213–3221 (1993).
    [CrossRef] [PubMed]
  18. P. V. Mamyshev and S. V. Chernikov, “Ultrashort pulse propagation in optical fibers,” Opt. Lett. 15, 1076–1078 (1990).
    [CrossRef] [PubMed]
  19. G. S. McDonald, K. S. Syed, and W. J. Firth, “Dark spatial soliton break-up in the transverse plane,” Opt. Commun. 95, 281–288 (1993).
    [CrossRef]

1993 (3)

C. S. West and T. A. Kennedy, “Optical multi-wave mixing: dark soliton wave trains and quasi-periodic dynamics,” Phys. Rev. A 47, 1252–1262 (1993).
[CrossRef] [PubMed]

N. Akhmediev and A. Ankiewicz, “First order exact solitons of the nonlinear Schrödinger equation in the normal dispersion regime,” Phys. Rev. A 47, 3213–3221 (1993).
[CrossRef] [PubMed]

G. S. McDonald, K. S. Syed, and W. J. Firth, “Dark spatial soliton break-up in the transverse plane,” Opt. Commun. 95, 281–288 (1993).
[CrossRef]

1992 (2)

S. V. Chernikov, P. V. Mamyshev, E. M. Dianov, D. J. Richardson, R. I. Laming, and D. N. Payne, “Cw soliton train generation in the repetition rate range 70–90 GHz using a dispersion decreasing fiber,” Sov. Lightwave Commun. 2, 161–169 (1992).

G. A. Swartzlander and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2506 (1992).
[CrossRef] [PubMed]

1991 (5)

S. R. Skinner, G. R. Allan, D. R. Anderson, and A. L. Smirl, “Dark spatial soliton propagation in bulk ZnSe,” IEEE J. Quantum Electron. 27, 2211–2219 (1991).
[CrossRef]

J. S. Aitchison, Y. Silberberg, A. M. Weiner, D. E. Leaird, M. K. Oliver, J. L. Jaeckel, E. M. Vogel, and P. W. E. Smith, “Spatial optical solitons in planar glass waveguides,” J. Opt. Soc. Am. B 8, 1290–1297 (1991).
[CrossRef]

J. R. Thompson and R. Roy, “Nonlinear dynamics of multiple four-wave mixing process in a single-mode fiber,” Phys. Rev. A 43, 4987–4996 (1991).
[CrossRef] [PubMed]

P. V. Mamyshev, S. V. Chernikov, and E. M. Dianov, “Generation of fundamental soliton trains for high-bit-rate optical fiber communication lines,” IEEE J. Quantum Electron. 27, 2347–2355 (1991).
[CrossRef]

G. A. Swartzlander, D. R. Anderson, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583–1586 (1991).
[CrossRef] [PubMed]

1990 (2)

1989 (1)

1988 (1)

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

1985 (1)

A. Barthelemy, S. Maneuf, and C. Froehly, “Propagation soliton et autoconfinement de faisceaus laser par nonlinearite de Kerr,” Opt. Commun. 55, 201–206 (1985); M. Shalaby and A. J. Barthelemy, “Observation of the self-guided propagation of a dark and bright soliton pair in a focusing nonlinear medium,” IEEE J. Quantum Electron. 28, 2736–2741 (1992).
[CrossRef]

1980 (1)

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

1972 (1)

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62–69 (1972); “Interactions between solitons in a stable medium,” Sov. Phys. JETP 37, 823–828 (1973).

Aitchison, J. S.

Akhmediev, N.

N. Akhmediev and A. Ankiewicz, “First order exact solitons of the nonlinear Schrödinger equation in the normal dispersion regime,” Phys. Rev. A 47, 3213–3221 (1993).
[CrossRef] [PubMed]

Allan, G. R.

S. R. Skinner, G. R. Allan, D. R. Anderson, and A. L. Smirl, “Dark spatial soliton propagation in bulk ZnSe,” IEEE J. Quantum Electron. 27, 2211–2219 (1991).
[CrossRef]

Anderson, D. R.

S. R. Skinner, G. R. Allan, D. R. Anderson, and A. L. Smirl, “Dark spatial soliton propagation in bulk ZnSe,” IEEE J. Quantum Electron. 27, 2211–2219 (1991).
[CrossRef]

G. A. Swartzlander, D. R. Anderson, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583–1586 (1991).
[CrossRef] [PubMed]

D. R. Anderson, D. E. Hooton, G. A. Swartzlander, and A. E. Kaplan, “Direct measurement of the transverse velocity of dark spatial solitons,” Opt. Lett. 15, 783–785 (1990).
[CrossRef]

Ankiewicz, A.

N. Akhmediev and A. Ankiewicz, “First order exact solitons of the nonlinear Schrödinger equation in the normal dispersion regime,” Phys. Rev. A 47, 3213–3221 (1993).
[CrossRef] [PubMed]

Barthelemy, A.

A. Barthelemy, S. Maneuf, and C. Froehly, “Propagation soliton et autoconfinement de faisceaus laser par nonlinearite de Kerr,” Opt. Commun. 55, 201–206 (1985); M. Shalaby and A. J. Barthelemy, “Observation of the self-guided propagation of a dark and bright soliton pair in a focusing nonlinear medium,” IEEE J. Quantum Electron. 28, 2736–2741 (1992).
[CrossRef]

Chernikov, S. V.

S. V. Chernikov, P. V. Mamyshev, E. M. Dianov, D. J. Richardson, R. I. Laming, and D. N. Payne, “Cw soliton train generation in the repetition rate range 70–90 GHz using a dispersion decreasing fiber,” Sov. Lightwave Commun. 2, 161–169 (1992).

P. V. Mamyshev, S. V. Chernikov, and E. M. Dianov, “Generation of fundamental soliton trains for high-bit-rate optical fiber communication lines,” IEEE J. Quantum Electron. 27, 2347–2355 (1991).
[CrossRef]

P. V. Mamyshev and S. V. Chernikov, “Ultrashort pulse propagation in optical fibers,” Opt. Lett. 15, 1076–1078 (1990).
[CrossRef] [PubMed]

E. M. Dianov, P. V. Mamyshev, A. M. Prokhorov, and S. V. Chernikov, “Generation of a train of fundamental solitons at a high repetition rate in optical fibers,” Opt. Lett. 14, 1008–1010 (1989).
[CrossRef] [PubMed]

Dianov, E. M.

S. V. Chernikov, P. V. Mamyshev, E. M. Dianov, D. J. Richardson, R. I. Laming, and D. N. Payne, “Cw soliton train generation in the repetition rate range 70–90 GHz using a dispersion decreasing fiber,” Sov. Lightwave Commun. 2, 161–169 (1992).

P. V. Mamyshev, S. V. Chernikov, and E. M. Dianov, “Generation of fundamental soliton trains for high-bit-rate optical fiber communication lines,” IEEE J. Quantum Electron. 27, 2347–2355 (1991).
[CrossRef]

E. M. Dianov, P. V. Mamyshev, A. M. Prokhorov, and S. V. Chernikov, “Generation of a train of fundamental solitons at a high repetition rate in optical fibers,” Opt. Lett. 14, 1008–1010 (1989).
[CrossRef] [PubMed]

Firth, W. J.

G. S. McDonald, K. S. Syed, and W. J. Firth, “Dark spatial soliton break-up in the transverse plane,” Opt. Commun. 95, 281–288 (1993).
[CrossRef]

Froehly, C.

A. Barthelemy, S. Maneuf, and C. Froehly, “Propagation soliton et autoconfinement de faisceaus laser par nonlinearite de Kerr,” Opt. Commun. 55, 201–206 (1985); M. Shalaby and A. J. Barthelemy, “Observation of the self-guided propagation of a dark and bright soliton pair in a focusing nonlinear medium,” IEEE J. Quantum Electron. 28, 2736–2741 (1992).
[CrossRef]

Gordon, J. P.

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

Hawkins, R. J.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

Heritage, J. P.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

Hooton, D. E.

Jaeckel, J. L.

Kaplan, A. E.

G. A. Swartzlander, D. R. Anderson, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583–1586 (1991).
[CrossRef] [PubMed]

D. R. Anderson, D. E. Hooton, G. A. Swartzlander, and A. E. Kaplan, “Direct measurement of the transverse velocity of dark spatial solitons,” Opt. Lett. 15, 783–785 (1990).
[CrossRef]

Kennedy, T. A.

C. S. West and T. A. Kennedy, “Optical multi-wave mixing: dark soliton wave trains and quasi-periodic dynamics,” Phys. Rev. A 47, 1252–1262 (1993).
[CrossRef] [PubMed]

Kirschner, E. M.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

Laming, R. I.

S. V. Chernikov, P. V. Mamyshev, E. M. Dianov, D. J. Richardson, R. I. Laming, and D. N. Payne, “Cw soliton train generation in the repetition rate range 70–90 GHz using a dispersion decreasing fiber,” Sov. Lightwave Commun. 2, 161–169 (1992).

Law, C. T.

G. A. Swartzlander and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2506 (1992).
[CrossRef] [PubMed]

Leaird, D. E.

J. S. Aitchison, Y. Silberberg, A. M. Weiner, D. E. Leaird, M. K. Oliver, J. L. Jaeckel, E. M. Vogel, and P. W. E. Smith, “Spatial optical solitons in planar glass waveguides,” J. Opt. Soc. Am. B 8, 1290–1297 (1991).
[CrossRef]

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

Mamyshev, P. V.

S. V. Chernikov, P. V. Mamyshev, E. M. Dianov, D. J. Richardson, R. I. Laming, and D. N. Payne, “Cw soliton train generation in the repetition rate range 70–90 GHz using a dispersion decreasing fiber,” Sov. Lightwave Commun. 2, 161–169 (1992).

P. V. Mamyshev, S. V. Chernikov, and E. M. Dianov, “Generation of fundamental soliton trains for high-bit-rate optical fiber communication lines,” IEEE J. Quantum Electron. 27, 2347–2355 (1991).
[CrossRef]

P. V. Mamyshev and S. V. Chernikov, “Ultrashort pulse propagation in optical fibers,” Opt. Lett. 15, 1076–1078 (1990).
[CrossRef] [PubMed]

E. M. Dianov, P. V. Mamyshev, A. M. Prokhorov, and S. V. Chernikov, “Generation of a train of fundamental solitons at a high repetition rate in optical fibers,” Opt. Lett. 14, 1008–1010 (1989).
[CrossRef] [PubMed]

P. V. Mamyshev, “Generation and compression of femtosecond solitons in optical fibers,” in Optical Solitons—Theory and Experiment, J. R. Taylor, ed. (Cambridge U. Press, Cambridge, 1992), Chap. 8, pp. 266–313.
[CrossRef]

P. V. Mamyshev, P. Wigley, J. Wilson, and G. I. Stegeman, “Restoration of dual-frequency signals with nonlinear propagation in fibers with positive group velocity dispersion,” Appl. Phys. Lett. (to be published).

Maneuf, S.

A. Barthelemy, S. Maneuf, and C. Froehly, “Propagation soliton et autoconfinement de faisceaus laser par nonlinearite de Kerr,” Opt. Commun. 55, 201–206 (1985); M. Shalaby and A. J. Barthelemy, “Observation of the self-guided propagation of a dark and bright soliton pair in a focusing nonlinear medium,” IEEE J. Quantum Electron. 28, 2736–2741 (1992).
[CrossRef]

McDonald, G. S.

G. S. McDonald, K. S. Syed, and W. J. Firth, “Dark spatial soliton break-up in the transverse plane,” Opt. Commun. 95, 281–288 (1993).
[CrossRef]

Mollenauer, L. F.

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

Oliver, M. K.

Payne, D. N.

S. V. Chernikov, P. V. Mamyshev, E. M. Dianov, D. J. Richardson, R. I. Laming, and D. N. Payne, “Cw soliton train generation in the repetition rate range 70–90 GHz using a dispersion decreasing fiber,” Sov. Lightwave Commun. 2, 161–169 (1992).

Prokhorov, A. M.

Regan, J. J.

G. A. Swartzlander, D. R. Anderson, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583–1586 (1991).
[CrossRef] [PubMed]

Richardson, D. J.

S. V. Chernikov, P. V. Mamyshev, E. M. Dianov, D. J. Richardson, R. I. Laming, and D. N. Payne, “Cw soliton train generation in the repetition rate range 70–90 GHz using a dispersion decreasing fiber,” Sov. Lightwave Commun. 2, 161–169 (1992).

Roy, R.

J. R. Thompson and R. Roy, “Nonlinear dynamics of multiple four-wave mixing process in a single-mode fiber,” Phys. Rev. A 43, 4987–4996 (1991).
[CrossRef] [PubMed]

Shabat, A. B.

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62–69 (1972); “Interactions between solitons in a stable medium,” Sov. Phys. JETP 37, 823–828 (1973).

Silberberg, Y.

Skinner, S. R.

S. R. Skinner, G. R. Allan, D. R. Anderson, and A. L. Smirl, “Dark spatial soliton propagation in bulk ZnSe,” IEEE J. Quantum Electron. 27, 2211–2219 (1991).
[CrossRef]

Smirl, A. L.

S. R. Skinner, G. R. Allan, D. R. Anderson, and A. L. Smirl, “Dark spatial soliton propagation in bulk ZnSe,” IEEE J. Quantum Electron. 27, 2211–2219 (1991).
[CrossRef]

Smith, P. W. E.

Stegeman, G. I.

P. V. Mamyshev, P. Wigley, J. Wilson, and G. I. Stegeman, “Restoration of dual-frequency signals with nonlinear propagation in fibers with positive group velocity dispersion,” Appl. Phys. Lett. (to be published).

Stolen, R. H.

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

Swartzlander, G. A.

G. A. Swartzlander and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2506 (1992).
[CrossRef] [PubMed]

G. A. Swartzlander, D. R. Anderson, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583–1586 (1991).
[CrossRef] [PubMed]

D. R. Anderson, D. E. Hooton, G. A. Swartzlander, and A. E. Kaplan, “Direct measurement of the transverse velocity of dark spatial solitons,” Opt. Lett. 15, 783–785 (1990).
[CrossRef]

Syed, K. S.

G. S. McDonald, K. S. Syed, and W. J. Firth, “Dark spatial soliton break-up in the transverse plane,” Opt. Commun. 95, 281–288 (1993).
[CrossRef]

Thompson, J. R.

J. R. Thompson and R. Roy, “Nonlinear dynamics of multiple four-wave mixing process in a single-mode fiber,” Phys. Rev. A 43, 4987–4996 (1991).
[CrossRef] [PubMed]

Thurston, R. N.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

Tomlinson, W. J.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

Vogel, E. M.

Weiner, A. M.

J. S. Aitchison, Y. Silberberg, A. M. Weiner, D. E. Leaird, M. K. Oliver, J. L. Jaeckel, E. M. Vogel, and P. W. E. Smith, “Spatial optical solitons in planar glass waveguides,” J. Opt. Soc. Am. B 8, 1290–1297 (1991).
[CrossRef]

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

West, C. S.

C. S. West and T. A. Kennedy, “Optical multi-wave mixing: dark soliton wave trains and quasi-periodic dynamics,” Phys. Rev. A 47, 1252–1262 (1993).
[CrossRef] [PubMed]

Wigley, P.

P. V. Mamyshev, P. Wigley, J. Wilson, and G. I. Stegeman, “Restoration of dual-frequency signals with nonlinear propagation in fibers with positive group velocity dispersion,” Appl. Phys. Lett. (to be published).

Wilson, J.

P. V. Mamyshev, P. Wigley, J. Wilson, and G. I. Stegeman, “Restoration of dual-frequency signals with nonlinear propagation in fibers with positive group velocity dispersion,” Appl. Phys. Lett. (to be published).

Yin, H.

G. A. Swartzlander, D. R. Anderson, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583–1586 (1991).
[CrossRef] [PubMed]

Zakharov, V. E.

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62–69 (1972); “Interactions between solitons in a stable medium,” Sov. Phys. JETP 37, 823–828 (1973).

IEEE J. Quantum Electron. (2)

S. R. Skinner, G. R. Allan, D. R. Anderson, and A. L. Smirl, “Dark spatial soliton propagation in bulk ZnSe,” IEEE J. Quantum Electron. 27, 2211–2219 (1991).
[CrossRef]

P. V. Mamyshev, S. V. Chernikov, and E. M. Dianov, “Generation of fundamental soliton trains for high-bit-rate optical fiber communication lines,” IEEE J. Quantum Electron. 27, 2347–2355 (1991).
[CrossRef]

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

Opt. Commun. (2)

A. Barthelemy, S. Maneuf, and C. Froehly, “Propagation soliton et autoconfinement de faisceaus laser par nonlinearite de Kerr,” Opt. Commun. 55, 201–206 (1985); M. Shalaby and A. J. Barthelemy, “Observation of the self-guided propagation of a dark and bright soliton pair in a focusing nonlinear medium,” IEEE J. Quantum Electron. 28, 2736–2741 (1992).
[CrossRef]

G. S. McDonald, K. S. Syed, and W. J. Firth, “Dark spatial soliton break-up in the transverse plane,” Opt. Commun. 95, 281–288 (1993).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (3)

N. Akhmediev and A. Ankiewicz, “First order exact solitons of the nonlinear Schrödinger equation in the normal dispersion regime,” Phys. Rev. A 47, 3213–3221 (1993).
[CrossRef] [PubMed]

J. R. Thompson and R. Roy, “Nonlinear dynamics of multiple four-wave mixing process in a single-mode fiber,” Phys. Rev. A 43, 4987–4996 (1991).
[CrossRef] [PubMed]

C. S. West and T. A. Kennedy, “Optical multi-wave mixing: dark soliton wave trains and quasi-periodic dynamics,” Phys. Rev. A 47, 1252–1262 (1993).
[CrossRef] [PubMed]

Phys. Rev. Lett. (4)

G. A. Swartzlander, D. R. Anderson, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583–1586 (1991).
[CrossRef] [PubMed]

G. A. Swartzlander and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2506 (1992).
[CrossRef] [PubMed]

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[CrossRef]

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

Sov. Lightwave Commun. (1)

S. V. Chernikov, P. V. Mamyshev, E. M. Dianov, D. J. Richardson, R. I. Laming, and D. N. Payne, “Cw soliton train generation in the repetition rate range 70–90 GHz using a dispersion decreasing fiber,” Sov. Lightwave Commun. 2, 161–169 (1992).

Sov. Phys. JETP (1)

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62–69 (1972); “Interactions between solitons in a stable medium,” Sov. Phys. JETP 37, 823–828 (1973).

Other (2)

P. V. Mamyshev, P. Wigley, J. Wilson, and G. I. Stegeman, “Restoration of dual-frequency signals with nonlinear propagation in fibers with positive group velocity dispersion,” Appl. Phys. Lett. (to be published).

P. V. Mamyshev, “Generation and compression of femtosecond solitons in optical fibers,” in Optical Solitons—Theory and Experiment, J. R. Taylor, ed. (Cambridge U. Press, Cambridge, 1992), Chap. 8, pp. 266–313.
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Numerical evolution of the signal [Eq. (2)] for the case without amplification. First column, near-field intensity profile; second column, phase profile; third column, far-field (spectrum) intensity profile. The parameters are μ = 0, A0 = 3. First row, (a)–(c), input signal (ξ = 0); second row, (d)–(f), ξ = 0.2; third row (g)–(i), ξ = 1.

Fig. 2
Fig. 2

Same as Fig. 1, but for the case of adiabatic amplification. The parameters are μ = 0.4, A0 = 0.25. First row, (a)–(c), input signal (ξ = 0); second row, (d)–(f), ξ = 8; third row, (g)–(i), ξ = 10; fourth row (j)–(l), the soliton array (ξ = 8) after amplification-free propagation for 25 soliton diffraction lengths.

Fig. 3
Fig. 3

Evolution of the dip width and the dip area for the case of Fig. 2. The analytical solution for the dip width [Eq. (3)] is also shown (see text).

Fig. 4
Fig. 4

Schematic experimental setup for the generation of a periodic array of dark spatial solitons. A cylindrical lens was used to induce the effective amplification.

Fig. 5
Fig. 5

Near-field [(a) and (c)] and far-field [(b) and (d)] patterns of the cell output (experiment). (a), (b), 30-mW input power [linear propagation; the input signal has the same near- and far-field profiles, not shown, as those of (a) and (b)]; (c), (d), 750-mW input power (formation of dark solitons). Figures have arbitrary y scales that are different for different figures.

Fig. 6
Fig. 6

Numerical simulations of the experimental results in Fig. 5. First row, input signal; second row, output signal.

Equations (6)

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i A / ξ - ½ 2 A / η 2 + A A 2 - i A μ / 2 = 0 ,
A ( 0 , η ) = A 0 sin ( π η / 2 ) .
d ( ξ ) = 1.763 [ ( 1 + 2 ) 1 / 2 - 1 ] /
( ξ ) = A 0 2 exp ( μ ξ ) .
P S A ( ω 1 , k 2 ) = χ ( 3 ) ( ω 1 = ω 1 + ω 1 - ω 1 , k 1 = k 1 + k 1 - k 1 ) × E 1 E 1 E 1 * + χ ( 3 ) ( ω 1 = ω 1 - ω 1 + ω 1 , k 1 = k 1 - k 1 + k 1 ) × E 1 E 1 * E 1 + χ ( 3 ) ( ω 1 = - ω 1 + ω 1 + ω 1 , k 1 = - k 1 + k 1 + k 1 ) × E 1 * E 1 E 1 ,
P X A ( ω 2 , B k 2 ) = χ ( 3 ) ( ω 2 = ω 1 + ω 2 - ω 1 , k 2 = k 1 + k 2 - k 1 ) × E 1 E 2 E 1 * + χ ( 3 ) ( ω 2 = ω 2 + ω 1 - ω 1 , k 2 = k 2 + k 1 - k 1 ) × E 2 E 1 E 1 * + χ ( 3 ) ( ω 2 = ω 1 + ω 2 , k 2 = k 1 - k 1 + k 2 ) × E 1 E 1 * E 2 + χ ( 3 ) ( ω 2 = ω 2 - ω 1 + ω 1 , k 2 = k 2 - k 1 + k 1 ) × E 2 E 1 * E 1 + χ ( 3 ) ( ω 2 = - ω 1 + ω 1 + ω 2 , k 2 = - k 1 + k 1 + k 2 ) × E 1 * E 1 E 2 + χ ( 3 ) ( ω 2 = - ω 1 + ω 2 + ω 1 , k 2 = - k 1 + k 2 + k 1 ) × E 1 * E 2 E 1 .

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