Abstract

We propose the modulation of dispersion to prevent collapse of planar pulsed beams that propagate in Kerr-type self-focusing optical media. As a result, we find a new type of two-dimensional spatiotemporal soliton stabilized by dispersion management. We have studied the existence and properties of these solitary waves both analytically and numerically. We show that the adequate choice of the modulation parameters optimizes the stabilization of the pulse.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. Sulem and P. Sulem, The Nonlinear Schrödinger Equation: Self-Focusing and Wave Collapse (Springer, 2000).
  2. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).
  3. 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).
  4. A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. 1. Anomalous dispersion," Appl. Phys. Lett. 23, 142-144 (1973).
    [CrossRef]
  5. S. Maneuf, A. Barthelemy, and C. Froehly, "Soliton beam propagation; space-time behaviour and spectral features," J. Opt. 17, 139-145 (1986).
    [CrossRef]
  6. A. A. Kanashov and A. M. Rubenchik, "Wave mutual focusing in media with quadratic nonlinearity," Opt. Commun. 24, 121-124 (1978).
    [CrossRef]
  7. B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, "Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity," Phys. Rev. E 4, 4725-4735 (1997).
    [CrossRef]
  8. X. Liu, K. Beckwitt, and F. Wise, "Two-dimensional optical spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 1328-1340 (2000).
    [CrossRef]
  9. I. G. Koprinkov, A. Suda, P. Q. Wang, and K. Midorikawa, "Self-compression of high-intensity femtosecond optical pulses and spatiotemporal soliton generation," Phys. Rev. Lett. 84, 3847-3850 (2000)
    [CrossRef] [PubMed]
  10. M. Segev and G. I. Stegeman, "Self-trapping of optical beams: spatial solitons," Phys. Today 51, 42-48 (1998).
    [CrossRef]
  11. H. Michinel, R. de la Fuente, and J. Linares, "Temporal modulation of spatial optical solitons," Appl. Opt. 33, 3384-3390 (1994).
    [CrossRef] [PubMed]
  12. L. Berge, V. K. Mezentsev, J. J. Rasmussen, P. L. Christiansen, and Y. B. Gaididei, "Self-guiding light in layered nonlinear media," Opt. Lett. 25, 1037-1039 (2000).
    [CrossRef]
  13. I. Towers and B. A. Malomed, "Stable (2+1)-dimensional solitons in a layered medium with sign-alternating Kerr nonlinearity," J. Opt. Soc. Am. B 19, 537-543 (2002).
    [CrossRef]
  14. G. D. Montesinos, V. M. Pérez-García, and H. Michinel, "Stabilized two-dimensional vector solitons," Phys. Rev. Lett. 92, 133901 (2004).
    [CrossRef] [PubMed]
  15. H. Saito and M. Ueda, "Dynamically stabilized bright solitons in a two-dimensional Bose-Einstein condensate," Phys. Rev. Lett. 90, 040403 (2003).
    [CrossRef] [PubMed]
  16. G. D. Montesinos, V. M. Pérez-García, and P. Torres, "Stabilization of solitons of the multidimensional nonlinear Schrödinger equation: matter-wave breathers," Physica D 191, 193-210 (2004).
    [CrossRef]
  17. L. Bergé, E. A. Kuznetsov, and J. J. Rasmussen, "Defocusing regimes of nonlinear waves in media with negative dispersion," Phys. Rev. E 53, R1340-R1343 (1996).
    [CrossRef]
  18. M. Matuszewski, M. Trippenbach, and B. A. Malomed, "Two-dimensional dispersion-managed light bullets in Kerr media," Phys. Rev. E 70, 016603 (2004).
    [CrossRef]
  19. V. Zharnitsky, E. Grenier, S. K. Turitsyn, C. K. R. T. Jones, and J. S. Hesthaven, "Ground states of dispersion-managed nonlinear Schrödinger equation," Phys. Rev. E 62, 7358-7364 (2000)
    [CrossRef]
  20. V. Zharnitsky, E. Grenier, C. K. R. T. Jones, and S. K. Turitsyn, "Stabilizing effects of dispersion management," Physica D 152, 794-817 (2001).
    [CrossRef]
  21. F. Abdullaev, B. Baizakov, and M. Salerno, "Stable two-dimensional dispersion-managed soliton," Phys. Rev. E 68, 066605 (2003).
    [CrossRef]
  22. F. Smektala, C. Quemard, V. Couderc, and A. Barthelemy, "Non-linear optical properties of chalcogenide glasses measured by Z-scan," J. Non-Cryst. Solids 274, 232-237 (2000).
    [CrossRef]
  23. D. Anderson and M. Lisak, "Bandwidth limits due to incoherent soliton interaction in optical-fiber communication systems," Phys. Rev. A 32, 2270-2274 (1985).
    [CrossRef] [PubMed]

2004 (3)

G. D. Montesinos, V. M. Pérez-García, and H. Michinel, "Stabilized two-dimensional vector solitons," Phys. Rev. Lett. 92, 133901 (2004).
[CrossRef] [PubMed]

G. D. Montesinos, V. M. Pérez-García, and P. Torres, "Stabilization of solitons of the multidimensional nonlinear Schrödinger equation: matter-wave breathers," Physica D 191, 193-210 (2004).
[CrossRef]

M. Matuszewski, M. Trippenbach, and B. A. Malomed, "Two-dimensional dispersion-managed light bullets in Kerr media," Phys. Rev. E 70, 016603 (2004).
[CrossRef]

2003 (2)

H. Saito and M. Ueda, "Dynamically stabilized bright solitons in a two-dimensional Bose-Einstein condensate," Phys. Rev. Lett. 90, 040403 (2003).
[CrossRef] [PubMed]

F. Abdullaev, B. Baizakov, and M. Salerno, "Stable two-dimensional dispersion-managed soliton," Phys. Rev. E 68, 066605 (2003).
[CrossRef]

2002 (1)

2001 (1)

V. Zharnitsky, E. Grenier, C. K. R. T. Jones, and S. K. Turitsyn, "Stabilizing effects of dispersion management," Physica D 152, 794-817 (2001).
[CrossRef]

2000 (5)

F. Smektala, C. Quemard, V. Couderc, and A. Barthelemy, "Non-linear optical properties of chalcogenide glasses measured by Z-scan," J. Non-Cryst. Solids 274, 232-237 (2000).
[CrossRef]

L. Berge, V. K. Mezentsev, J. J. Rasmussen, P. L. Christiansen, and Y. B. Gaididei, "Self-guiding light in layered nonlinear media," Opt. Lett. 25, 1037-1039 (2000).
[CrossRef]

V. Zharnitsky, E. Grenier, S. K. Turitsyn, C. K. R. T. Jones, and J. S. Hesthaven, "Ground states of dispersion-managed nonlinear Schrödinger equation," Phys. Rev. E 62, 7358-7364 (2000)
[CrossRef]

X. Liu, K. Beckwitt, and F. Wise, "Two-dimensional optical spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 1328-1340 (2000).
[CrossRef]

I. G. Koprinkov, A. Suda, P. Q. Wang, and K. Midorikawa, "Self-compression of high-intensity femtosecond optical pulses and spatiotemporal soliton generation," Phys. Rev. Lett. 84, 3847-3850 (2000)
[CrossRef] [PubMed]

1998 (1)

M. Segev and G. I. Stegeman, "Self-trapping of optical beams: spatial solitons," Phys. Today 51, 42-48 (1998).
[CrossRef]

1997 (1)

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, "Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity," Phys. Rev. E 4, 4725-4735 (1997).
[CrossRef]

1996 (1)

L. Bergé, E. A. Kuznetsov, and J. J. Rasmussen, "Defocusing regimes of nonlinear waves in media with negative dispersion," Phys. Rev. E 53, R1340-R1343 (1996).
[CrossRef]

1994 (1)

1986 (1)

S. Maneuf, A. Barthelemy, and C. Froehly, "Soliton beam propagation; space-time behaviour and spectral features," J. Opt. 17, 139-145 (1986).
[CrossRef]

1985 (1)

D. Anderson and M. Lisak, "Bandwidth limits due to incoherent soliton interaction in optical-fiber communication systems," Phys. Rev. A 32, 2270-2274 (1985).
[CrossRef] [PubMed]

1978 (1)

A. A. Kanashov and A. M. Rubenchik, "Wave mutual focusing in media with quadratic nonlinearity," Opt. Commun. 24, 121-124 (1978).
[CrossRef]

1973 (1)

A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. 1. Anomalous dispersion," Appl. Phys. Lett. 23, 142-144 (1973).
[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).

Abdullaev, F.

F. Abdullaev, B. Baizakov, and M. Salerno, "Stable two-dimensional dispersion-managed soliton," Phys. Rev. E 68, 066605 (2003).
[CrossRef]

Agrawal, G. P.

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).

Anderson, D.

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, "Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity," Phys. Rev. E 4, 4725-4735 (1997).
[CrossRef]

D. Anderson and M. Lisak, "Bandwidth limits due to incoherent soliton interaction in optical-fiber communication systems," Phys. Rev. A 32, 2270-2274 (1985).
[CrossRef] [PubMed]

Baizakov, B.

F. Abdullaev, B. Baizakov, and M. Salerno, "Stable two-dimensional dispersion-managed soliton," Phys. Rev. E 68, 066605 (2003).
[CrossRef]

Barthelemy, A.

F. Smektala, C. Quemard, V. Couderc, and A. Barthelemy, "Non-linear optical properties of chalcogenide glasses measured by Z-scan," J. Non-Cryst. Solids 274, 232-237 (2000).
[CrossRef]

S. Maneuf, A. Barthelemy, and C. Froehly, "Soliton beam propagation; space-time behaviour and spectral features," J. Opt. 17, 139-145 (1986).
[CrossRef]

Beckwitt, K.

X. Liu, K. Beckwitt, and F. Wise, "Two-dimensional optical spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 1328-1340 (2000).
[CrossRef]

Berge, L.

Bergé, L.

L. Bergé, E. A. Kuznetsov, and J. J. Rasmussen, "Defocusing regimes of nonlinear waves in media with negative dispersion," Phys. Rev. E 53, R1340-R1343 (1996).
[CrossRef]

Berntson, A.

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, "Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity," Phys. Rev. E 4, 4725-4735 (1997).
[CrossRef]

Christiansen, P. L.

Couderc, V.

F. Smektala, C. Quemard, V. Couderc, and A. Barthelemy, "Non-linear optical properties of chalcogenide glasses measured by Z-scan," J. Non-Cryst. Solids 274, 232-237 (2000).
[CrossRef]

de la Fuente, R.

Drummond, P.

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, "Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity," Phys. Rev. E 4, 4725-4735 (1997).
[CrossRef]

Froehly, C.

S. Maneuf, A. Barthelemy, and C. Froehly, "Soliton beam propagation; space-time behaviour and spectral features," J. Opt. 17, 139-145 (1986).
[CrossRef]

Gaididei, Y. B.

Grenier, E.

V. Zharnitsky, E. Grenier, C. K. R. T. Jones, and S. K. Turitsyn, "Stabilizing effects of dispersion management," Physica D 152, 794-817 (2001).
[CrossRef]

V. Zharnitsky, E. Grenier, S. K. Turitsyn, C. K. R. T. Jones, and J. S. Hesthaven, "Ground states of dispersion-managed nonlinear Schrödinger equation," Phys. Rev. E 62, 7358-7364 (2000)
[CrossRef]

Hasegawa, A.

A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. 1. Anomalous dispersion," Appl. Phys. Lett. 23, 142-144 (1973).
[CrossRef]

He, H.

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, "Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity," Phys. Rev. E 4, 4725-4735 (1997).
[CrossRef]

Hesthaven, J. S.

V. Zharnitsky, E. Grenier, S. K. Turitsyn, C. K. R. T. Jones, and J. S. Hesthaven, "Ground states of dispersion-managed nonlinear Schrödinger equation," Phys. Rev. E 62, 7358-7364 (2000)
[CrossRef]

Jones, C. K.

V. Zharnitsky, E. Grenier, C. K. R. T. Jones, and S. K. Turitsyn, "Stabilizing effects of dispersion management," Physica D 152, 794-817 (2001).
[CrossRef]

V. Zharnitsky, E. Grenier, S. K. Turitsyn, C. K. R. T. Jones, and J. S. Hesthaven, "Ground states of dispersion-managed nonlinear Schrödinger equation," Phys. Rev. E 62, 7358-7364 (2000)
[CrossRef]

Kanashov, A. A.

A. A. Kanashov and A. M. Rubenchik, "Wave mutual focusing in media with quadratic nonlinearity," Opt. Commun. 24, 121-124 (1978).
[CrossRef]

Kivshar, Yu. S.

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).

Koprinkov, I. G.

I. G. Koprinkov, A. Suda, P. Q. Wang, and K. Midorikawa, "Self-compression of high-intensity femtosecond optical pulses and spatiotemporal soliton generation," Phys. Rev. Lett. 84, 3847-3850 (2000)
[CrossRef] [PubMed]

Kuznetsov, E. A.

L. Bergé, E. A. Kuznetsov, and J. J. Rasmussen, "Defocusing regimes of nonlinear waves in media with negative dispersion," Phys. Rev. E 53, R1340-R1343 (1996).
[CrossRef]

Linares, J.

Lisak, M.

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, "Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity," Phys. Rev. E 4, 4725-4735 (1997).
[CrossRef]

D. Anderson and M. Lisak, "Bandwidth limits due to incoherent soliton interaction in optical-fiber communication systems," Phys. Rev. A 32, 2270-2274 (1985).
[CrossRef] [PubMed]

Liu, X.

X. Liu, K. Beckwitt, and F. Wise, "Two-dimensional optical spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 1328-1340 (2000).
[CrossRef]

Malomed, B. A.

M. Matuszewski, M. Trippenbach, and B. A. Malomed, "Two-dimensional dispersion-managed light bullets in Kerr media," Phys. Rev. E 70, 016603 (2004).
[CrossRef]

I. Towers and B. A. Malomed, "Stable (2+1)-dimensional solitons in a layered medium with sign-alternating Kerr nonlinearity," J. Opt. Soc. Am. B 19, 537-543 (2002).
[CrossRef]

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, "Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity," Phys. Rev. E 4, 4725-4735 (1997).
[CrossRef]

Maneuf, S.

S. Maneuf, A. Barthelemy, and C. Froehly, "Soliton beam propagation; space-time behaviour and spectral features," J. Opt. 17, 139-145 (1986).
[CrossRef]

Matuszewski, M.

M. Matuszewski, M. Trippenbach, and B. A. Malomed, "Two-dimensional dispersion-managed light bullets in Kerr media," Phys. Rev. E 70, 016603 (2004).
[CrossRef]

Mezentsev, V. K.

Michinel, H.

G. D. Montesinos, V. M. Pérez-García, and H. Michinel, "Stabilized two-dimensional vector solitons," Phys. Rev. Lett. 92, 133901 (2004).
[CrossRef] [PubMed]

H. Michinel, R. de la Fuente, and J. Linares, "Temporal modulation of spatial optical solitons," Appl. Opt. 33, 3384-3390 (1994).
[CrossRef] [PubMed]

Midorikawa, K.

I. G. Koprinkov, A. Suda, P. Q. Wang, and K. Midorikawa, "Self-compression of high-intensity femtosecond optical pulses and spatiotemporal soliton generation," Phys. Rev. Lett. 84, 3847-3850 (2000)
[CrossRef] [PubMed]

Montesinos, G. D.

G. D. Montesinos, V. M. Pérez-García, and H. Michinel, "Stabilized two-dimensional vector solitons," Phys. Rev. Lett. 92, 133901 (2004).
[CrossRef] [PubMed]

G. D. Montesinos, V. M. Pérez-García, and P. Torres, "Stabilization of solitons of the multidimensional nonlinear Schrödinger equation: matter-wave breathers," Physica D 191, 193-210 (2004).
[CrossRef]

Pérez-García, V. M.

G. D. Montesinos, V. M. Pérez-García, and P. Torres, "Stabilization of solitons of the multidimensional nonlinear Schrödinger equation: matter-wave breathers," Physica D 191, 193-210 (2004).
[CrossRef]

G. D. Montesinos, V. M. Pérez-García, and H. Michinel, "Stabilized two-dimensional vector solitons," Phys. Rev. Lett. 92, 133901 (2004).
[CrossRef] [PubMed]

Quemard, C.

F. Smektala, C. Quemard, V. Couderc, and A. Barthelemy, "Non-linear optical properties of chalcogenide glasses measured by Z-scan," J. Non-Cryst. Solids 274, 232-237 (2000).
[CrossRef]

Rasmussen, J. J.

L. Berge, V. K. Mezentsev, J. J. Rasmussen, P. L. Christiansen, and Y. B. Gaididei, "Self-guiding light in layered nonlinear media," Opt. Lett. 25, 1037-1039 (2000).
[CrossRef]

L. Bergé, E. A. Kuznetsov, and J. J. Rasmussen, "Defocusing regimes of nonlinear waves in media with negative dispersion," Phys. Rev. E 53, R1340-R1343 (1996).
[CrossRef]

Rubenchik, A. M.

A. A. Kanashov and A. M. Rubenchik, "Wave mutual focusing in media with quadratic nonlinearity," Opt. Commun. 24, 121-124 (1978).
[CrossRef]

Saito, H.

H. Saito and M. Ueda, "Dynamically stabilized bright solitons in a two-dimensional Bose-Einstein condensate," Phys. Rev. Lett. 90, 040403 (2003).
[CrossRef] [PubMed]

Salerno, M.

F. Abdullaev, B. Baizakov, and M. Salerno, "Stable two-dimensional dispersion-managed soliton," Phys. Rev. E 68, 066605 (2003).
[CrossRef]

Segev, M.

M. Segev and G. I. Stegeman, "Self-trapping of optical beams: spatial solitons," Phys. Today 51, 42-48 (1998).
[CrossRef]

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).

Smektala, F.

F. Smektala, C. Quemard, V. Couderc, and A. Barthelemy, "Non-linear optical properties of chalcogenide glasses measured by Z-scan," J. Non-Cryst. Solids 274, 232-237 (2000).
[CrossRef]

Stegeman, G. I.

M. Segev and G. I. Stegeman, "Self-trapping of optical beams: spatial solitons," Phys. Today 51, 42-48 (1998).
[CrossRef]

Suda, A.

I. G. Koprinkov, A. Suda, P. Q. Wang, and K. Midorikawa, "Self-compression of high-intensity femtosecond optical pulses and spatiotemporal soliton generation," Phys. Rev. Lett. 84, 3847-3850 (2000)
[CrossRef] [PubMed]

Sulem, C.

C. Sulem and P. Sulem, The Nonlinear Schrödinger Equation: Self-Focusing and Wave Collapse (Springer, 2000).

Sulem, P.

C. Sulem and P. Sulem, The Nonlinear Schrödinger Equation: Self-Focusing and Wave Collapse (Springer, 2000).

Tappert, F.

A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. 1. Anomalous dispersion," Appl. Phys. Lett. 23, 142-144 (1973).
[CrossRef]

Torres, P.

G. D. Montesinos, V. M. Pérez-García, and P. Torres, "Stabilization of solitons of the multidimensional nonlinear Schrödinger equation: matter-wave breathers," Physica D 191, 193-210 (2004).
[CrossRef]

Towers, I.

Trippenbach, M.

M. Matuszewski, M. Trippenbach, and B. A. Malomed, "Two-dimensional dispersion-managed light bullets in Kerr media," Phys. Rev. E 70, 016603 (2004).
[CrossRef]

Turitsyn, S. K.

V. Zharnitsky, E. Grenier, C. K. R. T. Jones, and S. K. Turitsyn, "Stabilizing effects of dispersion management," Physica D 152, 794-817 (2001).
[CrossRef]

V. Zharnitsky, E. Grenier, S. K. Turitsyn, C. K. R. T. Jones, and J. S. Hesthaven, "Ground states of dispersion-managed nonlinear Schrödinger equation," Phys. Rev. E 62, 7358-7364 (2000)
[CrossRef]

Ueda, M.

H. Saito and M. Ueda, "Dynamically stabilized bright solitons in a two-dimensional Bose-Einstein condensate," Phys. Rev. Lett. 90, 040403 (2003).
[CrossRef] [PubMed]

Wang, P. Q.

I. G. Koprinkov, A. Suda, P. Q. Wang, and K. Midorikawa, "Self-compression of high-intensity femtosecond optical pulses and spatiotemporal soliton generation," Phys. Rev. Lett. 84, 3847-3850 (2000)
[CrossRef] [PubMed]

Wise, F.

X. Liu, K. Beckwitt, and F. Wise, "Two-dimensional optical spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 1328-1340 (2000).
[CrossRef]

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).

Zharnitsky, V.

V. Zharnitsky, E. Grenier, C. K. R. T. Jones, and S. K. Turitsyn, "Stabilizing effects of dispersion management," Physica D 152, 794-817 (2001).
[CrossRef]

V. Zharnitsky, E. Grenier, S. K. Turitsyn, C. K. R. T. Jones, and J. S. Hesthaven, "Ground states of dispersion-managed nonlinear Schrödinger equation," Phys. Rev. E 62, 7358-7364 (2000)
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. 1. Anomalous dispersion," Appl. Phys. Lett. 23, 142-144 (1973).
[CrossRef]

J. Non-Cryst. Solids (1)

F. Smektala, C. Quemard, V. Couderc, and A. Barthelemy, "Non-linear optical properties of chalcogenide glasses measured by Z-scan," J. Non-Cryst. Solids 274, 232-237 (2000).
[CrossRef]

J. Opt. (1)

S. Maneuf, A. Barthelemy, and C. Froehly, "Soliton beam propagation; space-time behaviour and spectral features," J. Opt. 17, 139-145 (1986).
[CrossRef]

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

Opt. Commun. (1)

A. A. Kanashov and A. M. Rubenchik, "Wave mutual focusing in media with quadratic nonlinearity," Opt. Commun. 24, 121-124 (1978).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (1)

D. Anderson and M. Lisak, "Bandwidth limits due to incoherent soliton interaction in optical-fiber communication systems," Phys. Rev. A 32, 2270-2274 (1985).
[CrossRef] [PubMed]

Phys. Rev. E (6)

F. Abdullaev, B. Baizakov, and M. Salerno, "Stable two-dimensional dispersion-managed soliton," Phys. Rev. E 68, 066605 (2003).
[CrossRef]

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, "Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity," Phys. Rev. E 4, 4725-4735 (1997).
[CrossRef]

X. Liu, K. Beckwitt, and F. Wise, "Two-dimensional optical spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 1328-1340 (2000).
[CrossRef]

L. Bergé, E. A. Kuznetsov, and J. J. Rasmussen, "Defocusing regimes of nonlinear waves in media with negative dispersion," Phys. Rev. E 53, R1340-R1343 (1996).
[CrossRef]

M. Matuszewski, M. Trippenbach, and B. A. Malomed, "Two-dimensional dispersion-managed light bullets in Kerr media," Phys. Rev. E 70, 016603 (2004).
[CrossRef]

V. Zharnitsky, E. Grenier, S. K. Turitsyn, C. K. R. T. Jones, and J. S. Hesthaven, "Ground states of dispersion-managed nonlinear Schrödinger equation," Phys. Rev. E 62, 7358-7364 (2000)
[CrossRef]

Phys. Rev. Lett. (3)

G. D. Montesinos, V. M. Pérez-García, and H. Michinel, "Stabilized two-dimensional vector solitons," Phys. Rev. Lett. 92, 133901 (2004).
[CrossRef] [PubMed]

H. Saito and M. Ueda, "Dynamically stabilized bright solitons in a two-dimensional Bose-Einstein condensate," Phys. Rev. Lett. 90, 040403 (2003).
[CrossRef] [PubMed]

I. G. Koprinkov, A. Suda, P. Q. Wang, and K. Midorikawa, "Self-compression of high-intensity femtosecond optical pulses and spatiotemporal soliton generation," Phys. Rev. Lett. 84, 3847-3850 (2000)
[CrossRef] [PubMed]

Phys. Today (1)

M. Segev and G. I. Stegeman, "Self-trapping of optical beams: spatial solitons," Phys. Today 51, 42-48 (1998).
[CrossRef]

Physica D (2)

G. D. Montesinos, V. M. Pérez-García, and P. Torres, "Stabilization of solitons of the multidimensional nonlinear Schrödinger equation: matter-wave breathers," Physica D 191, 193-210 (2004).
[CrossRef]

V. Zharnitsky, E. Grenier, C. K. R. T. Jones, and S. K. Turitsyn, "Stabilizing effects of dispersion management," Physica D 152, 794-817 (2001).
[CrossRef]

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).

Other (2)

C. Sulem and P. Sulem, The Nonlinear Schrödinger Equation: Self-Focusing and Wave Collapse (Springer, 2000).

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).

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 (7)

Fig. 1
Fig. 1

(Color online) (top) Sketch of the propagation of a pulsed beam through a system with periodic modulation of dispersion made by our joining two different planar Kerr waveguides. The forward–backward trajectory can be obtained by reflection at mirrors M1 and M2. (bottom) Oscillations of the peak amplitude of stabilized pulsed beams propagating in the above system. The upper curve corresponds to a value g = 1.074 g c (surface plots in the top figure). For the lower curve, g = 1.034 g c . The modulation is of the form d a = 1 + 8 , d b = 1 8 , η a = η b = 0.02 . In (a) and (b) details of the fast oscillations are shown.

Fig. 2
Fig. 2

Oscillations of the spatial (lower) and temporal (upper) widths of the stabilized soliton with g = 1.074 g c from Fig. 1. (a) and (b) Insets display details of the curves. (c) and (d) Insets show the frequency spectra of the spatial and temporal width oscillations, respectively.

Fig. 3
Fig. 3

Comparison between the evolutions of the spatial and temporal widths of the stabilized soliton with g = 1.074 g c obtained from the variational equations (5) and from the NLSE [Eq. (2)]. The modulation is of the form d a = 1 + 8 , d b = 1 8 , η a = η b = 0.02 . The plots correspond to (a) ω τ (variational), (b) ω χ (variational), (c) ω τ (numerical), and (d) ω χ (numerical).

Fig. 4
Fig. 4

Oscillations of the (a) peak amplitudes and (b) widths of the same input solitons from Fig. 1. In this case the modulation is given by d a = 1 + 8 , d b = 1 8 , η a = η b = 0.01 . In (b) the oscillations of the spatial and temporal widths are overlapped (insets).

Fig. 5
Fig. 5

Oscillations of the (a) peak amplitudes and (b) widths of the same input solitons from Fig. 1. In this case the modulation is given by d a = 1 + 17 , d b = 1 17 3 , η a = 0.005 , η b = 0.015 . In (b) the oscillations of the spatial and temporal widths are overlapped.

Fig. 6
Fig. 6

Oscillations of the (a) peak amplitudes and (b) widths of the same input solitons from Fig. 1. In this case the modulation is given by a sinusoidal function with d 0 = 1 , d 1 = 8 , Ω = 80 . In (b) the oscillations of the spatial and temporal widths are overlapped.

Fig. 7
Fig. 7

Oscillations of the (a) peak amplitudes and (b) widths of the same input solitons from Fig. 1 when a random noise of 1% in amplitude is added to the initial data. In this case the modulation is sinusoidal with d 0 = 1 , d 1 = 8 , Ω = 157 . In (b) the oscillations of the spatial and temporal widths are overlapped.

Equations (6)

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

2 i ( E z + k 0 E t ) + k 0 2 E t 2 + 1 k 0 2 E x 2 + 2 k 0 n 2 n 0 E 2 E = 0 ,
i u η + 1 2 d ( η ) 2 u τ 2 + 1 2 2 u χ 2 + g u 2 u = 0 .
2 L = i ( u u ̇ * u * u ̇ ) + d ( η ) u τ 2 + u χ 2 g u 4 ,
u = A exp [ ( χ 2 2 w χ 2 + τ 2 2 w τ 2 ) + i ( β χ χ 2 + β τ τ 2 ) ] .
w ̈ χ = 1 w χ 3 1 2 π g w χ 2 w τ ,
w ̈ τ d ̇ ( η ) d ( η ) w ̇ τ = d 2 ( η ) w τ 3 1 2 π g d ( η ) w τ 2 w χ .

Metrics