Abstract

We study the propagation of spatial solitons close to the lateral boundaries of self-focusing nonlocal media. Using the Green function approach, we investigate the soliton induced index distribution and resulting trajectories in four cases of physical relevance.

© 2007 Optical Society of America

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  1. H. L. Pecseli and J. J. Rasmussen, "Nonlinear electron waves in strongly magnetized plasma," Plasma Phys. 22, 421-438 (1980).
    [Crossref]
  2. P. Pedri and L. Santos, "Two-dimensional bright solitons in dipolar Bose-Einstein condensates," Phys. Rev. Lett. 95, 200404 (2005).
    [Crossref] [PubMed]
  3. G. Vitrant, R. Reinisch, J. C. Paumier, G. Assanto, and G. I. Stegeman, "Nonlinear prism coupling with nonlocality," Opt. Lett. 14, 898-890 (1989).
    [Crossref] [PubMed]
  4. Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003).
  5. S. Trillo and W. E. Torruellas, eds., Spatial Solitons (Springer-Verlag, 2001).
  6. C. Conti and G. Assanto, "Nonlinear optics applications: bright spatial solitons," in Encyclopedia of Modern Optics, Vol. 5, pp. 43-55, R.D.Guenther, D.G.Steel, and L.Bayvel, eds. (Elsevier, 2004).
  7. E. Vanin, A. I. Korytin, A. M. Sergeev, D. Anderson, M. Lisak, and L. Vazquez, "Dissipative optical solitons," Phys. Rev. A 49, 2806-2811 (1994).
    [Crossref] [PubMed]
  8. S. Abe and A. Ogura, "Solitary waves and their critical behavior in a nonlinear nonlocal medium with power-law response," Phys. Rev. E 57, 6066-6070 (1998).
    [Crossref]
  9. D. J. Mitchell and A. W. Snyder, "Soliton dynamics in a nonlocal medium," J. Opt. Soc. Am. B 16, 236-239 (1999).
    [Crossref]
  10. W. Krolikowski and O. Bang, "Solitons in nonlocal nonlinear media: exact solutions," Phys. Rev. E 63, 016610 (2000).
    [Crossref]
  11. C. Conti, M. Peccianti, and G. Assanto, "Route to nonlocality and observation of accessible solitons," Phys. Rev. Lett. 91, 073901 (2003).
    [Crossref] [PubMed]
  12. G. Assanto and M. Peccianti, "Spatial solitons in nematic liquid crystals," IEEE J. Quantum Electron. 39, 13-21 (2003).
    [Crossref]
  13. M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, "Nonlocal optical propagation in nonlinear nematic liquid crystals," J. Nonlinear Opt. Phys. Mater. 12, 525-538 (2003).
    [Crossref]
  14. C. Conti, M. Peccianti, and G. Assanto, "Observation of optical spatial solitons in a highly nonlocal medium," Phys. Rev. Lett. 92, 113902 (2004).
    [Crossref] [PubMed]
  15. C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, "Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons," Phys. Rev. Lett. 95, 213904 (2005).
    [Crossref] [PubMed]
  16. Z. Xu, Y. V. Kartashov, and L. Torner, "Stabilization of vector soliton complexes in nonlocal nonlinear media," Phys. Rev. E 73, 055601 (2006).
    [Crossref]
  17. W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. Luther-Davies, "Observation of dipole-mode vector solitons," Phys. Rev. Lett. 85, 1424-1427 (2000).
    [Crossref] [PubMed]
  18. T. Carmon, C. Anastassiou, S. Lan, D. Kip, Z. H. Musslimani, M. Segev, and D. Christodoulides, "Observation of two-dimensional multimode solitons," Opt. Lett. 25, 1113-1115 (2000).
    [Crossref]
  19. Y. A. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, "Dynamics of two-dimensional coherent structures in nonlocal nonlinear media," Phys. Rev. E 73, 066605 (2006).
    [Crossref]
  20. A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, "Observation of attraction between dark solitons," Phys. Rev. Lett. 96, 043901 (2006).
    [Crossref] [PubMed]
  21. M. Segev, B. Crosignani, A. Yariv, and B. Fischer, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68, 923-926 (1992).
    [Crossref] [PubMed]
  22. W. Krolikowsky, B. Luther-Davies, and C. Denz, "Photorefractive solitons," Quantum Electron. 39, 3-12 (2003).
  23. C. Conti, G. Ruocco, and S. Trillo, "Optical spatial solitons in soft matter," Phys. Rev. Lett. 95, 183902 (2005).
    [Crossref] [PubMed]
  24. M. Warenghem, J. F. Henninot, F. Derrien, and G. Abbate, "Thermal and orientational 2D+1 spatial optical solitons in dye doped liquid crystals," Mol. Cryst. Liq. Cryst. 373, 213-225 (2002).
    [Crossref]
  25. M. Peccianti, K. Brzadkiewicz, and G. Assanto, "Nonlocal spatial soliton interactions in nematic liquid crystals," Opt. Lett. 27, 1460-1462 (2002).
    [Crossref]
  26. M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, "Routing of anisotropic spatial solitons and modulational instability in nematic liquid crystals," Nature 432, 733-737 (2004).
    [Crossref] [PubMed]
  27. A. Alberucci, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, "Two-color vector solitons in nonlocal media," Phys. Rev. Lett. 97, 153903 (2006).
    [Crossref] [PubMed]
  28. M. Peccianti, A. Fratalocchi, and G. Assanto, "Transverse dynamics of nematicons," Opt. Express 12, 6524-6529 (2004).
    [Crossref] [PubMed]
  29. B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, "Boundary force effects exerted on solitons in highly nonlocal nonlinear media," Opt. Lett. 32, 154-156 (2007).
    [Crossref]
  30. C. Rothschild, B. Alfassi, O. Cohen, and M. Segev, "Long-range interactions between optical solitons," Nat. Phys. 2, 769-774 (2006).
    [Crossref]
  31. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (Academic, 2001).

2007 (1)

2006 (5)

C. Rothschild, B. Alfassi, O. Cohen, and M. Segev, "Long-range interactions between optical solitons," Nat. Phys. 2, 769-774 (2006).
[Crossref]

Y. A. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, "Dynamics of two-dimensional coherent structures in nonlocal nonlinear media," Phys. Rev. E 73, 066605 (2006).
[Crossref]

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, "Observation of attraction between dark solitons," Phys. Rev. Lett. 96, 043901 (2006).
[Crossref] [PubMed]

A. Alberucci, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, "Two-color vector solitons in nonlocal media," Phys. Rev. Lett. 97, 153903 (2006).
[Crossref] [PubMed]

Z. Xu, Y. V. Kartashov, and L. Torner, "Stabilization of vector soliton complexes in nonlocal nonlinear media," Phys. Rev. E 73, 055601 (2006).
[Crossref]

2005 (3)

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, "Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons," Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

P. Pedri and L. Santos, "Two-dimensional bright solitons in dipolar Bose-Einstein condensates," Phys. Rev. Lett. 95, 200404 (2005).
[Crossref] [PubMed]

C. Conti, G. Ruocco, and S. Trillo, "Optical spatial solitons in soft matter," Phys. Rev. Lett. 95, 183902 (2005).
[Crossref] [PubMed]

2004 (4)

M. Peccianti, A. Fratalocchi, and G. Assanto, "Transverse dynamics of nematicons," Opt. Express 12, 6524-6529 (2004).
[Crossref] [PubMed]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, "Routing of anisotropic spatial solitons and modulational instability in nematic liquid crystals," Nature 432, 733-737 (2004).
[Crossref] [PubMed]

C. Conti and G. Assanto, "Nonlinear optics applications: bright spatial solitons," in Encyclopedia of Modern Optics, Vol. 5, pp. 43-55, R.D.Guenther, D.G.Steel, and L.Bayvel, eds. (Elsevier, 2004).

C. Conti, M. Peccianti, and G. Assanto, "Observation of optical spatial solitons in a highly nonlocal medium," Phys. Rev. Lett. 92, 113902 (2004).
[Crossref] [PubMed]

2003 (5)

C. Conti, M. Peccianti, and G. Assanto, "Route to nonlocality and observation of accessible solitons," Phys. Rev. Lett. 91, 073901 (2003).
[Crossref] [PubMed]

G. Assanto and M. Peccianti, "Spatial solitons in nematic liquid crystals," IEEE J. Quantum Electron. 39, 13-21 (2003).
[Crossref]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, "Nonlocal optical propagation in nonlinear nematic liquid crystals," J. Nonlinear Opt. Phys. Mater. 12, 525-538 (2003).
[Crossref]

Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003).

W. Krolikowsky, B. Luther-Davies, and C. Denz, "Photorefractive solitons," Quantum Electron. 39, 3-12 (2003).

2002 (2)

M. Warenghem, J. F. Henninot, F. Derrien, and G. Abbate, "Thermal and orientational 2D+1 spatial optical solitons in dye doped liquid crystals," Mol. Cryst. Liq. Cryst. 373, 213-225 (2002).
[Crossref]

M. Peccianti, K. Brzadkiewicz, and G. Assanto, "Nonlocal spatial soliton interactions in nematic liquid crystals," Opt. Lett. 27, 1460-1462 (2002).
[Crossref]

2001 (2)

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (Academic, 2001).

S. Trillo and W. E. Torruellas, eds., Spatial Solitons (Springer-Verlag, 2001).

2000 (3)

W. Krolikowski and O. Bang, "Solitons in nonlocal nonlinear media: exact solutions," Phys. Rev. E 63, 016610 (2000).
[Crossref]

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. Luther-Davies, "Observation of dipole-mode vector solitons," Phys. Rev. Lett. 85, 1424-1427 (2000).
[Crossref] [PubMed]

T. Carmon, C. Anastassiou, S. Lan, D. Kip, Z. H. Musslimani, M. Segev, and D. Christodoulides, "Observation of two-dimensional multimode solitons," Opt. Lett. 25, 1113-1115 (2000).
[Crossref]

1999 (1)

1998 (1)

S. Abe and A. Ogura, "Solitary waves and their critical behavior in a nonlinear nonlocal medium with power-law response," Phys. Rev. E 57, 6066-6070 (1998).
[Crossref]

1994 (1)

E. Vanin, A. I. Korytin, A. M. Sergeev, D. Anderson, M. Lisak, and L. Vazquez, "Dissipative optical solitons," Phys. Rev. A 49, 2806-2811 (1994).
[Crossref] [PubMed]

1992 (1)

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68, 923-926 (1992).
[Crossref] [PubMed]

1989 (1)

1980 (1)

H. L. Pecseli and J. J. Rasmussen, "Nonlinear electron waves in strongly magnetized plasma," Plasma Phys. 22, 421-438 (1980).
[Crossref]

Abbate, G.

M. Warenghem, J. F. Henninot, F. Derrien, and G. Abbate, "Thermal and orientational 2D+1 spatial optical solitons in dye doped liquid crystals," Mol. Cryst. Liq. Cryst. 373, 213-225 (2002).
[Crossref]

Abe, S.

S. Abe and A. Ogura, "Solitary waves and their critical behavior in a nonlinear nonlocal medium with power-law response," Phys. Rev. E 57, 6066-6070 (1998).
[Crossref]

Agrawal, G. P.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003).

Alberucci, A.

A. Alberucci, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, "Two-color vector solitons in nonlocal media," Phys. Rev. Lett. 97, 153903 (2006).
[Crossref] [PubMed]

Alfassi, B.

Anastassiou, C.

Anderson, D.

E. Vanin, A. I. Korytin, A. M. Sergeev, D. Anderson, M. Lisak, and L. Vazquez, "Dissipative optical solitons," Phys. Rev. A 49, 2806-2811 (1994).
[Crossref] [PubMed]

Arfken, G. B.

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (Academic, 2001).

Assanto, G.

A. Alberucci, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, "Two-color vector solitons in nonlocal media," Phys. Rev. Lett. 97, 153903 (2006).
[Crossref] [PubMed]

M. Peccianti, A. Fratalocchi, and G. Assanto, "Transverse dynamics of nematicons," Opt. Express 12, 6524-6529 (2004).
[Crossref] [PubMed]

C. Conti and G. Assanto, "Nonlinear optics applications: bright spatial solitons," in Encyclopedia of Modern Optics, Vol. 5, pp. 43-55, R.D.Guenther, D.G.Steel, and L.Bayvel, eds. (Elsevier, 2004).

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, "Routing of anisotropic spatial solitons and modulational instability in nematic liquid crystals," Nature 432, 733-737 (2004).
[Crossref] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, "Observation of optical spatial solitons in a highly nonlocal medium," Phys. Rev. Lett. 92, 113902 (2004).
[Crossref] [PubMed]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, "Nonlocal optical propagation in nonlinear nematic liquid crystals," J. Nonlinear Opt. Phys. Mater. 12, 525-538 (2003).
[Crossref]

C. Conti, M. Peccianti, and G. Assanto, "Route to nonlocality and observation of accessible solitons," Phys. Rev. Lett. 91, 073901 (2003).
[Crossref] [PubMed]

G. Assanto and M. Peccianti, "Spatial solitons in nematic liquid crystals," IEEE J. Quantum Electron. 39, 13-21 (2003).
[Crossref]

M. Peccianti, K. Brzadkiewicz, and G. Assanto, "Nonlocal spatial soliton interactions in nematic liquid crystals," Opt. Lett. 27, 1460-1462 (2002).
[Crossref]

G. Vitrant, R. Reinisch, J. C. Paumier, G. Assanto, and G. I. Stegeman, "Nonlinear prism coupling with nonlocality," Opt. Lett. 14, 898-890 (1989).
[Crossref] [PubMed]

Bang, O.

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, "Observation of attraction between dark solitons," Phys. Rev. Lett. 96, 043901 (2006).
[Crossref] [PubMed]

W. Krolikowski and O. Bang, "Solitons in nonlocal nonlinear media: exact solutions," Phys. Rev. E 63, 016610 (2000).
[Crossref]

Brzadkiewicz, K.

Carmon, T.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, "Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons," Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

T. Carmon, C. Anastassiou, S. Lan, D. Kip, Z. H. Musslimani, M. Segev, and D. Christodoulides, "Observation of two-dimensional multimode solitons," Opt. Lett. 25, 1113-1115 (2000).
[Crossref]

Christodoulides, D.

Christodoulides, D. N.

Cohen, O.

C. Rothschild, B. Alfassi, O. Cohen, and M. Segev, "Long-range interactions between optical solitons," Nat. Phys. 2, 769-774 (2006).
[Crossref]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, "Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons," Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

Conti, C.

C. Conti, G. Ruocco, and S. Trillo, "Optical spatial solitons in soft matter," Phys. Rev. Lett. 95, 183902 (2005).
[Crossref] [PubMed]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, "Routing of anisotropic spatial solitons and modulational instability in nematic liquid crystals," Nature 432, 733-737 (2004).
[Crossref] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, "Observation of optical spatial solitons in a highly nonlocal medium," Phys. Rev. Lett. 92, 113902 (2004).
[Crossref] [PubMed]

C. Conti and G. Assanto, "Nonlinear optics applications: bright spatial solitons," in Encyclopedia of Modern Optics, Vol. 5, pp. 43-55, R.D.Guenther, D.G.Steel, and L.Bayvel, eds. (Elsevier, 2004).

C. Conti, M. Peccianti, and G. Assanto, "Route to nonlocality and observation of accessible solitons," Phys. Rev. Lett. 91, 073901 (2003).
[Crossref] [PubMed]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, "Nonlocal optical propagation in nonlinear nematic liquid crystals," J. Nonlinear Opt. Phys. Mater. 12, 525-538 (2003).
[Crossref]

Crosignani, B.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68, 923-926 (1992).
[Crossref] [PubMed]

De Luca, A.

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, "Routing of anisotropic spatial solitons and modulational instability in nematic liquid crystals," Nature 432, 733-737 (2004).
[Crossref] [PubMed]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, "Nonlocal optical propagation in nonlinear nematic liquid crystals," J. Nonlinear Opt. Phys. Mater. 12, 525-538 (2003).
[Crossref]

Denz, C.

W. Krolikowsky, B. Luther-Davies, and C. Denz, "Photorefractive solitons," Quantum Electron. 39, 3-12 (2003).

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. Luther-Davies, "Observation of dipole-mode vector solitons," Phys. Rev. Lett. 85, 1424-1427 (2000).
[Crossref] [PubMed]

Derrien, F.

M. Warenghem, J. F. Henninot, F. Derrien, and G. Abbate, "Thermal and orientational 2D+1 spatial optical solitons in dye doped liquid crystals," Mol. Cryst. Liq. Cryst. 373, 213-225 (2002).
[Crossref]

Dreischuh, A.

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, "Observation of attraction between dark solitons," Phys. Rev. Lett. 96, 043901 (2006).
[Crossref] [PubMed]

Dyadyusha, A.

A. Alberucci, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, "Two-color vector solitons in nonlocal media," Phys. Rev. Lett. 97, 153903 (2006).
[Crossref] [PubMed]

Fischer, B.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68, 923-926 (1992).
[Crossref] [PubMed]

Fratalocchi, A.

Geisser, M.

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. Luther-Davies, "Observation of dipole-mode vector solitons," Phys. Rev. Lett. 85, 1424-1427 (2000).
[Crossref] [PubMed]

Henninot, J. F.

M. Warenghem, J. F. Henninot, F. Derrien, and G. Abbate, "Thermal and orientational 2D+1 spatial optical solitons in dye doped liquid crystals," Mol. Cryst. Liq. Cryst. 373, 213-225 (2002).
[Crossref]

Kaczmarek, M.

A. Alberucci, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, "Two-color vector solitons in nonlocal media," Phys. Rev. Lett. 97, 153903 (2006).
[Crossref] [PubMed]

Kartashov, Y. V.

Z. Xu, Y. V. Kartashov, and L. Torner, "Stabilization of vector soliton complexes in nonlocal nonlinear media," Phys. Rev. E 73, 055601 (2006).
[Crossref]

Kip, D.

Kivshar, Y. S.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003).

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. Luther-Davies, "Observation of dipole-mode vector solitons," Phys. Rev. Lett. 85, 1424-1427 (2000).
[Crossref] [PubMed]

Korytin, A. I.

E. Vanin, A. I. Korytin, A. M. Sergeev, D. Anderson, M. Lisak, and L. Vazquez, "Dissipative optical solitons," Phys. Rev. A 49, 2806-2811 (1994).
[Crossref] [PubMed]

Krolikowski, W.

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, "Observation of attraction between dark solitons," Phys. Rev. Lett. 96, 043901 (2006).
[Crossref] [PubMed]

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. Luther-Davies, "Observation of dipole-mode vector solitons," Phys. Rev. Lett. 85, 1424-1427 (2000).
[Crossref] [PubMed]

W. Krolikowski and O. Bang, "Solitons in nonlocal nonlinear media: exact solutions," Phys. Rev. E 63, 016610 (2000).
[Crossref]

Krolikowsky, W.

W. Krolikowsky, B. Luther-Davies, and C. Denz, "Photorefractive solitons," Quantum Electron. 39, 3-12 (2003).

Lan, S.

Lashkin, V. M.

Y. A. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, "Dynamics of two-dimensional coherent structures in nonlocal nonlinear media," Phys. Rev. E 73, 066605 (2006).
[Crossref]

Lisak, M.

E. Vanin, A. I. Korytin, A. M. Sergeev, D. Anderson, M. Lisak, and L. Vazquez, "Dissipative optical solitons," Phys. Rev. A 49, 2806-2811 (1994).
[Crossref] [PubMed]

Luther-Davies, B.

W. Krolikowsky, B. Luther-Davies, and C. Denz, "Photorefractive solitons," Quantum Electron. 39, 3-12 (2003).

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. Luther-Davies, "Observation of dipole-mode vector solitons," Phys. Rev. Lett. 85, 1424-1427 (2000).
[Crossref] [PubMed]

Manela, O.

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, "Boundary force effects exerted on solitons in highly nonlocal nonlinear media," Opt. Lett. 32, 154-156 (2007).
[Crossref]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, "Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons," Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

McCarthy, G.

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. Luther-Davies, "Observation of dipole-mode vector solitons," Phys. Rev. Lett. 85, 1424-1427 (2000).
[Crossref] [PubMed]

Mitchell, D. J.

Musslimani, Z. H.

Neshev, D. N.

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, "Observation of attraction between dark solitons," Phys. Rev. Lett. 96, 043901 (2006).
[Crossref] [PubMed]

Ogura, A.

S. Abe and A. Ogura, "Solitary waves and their critical behavior in a nonlinear nonlocal medium with power-law response," Phys. Rev. E 57, 6066-6070 (1998).
[Crossref]

Ostrovskaya, E. A.

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. Luther-Davies, "Observation of dipole-mode vector solitons," Phys. Rev. Lett. 85, 1424-1427 (2000).
[Crossref] [PubMed]

Paumier, J. C.

Peccianti, M.

A. Alberucci, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, "Two-color vector solitons in nonlocal media," Phys. Rev. Lett. 97, 153903 (2006).
[Crossref] [PubMed]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, "Routing of anisotropic spatial solitons and modulational instability in nematic liquid crystals," Nature 432, 733-737 (2004).
[Crossref] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, "Observation of optical spatial solitons in a highly nonlocal medium," Phys. Rev. Lett. 92, 113902 (2004).
[Crossref] [PubMed]

M. Peccianti, A. Fratalocchi, and G. Assanto, "Transverse dynamics of nematicons," Opt. Express 12, 6524-6529 (2004).
[Crossref] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, "Route to nonlocality and observation of accessible solitons," Phys. Rev. Lett. 91, 073901 (2003).
[Crossref] [PubMed]

G. Assanto and M. Peccianti, "Spatial solitons in nematic liquid crystals," IEEE J. Quantum Electron. 39, 13-21 (2003).
[Crossref]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, "Nonlocal optical propagation in nonlinear nematic liquid crystals," J. Nonlinear Opt. Phys. Mater. 12, 525-538 (2003).
[Crossref]

M. Peccianti, K. Brzadkiewicz, and G. Assanto, "Nonlocal spatial soliton interactions in nematic liquid crystals," Opt. Lett. 27, 1460-1462 (2002).
[Crossref]

Pecseli, H. L.

H. L. Pecseli and J. J. Rasmussen, "Nonlinear electron waves in strongly magnetized plasma," Plasma Phys. 22, 421-438 (1980).
[Crossref]

Pedri, P.

P. Pedri and L. Santos, "Two-dimensional bright solitons in dipolar Bose-Einstein condensates," Phys. Rev. Lett. 95, 200404 (2005).
[Crossref] [PubMed]

Petersen, D. E.

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, "Observation of attraction between dark solitons," Phys. Rev. Lett. 96, 043901 (2006).
[Crossref] [PubMed]

Prikhodko, O. O.

Y. A. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, "Dynamics of two-dimensional coherent structures in nonlocal nonlinear media," Phys. Rev. E 73, 066605 (2006).
[Crossref]

Rasmussen, J. J.

H. L. Pecseli and J. J. Rasmussen, "Nonlinear electron waves in strongly magnetized plasma," Plasma Phys. 22, 421-438 (1980).
[Crossref]

Reinisch, R.

Rothschild, C.

C. Rothschild, B. Alfassi, O. Cohen, and M. Segev, "Long-range interactions between optical solitons," Nat. Phys. 2, 769-774 (2006).
[Crossref]

Rotschild, C.

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, "Boundary force effects exerted on solitons in highly nonlocal nonlinear media," Opt. Lett. 32, 154-156 (2007).
[Crossref]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, "Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons," Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

Ruocco, G.

C. Conti, G. Ruocco, and S. Trillo, "Optical spatial solitons in soft matter," Phys. Rev. Lett. 95, 183902 (2005).
[Crossref] [PubMed]

Santos, L.

P. Pedri and L. Santos, "Two-dimensional bright solitons in dipolar Bose-Einstein condensates," Phys. Rev. Lett. 95, 200404 (2005).
[Crossref] [PubMed]

Segev, M.

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, "Boundary force effects exerted on solitons in highly nonlocal nonlinear media," Opt. Lett. 32, 154-156 (2007).
[Crossref]

C. Rothschild, B. Alfassi, O. Cohen, and M. Segev, "Long-range interactions between optical solitons," Nat. Phys. 2, 769-774 (2006).
[Crossref]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, "Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons," Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

T. Carmon, C. Anastassiou, S. Lan, D. Kip, Z. H. Musslimani, M. Segev, and D. Christodoulides, "Observation of two-dimensional multimode solitons," Opt. Lett. 25, 1113-1115 (2000).
[Crossref]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68, 923-926 (1992).
[Crossref] [PubMed]

Sergeev, A. M.

E. Vanin, A. I. Korytin, A. M. Sergeev, D. Anderson, M. Lisak, and L. Vazquez, "Dissipative optical solitons," Phys. Rev. A 49, 2806-2811 (1994).
[Crossref] [PubMed]

Snyder, A. W.

Stegeman, G. I.

Torner, L.

Z. Xu, Y. V. Kartashov, and L. Torner, "Stabilization of vector soliton complexes in nonlocal nonlinear media," Phys. Rev. E 73, 055601 (2006).
[Crossref]

Torruellas, W. E.

S. Trillo and W. E. Torruellas, eds., Spatial Solitons (Springer-Verlag, 2001).

Trillo, S.

C. Conti, G. Ruocco, and S. Trillo, "Optical spatial solitons in soft matter," Phys. Rev. Lett. 95, 183902 (2005).
[Crossref] [PubMed]

S. Trillo and W. E. Torruellas, eds., Spatial Solitons (Springer-Verlag, 2001).

Umeton, C.

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, "Routing of anisotropic spatial solitons and modulational instability in nematic liquid crystals," Nature 432, 733-737 (2004).
[Crossref] [PubMed]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, "Nonlocal optical propagation in nonlinear nematic liquid crystals," J. Nonlinear Opt. Phys. Mater. 12, 525-538 (2003).
[Crossref]

Vanin, E.

E. Vanin, A. I. Korytin, A. M. Sergeev, D. Anderson, M. Lisak, and L. Vazquez, "Dissipative optical solitons," Phys. Rev. A 49, 2806-2811 (1994).
[Crossref] [PubMed]

Vazquez, L.

E. Vanin, A. I. Korytin, A. M. Sergeev, D. Anderson, M. Lisak, and L. Vazquez, "Dissipative optical solitons," Phys. Rev. A 49, 2806-2811 (1994).
[Crossref] [PubMed]

Vitrant, G.

Warenghem, M.

M. Warenghem, J. F. Henninot, F. Derrien, and G. Abbate, "Thermal and orientational 2D+1 spatial optical solitons in dye doped liquid crystals," Mol. Cryst. Liq. Cryst. 373, 213-225 (2002).
[Crossref]

Weber, H. J.

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (Academic, 2001).

Weilnau, C.

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. Luther-Davies, "Observation of dipole-mode vector solitons," Phys. Rev. Lett. 85, 1424-1427 (2000).
[Crossref] [PubMed]

Xu, Z.

Z. Xu, Y. V. Kartashov, and L. Torner, "Stabilization of vector soliton complexes in nonlocal nonlinear media," Phys. Rev. E 73, 055601 (2006).
[Crossref]

Yakimenko, Y. A.

Y. A. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, "Dynamics of two-dimensional coherent structures in nonlocal nonlinear media," Phys. Rev. E 73, 066605 (2006).
[Crossref]

Yariv, A.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68, 923-926 (1992).
[Crossref] [PubMed]

IEEE J. Quantum Electron. (1)

G. Assanto and M. Peccianti, "Spatial solitons in nematic liquid crystals," IEEE J. Quantum Electron. 39, 13-21 (2003).
[Crossref]

J. Nonlinear Opt. Phys. Mater. (1)

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, "Nonlocal optical propagation in nonlinear nematic liquid crystals," J. Nonlinear Opt. Phys. Mater. 12, 525-538 (2003).
[Crossref]

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

Mol. Cryst. Liq. Cryst. (1)

M. Warenghem, J. F. Henninot, F. Derrien, and G. Abbate, "Thermal and orientational 2D+1 spatial optical solitons in dye doped liquid crystals," Mol. Cryst. Liq. Cryst. 373, 213-225 (2002).
[Crossref]

Nat. Phys. (1)

C. Rothschild, B. Alfassi, O. Cohen, and M. Segev, "Long-range interactions between optical solitons," Nat. Phys. 2, 769-774 (2006).
[Crossref]

Nature (1)

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, "Routing of anisotropic spatial solitons and modulational instability in nematic liquid crystals," Nature 432, 733-737 (2004).
[Crossref] [PubMed]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. A (1)

E. Vanin, A. I. Korytin, A. M. Sergeev, D. Anderson, M. Lisak, and L. Vazquez, "Dissipative optical solitons," Phys. Rev. A 49, 2806-2811 (1994).
[Crossref] [PubMed]

Phys. Rev. E (4)

S. Abe and A. Ogura, "Solitary waves and their critical behavior in a nonlinear nonlocal medium with power-law response," Phys. Rev. E 57, 6066-6070 (1998).
[Crossref]

W. Krolikowski and O. Bang, "Solitons in nonlocal nonlinear media: exact solutions," Phys. Rev. E 63, 016610 (2000).
[Crossref]

Z. Xu, Y. V. Kartashov, and L. Torner, "Stabilization of vector soliton complexes in nonlocal nonlinear media," Phys. Rev. E 73, 055601 (2006).
[Crossref]

Y. A. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, "Dynamics of two-dimensional coherent structures in nonlocal nonlinear media," Phys. Rev. E 73, 066605 (2006).
[Crossref]

Phys. Rev. Lett. (9)

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, "Observation of attraction between dark solitons," Phys. Rev. Lett. 96, 043901 (2006).
[Crossref] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68, 923-926 (1992).
[Crossref] [PubMed]

A. Alberucci, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, "Two-color vector solitons in nonlocal media," Phys. Rev. Lett. 97, 153903 (2006).
[Crossref] [PubMed]

C. Conti, G. Ruocco, and S. Trillo, "Optical spatial solitons in soft matter," Phys. Rev. Lett. 95, 183902 (2005).
[Crossref] [PubMed]

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. Luther-Davies, "Observation of dipole-mode vector solitons," Phys. Rev. Lett. 85, 1424-1427 (2000).
[Crossref] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, "Route to nonlocality and observation of accessible solitons," Phys. Rev. Lett. 91, 073901 (2003).
[Crossref] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, "Observation of optical spatial solitons in a highly nonlocal medium," Phys. Rev. Lett. 92, 113902 (2004).
[Crossref] [PubMed]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, "Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons," Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

P. Pedri and L. Santos, "Two-dimensional bright solitons in dipolar Bose-Einstein condensates," Phys. Rev. Lett. 95, 200404 (2005).
[Crossref] [PubMed]

Plasma Phys. (1)

H. L. Pecseli and J. J. Rasmussen, "Nonlinear electron waves in strongly magnetized plasma," Plasma Phys. 22, 421-438 (1980).
[Crossref]

Quantum Electron. (1)

W. Krolikowsky, B. Luther-Davies, and C. Denz, "Photorefractive solitons," Quantum Electron. 39, 3-12 (2003).

Other (4)

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (Academic, 2001).

Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003).

S. Trillo and W. E. Torruellas, eds., Spatial Solitons (Springer-Verlag, 2001).

C. Conti and G. Assanto, "Nonlinear optics applications: bright spatial solitons," in Encyclopedia of Modern Optics, Vol. 5, pp. 43-55, R.D.Guenther, D.G.Steel, and L.Bayvel, eds. (Elsevier, 2004).

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Figures (9)

Fig. 1
Fig. 1

(a), (b) Perturbation profiles versus ξ for ξ = 0.5 , 0.63, 0.76, and 0.9 (solid curve, squares, stars, and triangles, respectively) for (a) ω = 0.001 and (b) ω = 0.09 . The profile in (a) is very similar to the Green function, as the soliton is much narrower than the sample width. (c) Calculated α (squares) and α s for ξ = 0.54 (no symbols), ξ = 0.72 (stars), and ξ = 0.86 (triangles), respectively, versus normalized waist ω. (d) Calculated α g for the same set of soliton positions.

Fig. 2
Fig. 2

(a) θ n ξ calculated for ω = 0.02 , ξ = 0.5 (solid curve), ω = 0.02 , ξ = 0.75 (asterisks), ω = 0.1 , ξ = 0.5 , (triangles), and ω = 0.1 , ξ = 0.75 (squares), respectively. The numerical results are in complete agreement with the theoretical approximation. (b), (c) Calculated degree of nonlocality α along x and (d) along y for ξ = 0.5 (circles), ξ = 0.54 (solid curve), ξ = 0.68 (squares), and ξ = 0.81 (triangles), respectively.

Fig. 3
Fig. 3

Perturbation profiles for (a), (c) ω = 0.01 and (b),(d) ω = 0.1 for (a),(b) ξ = 0.5 and (c),(d) ξ = 0.75 . The dashed (solid) curves correspond to profiles along υ ( ξ ξ ) . The profiles are chosen to contain the perturbation peak. Squares (triangles) are the corresponding values computed using a full numerical approach.

Fig. 4
Fig. 4

Calculated figure of nonlocality α x (curves for α y and α x y g s are nearly identical) versus ω for ξ = 0.5 and (a), (b) μ κ = 10 2 or (c), (d) μ κ = 10 4 . In this range for μ κ , nonlocality does not depend on beam position. When α x = 1 , perturbation and excitation have the same profile, i.e., the medium is local. (b)–(d): beam profile along υ (symbols) and ξ ξ (solid curve) for μ κ = 10 2 and μ κ = 10 4 , respectively, when ω = 0.034 and ξ = 0.5 ; in both cases the perturbation possesses radial symmetry.

Fig. 5
Fig. 5

Plots of g 1 (a), (d) and g 2 (b), (e) for ξ = 0.5 . The corresponding profiles are plotted in (c) and (f) versus ξ ( g 1 solid curve, g 2 squares) and υ ( g 1 dashed curve, g 2 triangles), normalized to one (the cross sections are in υ = 0 and ξ = 0.5 , respectively). Results for g 1 and g 2 perfectly overlap. Excitation waists are ω = 0.03 (a)–(c) and ω = 0.1 (d)–(f), respectively.

Fig. 6
Fig. 6

As in Fig. 5 but with soliton beams centered in ξ = 0.75 .

Fig. 7
Fig. 7

Calculated perturbation ψ versus power for γ = 1.3 × 10 9 V 2 , L = 100 μ m , w = 2.6 μ m , and θ 0 = 0.42 . Dashed and solid curves stem from retaining first- and second-order terms in the perturbative series, respectively. Squares (and solid-curve linear interpolation) are numerical solutions obtained by a standard relaxation method. The beam is centered in the midplane x = 50 μ m .

Fig. 8
Fig. 8

(a) W 0 versus initial (i.e., at z = 0 ) beam position x for the Poisson equation in 1D [see Eq. (17)]; the curves for different ω overlap. In (b) the corresponding oscillation period Λ is graphed versus power density P L , with dependence on the square root of P L . Given the linearity of W 0 , Λ does not depend on the initial beam position. (c) W 0 in the screened Poisson case for μ κ = 0 , i.e., the 2D Poisson case (squares w = 10 μ m , solid curve w = 2.2 μ m ), and μ κ = 100 (triangles w = 10 μ m , circles w = 2.2 μ m ). (d) Soliton trajectories in the 2D Poisson case for different x ( z = 0 ) , considering a null initial velocity and a power of 2 mW . (e) Corresponding Λ versus initial soliton position. For all cases L = 100 μ m and κ = 1 .

Fig. 9
Fig. 9

(a) W 0 for NLC as computed from Eq. (19), for P = 2 2 mW (solid curve) and P = 3 2 2 mW (dashed curve). The curves for w = 2.2 and 2.8 μ m overlap. (b) Oscillation period Λ versus initial beam position for P = 2 2 mW (stars w = 2.8 μ m , solid curve w = 2.2 μ m ) and P = 3 2 2 mW (squares w = 2.8 μ m , triangles w = 2.2 μ m ). In all cases L = 100 μ m .

Equations (27)

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2 i k A z + T 2 A + 2 n 0 k 0 2 Δ n ( A ) A = 0 ,
α i = F W H M i A 2 F W H M i Δ n ( i = x , y ) .
α x y g s = F W H M x y A 2 ( 2 σ x y g s ) ,
β d 2 ψ d x 2 + A 2 = 0 ,
G ( ξ , ζ ) = ξ κ ( 1 ζ ) u ( ζ ξ ) + ζ κ ( 1 ξ ) u ( ξ ζ ) ,
ψ = ω 2 κ { N 1 + N 2 } ,
N 1 = π { erf ( 1 ξ ω ) ( 1 ξ ) ξ + erf ( ξ ξ ω ) ( ξ ξ ) + ξ ( ξ 1 ) erf ( ξ ω ) } ,
N 2 = ω [ exp ( ξ 2 ω 2 ) exp ( ( ξ ξ ) 2 ω 2 ) ξ ( exp ( ξ 2 ω 2 ) exp ( ( 1 ξ ) 2 ω 2 ) ) ] .
β 2 ψ ( x , y ) + A ( x , y ) 2 = 0 ,
G ( ξ , υ , ζ , η ) = n = 1 1 c n κ sin ( π n ζ ) exp ( c n υ η ) sin ( π n ξ ) ,
ψ ( ξ , υ ) = d η 0 1 G ( ξ , υ , ζ , η ) A ( ζ , η ) 2 d ζ = n = 1 1 π n κ sin ( π n ξ ) θ n ( υ ) ,
θ n υ ( υ ) = π 2 ω y exp ( π n ω y 2 ) [ erfc ( υ ω y + π n 2 ω y ) exp ( π n υ ) + erfc ( υ ω y + π n 2 ω y ) exp ( π n υ ) ] .
β 2 ψ ( x , y ) + μ ψ ( x , y ) + A ( x , y ) 2 = 0 ,
υ ξ 2 θ + γ sin [ 2 θ ] A 2 = 0
2 ψ 1 + γ sin [ 2 θ 0 ] A 2 = 0 ,
2 ψ 2 + 2 γ cos [ 2 θ 0 ] ψ 1 A 2 = 0 .
ψ = sin [ 2 θ 0 ] γ P g 1 ( ξ , υ ) + sin [ 4 θ 0 ] γ 2 P 2 g 2 ( ξ , υ ) ,
g 1 ( ξ , υ ) = G ( ξ , υ , ζ , η ) a ( ζ , η ) d ζ d η ,
g 2 ( ξ , υ ) = G ( ξ , υ , ζ , η ) a ( ζ , η ) { G ( ζ , η , ζ , η ) a ( ζ , η ) d ζ d η } d ζ d η .
k d 2 r d z 2 = φ 2 V d x d y ,
k d 2 x d z 2 = W 0 ( x , z ) ,
W 0 = k 0 P L κ { [ erf ( 1 x w ) + x L ( erf ( x w ) erf ( 1 x w ) ) ] w π L [ exp ( x 2 w 2 ) exp ( ( L x ) 2 w 2 ) ] } ,
W 0 ( x ) = k 0 P κ n = 1 R n υ θ n ξ ( x L ) cos ( π n L x ) ,
W 0 = k 0 ε a n 0 cos δ { sin [ 2 ( θ 0 δ ) ] W 0 L + cos [ 2 ( θ 0 δ ) ] W 0 N L } ,
W 0 L ( x ) = γ P C 2 n = 1 R n υ θ n ξ ( x L ) cos ( π n L x ) + γ 2 P 2 C 2 2 n = 1 cos ( π n L x ) m = 1 P m n G m n ( x L ) ,
W 0 N L ( x ) = γ 2 P 2 C 2 4 π 2 n = 1 m = 1 1 n m [ n cos ( π n L x ) sin ( π m L x ) + m cos ( π m L x ) sin ( π n L x ) ] M n m ( x ) ,
P n m = F m n ( η ) exp ( t 2 ω 2 ) e π n t η d η π ω 2

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