Abstract

Using a system of coupled nonlinear Schrödinger equations (CNLSEs), we show that nonlinear light propagation in self-focusing Kerr media can be controlled via a suitable combination of linear and circular birefringences. In particular, magneto-optical effects are taken as a specific physical example, which enables the introduction of both types of birefringences simultaneously via the joint action of the Cotton-Mouton and the Faraday effect. We demonstrate the efficient management of the collapse of (2 + 1)D beams in magneto-optic dielectric media, which may result in either the acceleration or the suppression of the collapse. However, our study also shows that a complete stabilization of the bimodal beams (i.e., the propagation of two-dimensional solitary waves) is not possible under the proposed conditions. The analysis is performed by directly numerically solving the CNLSEs, as well as by using the variational approximation, both showing consistent results. The investigated method allows high-power beam propagation in Kerr media while avoiding collapse, thus offering a viable alternative to the techniques applied in non-instantaneous and/or non-local nonlinear media.

© 2010 OSA

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. Sulem and P. L. Sulem, The nonlinear Schrödinger equation: self-focusing and wave collapse (Springer, New York 1999).
  2. E. Infeld and G. Rowlands, Nonlinear Waves, Solitons and Chaos (Cambridge Univ. Press, Cambridge 2000).
  3. R. W. Boyd, Nonlinear Optics (Academic Press, San Diego 2008).
  4. B. A. Malomed, “Nonlinear Schrödinger equations,” in Encyclopedia of Nonlinear Science, A. Scott, ed., (Routledge, New York 2005).
  5. Y. S. Kivshar, and P. G. Agrawal, Optical Solitons: From Fibers to Photonic Crystal (Academic Press, San Diego 2003).
  6. S. Trillo and W. Torruellas, Spatial Solitons (Springer-Verlag, Berlin 2001).
  7. G. I. Stegeman and M. Segev, “Optical Spatial Solitons and Their Interactions: Universality and Diversity,” Science 286(5444), 1518–1523 (1999).
    [CrossRef]
  8. R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-Trapping of Optical Beams,” Phys. Rev. Lett. 13(15), 479–482 (1964).
    [CrossRef]
  9. K. D. Moll, A. L. Gaeta, and G. Fibich, “Self-similar optical wave collapse: observation of the Townes profile,” Phys. Rev. Lett. 90(20), 203902 (2003).
    [CrossRef]
  10. G. Fibich and A. L. Gaeta, “Critical power for self-focusing in bulk media and in hollow waveguides,” Opt. Lett. 25(5), 335–337 (2000).
    [CrossRef]
  11. M. Weinstein, “Nonlinear Schrödinger Equations and Sharp Interpolation Estimates,” Commun. Math. Phys. 87(4), 567–576 (1983).
    [CrossRef]
  12. T. Lahaye, J. Metz, B. Fröhlich, T. Koch, M. Meister, A. Griesmaier, T. Pfau, H. Saito, Y. Kawaguchi, and M. Ueda, “d-wave collapse and explosion of a dipolar bose-einstein condensate,” Phys. Rev. Lett. 101(8), 080401 (2008).
    [CrossRef]
  13. T. Koch, T. Lahaye, J. Metz, B. Fröhlich, A. Griesmaier, and T. Pfau, “Stabilization of a purely dipolar quantum gas against collapse,” Nat. Phys. 4(3), 218–222 (2008).
    [CrossRef]
  14. P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15(26), 1005–1008 (1965).
    [CrossRef]
  15. L. Bergé, “Wave collapse in physics: principles and applications to light and plasma waves,” Phys. Rep. 303(5-6), 259–370 (1998).
    [CrossRef]
  16. T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, “Collapse and stability of necklace beams in Kerr media,” Phys. Rev. Lett. 99(13), 133902 (2007).
    [CrossRef]
  17. D. P. Lathrop, B. W. Zeff, B. Kleber, and J. Fineberg, “Singularity dynamics in curvature collapse and jet eruption on a fluid surface,” Nature 403(6768), 401–404 (2000).
    [CrossRef]
  18. P. A. Robinson, “Nonlinear wave collapse and strong turbulence,” Rev. Mod. Phys. 69(2), 507–574 (1997).
    [CrossRef]
  19. Y. R. Shen, “Recent advances in nonlinear optics,” Rev. Mod. Phys. 48(1), 1–32 (1976).
    [CrossRef]
  20. E. A. Kuznetsov, J. J. Rasmussen, K. Rypdal, and S. K. Turitsyn, “Shaper criteria for the wave collapse,” Physica D 87(1-4), 273–284 (1995).
    [CrossRef]
  21. Y. Silberberg, “Collapse of optical pulses,” Opt. Lett. 15(22), 1282–1284 (1990).
    [CrossRef]
  22. F. Wise and P. di Trapani, “The Hunt for Light Bullets – Spatiotemporal Solitons,” Opt. Photonics News 13(2), 29 (2002).
    [CrossRef]
  23. B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quant. Semicl. Opt. 7(5), R53–R72 (2005).
    [CrossRef]
  24. A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
    [CrossRef]
  25. Y. S. Kivshar and D. E. Pelinovsky, “Self-focusing and transverse instabilities of solitary waves,” Phys. Rep. 331(4), 117–195 (2000).
    [CrossRef]
  26. A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84(16), 3582–3585 (2000).
    [CrossRef]
  27. G. Fibich and G. C. Papanicolaou, “Self-focusing in the presence of small time dispersion and nonparaxiality,” Opt. Lett. 22(18), 1379–1381 (1997).
    [CrossRef]
  28. D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, “Strong spatiotemporal localization in a silica nonlinear waveguide array,” Phys. Rev. Lett. 91(22), 223901 (2003).
    [CrossRef]
  29. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Does the nonlinear Schrödinger equation correctly describe beam propagation?” Opt. Lett. 18(6), 411–413 (1993).
    [CrossRef]
  30. G. Fibich and B. Ilan, “Optical light bullets in a pure Kerr medium,” Opt. Lett. 29(8), 887–889 (2004).
    [CrossRef]
  31. O. Bang, J. J. Rasmussen, and P. L. Christiansen, “Subcritical localization in the discrete nonlinear Schrödinger equation with arbitrary power nonlinearity,” Nonlinearity 7(1), 205–218 (1994).
    [CrossRef]
  32. A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Two-dimensional soliton in cubic fs laser written waveguide arrays in fused silica,” Opt. Express 14(13), 6055–6062 (2006).
    [CrossRef]
  33. O. Bang, D. Edmundson, and W. Królikowski, “Collapse of incoherent light beams in inertial bulk Kerr media,” Phys. Rev. Lett. 83(26), 5479–5482 (1999).
    [CrossRef]
  34. A. S. Desyatnikov, D. Buccoliero, M. R. Dennis, and Y. S. Kivshar, “Suppression of collapse for spiraling elliptic solitons,” Phys. Rev. Lett. 104(5), 053902 (2010).
    [CrossRef]
  35. L. Bergé, O. Bang, J. J. Rasmussen, and V. K. Mezentsev, “Self-focusing and solitonlike structures in materials with competing quadratic and cubic nonlinearities,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 55(3), 3555–3570 (1997).
    [CrossRef]
  36. V. Skarka, V. I. Berezhiani, and R. Miklaszewski, “Spatiotemporal soliton propagation in saturating nonlinear optical media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 56(1), 1080–1087 (1997).
    [CrossRef]
  37. S. Gatz and J. Herrmann, “Propagation of optical beams and the properties of two-dimensional spatial solitons in media with a local saturable nonlinear refractive index,” J. Opt. Soc. Am. B 14(7), 1795 (1997).
    [CrossRef]
  38. O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046619 (2002).
    [CrossRef]
  39. M. Peccianti, K. A. Brzdkiewicz, and G. Assanto, “Nonlocal spatial soliton interactions in nematic liquid crystals,” Opt. Lett. 27(16), 1460–1462 (2002).
    [CrossRef]
  40. P. Pedri and L. Santos, “Two-dimensional bright solitons in dipolar Bose-Einstein condensates,” Phys. Rev. Lett. 95(20), 200404 (2005).
    [CrossRef]
  41. 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(3), 537 (2002).
    [CrossRef]
  42. F. Kh. Abdullaev, J. G. Caputo, R. A. Kraenkel, and B. A. Malomed, “Controlling collapse in Bose-Einstein condensation by temporal modulation of the scattering length,” Phys. Rev. A 67(1), 013605 (2003).
    [CrossRef]
  43. H. Saito and M. Ueda, “Dynamically stabilized bright solitons in a two-dimensional bose-einstein condensate,” Phys. Rev. Lett. 90(4), 040403 (2003).
    [CrossRef]
  44. S. Eisenmann, E. Louzon, Y. Katzir, T. Palchan, A. Zigler, Y. Sivan, and G. Fibich, “Control of the filamentation distance and pattern in long-range atmospheric propagation,” Opt. Express 15(6), 2779–2784 (2007).
    [CrossRef]
  45. J. Yang and Z. H. Musslimani, “Fundamental and vortex solitons in a two-dimensional optical lattice,” Opt. Lett. 28(21), 2094–2096 (2003).
    [CrossRef]
  46. C. R. Menyuk, “Stability of solitons in birefringent optical fibers. I: equal propagation amplitudes,” Opt. Lett. 12(8), 614–616 (1987).
    [CrossRef]
  47. S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Polarized soliton instability and branching in birefringent fibers,” Opt. Commun. 70(2), 166–172 (1989).
    [CrossRef]
  48. B. A. Malomed, “Polarization dynamics and interactions of solitons in a birefringent optical fiber,” Phys. Rev. A 43(1), 410–423 (1991).
    [CrossRef]
  49. Y. Barad and Y. Silberberg, “Polarization Evolution and Polarization Instability of Solitons in a Birefringent Optical Fiber,” Phys. Rev. Lett. 78(17), 3290–3293 (1997).
    [CrossRef]
  50. L. Bergé, O. Bang, and W. Królikowski, “Influence of four-wave mixing and walk-Off on the self-focusing of coupled waves,” Phys. Rev. Lett. 84(15), 3302–3305 (2000).
    [CrossRef]
  51. O. Bang, L. Bergé, and J. J. Rasmussen, “Fusion, collapse, and stationary bound states of incoherently coupled waves in bulk cubic media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 59(4), 4600–4613 (1999).
    [CrossRef]
  52. R. Kurzynowski and W. A. Wo?niak, “Superposition rule for the magneto-optic effects in isotropic media,” Optik (Stuttg.) 115(10), 473–475 (2004).
    [CrossRef]
  53. A. K. Zvezdin, and V. A. Kotov, Modern Magnetooptics and Magnetooptical Materials (Taylor & Francis Group, New York 1997).
  54. J. F. Dillon, J. P. Remeika, and C. R. Staton, “Linear Magnetic Birefringence in the Ferrimagnetic Garnets,” J. Appl. Phys. 41(11), 4613 (1970).
    [CrossRef]
  55. G. B. Scott, D. E. Lacklison, H. I. Ralph, and J. L. Page, “Magnetic circular dichroism and Faraday rotation spectra of Y3Fe5O12,” Phys. Rev. B 12(7), 2562 (1975).
    [CrossRef]
  56. G. A. Smolenskii, R. V. Pisarev, and I. G. Sinii, “Birefringence of light in magnetically ordered crystals,” Usp. Fiziol. Nauk 116, 231 (1975).
  57. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
    [CrossRef]
  58. R. J. Ballagh, K. Burnett, and T. F. Scott, “Theory of an Output Coupler for Bose-Einstein Condensated Atoms,” Phys. Rev. Lett. 78(9), 1607–1611 (1997).
    [CrossRef]
  59. B. A. Malomed, “Variational methods in nonlinear fiber optics and related fields,” Progr. Opt. 43, 71 (2002).
  60. M. Desaix, D. Anderson, and M. Lisak, “Variational approach to collapse of the optical pulses,” J. Opt. Soc. Am. B 8(10), 2082 (1991).
    [CrossRef]
  61. Y. Linzon, K. A. Rutkowska, B. A. Malomed, and R. Morandotti, “Magneto-optical control of light collapse in bulk Kerr media,” Phys. Rev. Lett. 103(5), 053902 (2009).
    [CrossRef]
  62. J.-M. Liu, Photonic Devices, Cambridge Univ. Press, New York 2005.
  63. O. Kamada, T. Nakaya, and S. Higuchi, “Magnetic field optical sensors using Ce:YIG single crystals as a Faraday element,” Sens. Actuators A Phys. 119(2), 345–348 (2005).
    [CrossRef]
  64. M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce: and Bi: co-modified epitaxial iron garnet thin films,” Appl. Phys. Lett. 94(18), 181916 (2009).
    [CrossRef]
  65. U. M. Ascher, Numerical methods for evolutionary differential equations (SIAM, Philadelphia 2008).
  66. J. C. Butcher, Numerical Methods for Ordinary Differential Equations (Wiley & Sons, West Sussex 2008).

2010 (2)

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[CrossRef]

A. S. Desyatnikov, D. Buccoliero, M. R. Dennis, and Y. S. Kivshar, “Suppression of collapse for spiraling elliptic solitons,” Phys. Rev. Lett. 104(5), 053902 (2010).
[CrossRef]

2009 (2)

Y. Linzon, K. A. Rutkowska, B. A. Malomed, and R. Morandotti, “Magneto-optical control of light collapse in bulk Kerr media,” Phys. Rev. Lett. 103(5), 053902 (2009).
[CrossRef]

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce: and Bi: co-modified epitaxial iron garnet thin films,” Appl. Phys. Lett. 94(18), 181916 (2009).
[CrossRef]

2008 (2)

T. Lahaye, J. Metz, B. Fröhlich, T. Koch, M. Meister, A. Griesmaier, T. Pfau, H. Saito, Y. Kawaguchi, and M. Ueda, “d-wave collapse and explosion of a dipolar bose-einstein condensate,” Phys. Rev. Lett. 101(8), 080401 (2008).
[CrossRef]

T. Koch, T. Lahaye, J. Metz, B. Fröhlich, A. Griesmaier, and T. Pfau, “Stabilization of a purely dipolar quantum gas against collapse,” Nat. Phys. 4(3), 218–222 (2008).
[CrossRef]

2007 (2)

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, “Collapse and stability of necklace beams in Kerr media,” Phys. Rev. Lett. 99(13), 133902 (2007).
[CrossRef]

S. Eisenmann, E. Louzon, Y. Katzir, T. Palchan, A. Zigler, Y. Sivan, and G. Fibich, “Control of the filamentation distance and pattern in long-range atmospheric propagation,” Opt. Express 15(6), 2779–2784 (2007).
[CrossRef]

2006 (2)

2005 (3)

O. Kamada, T. Nakaya, and S. Higuchi, “Magnetic field optical sensors using Ce:YIG single crystals as a Faraday element,” Sens. Actuators A Phys. 119(2), 345–348 (2005).
[CrossRef]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quant. Semicl. Opt. 7(5), R53–R72 (2005).
[CrossRef]

P. Pedri and L. Santos, “Two-dimensional bright solitons in dipolar Bose-Einstein condensates,” Phys. Rev. Lett. 95(20), 200404 (2005).
[CrossRef]

2004 (2)

R. Kurzynowski and W. A. Wo?niak, “Superposition rule for the magneto-optic effects in isotropic media,” Optik (Stuttg.) 115(10), 473–475 (2004).
[CrossRef]

G. Fibich and B. Ilan, “Optical light bullets in a pure Kerr medium,” Opt. Lett. 29(8), 887–889 (2004).
[CrossRef]

2003 (5)

J. Yang and Z. H. Musslimani, “Fundamental and vortex solitons in a two-dimensional optical lattice,” Opt. Lett. 28(21), 2094–2096 (2003).
[CrossRef]

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, “Strong spatiotemporal localization in a silica nonlinear waveguide array,” Phys. Rev. Lett. 91(22), 223901 (2003).
[CrossRef]

F. Kh. Abdullaev, J. G. Caputo, R. A. Kraenkel, and B. A. Malomed, “Controlling collapse in Bose-Einstein condensation by temporal modulation of the scattering length,” Phys. Rev. A 67(1), 013605 (2003).
[CrossRef]

H. Saito and M. Ueda, “Dynamically stabilized bright solitons in a two-dimensional bose-einstein condensate,” Phys. Rev. Lett. 90(4), 040403 (2003).
[CrossRef]

K. D. Moll, A. L. Gaeta, and G. Fibich, “Self-similar optical wave collapse: observation of the Townes profile,” Phys. Rev. Lett. 90(20), 203902 (2003).
[CrossRef]

2002 (5)

F. Wise and P. di Trapani, “The Hunt for Light Bullets – Spatiotemporal Solitons,” Opt. Photonics News 13(2), 29 (2002).
[CrossRef]

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046619 (2002).
[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(3), 537 (2002).
[CrossRef]

M. Peccianti, K. A. Brzdkiewicz, and G. Assanto, “Nonlocal spatial soliton interactions in nematic liquid crystals,” Opt. Lett. 27(16), 1460–1462 (2002).
[CrossRef]

B. A. Malomed, “Variational methods in nonlinear fiber optics and related fields,” Progr. Opt. 43, 71 (2002).

2000 (5)

G. Fibich and A. L. Gaeta, “Critical power for self-focusing in bulk media and in hollow waveguides,” Opt. Lett. 25(5), 335–337 (2000).
[CrossRef]

L. Bergé, O. Bang, and W. Królikowski, “Influence of four-wave mixing and walk-Off on the self-focusing of coupled waves,” Phys. Rev. Lett. 84(15), 3302–3305 (2000).
[CrossRef]

Y. S. Kivshar and D. E. Pelinovsky, “Self-focusing and transverse instabilities of solitary waves,” Phys. Rep. 331(4), 117–195 (2000).
[CrossRef]

A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84(16), 3582–3585 (2000).
[CrossRef]

D. P. Lathrop, B. W. Zeff, B. Kleber, and J. Fineberg, “Singularity dynamics in curvature collapse and jet eruption on a fluid surface,” Nature 403(6768), 401–404 (2000).
[CrossRef]

1999 (3)

G. I. Stegeman and M. Segev, “Optical Spatial Solitons and Their Interactions: Universality and Diversity,” Science 286(5444), 1518–1523 (1999).
[CrossRef]

O. Bang, L. Bergé, and J. J. Rasmussen, “Fusion, collapse, and stationary bound states of incoherently coupled waves in bulk cubic media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 59(4), 4600–4613 (1999).
[CrossRef]

O. Bang, D. Edmundson, and W. Królikowski, “Collapse of incoherent light beams in inertial bulk Kerr media,” Phys. Rev. Lett. 83(26), 5479–5482 (1999).
[CrossRef]

1998 (1)

L. Bergé, “Wave collapse in physics: principles and applications to light and plasma waves,” Phys. Rep. 303(5-6), 259–370 (1998).
[CrossRef]

1997 (7)

P. A. Robinson, “Nonlinear wave collapse and strong turbulence,” Rev. Mod. Phys. 69(2), 507–574 (1997).
[CrossRef]

L. Bergé, O. Bang, J. J. Rasmussen, and V. K. Mezentsev, “Self-focusing and solitonlike structures in materials with competing quadratic and cubic nonlinearities,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 55(3), 3555–3570 (1997).
[CrossRef]

V. Skarka, V. I. Berezhiani, and R. Miklaszewski, “Spatiotemporal soliton propagation in saturating nonlinear optical media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 56(1), 1080–1087 (1997).
[CrossRef]

S. Gatz and J. Herrmann, “Propagation of optical beams and the properties of two-dimensional spatial solitons in media with a local saturable nonlinear refractive index,” J. Opt. Soc. Am. B 14(7), 1795 (1997).
[CrossRef]

G. Fibich and G. C. Papanicolaou, “Self-focusing in the presence of small time dispersion and nonparaxiality,” Opt. Lett. 22(18), 1379–1381 (1997).
[CrossRef]

Y. Barad and Y. Silberberg, “Polarization Evolution and Polarization Instability of Solitons in a Birefringent Optical Fiber,” Phys. Rev. Lett. 78(17), 3290–3293 (1997).
[CrossRef]

R. J. Ballagh, K. Burnett, and T. F. Scott, “Theory of an Output Coupler for Bose-Einstein Condensated Atoms,” Phys. Rev. Lett. 78(9), 1607–1611 (1997).
[CrossRef]

1995 (1)

E. A. Kuznetsov, J. J. Rasmussen, K. Rypdal, and S. K. Turitsyn, “Shaper criteria for the wave collapse,” Physica D 87(1-4), 273–284 (1995).
[CrossRef]

1994 (1)

O. Bang, J. J. Rasmussen, and P. L. Christiansen, “Subcritical localization in the discrete nonlinear Schrödinger equation with arbitrary power nonlinearity,” Nonlinearity 7(1), 205–218 (1994).
[CrossRef]

1993 (1)

1991 (2)

M. Desaix, D. Anderson, and M. Lisak, “Variational approach to collapse of the optical pulses,” J. Opt. Soc. Am. B 8(10), 2082 (1991).
[CrossRef]

B. A. Malomed, “Polarization dynamics and interactions of solitons in a birefringent optical fiber,” Phys. Rev. A 43(1), 410–423 (1991).
[CrossRef]

1990 (1)

1989 (1)

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Polarized soliton instability and branching in birefringent fibers,” Opt. Commun. 70(2), 166–172 (1989).
[CrossRef]

1987 (1)

1983 (1)

M. Weinstein, “Nonlinear Schrödinger Equations and Sharp Interpolation Estimates,” Commun. Math. Phys. 87(4), 567–576 (1983).
[CrossRef]

1976 (1)

Y. R. Shen, “Recent advances in nonlinear optics,” Rev. Mod. Phys. 48(1), 1–32 (1976).
[CrossRef]

1975 (2)

G. B. Scott, D. E. Lacklison, H. I. Ralph, and J. L. Page, “Magnetic circular dichroism and Faraday rotation spectra of Y3Fe5O12,” Phys. Rev. B 12(7), 2562 (1975).
[CrossRef]

G. A. Smolenskii, R. V. Pisarev, and I. G. Sinii, “Birefringence of light in magnetically ordered crystals,” Usp. Fiziol. Nauk 116, 231 (1975).

1970 (1)

J. F. Dillon, J. P. Remeika, and C. R. Staton, “Linear Magnetic Birefringence in the Ferrimagnetic Garnets,” J. Appl. Phys. 41(11), 4613 (1970).
[CrossRef]

1965 (1)

P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15(26), 1005–1008 (1965).
[CrossRef]

1964 (1)

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-Trapping of Optical Beams,” Phys. Rev. Lett. 13(15), 479–482 (1964).
[CrossRef]

Abdullaev, F. Kh.

F. Kh. Abdullaev, J. G. Caputo, R. A. Kraenkel, and B. A. Malomed, “Controlling collapse in Bose-Einstein condensation by temporal modulation of the scattering length,” Phys. Rev. A 67(1), 013605 (2003).
[CrossRef]

Aitchison, J. S.

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, “Strong spatiotemporal localization in a silica nonlinear waveguide array,” Phys. Rev. Lett. 91(22), 223901 (2003).
[CrossRef]

Akhmediev, N.

Anderson, D.

Ankiewicz, A.

Assanto, G.

Ballagh, R. J.

R. J. Ballagh, K. Burnett, and T. F. Scott, “Theory of an Output Coupler for Bose-Einstein Condensated Atoms,” Phys. Rev. Lett. 78(9), 1607–1611 (1997).
[CrossRef]

Bang, O.

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046619 (2002).
[CrossRef]

L. Bergé, O. Bang, and W. Królikowski, “Influence of four-wave mixing and walk-Off on the self-focusing of coupled waves,” Phys. Rev. Lett. 84(15), 3302–3305 (2000).
[CrossRef]

O. Bang, L. Bergé, and J. J. Rasmussen, “Fusion, collapse, and stationary bound states of incoherently coupled waves in bulk cubic media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 59(4), 4600–4613 (1999).
[CrossRef]

O. Bang, D. Edmundson, and W. Królikowski, “Collapse of incoherent light beams in inertial bulk Kerr media,” Phys. Rev. Lett. 83(26), 5479–5482 (1999).
[CrossRef]

L. Bergé, O. Bang, J. J. Rasmussen, and V. K. Mezentsev, “Self-focusing and solitonlike structures in materials with competing quadratic and cubic nonlinearities,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 55(3), 3555–3570 (1997).
[CrossRef]

O. Bang, J. J. Rasmussen, and P. L. Christiansen, “Subcritical localization in the discrete nonlinear Schrödinger equation with arbitrary power nonlinearity,” Nonlinearity 7(1), 205–218 (1994).
[CrossRef]

Barad, Y.

Y. Barad and Y. Silberberg, “Polarization Evolution and Polarization Instability of Solitons in a Birefringent Optical Fiber,” Phys. Rev. Lett. 78(17), 3290–3293 (1997).
[CrossRef]

Bar-Ad, S.

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, “Strong spatiotemporal localization in a silica nonlinear waveguide array,” Phys. Rev. Lett. 91(22), 223901 (2003).
[CrossRef]

Berezhiani, V. I.

V. Skarka, V. I. Berezhiani, and R. Miklaszewski, “Spatiotemporal soliton propagation in saturating nonlinear optical media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 56(1), 1080–1087 (1997).
[CrossRef]

Bergé, L.

L. Bergé, O. Bang, and W. Królikowski, “Influence of four-wave mixing and walk-Off on the self-focusing of coupled waves,” Phys. Rev. Lett. 84(15), 3302–3305 (2000).
[CrossRef]

O. Bang, L. Bergé, and J. J. Rasmussen, “Fusion, collapse, and stationary bound states of incoherently coupled waves in bulk cubic media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 59(4), 4600–4613 (1999).
[CrossRef]

L. Bergé, “Wave collapse in physics: principles and applications to light and plasma waves,” Phys. Rep. 303(5-6), 259–370 (1998).
[CrossRef]

L. Bergé, O. Bang, J. J. Rasmussen, and V. K. Mezentsev, “Self-focusing and solitonlike structures in materials with competing quadratic and cubic nonlinearities,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 55(3), 3555–3570 (1997).
[CrossRef]

Brzdkiewicz, K. A.

Buccoliero, D.

A. S. Desyatnikov, D. Buccoliero, M. R. Dennis, and Y. S. Kivshar, “Suppression of collapse for spiraling elliptic solitons,” Phys. Rev. Lett. 104(5), 053902 (2010).
[CrossRef]

Burghoff, J.

Burnett, K.

R. J. Ballagh, K. Burnett, and T. F. Scott, “Theory of an Output Coupler for Bose-Einstein Condensated Atoms,” Phys. Rev. Lett. 78(9), 1607–1611 (1997).
[CrossRef]

Caputo, J. G.

F. Kh. Abdullaev, J. G. Caputo, R. A. Kraenkel, and B. A. Malomed, “Controlling collapse in Bose-Einstein condensation by temporal modulation of the scattering length,” Phys. Rev. A 67(1), 013605 (2003).
[CrossRef]

Cheskis, D.

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, “Strong spatiotemporal localization in a silica nonlinear waveguide array,” Phys. Rev. Lett. 91(22), 223901 (2003).
[CrossRef]

Chiao, R. Y.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-Trapping of Optical Beams,” Phys. Rev. Lett. 13(15), 479–482 (1964).
[CrossRef]

Chong, A.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[CrossRef]

Christiansen, P. L.

O. Bang, J. J. Rasmussen, and P. L. Christiansen, “Subcritical localization in the discrete nonlinear Schrödinger equation with arbitrary power nonlinearity,” Nonlinearity 7(1), 205–218 (1994).
[CrossRef]

Christodoulides, D. N.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[CrossRef]

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

Dennis, M. R.

A. S. Desyatnikov, D. Buccoliero, M. R. Dennis, and Y. S. Kivshar, “Suppression of collapse for spiraling elliptic solitons,” Phys. Rev. Lett. 104(5), 053902 (2010).
[CrossRef]

Desaix, M.

Desyatnikov, A. S.

A. S. Desyatnikov, D. Buccoliero, M. R. Dennis, and Y. S. Kivshar, “Suppression of collapse for spiraling elliptic solitons,” Phys. Rev. Lett. 104(5), 053902 (2010).
[CrossRef]

di Trapani, P.

F. Wise and P. di Trapani, “The Hunt for Light Bullets – Spatiotemporal Solitons,” Opt. Photonics News 13(2), 29 (2002).
[CrossRef]

Dillon, J. F.

J. F. Dillon, J. P. Remeika, and C. R. Staton, “Linear Magnetic Birefringence in the Ferrimagnetic Garnets,” J. Appl. Phys. 41(11), 4613 (1970).
[CrossRef]

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

Edmundson, D.

O. Bang, D. Edmundson, and W. Królikowski, “Collapse of incoherent light beams in inertial bulk Kerr media,” Phys. Rev. Lett. 83(26), 5479–5482 (1999).
[CrossRef]

Eisenberg, H. S.

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, “Strong spatiotemporal localization in a silica nonlinear waveguide array,” Phys. Rev. Lett. 91(22), 223901 (2003).
[CrossRef]

Eisenmann, S.

Ferrera, M.

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce: and Bi: co-modified epitaxial iron garnet thin films,” Appl. Phys. Lett. 94(18), 181916 (2009).
[CrossRef]

Fibich, G.

Fineberg, J.

D. P. Lathrop, B. W. Zeff, B. Kleber, and J. Fineberg, “Singularity dynamics in curvature collapse and jet eruption on a fluid surface,” Nature 403(6768), 401–404 (2000).
[CrossRef]

Fröhlich, B.

T. Koch, T. Lahaye, J. Metz, B. Fröhlich, A. Griesmaier, and T. Pfau, “Stabilization of a purely dipolar quantum gas against collapse,” Nat. Phys. 4(3), 218–222 (2008).
[CrossRef]

T. Lahaye, J. Metz, B. Fröhlich, T. Koch, M. Meister, A. Griesmaier, T. Pfau, H. Saito, Y. Kawaguchi, and M. Ueda, “d-wave collapse and explosion of a dipolar bose-einstein condensate,” Phys. Rev. Lett. 101(8), 080401 (2008).
[CrossRef]

Gaeta, A. L.

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, “Collapse and stability of necklace beams in Kerr media,” Phys. Rev. Lett. 99(13), 133902 (2007).
[CrossRef]

K. D. Moll, A. L. Gaeta, and G. Fibich, “Self-similar optical wave collapse: observation of the Townes profile,” Phys. Rev. Lett. 90(20), 203902 (2003).
[CrossRef]

G. Fibich and A. L. Gaeta, “Critical power for self-focusing in bulk media and in hollow waveguides,” Opt. Lett. 25(5), 335–337 (2000).
[CrossRef]

A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84(16), 3582–3585 (2000).
[CrossRef]

Garmire, E.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-Trapping of Optical Beams,” Phys. Rev. Lett. 13(15), 479–482 (1964).
[CrossRef]

Gatz, S.

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

Griesmaier, A.

T. Koch, T. Lahaye, J. Metz, B. Fröhlich, A. Griesmaier, and T. Pfau, “Stabilization of a purely dipolar quantum gas against collapse,” Nat. Phys. 4(3), 218–222 (2008).
[CrossRef]

T. Lahaye, J. Metz, B. Fröhlich, T. Koch, M. Meister, A. Griesmaier, T. Pfau, H. Saito, Y. Kawaguchi, and M. Ueda, “d-wave collapse and explosion of a dipolar bose-einstein condensate,” Phys. Rev. Lett. 101(8), 080401 (2008).
[CrossRef]

Grow, T. D.

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, “Collapse and stability of necklace beams in Kerr media,” Phys. Rev. Lett. 99(13), 133902 (2007).
[CrossRef]

Harnagea, C.

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce: and Bi: co-modified epitaxial iron garnet thin films,” Appl. Phys. Lett. 94(18), 181916 (2009).
[CrossRef]

Herrmann, J.

Higuchi, S.

O. Kamada, T. Nakaya, and S. Higuchi, “Magnetic field optical sensors using Ce:YIG single crystals as a Faraday element,” Sens. Actuators A Phys. 119(2), 345–348 (2005).
[CrossRef]

Hwang, J.-Y.

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce: and Bi: co-modified epitaxial iron garnet thin films,” Appl. Phys. Lett. 94(18), 181916 (2009).
[CrossRef]

Ilan, B.

Ishaaya, A. A.

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, “Collapse and stability of necklace beams in Kerr media,” Phys. Rev. Lett. 99(13), 133902 (2007).
[CrossRef]

Kamada, O.

O. Kamada, T. Nakaya, and S. Higuchi, “Magnetic field optical sensors using Ce:YIG single crystals as a Faraday element,” Sens. Actuators A Phys. 119(2), 345–348 (2005).
[CrossRef]

Katzir, Y.

Kawaguchi, Y.

T. Lahaye, J. Metz, B. Fröhlich, T. Koch, M. Meister, A. Griesmaier, T. Pfau, H. Saito, Y. Kawaguchi, and M. Ueda, “d-wave collapse and explosion of a dipolar bose-einstein condensate,” Phys. Rev. Lett. 101(8), 080401 (2008).
[CrossRef]

Kelley, P. L.

P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15(26), 1005–1008 (1965).
[CrossRef]

Kivshar, Y. S.

A. S. Desyatnikov, D. Buccoliero, M. R. Dennis, and Y. S. Kivshar, “Suppression of collapse for spiraling elliptic solitons,” Phys. Rev. Lett. 104(5), 053902 (2010).
[CrossRef]

Y. S. Kivshar and D. E. Pelinovsky, “Self-focusing and transverse instabilities of solitary waves,” Phys. Rep. 331(4), 117–195 (2000).
[CrossRef]

Kleber, B.

D. P. Lathrop, B. W. Zeff, B. Kleber, and J. Fineberg, “Singularity dynamics in curvature collapse and jet eruption on a fluid surface,” Nature 403(6768), 401–404 (2000).
[CrossRef]

Koch, T.

T. Koch, T. Lahaye, J. Metz, B. Fröhlich, A. Griesmaier, and T. Pfau, “Stabilization of a purely dipolar quantum gas against collapse,” Nat. Phys. 4(3), 218–222 (2008).
[CrossRef]

T. Lahaye, J. Metz, B. Fröhlich, T. Koch, M. Meister, A. Griesmaier, T. Pfau, H. Saito, Y. Kawaguchi, and M. Ueda, “d-wave collapse and explosion of a dipolar bose-einstein condensate,” Phys. Rev. Lett. 101(8), 080401 (2008).
[CrossRef]

Kraenkel, R. A.

F. Kh. Abdullaev, J. G. Caputo, R. A. Kraenkel, and B. A. Malomed, “Controlling collapse in Bose-Einstein condensation by temporal modulation of the scattering length,” Phys. Rev. A 67(1), 013605 (2003).
[CrossRef]

Krolikowski, W.

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046619 (2002).
[CrossRef]

Królikowski, W.

L. Bergé, O. Bang, and W. Królikowski, “Influence of four-wave mixing and walk-Off on the self-focusing of coupled waves,” Phys. Rev. Lett. 84(15), 3302–3305 (2000).
[CrossRef]

O. Bang, D. Edmundson, and W. Królikowski, “Collapse of incoherent light beams in inertial bulk Kerr media,” Phys. Rev. Lett. 83(26), 5479–5482 (1999).
[CrossRef]

Kurzynowski, R.

R. Kurzynowski and W. A. Wo?niak, “Superposition rule for the magneto-optic effects in isotropic media,” Optik (Stuttg.) 115(10), 473–475 (2004).
[CrossRef]

Kuznetsov, E. A.

E. A. Kuznetsov, J. J. Rasmussen, K. Rypdal, and S. K. Turitsyn, “Shaper criteria for the wave collapse,” Physica D 87(1-4), 273–284 (1995).
[CrossRef]

Lacklison, D. E.

G. B. Scott, D. E. Lacklison, H. I. Ralph, and J. L. Page, “Magnetic circular dichroism and Faraday rotation spectra of Y3Fe5O12,” Phys. Rev. B 12(7), 2562 (1975).
[CrossRef]

Lahaye, T.

T. Lahaye, J. Metz, B. Fröhlich, T. Koch, M. Meister, A. Griesmaier, T. Pfau, H. Saito, Y. Kawaguchi, and M. Ueda, “d-wave collapse and explosion of a dipolar bose-einstein condensate,” Phys. Rev. Lett. 101(8), 080401 (2008).
[CrossRef]

T. Koch, T. Lahaye, J. Metz, B. Fröhlich, A. Griesmaier, and T. Pfau, “Stabilization of a purely dipolar quantum gas against collapse,” Nat. Phys. 4(3), 218–222 (2008).
[CrossRef]

Lathrop, D. P.

D. P. Lathrop, B. W. Zeff, B. Kleber, and J. Fineberg, “Singularity dynamics in curvature collapse and jet eruption on a fluid surface,” Nature 403(6768), 401–404 (2000).
[CrossRef]

Lederer, F.

Linzon, Y.

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce: and Bi: co-modified epitaxial iron garnet thin films,” Appl. Phys. Lett. 94(18), 181916 (2009).
[CrossRef]

Y. Linzon, K. A. Rutkowska, B. A. Malomed, and R. Morandotti, “Magneto-optical control of light collapse in bulk Kerr media,” Phys. Rev. Lett. 103(5), 053902 (2009).
[CrossRef]

Lisak, M.

Louzon, E.

Malomed, B. A.

Y. Linzon, K. A. Rutkowska, B. A. Malomed, and R. Morandotti, “Magneto-optical control of light collapse in bulk Kerr media,” Phys. Rev. Lett. 103(5), 053902 (2009).
[CrossRef]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quant. Semicl. Opt. 7(5), R53–R72 (2005).
[CrossRef]

F. Kh. Abdullaev, J. G. Caputo, R. A. Kraenkel, and B. A. Malomed, “Controlling collapse in Bose-Einstein condensation by temporal modulation of the scattering length,” Phys. Rev. A 67(1), 013605 (2003).
[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(3), 537 (2002).
[CrossRef]

B. A. Malomed, “Variational methods in nonlinear fiber optics and related fields,” Progr. Opt. 43, 71 (2002).

B. A. Malomed, “Polarization dynamics and interactions of solitons in a birefringent optical fiber,” Phys. Rev. A 43(1), 410–423 (1991).
[CrossRef]

Meister, M.

T. Lahaye, J. Metz, B. Fröhlich, T. Koch, M. Meister, A. Griesmaier, T. Pfau, H. Saito, Y. Kawaguchi, and M. Ueda, “d-wave collapse and explosion of a dipolar bose-einstein condensate,” Phys. Rev. Lett. 101(8), 080401 (2008).
[CrossRef]

Menyuk, C. R.

Metz, J.

T. Lahaye, J. Metz, B. Fröhlich, T. Koch, M. Meister, A. Griesmaier, T. Pfau, H. Saito, Y. Kawaguchi, and M. Ueda, “d-wave collapse and explosion of a dipolar bose-einstein condensate,” Phys. Rev. Lett. 101(8), 080401 (2008).
[CrossRef]

T. Koch, T. Lahaye, J. Metz, B. Fröhlich, A. Griesmaier, and T. Pfau, “Stabilization of a purely dipolar quantum gas against collapse,” Nat. Phys. 4(3), 218–222 (2008).
[CrossRef]

Mezentsev, V. K.

L. Bergé, O. Bang, J. J. Rasmussen, and V. K. Mezentsev, “Self-focusing and solitonlike structures in materials with competing quadratic and cubic nonlinearities,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 55(3), 3555–3570 (1997).
[CrossRef]

Mihalache, D.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quant. Semicl. Opt. 7(5), R53–R72 (2005).
[CrossRef]

Miklaszewski, R.

V. Skarka, V. I. Berezhiani, and R. Miklaszewski, “Spatiotemporal soliton propagation in saturating nonlinear optical media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 56(1), 1080–1087 (1997).
[CrossRef]

Moll, K. D.

K. D. Moll, A. L. Gaeta, and G. Fibich, “Self-similar optical wave collapse: observation of the Townes profile,” Phys. Rev. Lett. 90(20), 203902 (2003).
[CrossRef]

Morandotti, R.

Y. Linzon, K. A. Rutkowska, B. A. Malomed, and R. Morandotti, “Magneto-optical control of light collapse in bulk Kerr media,” Phys. Rev. Lett. 103(5), 053902 (2009).
[CrossRef]

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce: and Bi: co-modified epitaxial iron garnet thin films,” Appl. Phys. Lett. 94(18), 181916 (2009).
[CrossRef]

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, “Strong spatiotemporal localization in a silica nonlinear waveguide array,” Phys. Rev. Lett. 91(22), 223901 (2003).
[CrossRef]

Musslimani, Z. H.

Nakaya, T.

O. Kamada, T. Nakaya, and S. Higuchi, “Magnetic field optical sensors using Ce:YIG single crystals as a Faraday element,” Sens. Actuators A Phys. 119(2), 345–348 (2005).
[CrossRef]

Nolte, S.

Page, J. L.

G. B. Scott, D. E. Lacklison, H. I. Ralph, and J. L. Page, “Magnetic circular dichroism and Faraday rotation spectra of Y3Fe5O12,” Phys. Rev. B 12(7), 2562 (1975).
[CrossRef]

Palchan, T.

Papanicolaou, G. C.

Peccianti, M.

Pedri, P.

P. Pedri and L. Santos, “Two-dimensional bright solitons in dipolar Bose-Einstein condensates,” Phys. Rev. Lett. 95(20), 200404 (2005).
[CrossRef]

Pelinovsky, D. E.

Y. S. Kivshar and D. E. Pelinovsky, “Self-focusing and transverse instabilities of solitary waves,” Phys. Rep. 331(4), 117–195 (2000).
[CrossRef]

Pertsch, T.

Pfau, T.

T. Koch, T. Lahaye, J. Metz, B. Fröhlich, A. Griesmaier, and T. Pfau, “Stabilization of a purely dipolar quantum gas against collapse,” Nat. Phys. 4(3), 218–222 (2008).
[CrossRef]

T. Lahaye, J. Metz, B. Fröhlich, T. Koch, M. Meister, A. Griesmaier, T. Pfau, H. Saito, Y. Kawaguchi, and M. Ueda, “d-wave collapse and explosion of a dipolar bose-einstein condensate,” Phys. Rev. Lett. 101(8), 080401 (2008).
[CrossRef]

Pignolet, A.

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce: and Bi: co-modified epitaxial iron garnet thin films,” Appl. Phys. Lett. 94(18), 181916 (2009).
[CrossRef]

Pisarev, R. V.

G. A. Smolenskii, R. V. Pisarev, and I. G. Sinii, “Birefringence of light in magnetically ordered crystals,” Usp. Fiziol. Nauk 116, 231 (1975).

Ralph, H. I.

G. B. Scott, D. E. Lacklison, H. I. Ralph, and J. L. Page, “Magnetic circular dichroism and Faraday rotation spectra of Y3Fe5O12,” Phys. Rev. B 12(7), 2562 (1975).
[CrossRef]

Rasmussen, J. J.

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046619 (2002).
[CrossRef]

O. Bang, L. Bergé, and J. J. Rasmussen, “Fusion, collapse, and stationary bound states of incoherently coupled waves in bulk cubic media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 59(4), 4600–4613 (1999).
[CrossRef]

L. Bergé, O. Bang, J. J. Rasmussen, and V. K. Mezentsev, “Self-focusing and solitonlike structures in materials with competing quadratic and cubic nonlinearities,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 55(3), 3555–3570 (1997).
[CrossRef]

E. A. Kuznetsov, J. J. Rasmussen, K. Rypdal, and S. K. Turitsyn, “Shaper criteria for the wave collapse,” Physica D 87(1-4), 273–284 (1995).
[CrossRef]

O. Bang, J. J. Rasmussen, and P. L. Christiansen, “Subcritical localization in the discrete nonlinear Schrödinger equation with arbitrary power nonlinearity,” Nonlinearity 7(1), 205–218 (1994).
[CrossRef]

Razzari, L.

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce: and Bi: co-modified epitaxial iron garnet thin films,” Appl. Phys. Lett. 94(18), 181916 (2009).
[CrossRef]

Remeika, J. P.

J. F. Dillon, J. P. Remeika, and C. R. Staton, “Linear Magnetic Birefringence in the Ferrimagnetic Garnets,” J. Appl. Phys. 41(11), 4613 (1970).
[CrossRef]

Renninger, W. H.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[CrossRef]

Robinson, P. A.

P. A. Robinson, “Nonlinear wave collapse and strong turbulence,” Rev. Mod. Phys. 69(2), 507–574 (1997).
[CrossRef]

Ross, D.

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, “Strong spatiotemporal localization in a silica nonlinear waveguide array,” Phys. Rev. Lett. 91(22), 223901 (2003).
[CrossRef]

Rutkowska, K. A.

Y. Linzon, K. A. Rutkowska, B. A. Malomed, and R. Morandotti, “Magneto-optical control of light collapse in bulk Kerr media,” Phys. Rev. Lett. 103(5), 053902 (2009).
[CrossRef]

Rypdal, K.

E. A. Kuznetsov, J. J. Rasmussen, K. Rypdal, and S. K. Turitsyn, “Shaper criteria for the wave collapse,” Physica D 87(1-4), 273–284 (1995).
[CrossRef]

Saito, H.

T. Lahaye, J. Metz, B. Fröhlich, T. Koch, M. Meister, A. Griesmaier, T. Pfau, H. Saito, Y. Kawaguchi, and M. Ueda, “d-wave collapse and explosion of a dipolar bose-einstein condensate,” Phys. Rev. Lett. 101(8), 080401 (2008).
[CrossRef]

H. Saito and M. Ueda, “Dynamically stabilized bright solitons in a two-dimensional bose-einstein condensate,” Phys. Rev. Lett. 90(4), 040403 (2003).
[CrossRef]

Santos, L.

P. Pedri and L. Santos, “Two-dimensional bright solitons in dipolar Bose-Einstein condensates,” Phys. Rev. Lett. 95(20), 200404 (2005).
[CrossRef]

Scott, G. B.

G. B. Scott, D. E. Lacklison, H. I. Ralph, and J. L. Page, “Magnetic circular dichroism and Faraday rotation spectra of Y3Fe5O12,” Phys. Rev. B 12(7), 2562 (1975).
[CrossRef]

Scott, T. F.

R. J. Ballagh, K. Burnett, and T. F. Scott, “Theory of an Output Coupler for Bose-Einstein Condensated Atoms,” Phys. Rev. Lett. 78(9), 1607–1611 (1997).
[CrossRef]

Segev, M.

G. I. Stegeman and M. Segev, “Optical Spatial Solitons and Their Interactions: Universality and Diversity,” Science 286(5444), 1518–1523 (1999).
[CrossRef]

Sekhar, M. C.

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce: and Bi: co-modified epitaxial iron garnet thin films,” Appl. Phys. Lett. 94(18), 181916 (2009).
[CrossRef]

Shen, Y. R.

Y. R. Shen, “Recent advances in nonlinear optics,” Rev. Mod. Phys. 48(1), 1–32 (1976).
[CrossRef]

Silberberg, Y.

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, “Strong spatiotemporal localization in a silica nonlinear waveguide array,” Phys. Rev. Lett. 91(22), 223901 (2003).
[CrossRef]

Y. Barad and Y. Silberberg, “Polarization Evolution and Polarization Instability of Solitons in a Birefringent Optical Fiber,” Phys. Rev. Lett. 78(17), 3290–3293 (1997).
[CrossRef]

Y. Silberberg, “Collapse of optical pulses,” Opt. Lett. 15(22), 1282–1284 (1990).
[CrossRef]

Sinii, I. G.

G. A. Smolenskii, R. V. Pisarev, and I. G. Sinii, “Birefringence of light in magnetically ordered crystals,” Usp. Fiziol. Nauk 116, 231 (1975).

Sivan, Y.

Skarka, V.

V. Skarka, V. I. Berezhiani, and R. Miklaszewski, “Spatiotemporal soliton propagation in saturating nonlinear optical media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 56(1), 1080–1087 (1997).
[CrossRef]

Smolenskii, G. A.

G. A. Smolenskii, R. V. Pisarev, and I. G. Sinii, “Birefringence of light in magnetically ordered crystals,” Usp. Fiziol. Nauk 116, 231 (1975).

Soto-Crespo, J. M.

Staton, C. R.

J. F. Dillon, J. P. Remeika, and C. R. Staton, “Linear Magnetic Birefringence in the Ferrimagnetic Garnets,” J. Appl. Phys. 41(11), 4613 (1970).
[CrossRef]

Stegeman, G. I.

G. I. Stegeman and M. Segev, “Optical Spatial Solitons and Their Interactions: Universality and Diversity,” Science 286(5444), 1518–1523 (1999).
[CrossRef]

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Polarized soliton instability and branching in birefringent fibers,” Opt. Commun. 70(2), 166–172 (1989).
[CrossRef]

Szameit, A.

Torner, L.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quant. Semicl. Opt. 7(5), R53–R72 (2005).
[CrossRef]

Towers, I.

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(3), 537 (2002).
[CrossRef]

Townes, C. H.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-Trapping of Optical Beams,” Phys. Rev. Lett. 13(15), 479–482 (1964).
[CrossRef]

Trillo, S.

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Polarized soliton instability and branching in birefringent fibers,” Opt. Commun. 70(2), 166–172 (1989).
[CrossRef]

Tünnermann, A.

Turitsyn, S. K.

E. A. Kuznetsov, J. J. Rasmussen, K. Rypdal, and S. K. Turitsyn, “Shaper criteria for the wave collapse,” Physica D 87(1-4), 273–284 (1995).
[CrossRef]

Ueda, M.

T. Lahaye, J. Metz, B. Fröhlich, T. Koch, M. Meister, A. Griesmaier, T. Pfau, H. Saito, Y. Kawaguchi, and M. Ueda, “d-wave collapse and explosion of a dipolar bose-einstein condensate,” Phys. Rev. Lett. 101(8), 080401 (2008).
[CrossRef]

H. Saito and M. Ueda, “Dynamically stabilized bright solitons in a two-dimensional bose-einstein condensate,” Phys. Rev. Lett. 90(4), 040403 (2003).
[CrossRef]

Vuong, L. T.

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, “Collapse and stability of necklace beams in Kerr media,” Phys. Rev. Lett. 99(13), 133902 (2007).
[CrossRef]

Wabnitz, S.

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Polarized soliton instability and branching in birefringent fibers,” Opt. Commun. 70(2), 166–172 (1989).
[CrossRef]

Weinstein, M.

M. Weinstein, “Nonlinear Schrödinger Equations and Sharp Interpolation Estimates,” Commun. Math. Phys. 87(4), 567–576 (1983).
[CrossRef]

Wise, F.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quant. Semicl. Opt. 7(5), R53–R72 (2005).
[CrossRef]

F. Wise and P. di Trapani, “The Hunt for Light Bullets – Spatiotemporal Solitons,” Opt. Photonics News 13(2), 29 (2002).
[CrossRef]

Wise, F. W.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[CrossRef]

Wozniak, W. A.

R. Kurzynowski and W. A. Wo?niak, “Superposition rule for the magneto-optic effects in isotropic media,” Optik (Stuttg.) 115(10), 473–475 (2004).
[CrossRef]

Wright, E. M.

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Polarized soliton instability and branching in birefringent fibers,” Opt. Commun. 70(2), 166–172 (1989).
[CrossRef]

Wyller, J.

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046619 (2002).
[CrossRef]

Yang, J.

Zaezjev, M.

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce: and Bi: co-modified epitaxial iron garnet thin films,” Appl. Phys. Lett. 94(18), 181916 (2009).
[CrossRef]

Zeff, B. W.

D. P. Lathrop, B. W. Zeff, B. Kleber, and J. Fineberg, “Singularity dynamics in curvature collapse and jet eruption on a fluid surface,” Nature 403(6768), 401–404 (2000).
[CrossRef]

Zigler, A.

Appl. Phys. Lett. (1)

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce: and Bi: co-modified epitaxial iron garnet thin films,” Appl. Phys. Lett. 94(18), 181916 (2009).
[CrossRef]

Commun. Math. Phys. (1)

M. Weinstein, “Nonlinear Schrödinger Equations and Sharp Interpolation Estimates,” Commun. Math. Phys. 87(4), 567–576 (1983).
[CrossRef]

J. Appl. Phys. (1)

J. F. Dillon, J. P. Remeika, and C. R. Staton, “Linear Magnetic Birefringence in the Ferrimagnetic Garnets,” J. Appl. Phys. 41(11), 4613 (1970).
[CrossRef]

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

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(3), 537 (2002).
[CrossRef]

J. Opt. B: Quant. Semicl. Opt. (1)

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quant. Semicl. Opt. 7(5), R53–R72 (2005).
[CrossRef]

J. Opt. Soc. Am. B (2)

Nat. Photonics (1)

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[CrossRef]

Nat. Phys. (1)

T. Koch, T. Lahaye, J. Metz, B. Fröhlich, A. Griesmaier, and T. Pfau, “Stabilization of a purely dipolar quantum gas against collapse,” Nat. Phys. 4(3), 218–222 (2008).
[CrossRef]

Nature (1)

D. P. Lathrop, B. W. Zeff, B. Kleber, and J. Fineberg, “Singularity dynamics in curvature collapse and jet eruption on a fluid surface,” Nature 403(6768), 401–404 (2000).
[CrossRef]

Nonlinearity (1)

O. Bang, J. J. Rasmussen, and P. L. Christiansen, “Subcritical localization in the discrete nonlinear Schrödinger equation with arbitrary power nonlinearity,” Nonlinearity 7(1), 205–218 (1994).
[CrossRef]

Opt. Commun. (1)

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Polarized soliton instability and branching in birefringent fibers,” Opt. Commun. 70(2), 166–172 (1989).
[CrossRef]

Opt. Express (2)

Opt. Lett. (8)

Opt. Photonics News (1)

F. Wise and P. di Trapani, “The Hunt for Light Bullets – Spatiotemporal Solitons,” Opt. Photonics News 13(2), 29 (2002).
[CrossRef]

Optik (Stuttg.) (1)

R. Kurzynowski and W. A. Wo?niak, “Superposition rule for the magneto-optic effects in isotropic media,” Optik (Stuttg.) 115(10), 473–475 (2004).
[CrossRef]

Phys. Rev. A (1)

F. Kh. Abdullaev, J. G. Caputo, R. A. Kraenkel, and B. A. Malomed, “Controlling collapse in Bose-Einstein condensation by temporal modulation of the scattering length,” Phys. Rev. A 67(1), 013605 (2003).
[CrossRef]

Phys. Rep. (2)

Y. S. Kivshar and D. E. Pelinovsky, “Self-focusing and transverse instabilities of solitary waves,” Phys. Rep. 331(4), 117–195 (2000).
[CrossRef]

L. Bergé, “Wave collapse in physics: principles and applications to light and plasma waves,” Phys. Rep. 303(5-6), 259–370 (1998).
[CrossRef]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

O. Bang, L. Bergé, and J. J. Rasmussen, “Fusion, collapse, and stationary bound states of incoherently coupled waves in bulk cubic media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 59(4), 4600–4613 (1999).
[CrossRef]

Phys. Rev. Lett. (1)

Y. Barad and Y. Silberberg, “Polarization Evolution and Polarization Instability of Solitons in a Birefringent Optical Fiber,” Phys. Rev. Lett. 78(17), 3290–3293 (1997).
[CrossRef]

Phys. Rev. A (1)

B. A. Malomed, “Polarization dynamics and interactions of solitons in a birefringent optical fiber,” Phys. Rev. A 43(1), 410–423 (1991).
[CrossRef]

Phys. Rev. B (1)

G. B. Scott, D. E. Lacklison, H. I. Ralph, and J. L. Page, “Magnetic circular dichroism and Faraday rotation spectra of Y3Fe5O12,” Phys. Rev. B 12(7), 2562 (1975).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046619 (2002).
[CrossRef]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

V. Skarka, V. I. Berezhiani, and R. Miklaszewski, “Spatiotemporal soliton propagation in saturating nonlinear optical media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 56(1), 1080–1087 (1997).
[CrossRef]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

L. Bergé, O. Bang, J. J. Rasmussen, and V. K. Mezentsev, “Self-focusing and solitonlike structures in materials with competing quadratic and cubic nonlinearities,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 55(3), 3555–3570 (1997).
[CrossRef]

Phys. Rev. Lett. (14)

O. Bang, D. Edmundson, and W. Królikowski, “Collapse of incoherent light beams in inertial bulk Kerr media,” Phys. Rev. Lett. 83(26), 5479–5482 (1999).
[CrossRef]

A. S. Desyatnikov, D. Buccoliero, M. R. Dennis, and Y. S. Kivshar, “Suppression of collapse for spiraling elliptic solitons,” Phys. Rev. Lett. 104(5), 053902 (2010).
[CrossRef]

A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84(16), 3582–3585 (2000).
[CrossRef]

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, “Strong spatiotemporal localization in a silica nonlinear waveguide array,” Phys. Rev. Lett. 91(22), 223901 (2003).
[CrossRef]

P. Pedri and L. Santos, “Two-dimensional bright solitons in dipolar Bose-Einstein condensates,” Phys. Rev. Lett. 95(20), 200404 (2005).
[CrossRef]

H. Saito and M. Ueda, “Dynamically stabilized bright solitons in a two-dimensional bose-einstein condensate,” Phys. Rev. Lett. 90(4), 040403 (2003).
[CrossRef]

L. Bergé, O. Bang, and W. Królikowski, “Influence of four-wave mixing and walk-Off on the self-focusing of coupled waves,” Phys. Rev. Lett. 84(15), 3302–3305 (2000).
[CrossRef]

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, “Collapse and stability of necklace beams in Kerr media,” Phys. Rev. Lett. 99(13), 133902 (2007).
[CrossRef]

P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15(26), 1005–1008 (1965).
[CrossRef]

T. Lahaye, J. Metz, B. Fröhlich, T. Koch, M. Meister, A. Griesmaier, T. Pfau, H. Saito, Y. Kawaguchi, and M. Ueda, “d-wave collapse and explosion of a dipolar bose-einstein condensate,” Phys. Rev. Lett. 101(8), 080401 (2008).
[CrossRef]

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-Trapping of Optical Beams,” Phys. Rev. Lett. 13(15), 479–482 (1964).
[CrossRef]

K. D. Moll, A. L. Gaeta, and G. Fibich, “Self-similar optical wave collapse: observation of the Townes profile,” Phys. Rev. Lett. 90(20), 203902 (2003).
[CrossRef]

Y. Linzon, K. A. Rutkowska, B. A. Malomed, and R. Morandotti, “Magneto-optical control of light collapse in bulk Kerr media,” Phys. Rev. Lett. 103(5), 053902 (2009).
[CrossRef]

R. J. Ballagh, K. Burnett, and T. F. Scott, “Theory of an Output Coupler for Bose-Einstein Condensated Atoms,” Phys. Rev. Lett. 78(9), 1607–1611 (1997).
[CrossRef]

Physica D (1)

E. A. Kuznetsov, J. J. Rasmussen, K. Rypdal, and S. K. Turitsyn, “Shaper criteria for the wave collapse,” Physica D 87(1-4), 273–284 (1995).
[CrossRef]

Progr. Opt. (1)

B. A. Malomed, “Variational methods in nonlinear fiber optics and related fields,” Progr. Opt. 43, 71 (2002).

Rev. Mod. Phys. (3)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

P. A. Robinson, “Nonlinear wave collapse and strong turbulence,” Rev. Mod. Phys. 69(2), 507–574 (1997).
[CrossRef]

Y. R. Shen, “Recent advances in nonlinear optics,” Rev. Mod. Phys. 48(1), 1–32 (1976).
[CrossRef]

Science (1)

G. I. Stegeman and M. Segev, “Optical Spatial Solitons and Their Interactions: Universality and Diversity,” Science 286(5444), 1518–1523 (1999).
[CrossRef]

Sens. Actuators A Phys. (1)

O. Kamada, T. Nakaya, and S. Higuchi, “Magnetic field optical sensors using Ce:YIG single crystals as a Faraday element,” Sens. Actuators A Phys. 119(2), 345–348 (2005).
[CrossRef]

Usp. Fiziol. Nauk (1)

G. A. Smolenskii, R. V. Pisarev, and I. G. Sinii, “Birefringence of light in magnetically ordered crystals,” Usp. Fiziol. Nauk 116, 231 (1975).

Other (10)

A. K. Zvezdin, and V. A. Kotov, Modern Magnetooptics and Magnetooptical Materials (Taylor & Francis Group, New York 1997).

J.-M. Liu, Photonic Devices, Cambridge Univ. Press, New York 2005.

U. M. Ascher, Numerical methods for evolutionary differential equations (SIAM, Philadelphia 2008).

J. C. Butcher, Numerical Methods for Ordinary Differential Equations (Wiley & Sons, West Sussex 2008).

C. Sulem and P. L. Sulem, The nonlinear Schrödinger equation: self-focusing and wave collapse (Springer, New York 1999).

E. Infeld and G. Rowlands, Nonlinear Waves, Solitons and Chaos (Cambridge Univ. Press, Cambridge 2000).

R. W. Boyd, Nonlinear Optics (Academic Press, San Diego 2008).

B. A. Malomed, “Nonlinear Schrödinger equations,” in Encyclopedia of Nonlinear Science, A. Scott, ed., (Routledge, New York 2005).

Y. S. Kivshar, and P. G. Agrawal, Optical Solitons: From Fibers to Photonic Crystal (Academic Press, San Diego 2003).

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

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.


Metrics