Abstract

Very narrow, with the width smaller than a wavelength, solitons in (1+1)-dimensional and (2+1)-dimensional versions of cubic–quintic and full saturable models are studied, starting with the full system of the Maxwell’s equations rather than the paraxial (nonlinear Schrödinger) approximation. For the solitons with both TE and TM polarizations it is shown that there always exists a finite minimum width, and the solitons cease to exist at a critical value of the propagation constant, at which their width diverges. Full similarity of the results obtained for both nonlinearities suggests that the same general conclusions apply to narrow solitons in any non-Kerr model.

© 2001 Optical Society of America

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References

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  1. A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford University, Oxford, UK, 1995).
  2. D. Pohl, “Vectorial theory of self-trapped light beams,” Opt. Commun. 2, 305–308 (1970).
    [CrossRef]
  3. V. M. Eleonskii, L. G. Oganes’yants, and V. P. Silin, “Stationary solutions of the wave equation in the medium with nonlinearity saturation,” Sov. Phys. JETP 36, 282–285 (1973).
  4. A. W. Snyder, D. J. Mitchell, and Y. Chen, “Spatial solitons of Maxwell’s equations,” Opt. Lett. 19, 524–526 (1994).
    [CrossRef] [PubMed]
  5. E. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, “Subwavelength spatial solitons,” Opt. Lett. 22, 1290–1292 (1997).
    [CrossRef]
  6. C. Chen and S. Chi, “Subwavelength spatial solitons of TE mode,” Opt. Commun. 157, 170–172 (1998).
    [CrossRef]
  7. E. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, “On the existence of subwavelength spatial solitons,” Opt. Commun. 178, 431–435 (2000).
    [CrossRef]
  8. R. H. Enns, D. E. Edmundson, S. S. Rangneker, and A. E. Kaplan, “Optical switching between bistable soliton states: a theoretical review,” Opt. Quantum Electron. 24, S1295–S1314 (1992).
    [CrossRef]
  9. D. E. Edmundson and R. H. Enns, “Particlelike nature of colliding three-dimensional optical solitons,” Phys. Rev. A 51, 2491–2498 (1995).
    [CrossRef] [PubMed]
  10. D. E. Edmundson, “Unstable higher modes of a three-dimensional nonlinear Schrödinger equation,” Phys. Rev. E 55, 7636–7644 (1997).
    [CrossRef]
  11. C. De Angelis, “Self-trapped propagation in the nonlinear cubic-quintic Schrödinger equation: a variational approach,” IEEE J. Quantum Electron. QE-30, 818–821 (1994).
    [CrossRef]
  12. K. Dimitrievski, E. Reimhult, E. Svenssen, A. Ohgren, D. Anderson, A. Berston, M. Lisak, and M. Quiroga-Teixeiro, “Analysis of stable self-trapping of laser beams in cubic-quintic nonlinear media,” Phys. Lett. A 248, 369–376 (1998).
    [CrossRef]
  13. M. Quiroga-Teixeiro, A. Berntson, and H. Michinel, “Internal dynamics of nonlinear beams in their ground states: short- and long-lived excitation,” J. Opt. Soc. Am. B 16, 1697–1704 (1999).
    [CrossRef]
  14. M. Quiroga-Teixeiro and H. Michinel, “Stable azimuthalstationary state in quintic nonlinear media,” J. Opt. Soc. Am. B 14, 2004–2009 (1997).
    [CrossRef]
  15. A. Desyatnikov, A. I. Maimistov, and B. A. Malomed, “Three-dimensional spinning solitons in dispersive media with the cubic-quintic nonlinearity,” Phys. Rev. E 61, 3107–3113 (2000).
    [CrossRef]
  16. D. Mihalache, D. Mazilu, L.-C. Crasovan, B. A. Malomed, and F. Lederer, “Azimuthal instability of three-dimensional spinning solitons in cubic-quintic nonlinear media,” Phys. Rev. E 61, 7142–7145 (2000).
    [CrossRef]
  17. V. Tikhonenko, J. Christou, and B. Luther-Davies, “Three dimensional bright spatial solitons collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76, 2698–2701 (1996).
    [CrossRef] [PubMed]
  18. B. L. Lawrence, M. Cha, J. U. Kang, W. Torruellas, G. Stegeman, G. Baker, J. Meth, and S. Etemad, “Large purely refractive nonlinear index of single crystal P-toluene sul-phonate (PTS) at 1600 nm,” Electron. Lett. 30, 447–448 (1994).
    [CrossRef]
  19. E. W. Wright, B. L. Lawrence, W. Torruellas, and G. I. Stegeman, “Stable self-trapping and ring formation in polydiacetylene paratoluene sulphonate,” Opt. Lett. 20, 2481–2483 (1995).
    [CrossRef]
  20. B. L. Lawrence and G. I. Stegeman, “Two-dimensional bright spatial solitons stable over limited intensities and ring formation in polydiacetylene paratoluene sulphonate,” Opt. Lett. 23, 591–593 (1998).
    [CrossRef]
  21. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1991).
  22. M. G. Vakhitov and A. A. Kolokolov, “Stationary solutions of the wave equation in the medium with nonlinearity saturation,” Sov. J. Radiophys. Quantum Electron. 16, 783–789 (1973).
    [CrossRef]

2000 (3)

E. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, “On the existence of subwavelength spatial solitons,” Opt. Commun. 178, 431–435 (2000).
[CrossRef]

A. Desyatnikov, A. I. Maimistov, and B. A. Malomed, “Three-dimensional spinning solitons in dispersive media with the cubic-quintic nonlinearity,” Phys. Rev. E 61, 3107–3113 (2000).
[CrossRef]

D. Mihalache, D. Mazilu, L.-C. Crasovan, B. A. Malomed, and F. Lederer, “Azimuthal instability of three-dimensional spinning solitons in cubic-quintic nonlinear media,” Phys. Rev. E 61, 7142–7145 (2000).
[CrossRef]

1999 (1)

1998 (3)

C. Chen and S. Chi, “Subwavelength spatial solitons of TE mode,” Opt. Commun. 157, 170–172 (1998).
[CrossRef]

K. Dimitrievski, E. Reimhult, E. Svenssen, A. Ohgren, D. Anderson, A. Berston, M. Lisak, and M. Quiroga-Teixeiro, “Analysis of stable self-trapping of laser beams in cubic-quintic nonlinear media,” Phys. Lett. A 248, 369–376 (1998).
[CrossRef]

B. L. Lawrence and G. I. Stegeman, “Two-dimensional bright spatial solitons stable over limited intensities and ring formation in polydiacetylene paratoluene sulphonate,” Opt. Lett. 23, 591–593 (1998).
[CrossRef]

1997 (3)

1996 (1)

V. Tikhonenko, J. Christou, and B. Luther-Davies, “Three dimensional bright spatial solitons collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76, 2698–2701 (1996).
[CrossRef] [PubMed]

1995 (2)

D. E. Edmundson and R. H. Enns, “Particlelike nature of colliding three-dimensional optical solitons,” Phys. Rev. A 51, 2491–2498 (1995).
[CrossRef] [PubMed]

E. W. Wright, B. L. Lawrence, W. Torruellas, and G. I. Stegeman, “Stable self-trapping and ring formation in polydiacetylene paratoluene sulphonate,” Opt. Lett. 20, 2481–2483 (1995).
[CrossRef]

1994 (3)

A. W. Snyder, D. J. Mitchell, and Y. Chen, “Spatial solitons of Maxwell’s equations,” Opt. Lett. 19, 524–526 (1994).
[CrossRef] [PubMed]

B. L. Lawrence, M. Cha, J. U. Kang, W. Torruellas, G. Stegeman, G. Baker, J. Meth, and S. Etemad, “Large purely refractive nonlinear index of single crystal P-toluene sul-phonate (PTS) at 1600 nm,” Electron. Lett. 30, 447–448 (1994).
[CrossRef]

C. De Angelis, “Self-trapped propagation in the nonlinear cubic-quintic Schrödinger equation: a variational approach,” IEEE J. Quantum Electron. QE-30, 818–821 (1994).
[CrossRef]

1992 (1)

R. H. Enns, D. E. Edmundson, S. S. Rangneker, and A. E. Kaplan, “Optical switching between bistable soliton states: a theoretical review,” Opt. Quantum Electron. 24, S1295–S1314 (1992).
[CrossRef]

1973 (2)

V. M. Eleonskii, L. G. Oganes’yants, and V. P. Silin, “Stationary solutions of the wave equation in the medium with nonlinearity saturation,” Sov. Phys. JETP 36, 282–285 (1973).

M. G. Vakhitov and A. A. Kolokolov, “Stationary solutions of the wave equation in the medium with nonlinearity saturation,” Sov. J. Radiophys. Quantum Electron. 16, 783–789 (1973).
[CrossRef]

1970 (1)

D. Pohl, “Vectorial theory of self-trapped light beams,” Opt. Commun. 2, 305–308 (1970).
[CrossRef]

Anderson, D.

K. Dimitrievski, E. Reimhult, E. Svenssen, A. Ohgren, D. Anderson, A. Berston, M. Lisak, and M. Quiroga-Teixeiro, “Analysis of stable self-trapping of laser beams in cubic-quintic nonlinear media,” Phys. Lett. A 248, 369–376 (1998).
[CrossRef]

Baker, G.

B. L. Lawrence, M. Cha, J. U. Kang, W. Torruellas, G. Stegeman, G. Baker, J. Meth, and S. Etemad, “Large purely refractive nonlinear index of single crystal P-toluene sul-phonate (PTS) at 1600 nm,” Electron. Lett. 30, 447–448 (1994).
[CrossRef]

Berntson, A.

Berston, A.

K. Dimitrievski, E. Reimhult, E. Svenssen, A. Ohgren, D. Anderson, A. Berston, M. Lisak, and M. Quiroga-Teixeiro, “Analysis of stable self-trapping of laser beams in cubic-quintic nonlinear media,” Phys. Lett. A 248, 369–376 (1998).
[CrossRef]

Cha, M.

B. L. Lawrence, M. Cha, J. U. Kang, W. Torruellas, G. Stegeman, G. Baker, J. Meth, and S. Etemad, “Large purely refractive nonlinear index of single crystal P-toluene sul-phonate (PTS) at 1600 nm,” Electron. Lett. 30, 447–448 (1994).
[CrossRef]

Chen, C.

C. Chen and S. Chi, “Subwavelength spatial solitons of TE mode,” Opt. Commun. 157, 170–172 (1998).
[CrossRef]

Chen, Y.

Chi, S.

C. Chen and S. Chi, “Subwavelength spatial solitons of TE mode,” Opt. Commun. 157, 170–172 (1998).
[CrossRef]

Christou, J.

V. Tikhonenko, J. Christou, and B. Luther-Davies, “Three dimensional bright spatial solitons collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76, 2698–2701 (1996).
[CrossRef] [PubMed]

Crasovan, L.-C.

D. Mihalache, D. Mazilu, L.-C. Crasovan, B. A. Malomed, and F. Lederer, “Azimuthal instability of three-dimensional spinning solitons in cubic-quintic nonlinear media,” Phys. Rev. E 61, 7142–7145 (2000).
[CrossRef]

De Angelis, C.

C. De Angelis, “Self-trapped propagation in the nonlinear cubic-quintic Schrödinger equation: a variational approach,” IEEE J. Quantum Electron. QE-30, 818–821 (1994).
[CrossRef]

Desyatnikov, A.

A. Desyatnikov, A. I. Maimistov, and B. A. Malomed, “Three-dimensional spinning solitons in dispersive media with the cubic-quintic nonlinearity,” Phys. Rev. E 61, 3107–3113 (2000).
[CrossRef]

Dimitrievski, K.

K. Dimitrievski, E. Reimhult, E. Svenssen, A. Ohgren, D. Anderson, A. Berston, M. Lisak, and M. Quiroga-Teixeiro, “Analysis of stable self-trapping of laser beams in cubic-quintic nonlinear media,” Phys. Lett. A 248, 369–376 (1998).
[CrossRef]

Edmundson, D. E.

D. E. Edmundson, “Unstable higher modes of a three-dimensional nonlinear Schrödinger equation,” Phys. Rev. E 55, 7636–7644 (1997).
[CrossRef]

D. E. Edmundson and R. H. Enns, “Particlelike nature of colliding three-dimensional optical solitons,” Phys. Rev. A 51, 2491–2498 (1995).
[CrossRef] [PubMed]

R. H. Enns, D. E. Edmundson, S. S. Rangneker, and A. E. Kaplan, “Optical switching between bistable soliton states: a theoretical review,” Opt. Quantum Electron. 24, S1295–S1314 (1992).
[CrossRef]

Eleonskii, V. M.

V. M. Eleonskii, L. G. Oganes’yants, and V. P. Silin, “Stationary solutions of the wave equation in the medium with nonlinearity saturation,” Sov. Phys. JETP 36, 282–285 (1973).

Enns, R. H.

D. E. Edmundson and R. H. Enns, “Particlelike nature of colliding three-dimensional optical solitons,” Phys. Rev. A 51, 2491–2498 (1995).
[CrossRef] [PubMed]

R. H. Enns, D. E. Edmundson, S. S. Rangneker, and A. E. Kaplan, “Optical switching between bistable soliton states: a theoretical review,” Opt. Quantum Electron. 24, S1295–S1314 (1992).
[CrossRef]

Etemad, S.

B. L. Lawrence, M. Cha, J. U. Kang, W. Torruellas, G. Stegeman, G. Baker, J. Meth, and S. Etemad, “Large purely refractive nonlinear index of single crystal P-toluene sul-phonate (PTS) at 1600 nm,” Electron. Lett. 30, 447–448 (1994).
[CrossRef]

Granot, E.

E. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, “On the existence of subwavelength spatial solitons,” Opt. Commun. 178, 431–435 (2000).
[CrossRef]

E. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, “Subwavelength spatial solitons,” Opt. Lett. 22, 1290–1292 (1997).
[CrossRef]

Hasegawa, A.

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford University, Oxford, UK, 1995).

Isbi, Y.

E. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, “On the existence of subwavelength spatial solitons,” Opt. Commun. 178, 431–435 (2000).
[CrossRef]

E. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, “Subwavelength spatial solitons,” Opt. Lett. 22, 1290–1292 (1997).
[CrossRef]

Kang, J. U.

B. L. Lawrence, M. Cha, J. U. Kang, W. Torruellas, G. Stegeman, G. Baker, J. Meth, and S. Etemad, “Large purely refractive nonlinear index of single crystal P-toluene sul-phonate (PTS) at 1600 nm,” Electron. Lett. 30, 447–448 (1994).
[CrossRef]

Kaplan, A. E.

R. H. Enns, D. E. Edmundson, S. S. Rangneker, and A. E. Kaplan, “Optical switching between bistable soliton states: a theoretical review,” Opt. Quantum Electron. 24, S1295–S1314 (1992).
[CrossRef]

Kodama, Y.

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford University, Oxford, UK, 1995).

Kolokolov, A. A.

M. G. Vakhitov and A. A. Kolokolov, “Stationary solutions of the wave equation in the medium with nonlinearity saturation,” Sov. J. Radiophys. Quantum Electron. 16, 783–789 (1973).
[CrossRef]

Lawrence, B. L.

Lederer, F.

D. Mihalache, D. Mazilu, L.-C. Crasovan, B. A. Malomed, and F. Lederer, “Azimuthal instability of three-dimensional spinning solitons in cubic-quintic nonlinear media,” Phys. Rev. E 61, 7142–7145 (2000).
[CrossRef]

Lewis, A.

E. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, “On the existence of subwavelength spatial solitons,” Opt. Commun. 178, 431–435 (2000).
[CrossRef]

E. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, “Subwavelength spatial solitons,” Opt. Lett. 22, 1290–1292 (1997).
[CrossRef]

Lisak, M.

K. Dimitrievski, E. Reimhult, E. Svenssen, A. Ohgren, D. Anderson, A. Berston, M. Lisak, and M. Quiroga-Teixeiro, “Analysis of stable self-trapping of laser beams in cubic-quintic nonlinear media,” Phys. Lett. A 248, 369–376 (1998).
[CrossRef]

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1991).

Luther-Davies, B.

V. Tikhonenko, J. Christou, and B. Luther-Davies, “Three dimensional bright spatial solitons collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76, 2698–2701 (1996).
[CrossRef] [PubMed]

Maimistov, A. I.

A. Desyatnikov, A. I. Maimistov, and B. A. Malomed, “Three-dimensional spinning solitons in dispersive media with the cubic-quintic nonlinearity,” Phys. Rev. E 61, 3107–3113 (2000).
[CrossRef]

Malomed, B.

E. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, “On the existence of subwavelength spatial solitons,” Opt. Commun. 178, 431–435 (2000).
[CrossRef]

E. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, “Subwavelength spatial solitons,” Opt. Lett. 22, 1290–1292 (1997).
[CrossRef]

Malomed, B. A.

A. Desyatnikov, A. I. Maimistov, and B. A. Malomed, “Three-dimensional spinning solitons in dispersive media with the cubic-quintic nonlinearity,” Phys. Rev. E 61, 3107–3113 (2000).
[CrossRef]

D. Mihalache, D. Mazilu, L.-C. Crasovan, B. A. Malomed, and F. Lederer, “Azimuthal instability of three-dimensional spinning solitons in cubic-quintic nonlinear media,” Phys. Rev. E 61, 7142–7145 (2000).
[CrossRef]

Mazilu, D.

D. Mihalache, D. Mazilu, L.-C. Crasovan, B. A. Malomed, and F. Lederer, “Azimuthal instability of three-dimensional spinning solitons in cubic-quintic nonlinear media,” Phys. Rev. E 61, 7142–7145 (2000).
[CrossRef]

Meth, J.

B. L. Lawrence, M. Cha, J. U. Kang, W. Torruellas, G. Stegeman, G. Baker, J. Meth, and S. Etemad, “Large purely refractive nonlinear index of single crystal P-toluene sul-phonate (PTS) at 1600 nm,” Electron. Lett. 30, 447–448 (1994).
[CrossRef]

Michinel, H.

Mihalache, D.

D. Mihalache, D. Mazilu, L.-C. Crasovan, B. A. Malomed, and F. Lederer, “Azimuthal instability of three-dimensional spinning solitons in cubic-quintic nonlinear media,” Phys. Rev. E 61, 7142–7145 (2000).
[CrossRef]

Mitchell, D. J.

Oganes’yants, L. G.

V. M. Eleonskii, L. G. Oganes’yants, and V. P. Silin, “Stationary solutions of the wave equation in the medium with nonlinearity saturation,” Sov. Phys. JETP 36, 282–285 (1973).

Ohgren, A.

K. Dimitrievski, E. Reimhult, E. Svenssen, A. Ohgren, D. Anderson, A. Berston, M. Lisak, and M. Quiroga-Teixeiro, “Analysis of stable self-trapping of laser beams in cubic-quintic nonlinear media,” Phys. Lett. A 248, 369–376 (1998).
[CrossRef]

Pohl, D.

D. Pohl, “Vectorial theory of self-trapped light beams,” Opt. Commun. 2, 305–308 (1970).
[CrossRef]

Quiroga-Teixeiro, M.

Rangneker, S. S.

R. H. Enns, D. E. Edmundson, S. S. Rangneker, and A. E. Kaplan, “Optical switching between bistable soliton states: a theoretical review,” Opt. Quantum Electron. 24, S1295–S1314 (1992).
[CrossRef]

Reimhult, E.

K. Dimitrievski, E. Reimhult, E. Svenssen, A. Ohgren, D. Anderson, A. Berston, M. Lisak, and M. Quiroga-Teixeiro, “Analysis of stable self-trapping of laser beams in cubic-quintic nonlinear media,” Phys. Lett. A 248, 369–376 (1998).
[CrossRef]

Silin, V. P.

V. M. Eleonskii, L. G. Oganes’yants, and V. P. Silin, “Stationary solutions of the wave equation in the medium with nonlinearity saturation,” Sov. Phys. JETP 36, 282–285 (1973).

Snyder, A. W.

Stegeman, G.

B. L. Lawrence, M. Cha, J. U. Kang, W. Torruellas, G. Stegeman, G. Baker, J. Meth, and S. Etemad, “Large purely refractive nonlinear index of single crystal P-toluene sul-phonate (PTS) at 1600 nm,” Electron. Lett. 30, 447–448 (1994).
[CrossRef]

Stegeman, G. I.

Sternklar, S.

E. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, “On the existence of subwavelength spatial solitons,” Opt. Commun. 178, 431–435 (2000).
[CrossRef]

E. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, “Subwavelength spatial solitons,” Opt. Lett. 22, 1290–1292 (1997).
[CrossRef]

Svenssen, E.

K. Dimitrievski, E. Reimhult, E. Svenssen, A. Ohgren, D. Anderson, A. Berston, M. Lisak, and M. Quiroga-Teixeiro, “Analysis of stable self-trapping of laser beams in cubic-quintic nonlinear media,” Phys. Lett. A 248, 369–376 (1998).
[CrossRef]

Tikhonenko, V.

V. Tikhonenko, J. Christou, and B. Luther-Davies, “Three dimensional bright spatial solitons collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76, 2698–2701 (1996).
[CrossRef] [PubMed]

Torruellas, W.

E. W. Wright, B. L. Lawrence, W. Torruellas, and G. I. Stegeman, “Stable self-trapping and ring formation in polydiacetylene paratoluene sulphonate,” Opt. Lett. 20, 2481–2483 (1995).
[CrossRef]

B. L. Lawrence, M. Cha, J. U. Kang, W. Torruellas, G. Stegeman, G. Baker, J. Meth, and S. Etemad, “Large purely refractive nonlinear index of single crystal P-toluene sul-phonate (PTS) at 1600 nm,” Electron. Lett. 30, 447–448 (1994).
[CrossRef]

Vakhitov, M. G.

M. G. Vakhitov and A. A. Kolokolov, “Stationary solutions of the wave equation in the medium with nonlinearity saturation,” Sov. J. Radiophys. Quantum Electron. 16, 783–789 (1973).
[CrossRef]

Wright, E. W.

Electron. Lett. (1)

B. L. Lawrence, M. Cha, J. U. Kang, W. Torruellas, G. Stegeman, G. Baker, J. Meth, and S. Etemad, “Large purely refractive nonlinear index of single crystal P-toluene sul-phonate (PTS) at 1600 nm,” Electron. Lett. 30, 447–448 (1994).
[CrossRef]

IEEE J. Quantum Electron. (1)

C. De Angelis, “Self-trapped propagation in the nonlinear cubic-quintic Schrödinger equation: a variational approach,” IEEE J. Quantum Electron. QE-30, 818–821 (1994).
[CrossRef]

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

Opt. Commun. (3)

D. Pohl, “Vectorial theory of self-trapped light beams,” Opt. Commun. 2, 305–308 (1970).
[CrossRef]

C. Chen and S. Chi, “Subwavelength spatial solitons of TE mode,” Opt. Commun. 157, 170–172 (1998).
[CrossRef]

E. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, “On the existence of subwavelength spatial solitons,” Opt. Commun. 178, 431–435 (2000).
[CrossRef]

Opt. Lett. (4)

Opt. Quantum Electron. (1)

R. H. Enns, D. E. Edmundson, S. S. Rangneker, and A. E. Kaplan, “Optical switching between bistable soliton states: a theoretical review,” Opt. Quantum Electron. 24, S1295–S1314 (1992).
[CrossRef]

Phys. Lett. A (1)

K. Dimitrievski, E. Reimhult, E. Svenssen, A. Ohgren, D. Anderson, A. Berston, M. Lisak, and M. Quiroga-Teixeiro, “Analysis of stable self-trapping of laser beams in cubic-quintic nonlinear media,” Phys. Lett. A 248, 369–376 (1998).
[CrossRef]

Phys. Rev. A (1)

D. E. Edmundson and R. H. Enns, “Particlelike nature of colliding three-dimensional optical solitons,” Phys. Rev. A 51, 2491–2498 (1995).
[CrossRef] [PubMed]

Phys. Rev. E (3)

D. E. Edmundson, “Unstable higher modes of a three-dimensional nonlinear Schrödinger equation,” Phys. Rev. E 55, 7636–7644 (1997).
[CrossRef]

A. Desyatnikov, A. I. Maimistov, and B. A. Malomed, “Three-dimensional spinning solitons in dispersive media with the cubic-quintic nonlinearity,” Phys. Rev. E 61, 3107–3113 (2000).
[CrossRef]

D. Mihalache, D. Mazilu, L.-C. Crasovan, B. A. Malomed, and F. Lederer, “Azimuthal instability of three-dimensional spinning solitons in cubic-quintic nonlinear media,” Phys. Rev. E 61, 7142–7145 (2000).
[CrossRef]

Phys. Rev. Lett. (1)

V. Tikhonenko, J. Christou, and B. Luther-Davies, “Three dimensional bright spatial solitons collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76, 2698–2701 (1996).
[CrossRef] [PubMed]

Sov. J. Radiophys. Quantum Electron. (1)

M. G. Vakhitov and A. A. Kolokolov, “Stationary solutions of the wave equation in the medium with nonlinearity saturation,” Sov. J. Radiophys. Quantum Electron. 16, 783–789 (1973).
[CrossRef]

Sov. Phys. JETP (1)

V. M. Eleonskii, L. G. Oganes’yants, and V. P. Silin, “Stationary solutions of the wave equation in the medium with nonlinearity saturation,” Sov. Phys. JETP 36, 282–285 (1973).

Other (2)

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1991).

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford University, Oxford, UK, 1995).

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Figures (2)

Fig. 1
Fig. 1

Typical examples of the fundamental spatial TM soliton in (a) the (1+1)D and (b) the (2+1)D geometries. The relative propagation constant is β/β0=1.05, and material constant (20) is s=1. In this and the next figures the solid and dotted curves pertain to the cubic–quintic and saturable models, respectively.

Fig. 2
Fig. 2

Width of (a) the (1+1)D and (b) the (2+1)D fundamental spatial TM solitons versus the relative propagation constant β/β0 at various fixed values of the material constant s. For the saturable model the deviation of the relative propagation constant from 1 is five times that shown on the horizontal axis for the cubic–quintic model.

Equations (38)

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Hy=-H(x)cos Φ,Hx=Hz=0,
Ex=E(x)cos Φ,Ez=Ez(x)sin Φ,Ey=0,
Hx=(y/r)H(r)cos Φ,Hy=-(x/r)H(r)cos Φ,Hz=0,
Ex=(x/r)E(r)cos Φ,Ey=(y/r)E(r)cos Φ,
Ez=Ez(r)sin Φ;
Dsat=0E1+(2/0)E21+(4/2)E2
DCQ=E(0+2E2-4E4).
Dx, y=tEx, y,Dz=lEz,
t0+142(3E2+Ez2)-184(5E4+2E2Ez2+Ez4),
l0+142(E2+3Ez2)-184(E4+2E2Ez2+5Ez4).
×E=-1c Ht,
Ez+βE=-(ω/c)H,
×H=1c Dt.
tr1-D(rD-1H)=(ω/c)Ezl,
βH=-(ω/c)E,
Ez=E(1-P),
r1-D(rD-1Ev1)=-Ezv2.
γ1-(β0/β)2,
PE2+γ3Ez2+σE4+2γ5E2Ez2+γ25Ez4,
v11+γ1-γP,
v21+γ1-γ 13E2+γEz2+σ15E4+2γ5E2Ez2+γ2Ez4,
σ-γ(1-γ)-1s,
s(10/9)042-2.
E2(x)1,(E)21.
E-γE+E2+13(E)2E=0,
Esol(x)=2γ1+γ18sech(γξ)-γ9 sech3(γξ).
E=E-E3-σE5,
4/E2(x)=1+1+16σ/3 cosh(2x).
(β/β0)2<(β/β0)cr21+3/(16s).
cosh Δ=(1+16σ/3)-1/2+2.
W=(4λ/3πn0)sF(16σ/3),
F(y)|y|-1/2 ln[(1+y)-1/2+2
+3+4(1+y)-1/2+(1+y)-1].
Wmin(TE)/λ=0.8254/2.
d2Ed2r+1r dEdr-1r2E=E-E3-σE5.
Q=ExDx+EyDy+EzDz+HxHx+HyHy,
W=0QrDdr0QrD-1dr.
N=22-D(2π)D-10(Ex2+Ey2+Ez2)rD-1dr

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