Abstract

We address ring-shaped surface waves supported by defocusing thermal media with circular cross-section. Such waves exist because of the balance between repulsion from the interface and deflection of light from the bulk medium due to defocusing nonlocal nonlinearity. The properties of such surface waves are determined by the geometry of the sample. Nodeless ring surface waves are stable for all values of their winding number, while surface waves with a small number of azimuthal nodes can be metastable.

© 2007 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, "Routing of anisotropic spatial solitons and modulational instability in liquid crystals," Nature 432, 733 (2004).
    [CrossRef] [PubMed]
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    [CrossRef]
  6. 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]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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  18. D. Mihalache, M. Bertolotti, and C. Sibilia, "Nonlinear wave propagation in planar structures," Prog. Opt. 27, 229 (1989).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2007 (4)

2006 (6)

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]

D. Briedis, D. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, "Ring vortex solitons in nonlocal nonlinear media," Opt. Express 13, 435 (2005).
[CrossRef] [PubMed]

M. Peccianti, C. Conti, and G. Assanto, "Interplay between nonlocality and nonlinearity in nematic liquid crystals," Opt. Lett. 30, 415 (2005).
[CrossRef] [PubMed]

2004 (3)

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, "Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media," J. Opt. B: Quantum and Semiclass. Opt. 6, S288 (2004).
[CrossRef]

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

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

2001 (1)

1989 (1)

D. Mihalache, M. Bertolotti, and C. Sibilia, "Nonlinear wave propagation in planar structures," Prog. Opt. 27, 229 (1989).

1988 (2)

1985 (1)

N. N. Akhmediev, V. I. Korneyev, and Y. V. Kuzmenko, "Excitation of nonlinear surface-waves by Gaussian light-beams," Zh. Eksp. Teor. Fiz. 88, 107 (1985).

J. Opt. B: Quantum and Semiclass. Opt. (1)

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, "Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media," J. Opt. B: Quantum and Semiclass. Opt. 6, S288 (2004).
[CrossRef]

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

Nat. Phys. (1)

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, "Long-range interactions between optical solitons," Nat. Phys. 2, 769 (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 liquid crystals," Nature 432, 733 (2004).
[CrossRef] [PubMed]

Nature Physics (1)

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, "Tunable refraction and reflection of self-confined light beams," Nature Physics 2, 737 (2006).
[CrossRef]

Opt. Express (1)

Opt. Lett. (9)

M. Peccianti, C. Conti, and G. Assanto, "Interplay between nonlocality and nonlinearity in nematic liquid crystals," Opt. Lett. 30, 415 (2005).
[CrossRef] [PubMed]

S. Lopez-Aguayo, A. S. Desyatnikov, Y. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, "Stable rotating dipole solitons in nonlocal optical media," Opt. Lett. 31, 1100 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, L. Torner, V. A. Vysloukh, and D. Mihalache, "Multipole vector solitons in nonlocal nonlinear media," Opt. Lett. 31, 1483 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, L. Torner, and V. A. Vysloukh, "Lattice-supported surface solitons in nonlocal nonlinear media," Opt. Lett. 31, 2595 (2006).
[CrossRef] [PubMed]

C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, L. Torner, and O. Cohen, "Two-dimensional multipole solitons in nonlocal nonlinear media," Opt. Lett. 31, 3312 (2006).
[CrossRef] [PubMed]

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 (2007).
[CrossRef]

A. Minovich, D. Neshev, A. Dreischuh, W. Krolikowski, and Y. Kivshar, "Experimental reconstruction of nonlocal response of thermal nonlinear optical media," Opt. Lett. 32, 1599 (2007).
[CrossRef] [PubMed]

Y. V. Kartashov, F. Ye, V. A. Vysloukh, and L. Torner, "Surface waves in defocusing thermal media," Opt. Lett. 32, 2260 (2007).
[CrossRef] [PubMed]

P. Varatharajah, A. Aceves, J. V. Moloney, D. R. Heatley, and E. M. Wright, "Stationary nonlinear surface waves and their stability in diffusive Kerr media," Opt. Lett. 13, 690 (1988).
[CrossRef] [PubMed]

Phys. Rev. A (1)

D. R. Andersen, "Surface-wave excitation at the interface between diffusive Kerr-like nonlinear and linear media," Phys. Rev. A 37, 189 (1988).
[CrossRef] [PubMed]

Phys. Rev. E (1)

A. I. Yakimenko, Y. A. Zaliznyak, and Y. Kivshar, "Stable vortex solitons in nonlocal self-focusing nonlinear media," Phys. Rev. E 71, 065603(R).

Phys. Rev. Lett. (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]

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, "Nonlocal surface-wave solitons," Phys. Rev. Lett. 98, 213901 (2007).
[CrossRef] [PubMed]

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

Prog. Opt. (1)

D. Mihalache, M. Bertolotti, and C. Sibilia, "Nonlinear wave propagation in planar structures," Prog. Opt. 27, 229 (1989).

Zh. Eksp. Teor. Fiz. (1)

N. N. Akhmediev, V. I. Korneyev, and Y. V. Kuzmenko, "Excitation of nonlinear surface-waves by Gaussian light-beams," Zh. Eksp. Teor. Fiz. 88, 107 (1985).

Other (2)

Nonlinear waves in solid state physics, Ed. by A. D. Boardman, M. Bertolotti, and T. Twardowski, NATO ASI 247, Plenum Press, New York (1989).

A. D. Boardman, P. Egan, F. Lederer, U. Langbein, and D. Mihalache, "Third-order nonlinear electromagnetic TE and TM guided waves," in Nonlinear Surface Electromagnetic Phenomena, Ed. by H. E. Ponath and G. I. Stegeman (North Holland, Amsterdam, 1991), 73-287.

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Figures (3)

Fig. 1.
Fig. 1.

Profiles (a) and refractive index distributions (b) for nodeless surface waves with m=0, nr =0 for different b values. (c) Profiles of surface waves with different nr at b=-4, m=0. (d) Energy flow versus b for surface waves with different nr at m=0. (e) Integral width of surface wave with nr =0, m=0 versus b. Points marked by circles in (d) and (e) correspond to waves shown in (a). (f) Real part of perturbation growth rate corresponding to k=1 for wave with m=0, nr =1 versus b.

Fig. 2.
Fig. 2.

Propagation of perturbed surface waves with different nr . Field modulus distributions for waves with nr =0, m=0 (top, left), nr =0, m=3 (top, right), nr =2, m=0 (bottom) are shown at different distances. All waves correspond to b=-4.

Fig. 3.
Fig. 3.

Propagation of perturbed surface waves with different nϕ . Field modulus distributions for waves with nϕ =2 (top, left), nϕ =6 (top, right), and nϕ =26 (bottom) are shown at different distances. All waves correspond to b=-2.

Equations (7)

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i q ξ = 1 2 ( 2 q r 2 + 1 r q r + 1 r 2 2 q ϕ 2 ) qn ,
2 n r 2 + 1 r n r + 1 r 2 2 n ϕ 2 = q 2 .
n ( r , ξ ) = 0 R G 0 ( r , ρ ) q ( ρ , ξ ) 2 d ρ ,
i δ u = 1 2 [ d 2 u d r 2 + 1 r du dr ( m + k ) 2 r 2 u ] w Δ n k un + bu ,
i δ v = 1 2 [ d 2 v d r 2 + 1 r dv dr ( m k ) 2 r 2 v ] + w Δ n k + vn bv ,
Δ n k = 0 R G k ( r , ρ ) w ( ρ ) [ u ( ρ ) + v ( ρ ) ] d ρ
U = 2 π 0 R r w 2 dr

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