Abstract

A class of optical spatial solitons exhibiting propagation in a closed-loop orbit in a two-dimensional plane is presented. A closed-form particlelike model is derived, indicating that the quasi-centrifugal force acting on these solitons can be balanced by an inhomogeneity in the nonlinear index of refraction. Specifically, a circular-shaped nonlinear interface is shown to facilitate stable orbital propagation of solitons that carve their own circular cavity for a wide range of nonlinearity parameters.

© 2006 Optical Society of America

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References

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  1. G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
    [CrossRef] [PubMed]
  2. Y. S. Kivshar and G. I. Stegeman, Opt. Photonics News 13, 59 (2002).
    [CrossRef]
  3. B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, J. Opt. B: Quantum Semiclassical Opt. 7, R53 (2005).
    [CrossRef]
  4. J. Scheuer and M. Orenstein, Opt. Lett. 24, 1735 (1999).
    [CrossRef]
  5. E. Alvarado-Méndez, G. E. Torres-Cisneros, M. Torres-Cisneros, J. J. Sánchez-Mondragón, and V. Vysloukh, Opt. Quantum Electron. 30, 687 (1998).
    [CrossRef]
  6. A. B. Aceves, P. Varatharajah, A. C. Newell, E. M. Wright, G. I. Stegeman, D. R. Heatley, J. V. Moloney, and H. Adachihara, J. Opt. Soc. Am. B 7, 963 (1990).
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  7. L. Djaloshinski and M. Orenstein, IEEE J. Quantum Electron. 35, 737 (1999).
    [CrossRef]
  8. M. Heiblum and J. H. Harris, IEEE J. Quantum Electron. 11, 75 (1975).
    [CrossRef]
  9. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995).
  10. H. A. Haus and W. S. Wong, Rev. Mod. Phys. 68, 423 (1996).
    [CrossRef]

2005 (1)

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, J. Opt. B: Quantum Semiclassical Opt. 7, R53 (2005).
[CrossRef]

2002 (1)

Y. S. Kivshar and G. I. Stegeman, Opt. Photonics News 13, 59 (2002).
[CrossRef]

1999 (3)

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

L. Djaloshinski and M. Orenstein, IEEE J. Quantum Electron. 35, 737 (1999).
[CrossRef]

J. Scheuer and M. Orenstein, Opt. Lett. 24, 1735 (1999).
[CrossRef]

1998 (1)

E. Alvarado-Méndez, G. E. Torres-Cisneros, M. Torres-Cisneros, J. J. Sánchez-Mondragón, and V. Vysloukh, Opt. Quantum Electron. 30, 687 (1998).
[CrossRef]

1996 (1)

H. A. Haus and W. S. Wong, Rev. Mod. Phys. 68, 423 (1996).
[CrossRef]

1995 (1)

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995).

1990 (1)

1975 (1)

M. Heiblum and J. H. Harris, IEEE J. Quantum Electron. 11, 75 (1975).
[CrossRef]

Aceves, A. B.

Adachihara, H.

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995).

Alvarado-Méndez, E.

E. Alvarado-Méndez, G. E. Torres-Cisneros, M. Torres-Cisneros, J. J. Sánchez-Mondragón, and V. Vysloukh, Opt. Quantum Electron. 30, 687 (1998).
[CrossRef]

Djaloshinski, L.

L. Djaloshinski and M. Orenstein, IEEE J. Quantum Electron. 35, 737 (1999).
[CrossRef]

Harris, J. H.

M. Heiblum and J. H. Harris, IEEE J. Quantum Electron. 11, 75 (1975).
[CrossRef]

Haus, H. A.

H. A. Haus and W. S. Wong, Rev. Mod. Phys. 68, 423 (1996).
[CrossRef]

Heatley, D. R.

Heiblum, M.

M. Heiblum and J. H. Harris, IEEE J. Quantum Electron. 11, 75 (1975).
[CrossRef]

Kivshar, Y. S.

Y. S. Kivshar and G. I. Stegeman, Opt. Photonics News 13, 59 (2002).
[CrossRef]

Malomed, B. A.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, J. Opt. B: Quantum Semiclassical Opt. 7, R53 (2005).
[CrossRef]

Mihalache, D.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, J. Opt. B: Quantum Semiclassical Opt. 7, R53 (2005).
[CrossRef]

Moloney, J. V.

Newell, A. C.

Orenstein, M.

J. Scheuer and M. Orenstein, Opt. Lett. 24, 1735 (1999).
[CrossRef]

L. Djaloshinski and M. Orenstein, IEEE J. Quantum Electron. 35, 737 (1999).
[CrossRef]

Sánchez-Mondragón, J. J.

E. Alvarado-Méndez, G. E. Torres-Cisneros, M. Torres-Cisneros, J. J. Sánchez-Mondragón, and V. Vysloukh, Opt. Quantum Electron. 30, 687 (1998).
[CrossRef]

Scheuer, J.

Segev, M.

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

Stegeman, G. I.

Torner, L.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, J. Opt. B: Quantum Semiclassical Opt. 7, R53 (2005).
[CrossRef]

Torres-Cisneros, G. E.

E. Alvarado-Méndez, G. E. Torres-Cisneros, M. Torres-Cisneros, J. J. Sánchez-Mondragón, and V. Vysloukh, Opt. Quantum Electron. 30, 687 (1998).
[CrossRef]

Torres-Cisneros, M.

E. Alvarado-Méndez, G. E. Torres-Cisneros, M. Torres-Cisneros, J. J. Sánchez-Mondragón, and V. Vysloukh, Opt. Quantum Electron. 30, 687 (1998).
[CrossRef]

Varatharajah, P.

Vysloukh, and V.

E. Alvarado-Méndez, G. E. Torres-Cisneros, M. Torres-Cisneros, J. J. Sánchez-Mondragón, and V. Vysloukh, Opt. Quantum Electron. 30, 687 (1998).
[CrossRef]

Wise, F.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, J. Opt. B: Quantum Semiclassical Opt. 7, R53 (2005).
[CrossRef]

Wong, W. S.

H. A. Haus and W. S. Wong, Rev. Mod. Phys. 68, 423 (1996).
[CrossRef]

Wright, E. M.

IEEE J. Quantum Electron. (2)

L. Djaloshinski and M. Orenstein, IEEE J. Quantum Electron. 35, 737 (1999).
[CrossRef]

M. Heiblum and J. H. Harris, IEEE J. Quantum Electron. 11, 75 (1975).
[CrossRef]

J. Opt. B: Quantum Semiclassical Opt. (1)

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, J. Opt. B: Quantum Semiclassical Opt. 7, R53 (2005).
[CrossRef]

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

Opt. Lett. (1)

Opt. Photonics News (1)

Y. S. Kivshar and G. I. Stegeman, Opt. Photonics News 13, 59 (2002).
[CrossRef]

Opt. Quantum Electron. (1)

E. Alvarado-Méndez, G. E. Torres-Cisneros, M. Torres-Cisneros, J. J. Sánchez-Mondragón, and V. Vysloukh, Opt. Quantum Electron. 30, 687 (1998).
[CrossRef]

Rev. Mod. Phys. (1)

H. A. Haus and W. S. Wong, Rev. Mod. Phys. 68, 423 (1996).
[CrossRef]

Science (1)

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995).

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Figures (3)

Fig. 1
Fig. 1

Resent figure files on 12/8. Resolution too low, size wrong in original files.(a) Refractive index profile ( n 0 , linear; n 2 , Kerr). (b) Potential well formation. ϵ = 1 , 2 π R λ 0 = 200 , u 0 = u = 5 , n 0 = 1.45 , n 2 = 0.1 , Δ n 0 = 0.1 , Δ n 2 = 0.05 .

Fig. 2
Fig. 2

Simulation trajectories. ϵ = 1 , R = 2 π × 100 λ 0 , u = 0 , n 0 = 1.45 , n 2 = 0.1 , k θ = 1000 . (a) k u = 0 , u 0 = 0 , Δ n 0 = 0.05 . (b)–(d) Δ n 0 = 0.01 , u 0 = 10 , Δ n 2 = 0.03 . SP, starting point.

Fig. 3
Fig. 3

(a) Closed-loop oscillating soliton trajectories for initial shifts of 5 (dashed curve) and 8.6 (solid curve). (b) Polar view of the latter. The structure parameters are R k 0 = 500 , n 01 = 1.5 , n 02 = 1.45 , and n 21 = n 22 = 0.0625 .

Equations (13)

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2 A r 2 + 1 r A r + 2 j k θ r 2 A θ + ( k 0 2 n 0 2 + 2 k 0 2 n 0 n 2 A 2 k θ 2 r 2 ) A = 0 ,
A V = j R 2 k θ 2 A U 2 + j k 0 2 n 0 n 2 R k θ exp ( 2 U R ) A 2 A + j 2 [ k 0 2 n 0 2 R k θ exp ( 2 U R ) k θ R ] A ,
n 0 k θ k 0 1 r , n 2 1 r .
v E = j 2 2 E u 2 + j E 2 E + j ( n 0 2 + 2 E 2 ) u k 0 R E ,
u k 0 U , v k 0 2 R k θ V ,
A ( u , v ) E ( u , v ) n 0 n 2 exp [ j ( k θ 2 2 k 0 2 R 2 n 0 2 2 ) v ] ,
F r = 1 k 0 R ( n 0 2 + 2 3 ϵ 2 ) .
s n = j Δ ( n 0 n 2 ) n 0 n 2 1 ( u u ) E 2 E , 1 ( u u ) { 1 u > u 0 u < u ,
F n = ϵ 3 Δ ( n 0 n 2 ) 4 ( n 0 n 2 ) sech 4 [ ϵ ( u u 0 ) ] .
0 n 0 2 + 2 3 ϵ 2 k 0 R 4 ( n 0 n 2 ) ϵ 3 Δ ( n 0 n 2 ) 1.
min ( Δ n 2 ) = n 2 n 0 Δ n 0 + 4 n 2 ( n 0 2 + 2 3 ϵ 2 ) k 0 R ϵ 3 .
k 0 r = ( k 0 R ) exp ( u k 0 R ) , θ = k θ ( k 0 R ) 2 v .
m k θ = l = 2 π ( k 0 R ) 2 v per ,

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