Abstract

We study, numerically and analytically, linear and nonlinear waveguides induced by optical vortex solitons in a Kerr medium. Both fundamental and first-order guided modes are analyzed, as well as cases of effective defocusing and focusing nonlinearity.

© 2000 Optical Society of America

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References

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  1. See, e.g., Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998), and references therein.
    [CrossRef]
  2. M. Shih, Z. Chen, M. Mitchell, M. Segev, H. Lee, R. S. Fiegelson, and J. P. Wilde, J. Opt. Soc. Am. B 14, 3091 (1997).
    [CrossRef]
  3. E. A. Ostrovskaya and Yu. S. Kivshar, Opt. Lett. 23, 1268 (1998).
    [CrossRef]
  4. R. de la Fuente and A. Barthelemy, IEEE J. Quantum Electron. 28, 547 (1992); B. Luther-Davies and Y. Xiaoping, Opt. Lett. 17, 496 (1992); M. Morin, G. Duree, G. Salamo, and M. Segev, Opt. Lett. 20, 2066 (1995); J. U. Kang, G. I. Stegeman, and J. S. Aitchison, Opt. Lett. 20, 2069 (1995).
    [CrossRef] [PubMed]
  5. K. T. Gahagan and G. A. Swartzlander, Opt. Lett. 21, 827 (1996).
    [CrossRef] [PubMed]
  6. A. P. Sheppard and M. Haelterman, Opt. Lett. 19, 859 (1993).
    [CrossRef]
  7. C. T. Law, X. Zhang, and G. A. Swartzlander, Opt. Lett. 25, 55 (2000).
    [CrossRef]
  8. See, e.g., H. T. Tran and R. A. Sammut, Phys. Rev. A 52, 3170 (1995).
    [CrossRef] [PubMed]
  9. W. Królikowski, N. Akhmediev, and B. Luther-Davies, Opt. Lett. 21, 782 (1996).
    [CrossRef]
  10. R. W. Boyd, Nonlinear Optics (Academic, London, 1992).
  11. A. P. Sheppard and Yu. S. Kivshar, Phys. Rev. E 55, 4773 (1997).
    [CrossRef]
  12. B. V. Gisin and A. A. Hordy, Phys. Rev. A 48, 3466 (1993).
    [CrossRef] [PubMed]

2000 (1)

1998 (2)

See, e.g., Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998), and references therein.
[CrossRef]

E. A. Ostrovskaya and Yu. S. Kivshar, Opt. Lett. 23, 1268 (1998).
[CrossRef]

1997 (2)

1996 (2)

1995 (1)

See, e.g., H. T. Tran and R. A. Sammut, Phys. Rev. A 52, 3170 (1995).
[CrossRef] [PubMed]

1993 (2)

A. P. Sheppard and M. Haelterman, Opt. Lett. 19, 859 (1993).
[CrossRef]

B. V. Gisin and A. A. Hordy, Phys. Rev. A 48, 3466 (1993).
[CrossRef] [PubMed]

1992 (1)

R. de la Fuente and A. Barthelemy, IEEE J. Quantum Electron. 28, 547 (1992); B. Luther-Davies and Y. Xiaoping, Opt. Lett. 17, 496 (1992); M. Morin, G. Duree, G. Salamo, and M. Segev, Opt. Lett. 20, 2066 (1995); J. U. Kang, G. I. Stegeman, and J. S. Aitchison, Opt. Lett. 20, 2069 (1995).
[CrossRef] [PubMed]

Akhmediev, N.

Barthelemy, A.

R. de la Fuente and A. Barthelemy, IEEE J. Quantum Electron. 28, 547 (1992); B. Luther-Davies and Y. Xiaoping, Opt. Lett. 17, 496 (1992); M. Morin, G. Duree, G. Salamo, and M. Segev, Opt. Lett. 20, 2066 (1995); J. U. Kang, G. I. Stegeman, and J. S. Aitchison, Opt. Lett. 20, 2069 (1995).
[CrossRef] [PubMed]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, London, 1992).

Chen, Z.

de la Fuente, R.

R. de la Fuente and A. Barthelemy, IEEE J. Quantum Electron. 28, 547 (1992); B. Luther-Davies and Y. Xiaoping, Opt. Lett. 17, 496 (1992); M. Morin, G. Duree, G. Salamo, and M. Segev, Opt. Lett. 20, 2066 (1995); J. U. Kang, G. I. Stegeman, and J. S. Aitchison, Opt. Lett. 20, 2069 (1995).
[CrossRef] [PubMed]

Fiegelson, R. S.

Gahagan, K. T.

Gisin, B. V.

B. V. Gisin and A. A. Hordy, Phys. Rev. A 48, 3466 (1993).
[CrossRef] [PubMed]

Haelterman, M.

Hordy, A. A.

B. V. Gisin and A. A. Hordy, Phys. Rev. A 48, 3466 (1993).
[CrossRef] [PubMed]

Kivshar, Yu. S.

E. A. Ostrovskaya and Yu. S. Kivshar, Opt. Lett. 23, 1268 (1998).
[CrossRef]

See, e.g., Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998), and references therein.
[CrossRef]

A. P. Sheppard and Yu. S. Kivshar, Phys. Rev. E 55, 4773 (1997).
[CrossRef]

Królikowski, W.

Law, C. T.

Lee, H.

Luther-Davies, B.

See, e.g., Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998), and references therein.
[CrossRef]

W. Królikowski, N. Akhmediev, and B. Luther-Davies, Opt. Lett. 21, 782 (1996).
[CrossRef]

Mitchell, M.

Ostrovskaya, E. A.

Sammut, R. A.

See, e.g., H. T. Tran and R. A. Sammut, Phys. Rev. A 52, 3170 (1995).
[CrossRef] [PubMed]

Segev, M.

Sheppard, A. P.

A. P. Sheppard and Yu. S. Kivshar, Phys. Rev. E 55, 4773 (1997).
[CrossRef]

A. P. Sheppard and M. Haelterman, Opt. Lett. 19, 859 (1993).
[CrossRef]

Shih, M.

Swartzlander, G. A.

Tran, H. T.

See, e.g., H. T. Tran and R. A. Sammut, Phys. Rev. A 52, 3170 (1995).
[CrossRef] [PubMed]

Wilde, J. P.

Zhang, X.

IEEE J. Quantum Electron. (1)

R. de la Fuente and A. Barthelemy, IEEE J. Quantum Electron. 28, 547 (1992); B. Luther-Davies and Y. Xiaoping, Opt. Lett. 17, 496 (1992); M. Morin, G. Duree, G. Salamo, and M. Segev, Opt. Lett. 20, 2066 (1995); J. U. Kang, G. I. Stegeman, and J. S. Aitchison, Opt. Lett. 20, 2069 (1995).
[CrossRef] [PubMed]

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

Opt. Lett. (5)

Phys. Rep. (1)

See, e.g., Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998), and references therein.
[CrossRef]

Phys. Rev. A (2)

B. V. Gisin and A. A. Hordy, Phys. Rev. A 48, 3466 (1993).
[CrossRef] [PubMed]

See, e.g., H. T. Tran and R. A. Sammut, Phys. Rev. A 52, 3170 (1995).
[CrossRef] [PubMed]

Phys. Rev. E (1)

A. P. Sheppard and Yu. S. Kivshar, Phys. Rev. E 55, 4773 (1997).
[CrossRef]

Other (1)

R. W. Boyd, Nonlinear Optics (Academic, London, 1992).

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Figures (3)

Fig. 1
Fig. 1

Top, existence domain (hatched) for the fundamental mode guided by a vortex. Points a, b, c, and d correspond to the modal structure example (a), (b), (c), and (d), respectively (bottom). Parameters are (a)–(c) σ=3 and (d) σ=0.8. Dashed–dotted curve, cutoff calculated by the variational approach.

Fig. 2
Fig. 2

Existence domain (hatched) and characteristic examples for (a) a first-order mode guided by a vortex and (b) the corresponding vector soliton.

Fig. 3
Fig. 3

Existence domain of vector solitons (hatched) and (a), (b) two examples of the solutions in the antiwaveguiding regime.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

iE1z+ΔE1-η-1E12+σE22E1=0,  iκE2z+ΔE2-γηE22+σE12E2=0,
E1=η1/2E0uRexp-iE02zexpinφ,  E2=η-1/2E0vRexp-iλ/κE02zexpimφ,
Δru-n2r2u+u-u2+σ/ηv2u=0,  Δrv-m2r2v+λv-γv2+ησu2v=0,
Δru0-n2r2u0-u0+u03=0,  Δrv-m2r2v-λv+W0rv=0,
Lu=rdu0dr2+n2r2u02+r21+u022.
Lv=-rdvdr2+λr-σu02r-rv22v2,
σ=1321+24λ+16λ2-1-4λ1-4λ.

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