Abstract

We demonstrate that a concentric ring coupler can be employed for nonlinear switching of the angular momentum of light carried by an optical vortex. We find different types of stationary vortex states in the nonlinear coupler and study coupling of both power and momentum of an optical vortex launched into one of the rings, demonstrating that the switching takes place well below the collapse threshold. The switching is more effective for the inner-ring excitation since it triggers more sharply and for the powers low enough to avoid the vortex instability and breakup.

© 2007 Optical Society of America

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References

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  1. M. S. Soskin and M. V. Vasnetsov, "Singular optics," in Progress in Optics, E. Wolf, ed., vol. 42, p. 219 (North-Holand, Amsterdam, 2001).
  2. A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, "Optical vortices and vortex solitons," in Progress in Optics, E. Wolf, ed., vol. 47, pp. 291-391 (North-Holand, Amsterdam, 2005).
  3. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, San Diego, 2003), 520 pp.
  4. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Rotary solitons in Bessel optical lattices," Phys. Rev. Lett. 93, 093904-4 (2004).
    [CrossRef] [PubMed]
  5. X. Wang, Z. Chen, and P. G. Kevrekidis, "Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices," Phys. Rev. Lett. 96, 083,904 (2006).
    [PubMed]
  6. Q. E. Hoq, P. G. Kevrekidis, D. J. Frantzeskakis, and B. A. Malomed, "Ring-shaped solitons in a dartboard photonic lattice," Phys. Lett. A 341, 341-155 (2006).
  7. L. Djaloshinski and M. Orenstein, "Disk and ring microcavity lasers and their concentric coupling," IEEE J. Quantum Electron. 35, 737-744 (1999).
    [CrossRef]
  8. M. Heiblum and J. H. Harris, "Analysis of curved optical waveguides by conformal transformation," IEEE J. Quantum Electron. 11, 75-83 (1975).
    [CrossRef]
  9. N. N. Akhmediev and A. Ankiewicz, Solitons: Nonlinear Pulses and Beams (Chapman & Hall, Cornwall, 1997).
  10. J. F. Nye, Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations (Taylor & Francis, 1999).

2006

X. Wang, Z. Chen, and P. G. Kevrekidis, "Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices," Phys. Rev. Lett. 96, 083,904 (2006).
[PubMed]

Q. E. Hoq, P. G. Kevrekidis, D. J. Frantzeskakis, and B. A. Malomed, "Ring-shaped solitons in a dartboard photonic lattice," Phys. Lett. A 341, 341-155 (2006).

2004

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Rotary solitons in Bessel optical lattices," Phys. Rev. Lett. 93, 093904-4 (2004).
[CrossRef] [PubMed]

1999

L. Djaloshinski and M. Orenstein, "Disk and ring microcavity lasers and their concentric coupling," IEEE J. Quantum Electron. 35, 737-744 (1999).
[CrossRef]

1975

M. Heiblum and J. H. Harris, "Analysis of curved optical waveguides by conformal transformation," IEEE J. Quantum Electron. 11, 75-83 (1975).
[CrossRef]

Chen, Z.

X. Wang, Z. Chen, and P. G. Kevrekidis, "Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices," Phys. Rev. Lett. 96, 083,904 (2006).
[PubMed]

Djaloshinski, L.

L. Djaloshinski and M. Orenstein, "Disk and ring microcavity lasers and their concentric coupling," IEEE J. Quantum Electron. 35, 737-744 (1999).
[CrossRef]

Frantzeskakis, D. J.

Q. E. Hoq, P. G. Kevrekidis, D. J. Frantzeskakis, and B. A. Malomed, "Ring-shaped solitons in a dartboard photonic lattice," Phys. Lett. A 341, 341-155 (2006).

Harris, J. H.

M. Heiblum and J. H. Harris, "Analysis of curved optical waveguides by conformal transformation," IEEE J. Quantum Electron. 11, 75-83 (1975).
[CrossRef]

Heiblum, M.

M. Heiblum and J. H. Harris, "Analysis of curved optical waveguides by conformal transformation," IEEE J. Quantum Electron. 11, 75-83 (1975).
[CrossRef]

Hoq, Q. E.

Q. E. Hoq, P. G. Kevrekidis, D. J. Frantzeskakis, and B. A. Malomed, "Ring-shaped solitons in a dartboard photonic lattice," Phys. Lett. A 341, 341-155 (2006).

Kartashov, Y. V.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Rotary solitons in Bessel optical lattices," Phys. Rev. Lett. 93, 093904-4 (2004).
[CrossRef] [PubMed]

Kevrekidis, P. G.

Q. E. Hoq, P. G. Kevrekidis, D. J. Frantzeskakis, and B. A. Malomed, "Ring-shaped solitons in a dartboard photonic lattice," Phys. Lett. A 341, 341-155 (2006).

X. Wang, Z. Chen, and P. G. Kevrekidis, "Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices," Phys. Rev. Lett. 96, 083,904 (2006).
[PubMed]

Malomed, B. A.

Q. E. Hoq, P. G. Kevrekidis, D. J. Frantzeskakis, and B. A. Malomed, "Ring-shaped solitons in a dartboard photonic lattice," Phys. Lett. A 341, 341-155 (2006).

Orenstein, M.

L. Djaloshinski and M. Orenstein, "Disk and ring microcavity lasers and their concentric coupling," IEEE J. Quantum Electron. 35, 737-744 (1999).
[CrossRef]

Torner, L.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Rotary solitons in Bessel optical lattices," Phys. Rev. Lett. 93, 093904-4 (2004).
[CrossRef] [PubMed]

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Rotary solitons in Bessel optical lattices," Phys. Rev. Lett. 93, 093904-4 (2004).
[CrossRef] [PubMed]

Wang, X.

X. Wang, Z. Chen, and P. G. Kevrekidis, "Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices," Phys. Rev. Lett. 96, 083,904 (2006).
[PubMed]

IEEE J. Quantum Electron.

L. Djaloshinski and M. Orenstein, "Disk and ring microcavity lasers and their concentric coupling," IEEE J. Quantum Electron. 35, 737-744 (1999).
[CrossRef]

M. Heiblum and J. H. Harris, "Analysis of curved optical waveguides by conformal transformation," IEEE J. Quantum Electron. 11, 75-83 (1975).
[CrossRef]

Phys. Lett. A

Q. E. Hoq, P. G. Kevrekidis, D. J. Frantzeskakis, and B. A. Malomed, "Ring-shaped solitons in a dartboard photonic lattice," Phys. Lett. A 341, 341-155 (2006).

Phys. Rev. Lett.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Rotary solitons in Bessel optical lattices," Phys. Rev. Lett. 93, 093904-4 (2004).
[CrossRef] [PubMed]

X. Wang, Z. Chen, and P. G. Kevrekidis, "Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices," Phys. Rev. Lett. 96, 083,904 (2006).
[PubMed]

Other

M. S. Soskin and M. V. Vasnetsov, "Singular optics," in Progress in Optics, E. Wolf, ed., vol. 42, p. 219 (North-Holand, Amsterdam, 2001).

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, "Optical vortices and vortex solitons," in Progress in Optics, E. Wolf, ed., vol. 47, pp. 291-391 (North-Holand, Amsterdam, 2005).

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, San Diego, 2003), 520 pp.

N. N. Akhmediev and A. Ankiewicz, Solitons: Nonlinear Pulses and Beams (Chapman & Hall, Cornwall, 1997).

J. F. Nye, Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations (Taylor & Francis, 1999).

Supplementary Material (3)

» Media 1: AVI (3622 KB)     
» Media 2: AVI (3714 KB)     
» Media 3: AVI (3167 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

(a) Power diagram of the ring nonlinear coupler. Dashed lines represent the unstable collapsing solutions. Inset: Sketch of the concentric ring coupler. Values used (in normalized units) are: r 1 = 5, r 2 = 8, r 3 = 11 and r 4 = 14 for radii and n 0 = 1, n 1 = 2 for indices. (b) Examples of nonlinear stationary states corresponding to the points marked on the power diagram (labels A to F are correspondent in both subfigures).

Fig. 2.
Fig. 2.

Distribution of the light intensities in the coupler for different propagation distance z, for three different regimes. Top: external core excitation for the initial power P = 5 [Media 1]. Center: external core excitation, at P = 20 [Media 2]. Bottom: internal core excitation, at P = 20 [Media 3].

Fig. 3.
Fig. 3.

Normalized power (dashed) and angular momentum (solid) vs. propagation distance for ring excitation with a single- charged vortex. The individual values for each core are plotted, together with the total values. (a) simulation for external-core excitation at P=5; (b) the same at P=20; (c) simulation for internal-core excitation at P=5; (d) the same at P=20.

Fig. 4.
Fig. 4.

Switching curves for the power (dark dashed lines) and angular momentum (light continuous lines) for (a) outer-waveguide excitation, and (b) inner-waveguide excitation. Also shown is the total angular momentum (dotted line).

Equations (4)

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i ψ z + 2 ψ + [ V ( r ) + ψ 2 ] ψ = 0 ,
ψ ( r , ϕ , z ) = u ( r ) exp ( i ϕ ) exp ( iβz ) ,
βu + d 2 u d r 2 + 1 r du dr 2 u r 2 + [ V ( r ) + u 2 ] u = 0 .
L z = Im { ψ 0 * ϕ ψ 0 rdrdϕ } = 2 πℓ u 0 ( r ) 2 rdr = ℓP .

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