Abstract

We present a new type of soliton solutions in nonlinear photonic systems with discrete point-symmetry. These solitons have their origin in a novel mechanism of breaking of discrete symmetry by the presence of nonlinearities. These so-called nodal solitons are characterized by nodal lines determined by the discrete symmetry of the system. Our physical realization of such a system is a 2D nonlinear photonic crystal fiber owning 𝓒 symmetry.

© 2005 Optical Society of America

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References

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  1. K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, Berlin, 2001)
  2. J.W. Fleischer,M. Segev, N. K. Efremedis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422, 147–150 (2003)
    [CrossRef] [PubMed]
  3. D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. G. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92, 123903 (2004)
    [CrossRef] [PubMed]
  4. J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, “Observation of vortex-ring “discrete” solitons in 2D photonic lattices,” Phys. Rev. Lett. 92, 123904 (2004)
    [CrossRef] [PubMed]
  5. A. Ferrando, M. Zacarés, P. F. de Córdoba, D. Binosi, and J. A. Monsoriu, “Vortex solitons in photonic crystal fibers,” Opt. Express 12, 817–822 (2004).
    [CrossRef] [PubMed]
  6. M. Hamermesh, Group theory and its application to physical problems, Addison-Wesley series in physics, 1st ed. (Addison-Wesley, Reading, Massachusetts, 1964).
  7. A. Ferrando, M. Zacarés, P. F. de Córdoba, D. Binosi, and J. A. Monsoriu, “Spatial soliton formation in photonic crystal fibers,” Opt. Express 11, 452–459 (2003).
    [CrossRef] [PubMed]
  8. Z. H. Musslimani and J. Yang, “Self-trapping of light in a two-dimensional photonic lattice,” J. Opt. Soc. Am. B 21, 973–981 (2004)
    [CrossRef]
  9. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Does the nonlinear Schrödinger equation correctly describe beam propagation?,” Opt. Lett. 18, 411–413 (1993).
    [CrossRef] [PubMed]
  10. G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518 (1999)
    [CrossRef] [PubMed]
  11. T. J. Alexander, A. A. Sukhorukov, and Y. S. Kivshar, “Asymmetric vortex solitons in nonlinear periodic lattices,” Phys. Rev. Lett 93, 063901 (2004)
    [CrossRef] [PubMed]

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

Nature (1)

J.W. Fleischer,M. Segev, N. K. Efremedis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422, 147–150 (2003)
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. Lett (1)

T. J. Alexander, A. A. Sukhorukov, and Y. S. Kivshar, “Asymmetric vortex solitons in nonlinear periodic lattices,” Phys. Rev. Lett 93, 063901 (2004)
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. G. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92, 123903 (2004)
[CrossRef] [PubMed]

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, “Observation of vortex-ring “discrete” solitons in 2D photonic lattices,” Phys. Rev. Lett. 92, 123904 (2004)
[CrossRef] [PubMed]

Science (1)

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518 (1999)
[CrossRef] [PubMed]

Other (2)

K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, Berlin, 2001)

M. Hamermesh, Group theory and its application to physical problems, Addison-Wesley series in physics, 1st ed. (Addison-Wesley, Reading, Massachusetts, 1964).

Supplementary Material (2)

» Media 1: GIF (749 KB)     
» Media 2: GIF (576 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

Two nodal solitons for l=1 (Λ=23µm, a=8µm, γ=0.006 and wavelength λ=1064nm): (a)–(b) amplitude and phase, respectively, of the S nodal soliton; (c)–(d) amplitude and phase, respectively, of the A nodal soliton. Inset: schematic transverse representation of a PCF.

Fig. 2.
Fig. 2.

Effective index of a soliton solution, n sol vs the nonlinear coupling γ for symmetric (dotted line) and antisymmetric (dashed line) solitons and vortex and antivortex solitons with l=1 (solid line).

Fig. 3.
Fig. 3.

Evolution of a diagonal perturbation of a S nodal soliton showing asymptotic stability. (749 KB)

Fig. 4.
Fig. 4.

Non-diagonal perturbation of a S nodal soliton. In this case, an oscillatory instability occurs. (576 KB)

Equations (3)

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( L 0 + L N L ( Φ ) ) Φ = 2 Φ z 2 ,
( L 0 + L N L ( ϕ ) ) ϕ = β 2 ϕ .
ϕ δ l ( r , θ ) = 2 r ϕ l s ( r , θ ) cos [ l θ + ϕ l p ( r , θ ) + δ ] , l = 1 , 2 .

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