Stability of vortex solitons in a photorefractive optical lattice

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10 DEUTSCHE PHYSIKALISCHE GESELLSCHAFT(a) (b) (c)(d) (e) (f)Figure 7. (a) Intensity field of the optical lattice with I 0 = 1.5I d ; (b, c, e, f)intensity fields of on-site lattice vortices with peak intensities 10, 5.5, 2 and0.55I d , respectively, under the applied bias field E 0 = 5.5; (d) phase structureof these vortices.(a)10 2 power10 110 0peak intensity2.5 3 3.5 4Propagation constant µGrowth rates0.20.150.10.050(b)E 0=5.5E 0=5.3stable2 4 6Vortex peak intensityFigure 8. (a) Power and peak-intensity diagrams of on-site lattice vorticesat I 0 = 1.5I d and E 0 = 5.5; ——, stable vortices; ----, unstable vortices.(b) Growth rates of on-site vortices versus their peak intensity at two appliedbias fields E 0 = 5.3 and 5.5.New Journal of Physics 6 (2004) 47 (http://www.njp.org/)
11 DEUTSCHE PHYSIKALISCHE GESELLSCHAFTLattice Peak Intensity3.532.521.51stableE 0=5.3E 0=5.50.5unstable00 1 2 3 4 5Vortex Peak IntensityFigure 9. Stability boundaries of on-site lattice vortex solitons in the (I p ,I 0 )plane at two applied bias fields E 0 = 5.3 and 5.5. Vortices inside the boundaryare linearly stable.than that for off-site vortices, another sign that on-site vortices are generally more stable.Note that when E 0 >E 0c , even though stable on-site vortices exist, they have to be in theintermediate-intensity regime. In addition, the lattice intensity has to be in the intermediatevalue range too, similar to off-site vortices. Non-linear evolution of stable and unstable onsitevortex solitons under random-noise perturbations is qualitatively similar to that of off-sitevortices (see figures 3–5), and will not be repeated here.4. SummaryIn summary, we have carried out a numerical stability analysis for both the on- and off-sitelattice vortices with unit charge in a 2D photorefractive optical lattice. We have shown thathigh- and low-intensity lattice vortices of both types suffer oscillatory and VK instabilities, butintermediate-intensity vortices can be stable if the lattice intensity is moderate, and the appliedDC field is above a certain threshold value. Under the same physical conditions, on-site vorticesare more stable than off-site ones. Higher bias field stabilizes lattice vortices.AcknowledgmentsThis work was supported in part by a NASA EPSCoR grant.References[1] Kivshar Y S and Luther-Davies B 1998 Phys. Rep. 298 81[2] Matthews M R, Anderson B P, Haljan P C, Hall D S, Wieman C E and Cornell E A 1999 Phys. Rev. Lett.83 2498[3] Madison K W, Chevy F, Wohlleben W and Dalibard J 2000 Phys. Rev. Lett. 84 806New Journal of Physics 6 (2004) 47 (http://www.njp.org/)
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Stability of vortex solitons in a photorefractive optical lattice

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