Dynamics of two-dimensional coherent structures in nonlocal nonlinear media

Yakimenko, A. I.; Lashkin, Volodymyr M.; Prikhodko, O. O.

doi:10.1103/physreve.73.066605

Cited by 154 publications

(104 citation statements)

References 28 publications

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“…In this way, the generalized Vakhitov -Kolokolov (VK) stability criterion for two-component solitary waves can be applied here [16,17]. In related two-component continuous systems [18][19][20][21], modeled by coupled continual NLS equation, one can introduce a new parameter (the ratio of λ and µ) and rescale the variables, to make the stationary states depending on one (rather than two) effective chemical potential [21]. Moreover, a generalized VK stability criteria was developed for a system of N incoherently coupled continuous NLS equations in Ref.…”

Section: The Modelmentioning

confidence: 99%

Unstaggered-staggered solitons in two-component discrete nonlinear Schrödinger lattices

2012

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We present stable bright solitons built of coupled unstaggered and staggered components in a symmetric system of two discrete nonlinear Schrödinger (DNLS) equations with the attractive selfphase-modulation (SPM) nonlinearity, coupled by the repulsive cross-phase-modulation (XPM) interaction. These mixed modes are of a "symbiotic" type, as each component in isolation may only carry ordinary unstaggered solitons. The results are obtained in an analytical form, using the variational and Thomas-Fermi approximations (VA and TFA), and the generalized Vakhitov-Kolokolov (VK) criterion for the evaluation of the stability. The analytical predictions are verified against numerical results. Almost all the symbiotic solitons are predicted by the VA quite accurately, and are stable. Close to a boundary of the existence region of the solitons (which may feature several connected branches), there are broad solitons which are not well approximated by the VA, and are unstable.

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Section: The Modelmentioning

confidence: 99%

Unstaggered-staggered solitons in two-component discrete nonlinear Schrödinger lattices

2012

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“…Gaussian profiles were found to be a good approximation near the peak of a one-dimensional nematicon but decayed too fast in its tail. Lagrangian methods were also employed to find approximations to the steady twodimensional solitary wave solutions of a nonlocal nonlinear Schrödinger (NLS) equation with a Gaussian kernel in the nonlinear, nonlocal term [10]. However, such a Gaussian kernel is not applicable to liquid crystals.…”

Section: Introductionmentioning

confidence: 99%

Modulation solutions for nematicon propagation in nonlocal liquid crystals

2007

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The propagation of solitary waves, so-called nematicons, in a nonlinear nematic liquid crystal is considered in the nonlocal regime. Approximate modulation equations governing the evolution of input beams into steady nematicons are derived by using suitable trial functions in a Lagrangian formulation of the equations for a nematic liquid crystal. The variational equations are then extended to include the effect of diffractive loss as the beam evolves. It is found that the nonlocal nature of the interaction between the light and the nematic has a significant effect on the form of this diffractive radiation. Furthermore, it is this shed radiation that allows the input beam to evolve to a steady nematicon. Finally, excellent agreement is found between solutions of the modulation equations and numerical solutions of the nematic liquid-crystal equations. Disciplines Physical Sciences and Mathematics Publication DetailsMinzoni, A., Smyth, N. The propagation of solitary waves, so-called nematicons, in a nonlinear nematic liquid crystal is considered in the nonlocal regime. Approximate modulation equations governing the evolution of input beams into steady nematicons are derived by using suitable trial functions in a Lagrangian formulation of the equations for a nematic liquid crystal. The variational equations are then extended to include the effect of diffractive loss as the beam evolves. It is found that the nonlocal nature of the interaction between the light and the nematic has a significant effect on the form of this diffractive radiation. Furthermore, it is this shed radiation that allows the input beam to evolve to a steady nematicon. Finally, excellent agreement is found between solutions of the modulation equations and numerical solutions of the nematic liquid-crystal equations.

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“…The picture changes drastically when the nonlinear material response is nonlocal. Nonlocality has profound effects on the complexity of solitons since it allows to overcome repulsion between out-of-phase bright [10][11][12][13][14][15][16][17] or in-phase dark solitons [18] that can form bound states observed in one-dimensional settings [19,20]. In two transverse dimensions, however, the only complex structures thus far observed with scalar solitons were bright vortex-rings [21].…”

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confidence: 99%