Nematicons: self-localised beams in nematic liquid crystals

Assanto, Gaetano; Karpierz, Mirosław A.

doi:10.1080/02678290903033441

Cited by 90 publications

(66 citation statements)

References 66 publications

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“…The distinction between solitary wave and soliton solutions is that when any number of solitons interact they do not change form and the only outcome of the interaction is a phase shift. Various generalisations of the NLS equation (1) arise in optics [2] and possess solitary wave, but not soliton, solutions, including nonlinear beams in reorientational media such as nematic liquid crystals, which is of particular relevance to the present work [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

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Reorientational versus Kerr dark and gray solitary waves using modulation theory

et al. 2011

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We develop a modulation theory model based on a Lagrangian formulation to investigate the evolution of dark and gray optical spatial solitary waves for both the defocusing nonlinear Schr¨odinger (NLS) equation and the nematicon equations describing nonlinear beams, nematicons, in self-defocusing nematic liquid crystals. Since it has an exact soliton solution, the defocusing NLS equation is used as a test bed for the modulation theory applied to the nematicon equations,which have no exact solitarywave solution.We find that the evolution of dark and gray NLS solitons, as well as nematicons, is entirely driven by the emission of diffractive radiation, in contrast to the evolution of bright NLS solitons and bright nematicons.Moreover, the steady nematicon profile is nonmonotonic due to the long-range nonlocality associated with the perturbation of the optic axis. Excellent agreement is obtained with numerical solutions of both the defocusing NLS and nematicon equations. The comparisons for the nematicon solutions raise a number of subtle issues relating to the definition and measurement of the width of a dark or gray nematicon. Disciplines Physical Sciences and Mathematics Publication DetailsAssanto, G., Marchant, T. R., Minzoni, A. A. & Smyth, N. F. (2011 We develop a modulation theory model based on a Lagrangian formulation to investigate the evolution of dark and grey optical spatial solitary waves for both the defocusing nonlinear Schrödinger (NLS) equation and the nematicon equations describing nonlinear beams, nematicons, in selfdefocusing nematic liquid crystals. Since it has an exact soliton solution, the defocusing NLS equation is used as a test bed for the modulation theory applied to the nematicon equations, which have no exact solitary wave solution. We find that the evolution of dark and grey NLS solitons, as well as nematicons, is entirely driven by the emission of diffractive radiation, in contrast to the evolution of bright NLS solitons and bright nematicons. Moreover, the steady nematicon profile is non-monotonic due to the long range nonlocality associated with the perturbation of the optic axis. Excellent agreement is obtained with numerical solutions of both the defocusing NLS and nematicon equations. The comparisons for the nematicon solutions raise a number of subtle issues relating to the definition and measurement of the width of a dark or grey nematicon.

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Section: Introductionmentioning

confidence: 99%

“…The steady state value w f is just the relation for the exact dark (grey) soliton solution (3). Finally, the modulation equations for the evolution of a dark (grey) NLS soliton have a simple analytical solution, unlike those for the evolution of a bright NLS soliton [8].…”

Section: Radiation Loss For Dark and Grey Nls Solitonsmentioning

confidence: 99%

Reorientational versus Kerr dark and gray solitary waves using modulation theory

et al. 2011

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“…24 Equations (1)- (2) support the generation of stable nonlocal spatial optical solitons in NLCs, self-confined extraordinarily polarized wavepackets also termed nematicons. 23,25,26 From Eqs. (1) and (2), an equivalent nonlocal Kerr coefficient n 2 = 2ϵ 0 ∆ϵ sin(2θ 0 )n 2 e (θ 0 )/(4K) can be derived.…”

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Voltage-driven beam bistability in a reorientational uniaxial dielectric

et al. 2016

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We report on voltage controlled bistability of optical beams propagating in a nonlocal reorientational uniaxial dielectric, namely, nematic liquid crystals. In the nonlinear regime where spatial solitons can be generated, two stable states are accessible to a beam of given power in a finite interval of applied voltages, one state corresponding to linear diffraction and the other to self-confinement. We observe such a first-order transition and the associated hysteresis in a configuration when both the beam and the voltage reorientate the molecules beyond a threshold.

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“…The most important mechanism is reorientational nonlinearity as the molecules react to the electric and magnetic fields and change their average orientation i.e. director n. To describe the optical properties of liquid crystals it is crucial to model molecular reorientation as it influences refractive indexes and absorption which strongly affect light propagation in such materials [1][2][3]. However, there are some analytical solutions of molecular reorientation for simplified cases [4][5]; in more complex configurations, numerical methods have to be employed.…”

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Modeling of molecular reorientation in nematic liquid crystals

Sala

Bujok

Karpierz

2016

Photon. Lett. Poland

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Abstract-In this paper, the modeling of molecular reorientation in nematic liquid crystals is described. The theoretical model is based on Frank-Oseen elastic theory. By minimizing the equation on free energy, an equation describing molecular reorientation is obtained. To get a solution, two numerical methods (Successive Over-Relaxation and Multigrid) are employed and compared for the numerical results of director orientation and computation time.

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Nematicons: self-localised beams in nematic liquid crystals

Cited by 90 publications

References 66 publications

Reorientational versus Kerr dark and gray solitary waves using modulation theory

Reorientational versus Kerr dark and gray solitary waves using modulation theory

Voltage-driven beam bistability in a reorientational uniaxial dielectric

Modeling of molecular reorientation in nematic liquid crystals

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