Optical solitary waves escaping a wide trapping potential in nematic liquid crystals: Modulation theory

Assanto, Gaetano; Minzoni, Antonmaria A.; Peccianti, Marco; Smyth, Noel F.

doi:10.1103/physreva.79.033837

Cited by 57 publications

(112 citation statements)

References 21 publications

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“…In fact, the equations analyzed here, predict the formation of solitary-like structures for both atoms and light which can move away from the region where they were generated. Although in our case there is no external trapping but only the self-consistent interaction of atoms and laser, these results are suggestively similar to escaping solitons described and observed in com-pletely different environments, for instance in nematic liquid crystals, [11]. We will breafly review the basic physics of the semiclassical model and the limitations to be considered in Sec.II.…”

Section: Introductionsupporting

confidence: 83%

Co-propagating Bose-Einstein condensates and electromagnetic radiation: Emission of mutually localized structures

et al. 2011

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Section: Introductionsupporting

confidence: 83%

Co-propagating Bose-Einstein condensates and electromagnetic radiation: Emission of mutually localized structures

et al. 2011

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“…This integral does not have an exact, closed form and the approximation used is valid in the experimental nonlocal limit [7,29]. For physically realistic experimental scenarios ν = O(100) [11], in which case the used approximation is accurate.…”

Section: B Dark and Grey Nematiconsmentioning

confidence: 99%

“…For NLS equations which do possess an exact solitary wave solution, this modulation theory approach reduces to standard perturbation theory [8]. Modulation theory has proven to be a successful approximate analytical theory providing solutions in excellent agreement with numerical [9,10] and experimental results [5,11,12], even for the refraction of nematicons in non-uniform media [12][13][14][15]. In addition, it has been found to give excellent results for more complicated structures, such as undular bores [16] and optical vortices [17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

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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“…The accuracy of the modulation solution with respect to the angle of refraction for different initial V values is shown in Fig. 4, using physical parameter values [17]. It is clear that the modulation solution is highly accurate for all values of V 0 , particularly for values close to 0.…”

Section: Optical Path Control Of Solitary Waves In Dye-doped Nematic mentioning

confidence: 93%

Optical path control of solitary waves in dye-doped nematic liquid crystals

Assanto

Skuse

Smyth³

2009

Photon. Lett. Poland

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Abstract-The light-induced steering of spatial optical solitary waves in dye-doped nematic liquid crystals is analyzed. Shining a control beam through the cell results in a boundary mediated change in the orientation of the molecular director, thereby a perturbation in the refractive index of the medium. This re-orientational effect can optically steer spatial solitary waves propagating in an orthogonal plane within the liquid crystal layer. The equations governing this steering are solved using a Lagrangian formulation, resulting in modulation equations for the self-trapped beam path. Very good agreement is obtained between solutions of the modulation equations and numerical solutions of the full governing equations.Nematicons-spatial optical solitary waves in nematic liquid crystals-result from a balance between linear diffraction and nonlinear self-focusing of an input beam in the presence of nonlocality, an effect brought about by the thermal or reorientational response of the material to light [1][2]. Once created, nematicons are stable and robust, with the ability to survive defects and perturbations [3][4][5][6][7]. An approach to introducing a defect into nematic liquid crystals (NLC) is to alter the response of the medium to light by introducing a small amount of dye molecules, a technique known as doping [8]. Dyedoping causes a change in the absorption of the NLC. In specific spectral intervals, an external illumination, i.e. a control beam, impinging onto the medium can perturb the molecular reorientation according to the control beam intensity and/or polarisation [9][10][11]. Whilst nematicons can survive the interaction with such defects, their evolution will be somehow affected, with a change in trajectory. Piccardi, Assanto, Lucchetti and Simoni [11] experimentally observed nematicons propagating in a dye-doped cell where control beams induced refractive defects; they demonstrated solitary wave steering dependent on power, shape and relative position of the external perturbation with respect to the nematicon. They also reported solitary wave refraction and total internal reflection [11]. In this Letter we investigate theoretically the steering of a nematicon by an optically driven refractive index change. Modulation equations describing * E-mail: N.Smyth@ed.ac.uk the beam path are derived and solutions of these equations are found to be in excellent agreement with numerical solutions of the governing equations.Let us consider a linearly polarised, coherent light beam propagating through a cell filled with a dye-doped nematic liquid crystal (DD-NLC), as illustrated in Fig. 1. The input beam is launched so that it initially propagates at an arbitrary angle with respect to the direction z down the cell. The coordinates (x,y) are orthogonal to the z direction. The input beam is polarised with its electric field along x, i.e. it is an extraordinary wave in the NLC equivalent uniaxial. In the bulk NLC the molecules are pre-tilted at an angle θ 0 in the plane (x,z) by an external electric field (voltage)...

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Optical solitary waves escaping a wide trapping potential in nematic liquid crystals: Modulation theory

Cited by 57 publications

References 21 publications

Co-propagating Bose-Einstein condensates and electromagnetic radiation: Emission of mutually localized structures

Co-propagating Bose-Einstein condensates and electromagnetic radiation: Emission of mutually localized structures

Reorientational versus Kerr dark and gray solitary waves using modulation theory

Optical path control of solitary waves in dye-doped nematic liquid crystals

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