Vortices in Nematic Liquid Crystals

Minzoni, Antonmaria A.; Sciberras, Luke W.; Smyth, Noel F.; Worthy, Annette L.

doi:10.1002/9781118414637.ch15

Cited by 3 publications

(7 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As the vortex was not given an initial velocity, the vortex's initial motion arises from this repulsive force. Thus, if the interaction with the boundary does not disturb the phase singularity at the center of the vortex, the cell walls will completely repel the vortex and stability will be maintained, as in a circular cell [17,18]. Figure 3(d) confirms the conclusions drawn from Figs.…”

Section: Resultssupporting

confidence: 76%

“…An optical vortex shows the same "bouncing" as a nematicon, for the same reasons as for a nematicon [33,34]. The vortex is also stable if it is sufficiently far from a wall, as found for a vortex in a circular cell [17,18]. The parameter values were chosen so that the vortex solitary wave is above the minimum power threshold for its existence and below the threshold at which it will split into two.…”

Section: Resultsmentioning

confidence: 99%

“…In addition, optical vortex solitary waves are unstable in local media, but are stable in nonlocal media, such as nematic liquid crystals, as the symmetry-breaking mode-2 azimuthal instability is suppressed if the nonlocality is large enough [13,14]. In contrast to local media [11,15], optical vortex solitary waves in nonlocal media have received considerably less attention, especially in a NLC [14,[16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

“…. is the topological charge of the vortex [17]. A gradient of circulation is forced in the angular variable around the vortex, with the amplitude zero at the center to compensate for the phase singularity, as discussed above.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Optical vortex solitary wave in a bounded nematic-liquid-crystal cell

et al. 2013

Self Cite

View full text Add to dashboard Cite

Modulation theory, based on a Lagrangian formulation of the governing equations, is used to investigate the propagation of a nonlinear, nonlocal optical vortex solitary wave in a finite nematic-liquid-crystal cell. The nematic response to the vortex is calculated using the approach of themethod of images (MOI). It is demonstrated that the MOI is a reliable alternative to the usual Fourier series solution as it requires an order of magnitude fewer terms to obtain excellent agreement with numerical solutions. It is found that the cell walls, in addition to repelling the optical vortex solitary wave, as for an optical solitary wave, can destabilize it due to the fixed director orientation at the walls. A linearized stability analysis is used to explain and analyze this instability. In particular, the minimum distance of approach of a stable vortex to the wall is determined from the stability analysis. Good agreement is found with numerical minimum approach distances. Modulation theory, based on a Lagrangian formulation of the governing equations, is used to investigate the propagation of a nonlinear, nonlocal optical vortex solitary wave in a finite nematic-liquid-crystal cell. The nematic response to the vortex is calculated using the approach of the method of images (MOI). It is demonstrated that the MOI is a reliable alternative to the usual Fourier series solution as it requires an order of magnitude fewer terms to obtain excellent agreement with numerical solutions. It is found that the cell walls, in addition to repelling the optical vortex solitary wave, as for an optical solitary wave, can destabilize it due to the fixed director orientation at the walls. A linearized stability analysis is used to explain and analyze this instability. In particular, the minimum distance of approach of a stable vortex to the wall is determined from the stability analysis. Good agreement is found with numerical minimum approach distances. Optical vortex solitary wave in a bounded nematic-liquid-crystal cell

show abstract

Section: Resultssupporting

confidence: 76%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optical vortex solitary wave in a bounded nematic-liquid-crystal cell

et al. 2013

Self Cite

View full text Add to dashboard Cite

show abstract

“…Indeed, this method can be used for the equations describing nonlinear beam evolution in other bulk media [11][12][13][14][15][16][17][18]. In this regard, the view of the effect of the cell walls as due to image sources has promise [47]. The Green's function for the images solution used in the present work was that for the half plane mapped conformally onto a rectangle.…”

Section: Discussionmentioning

confidence: 99%

Propagation of optical spatial solitary waves in bias-free nematic-liquid-crystal cells

et al. 2011

Self Cite

View full text Add to dashboard Cite

The propagation of a bulk optical solitary wave in a rectangular cell filled with a nematic liquid crystal-a nematicon-is mathematically modelled. In order to overcome the Freédricksz threshold the cell walls are rubbed to pretilt the nematic. A modulation theory, based on a Lagrangian formulation, is developed for the (2 + 1)-dimensional propagation of the solitary wave beam down the cell. This modulation theory is based on two different formulations of the director distribution. The relative advantages and disadvantages of these two methods are discussed. A previously unexplored method based on images is found to possess significant advantages. Excellent agreement with full numerical solutions of the nematicon equations is found for both methods. Finally, the implications of the results obtained for some widely used approximations to the nematicon equations are discussed, particularly their use in comparisons with experimental results.

show abstract

Soliton Gyroscopes in Media with Spatially Growing Repulsive Nonlinearity

et al. 2014

View full text Add to dashboard Cite

We find that the recently introduced model of self-trapping supported by a spatially growing strength of a repulsive nonlinearity gives rise to robust vortex-soliton tori, i.e., three-dimensional vortex solitons, with topological charges S≥1. The family with S=1 is completely stable, while the one with S=2 has alternating regions of stability and instability. The families are nearly exactly reproduced in an analytical form by the Thomas-Fermi approximation. Unstable states with S=2 and 3 split into persistently rotating pairs or triangles of unitary vortices. Application of a moderate torque to the vortex torus initiates a persistent precession mode, with the torus' axle moving along a conical surface. A strong torque heavily deforms the vortex solitons, but, nonetheless, they restore themselves with the axle oriented according to the vectorial addition of angular momenta.

show abstract

Vortices in Nematic Liquid Crystals

Cited by 3 publications

References 21 publications

Optical vortex solitary wave in a bounded nematic-liquid-crystal cell

Optical vortex solitary wave in a bounded nematic-liquid-crystal cell

Propagation of optical spatial solitary waves in bias-free nematic-liquid-crystal cells

Soliton Gyroscopes in Media with Spatially Growing Repulsive Nonlinearity

Contact Info

Product

Resources

About