Stability of an optical vortex in a circular nematic cell

Minzoni, Antonmaria A.; Smyth, Noel F.; Xu, Zhiyong

doi:10.1103/physreva.81.033816

Cited by 18 publications

(20 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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]. An advantage of using modulation theory to develop approximate solutions is that the diffractive radiation shed when a solitary wave evolves can be incorporated [8,9,21].…”

Section: Introductionmentioning

confidence: 76%

Reorientational versus Kerr dark and gray solitary waves using modulation theory

et al. 2011

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 76%

Reorientational versus Kerr dark and gray solitary waves using modulation theory

et al. 2011

Self Cite

View full text Add to dashboard Cite

show abstract

“…To achieve this task, a blend of an exact solution found using the method of images (MOI) and a trial function, coupled with a Lagrangian formulation and modulation theory [35], is used. Modulation theory based on suitable trial functions has been found to be a useful and successful technique for giving results in excellent agreement with full numerical solutions [14,16,18,27,28,30,36] and experimental results [37,38]. In addition, it is found that the method of images possesses distinct advantages over other solution methods in that it requires an order of magnitude fewer terms to obtain accurate solutions [34].…”

Section: Introductionmentioning

confidence: 91%

“…I. The analysis presented here combines an exact solution and a trial-functionbased averaged Lagrangian method [18,26,34]. A Gaussian profile is used for the trial function of the electric field of the optical vortex and is…”

Section: Evolution Equationsmentioning

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%

See 1 more Smart Citation

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

“…Spatially nonlocality is a generic property in different materials including the photorefractive media [1,2], thermal nonlinear media [3][4][5][6][7], liquid crystals [8][9][10][11][12][13], and so on. Nonlocality can lead to new kinds of waves that would have been otherwise impossible in local nonlinear media.…”

Section: Introductionmentioning

confidence: 99%

(2+1)D surface solitons at the interface between a linear medium and a nonlocal nonlinear medium

Shi

Guo

2011

J. Opt. Soc. Am. B

View full text Add to dashboard Cite

We address (2+1)D surface solitons occurring at the interface between a linear medium and a nonlocal nonlinear medium whose nonlinear contribution to the refractive index has a initial value at the interface. We find that there exist stable single and dipole surface solitons which do not exhibit a power threshold. The properties of the surface solitons can be affected by the initial value and the degree of nonlocality. When a laser beam is launched away from the interface, the beam will be periodic oscillations.

show abstract

Stability of an optical vortex in a circular nematic cell

Cited by 18 publications

References 24 publications

Reorientational versus Kerr dark and gray solitary waves using modulation theory

Reorientational versus Kerr dark and gray solitary waves using modulation theory

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

(2+1)D surface solitons at the interface between a linear medium and a nonlocal nonlinear medium

Contact Info

Product

Resources

About