Liquid Crystal Light Valves: a versatile platform for Nematicons

The propagation of solitary waves in nematic liquid crystals in the presence of localized nonuniformities is studied. These nonuniformities can be caused by external electric fields, other light beams, or any other mechanism which results in a modified director orientation in a localized region of the liquid-crystal cell. The net effect is that the solitary wave undergoes refraction and trajectory bending. A general modulation theory for this refraction is developed, and particular cases of circular, elliptical, and rectangular perturbations are considered. The results are found to be in excellent agreement with numerical solutions

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“…(e κz 2 − e κz 1 ), as found in [16,20]. Poisson's equation (1) also has a simple exact solution for a circular region.…”

Section: Background Director Fieldmentioning

confidence: 71%

“…In Eqs. (20) and (21), the nonlinear correction to the walk-off, i θ n E nx , has been neglected as this term is O(V θ n ), where both V and θ n are O(0.1). The major nonlinear contribution comes from the last term in (20).…”

Section: Modulation Equationsmentioning

confidence: 99%

Refraction of nonlinear beams by localized refractive index changes in nematic liquid crystals

et al. 2010

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“…seen that both modulation solutions give identical results that are in excellent agreement with the full numerical trajectory. This is because the amplitude-width and position-velocity oscillations of nonlinear beams in liquid crystals tend to decouple [28,36,55,56], so even though the method-of-images and Fourier series solutions give different amplitudes, they can agree in the position. Again, the first eight nearest-neighbor images give a very good comparison with the numerical position.…”

Section: Resultsmentioning

confidence: 99%

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

et al. 2013

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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

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“…The most innovative way seems to be a nonlinear waveguides array first introduced by Christodoulides et al [2]. This concept has been widely developed by Assanto, and also by Assanto and Karpierz et al [3][4][5]. The authors used the interaction of a laser beam with an lc layer driven by patterned electrodes forming light guiding channels.…”

mentioning

confidence: 99%

Electromagnetic wave beam self - guidance in liquid crystal - semiconductor cell

Walczak

2010

Photon. Lett. Poland

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Liquid Crystal Light Valves: a versatile platform for Nematicons

Cited by 11 publications

References 11 publications

Refraction of nonlinear beams by localized refractive index changes in nematic liquid crystals

Refraction of nonlinear beams by localized refractive index changes in nematic liquid crystals

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

Electromagnetic wave beam self - guidance in liquid crystal - semiconductor cell

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