Vector vortex solitons in nematic liquid crystals

Abstract

We analyze the existence and stability of two-component vector solitons in nematic liquid crystals for which one of the components carries angular momentum and describes a vortex beam. We demonstrate that the nonlocal, nonlinear response can dramatically enhance the field coupling leading to the stabilization of the vortex beam when the amplitude of the second beam exceeds some threshold value. We develop a variational approach to describe this effect analytically. c 2013 Optical Society of America OCIS codes: 190.4420; 190.5530; 190.5940 Optical vortices are usually introduced as phase singularities in diffracting optical beams [1] and can be generated in both linear and nonlinear media. The well known effect accompanying the propagation of such singular beams and vortex solitons in self-focusing, nonlinear media is vortex breakup into several fundamental solitons via a symmetry-breaking azimuthal instability [2]. However, recent numerical studies have revealed that spatially localized vortex solitons can be stabilized in highly nonlocal self-focusing nonlinear media [3][4][5]. This stabilization effect was later explained analytically [6] by employing a modulation theory for the vortex parameters based on an averaged Lagrangian.Spatial optical vector solitons can form when several beams propagate together, interacting parametrically or via the effect of cross-phase modulation [7]. The simplest vector solitons are known as shape-preserving, selflocalized solutions of coupled nonlinear evolution equations [7]. A novel class of vector solitons in the form of two color spatial solitons in a highly nonlocal and anisotropic Kerr-like medium were predicted to exist in nematic liquid crystals [8][9][10]. The first experimental observations of anisotropic, nonlocal vector solitons in unbiased nematic liquid crystals were reported by Alberucci et al. [10], who investigated the interaction between two beams of different wavelengths and observed that two extraordinarily polarized beams of different wavelengths can nonlinearly couple, compensating for the beam walk-off, so creating a vector soliton.The main purpose of this Letter is twofold. Firstly, we introduce a novel class of vector solitons in nonlocal, nonlinear media, such as nematic liquid crystals and study their properties. These vector solitons appear as two color, self-trapped beams for which one of the components carries angular momentum and describes a vortex beam. Secondly, we demonstrate that the nonlocal, nonlinear response may dramatically enhance the field coupling, leading to the stabilization of the vortex for much weaker nonlocality when the amplitude of the second beam exceeds some threshold value. We develop a variational approach to describe this effect analytically.We consider the propagation of two light beams of different wavelengths in a cell filled with a nematic liquid crystal. The light propagates in the z direction, with the (x, y) plane orthogonal to this. The electric fields of the light beams are assumed to be polarized in the x dire...

Optical vortices in antiguides

“…Hence, it can neither spontaneously split into separate vortices of smaller charge, nor can it vanish owing to the conservation of the total topological charge. In a standard waveguide (positive A) the vortex can be confined by the refractive potential, consistent with previous studies on vortex stabilization by means of nonlocal spatial solitons [6,10,11,17]. In a curved positive waveguide, the vortex path can bend, undergoing profile distortions, vortexantivortex pair generation, and radiation losses related to the curvature and to the waveguide core size relative to the input beam.…”

Reorientational versus Kerr dark and gray solitary waves using modulation theory

“…where the over bar denotes the Laplace transform, D is an integration constant and λ − is given by (18). It is not possible to invert this Laplace transform, but a large z expansion, i.e.…”

“…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].…”

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