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Register a new userReorientational solitons in nematic liquid crystals with modulated alignment
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In uniaxial soft matter with a reorientational nonlinearity, such as nematic liquid crystals, a light beam in the extraordinary polarization walks off its wavevector due to birefringence, while it undergoes self-focusing via an increase in refractive index and eventually forms a spatial soliton. Hereby the trajectory evolution of solitons in nematic liquid crystals- nematicons- in the presence of a linearly varying transverse orientation of the optic axis is analysed. In this study we use and compare two approaches: i) a slowly varying (adiabatic) approximation based on momentum conservation of the soliton in a Hamiltonian sense; ii) the Frank-Oseen elastic theory coupled with a fully vectorial and nonlinear beam propagation method. The models provide comparable results in such a non-homogeneously oriented uniaxial medium and predict curved soliton paths with either monotonic or non-monotonic curvatures. The minimal power needed to excite a solitary wave via reorientation remains essentially the same in both uniform and modulated cases.
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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.
Thanks to their unique properties, nematic liquid crystals feature a variety of mechanisms for light-matter interactions. For continuous-wave optical excitations, the two dominant contributions stem from reorientational and thermal nonlinearities. We thoroughly analyze the competing roles of these two nonlinear responses with reference to self-focusing/defocusing and, eventually, the formation of nonlinear diffraction-free wavepackets, the so-called spatial optical solitons. To this extent we refer to dye-doped nematic liquid crystals in planar cells and continuous-wave beams at two distinct wavelengths in order to adjust the relative weights of the two responses. The theoretical analysis is complemented by numerical simulations in the highly nonlocal approximation and compared to experimental results.
Motivated by experiments in electroconvection in nematic liquid crystals with homeotropic alignment we study the coupled amplitude equations describing the formation of a stationary roll pattern in the presence of a weakly-damped mode that breaks isotropy. The equations can be generalized to describe the planarly aligned case if the orienting effect of the boundaries is small, which can be achieved by a destabilizing magnetic field. The slow mode represents the in-plane director at the center of the cell. The simplest uniform states are normal rolls which may undergo a pitchfork bifurcation to abnormal rolls with a misaligned in-plane director.We present a new class of defect-free solutions with spatial modulations perpendicular to the rolls. In a parameter range where the zig-zag instability is not relevant these solutions are stable attractors, as observed in experiments. We also present two-dimensionally modulated states with and without defects which result from the destabilization of the one-dimensionally modulated structures. Finally, for no (or very small) damping, and away from the rotationally symmetric case, we find static chevrons made up of a periodic arrangement of defect chains (or bands of defects) separating homogeneous regions of oblique rolls with very small amplitude. These states may provide a model for a class of poorly understood stationary structures observed in various highly-conducting materials (prechevrons or broad domains).
The director configuration of disclination lines in nematic liquid crystals in the presence of an external magnetic field is evaluated. Our method is a combination of a polynomial expansion for the director and of further analytical approximations which are tested against a numerical shooting method. The results are particularly simple when the elastic constants are equal, but we discuss the general case of elastic anisotropy. The director field is continuous everywhere apart from a straight line segment whose length depends on the value of the magnetic field. This indicates the possibility of an elongated defect core for disclination lines in nematics due to an external magnetic field.
We consider the simplified Ericksen-Leslie model in three dimensional bounded Lipschitz domains. Applying a semilinear approach, we prove local and global well-posedness (assuming a smallness condition on the initial data) in critical spaces for initial data in $L^3_{sigma}$ for the fluid and $W^{1,3}$ for the director field. The analysis of such models, so far, has been restricted to domains with smooth boundaries.
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