Relatore
Prof.
Luigi Martina
(Universita' del Salento - Lecce)
Descrizione
Within the framework of Oseen-Frank
theory, we analyse the static configurations for chiral liquid crystals.
In particular, we find numerical solutions for localised axisymmetric
states in confined chiral liquid crystals with weak homeotropic
anchoring at the boundaries. These solutions describe the distortions of
two-dimensional skyrmions, known as either textit{spherulites} or
textit{cholesteric bubbles}, which have been observed experimentally in
these systems. Relations with nonlinear integrable equations have been
outlined and are used to study asymptotic behaviours of the solutions.
By using analytical methods, we build approximated solutions of the
equilibrium equations and we analyse the generation and stabilisation of
these states in relation to the material parameters, the external fields
and the anchoring boundary conditions.
Because of the anisotropic
optical properties of the medium and the peculiar shape of such an
excitation, we quantitatively evaluate the cross section for the
axis-rotation of polarised light, by resorting to the Born
approximation. The analysis suggests the use of the spherulites as
elements of photonics circuits.
On the other hand the same confined
cholesteric liquid crystals admit special nonlinear static elongated
configurations, described by integrable nonlinear equations with
boundary conditions. Thus, confined helicoidal with disclination type
singularities appear. Differently from the well known linear case, we
explicitly find $pi$ or $2pi$ helicoids and analyse their properties
both by analytical and numerical tools.
Autore principale
Prof.
Luigi Martina
(Universita' del Salento - Lecce)
