Principles of thermal design with nematic liquid crystals.

Highly engineered materials are arousing great interest because of their ability to manipulate heat, as described by the coordinate transformation approach. Based on recently developed analog gravity models, we present how a simple device based on nematic liquid crystals can achieve in principle either thermal concentration or expulsion. These outcomes are shown to stem from the topological properties of a disclination-like structure, induced in the nematic phase by anchoring conditions.

Metric approach for sound propagation in nematic liquid crystals.

In the eikonal approach, we describe sound propagation near topological defects of nematic liquid crystals as geodesics of a non-Euclidian manifold endowed with an effective metric tensor. The relation between the acoustics of the medium and this geometrical description is given by Fermat's principle. We calculate the ray trajectories and propose a diffraction experiment to retrieve information about the elastic constants.

Structure of the dielectric tensor in nematic liquid crystals with topological charge.

A q-plate is a stratified medium composed of a uniaxial nematic liquid crystal with an inhomogeneous orientation of the optical axis possessing a topological charge q, which looks promising as a switching device. This work reports an approach to diagonalizing the dielectric tensor in q-plates, giving a detailed study of nontrivial tensor coordinate transformations. The relationship between the diagonal dielectric tensor and the topological charge of the plate is established. From that, the dielectric tensor for a given q-plate can be explicitly calculated in a convenient frame, and hence the field propagation equations can be derived. These studies establish a theoretical basis that could further deepen the research on these particular structures for nonconventional manipulation of the light.