Diffraction of light by topological defects in liquid crystals

Abstract

We study light scattering by a hedgehog-like and linear disclination topological defects in a nematic liquid crystal by a metric approach. Light propagating near such defects feels an effective metric equivalent to the spatial part of the global monopole and cosmic string geometries. We obtain the scattering amplitude and the differential and total scattering cross section for the case of the hedgehog defect, in terms of the characteristic parameters of the liquid crystal. Studying the disclination case, a cylindrical partial wave method is developed. As an application of the previous developments, we also examine the temperature influence on the localization of the diffraction patterns.