Interferences and dispersion of developable domains in columnar liquid crystal

Abstract

We are interested in characteristic defects S1/2 in an optically anisotropic columnar liquid crystal (C8HET) where the growth of the columns develops cylinders or semi-spherical topology around a core of radius rc. We have described the growth of an S1/2 defect in a columnar liquid crystal (CLC). The conservation of several director columns n→ carried by directions (div n→ = 0) gives structures in half-spheres surfaces.In the structure of the half-drop, we compare the growth of the transversal radius RT and the longitudinal radius RL to discuss the topology of the surface structure. We show the existence of destructive fringes on the surface of the half-drop characterized by a black ring. Furthermore, we characterize the interference phenomena between the incident ray and the reflected one in tangential incidence on the surface of the half-drop by the localization of the interference field, the interfringe and the dispersion in polychromatic light.The present work shows that the liquid index nl exhibits a noticeable difference versus the wavelength λ, the liquid index nl is given by the relationship: nl=1.4763+0.0067λ2.