Universality of the Quasi-linear Relation Between the Order Parameter and the Normalized Birefringence of Aligned Uniaxially Anisotropic Molecules

Abstract

The universality of the quasi-linear relation between the order parameter  and the normalized birefringence   ,           is confirmed. It is verified that the refractive index of liquid crystals distributed with regular polyhedral symmetry is isotropic and it is given as.  and   of angular weighted liquid crystals that are initially distributed with regular polyhedral symmetry, are numerically calculated. Also   and  of liquid crystals that are conically distributed, keeping the rotational symmetry about z-axis are calculated as the apex angle of the cone is varied. Based on these calculated results, it is confirmed that the quasi-linear relation between  and   is universal, independent of the details of the distribution function.