• Korean Journal of Optics and Photonics
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• v.28 no.1
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• pp.33-38
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• 2017

The universality of the quasi-linear relation between the order parameter S and the normalized birefringence ${\Delta}n_{rel}$, $S=(1+a){\Delta}n_{rel}-a{\Delta}n^2_{rel}$ is confirmed. It is verified that the refractive index of liquid crystals distributed with regular polyhedral symmetry is isotropic and it is given as $\frac{1}{n^2_{av}}=\frac{1}{3}\(\frac{1}{n^2_e}+\frac{2}{n^2_o}\){\cdot}S$ and ${\Delta}n_{rel}$ of angular weighted liquid crystals that are initially distributed with regular polyhedral symmetry, are numerically calculated. Also ${\Delta}n_{rel}$ and S 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 S and ${\Delta}n_{rel}$ is universal, independent of the details of the distribution function.