Korean Journal of Optics and Photonics (한국광학회지)

Optical Society of Korea (한국광학회)
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Universality of the Quasi-linear Relation Between the Order Parameter and the Normalized Birefringence of Aligned Uniaxially Anisotropic Molecules

정렬된 단축이방성 분자들의 질서변수와 상대 복굴절간 준선형 관계식의 보편성

  • Received : 2016.11.08
  • Accepted : 2016.12.23
  • Published : 2017.02.25
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Abstract

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.

액정과 같은 단축 이방성 분자들의 상대 복굴절 ${\Delta}n_{rel}$과 질서변수 S가 만족하는 준선형 관계식인 $S=(1+a){\Delta}n_{rel}-a{\Delta}n^2_{rel}$이 보편적인 관계식임을 확인하였다. 액정분자들이 정다면체 대칭분포를 할 경우 굴절률은 등방적이며 $\frac{1}{n^2_{av}}=\frac{1}{3}\(\frac{1}{n^2_e}+\frac{2}{n^2_o}\)$와 같이 구해짐을 확인하였다. 정다면체 대칭성을 가지는 액정의 기본 분포에 분포함수 가중치를 가하여 액정의 정렬정도를 바꾸며 ${\Delta}n_{rel}$과 S를 수치계산 하였다. 또한 액정이 z축 주위 회전대칭성을 가지는 깔때기 모양으로 분포하고 있을 때 깔때기의 중심각을 변화시키며 ${\Delta}n_{rel}$과 S를 수치계산 하였다. 이로부터 S와 ${\Delta}n_{rel}$의 준선형 관계식이 액정의 분포형태와는 무관한 보편적인 관계식임을 보였다.

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References

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