具不同缺陷的膽固醇液晶之理論模擬

The Theoretical Simulation of Cholesteric Liquid Crystals with Various Defects

曾昱嘉(Yu-Chia Zeng)

指導教授 ： 劉育松

國立虎尾科技大學/電機資訊學院/電子工程系碩士班/碩士(2017年)

摘要

本論文利用Pochi Yeh等人發展之擴展Jones 4X4矩陣(extended Jones 4x4 matrix method)理論來模擬具缺陷(defect)的膽固醇液晶之光學行為，模擬的缺陷主要包括對膽固醇液晶分子的導軸(director)引入一不同的相位跳躍(phase jump)、在膽固醇分子螺旋軸(helical axis)中插入一不同厚度之折射率均向性介質缺陷層(isotropic defect layer)、及對膽固醇液晶分子螺旋軸裡眾多螺距之其中一螺距長度改變(局部螺旋形變，local helix deformation)等三種缺陷。擴展Jones 4X4矩陣為分析非均向性光學介質(anisotropic media) 之光學行為的重要數學工具，其可得各介質層中光場之精確解，據我們所知，此方法首次應用來解決類光子晶體(quasi photonic crystals)材料，即非均向性光學介質之光軸呈週期性轉動變化的膽固醇液晶之光學行為。
研究中發現膽固醇液晶結構之反射光譜呈現光子帶隙(photonic band gap)，在引入缺陷後，則缺陷誘導衰減模態(defect-induced evanescence mode)允許存在其光子帶隙中，空間中形成一共振腔，調整缺陷(即共振腔)之幾何結構，可調整共振模態之行為，此行為亦用Fabry-Perot共振腔之模擬結果作為比對。

關鍵字

膽固醇液晶 ； 擴展Jones 4X4矩陣 ； 缺陷態雷射 ； 光子晶體 ； Fabry-Peort

並列摘要

In this paper, the optical behavior of defective cholesterol liquid crystals is simulated by the extended Jones 4x4 matrix method which is developed by Pochi Yeh et al. There are three main types of simulated defects, including the introduction of a different phase jump for the director of the cholesterol liquid crystal molecule, the insertion of different thickness of the refractive index of the isotropic defect layer into the helical axis of the cholesterol molecule, and the local helix deformation of the many pitch in the spiral axis of the cholesterol liquid crystal molecule.Extending the Jones 4X4 matrix is an important mathematical tool for analyzing the optical behavior of anisotropic media, which gives the exact solution of the light field in each dielectric layer. As far as we know, this method is first applied to solve the material of quasi photonic crystals, that is, the optical behavior of cholesterol liquid crystal which the optical axis of the optical behavior of anisotropic media periodically change the rotation.
In the research, it is found that the reflection spectrum of the cholesterol liquid crystal structure shows a photonic band gap. After the defect is introduced, the defect-induced evanescence mode is allowed to exist in its photonic band gap, and it forms a resonance in the space. Adjust the geometry of the defect (ie, the resonance), you can also adjust the behavior of the resonant mode. This behavior is also compared with the simulation results of the resonance of Fabry-Perot.

並列關鍵字

Cholesteric Liquid Crystal ； Extended Jones 4X4 Matrix ； Defect Mode Laser ； Photonic Crystals ； Fabry-Peort

參考文獻

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