臺灣博碩士論文加值系統

本論文提出了一種推導非等向性晶體(anisotropic crystal)穆勒矩陣(Mueller Matrix)的新方法，這類晶體如鈮酸鋰(LiNbO3)，經常用於電光調變器。非等向性電光晶體中的偏振光波傳播可以透過向量波方程式(vector wave equation)來描述，而晶體的介電常數張量會隨著所施加的外部電信號偏壓產生微擾的情形。利用史托克斯向量(Stokes Vector)形式表示的入射偏振光，可以使用系統概念將非等向性晶體建模為一個從向量波方程式推導出的四乘四矩陣，即為穆勒矩陣。

輸出偏振光的史托克斯向量可以經由輸入光的史托克斯向量和晶體的穆勒矩陣的矩陣乘法運算獲得。為了驗證該理論，我們將三種不同相位的偏振光入射到內部具有鈮酸鋰晶體的電光調變器中來計算出輸出光的史托克斯向量。此外，利用邦加球(Poincaré sphere)的模擬結果、晶體中的方位角和橢圓角，我們可以找出輸出光的偏振態。

This thesis proposes a novel method to derive a Mueller Matrix of an anisotropic crystal, the Lithium Niobate (LiNbO3) which is common used in electro-optic modulators. The polarized optical wave propagation in an anisotropic electro-optic crystal can be properly described by the vector wave equation with the permittivity tensor is perturbed by the applied, external electrical signal. With the incident polarized optical wave represented in the form of the Stokes vector, the anisotropic crystal can be modeled using the system concept as a four-by-four matrix which is derived from the vector wave equation and is named as a Mueller Matrix of the crystal. The Stokes vector of the output polarized light wave can be simply obtained by a matrix multiplication operation of the input light Stokes vector and the Mueller Matrix of the crystal. To verify the theory, we simulate the Stokes vector of the output light by injecting three different phases polarized light into the electro-optic modulator which has a Lithium Niobate crystal inside. Moreover, with the simulation result of the Poincaré sphere, azimuth angle and ellipse angle in crystal, we can find the polarization states of the output light.

摘要 i
Abstract ii
致謝 iii
目錄 iv
圖目錄 vi
表目錄 viii
第一章 緒論 1
1.1 前言 1
1.2 研究方法與動機 2
1.3 論文架構 3
第二章 基本理論 4
2.1 Maxwell’s Equations 4
2.2 電磁波在物質中的傳播 5
2.2.1 自由空間中的波動方程式 5
2.2.2 非等向性材料(Anisotropic material)的波動方程式 7
2.2.3 單軸晶體(Uniaxial Crystal) 8
2.3 電光效應 9
2.3.1 原理 9
2.3.2 折射率橢圓(Index Ellipsoid)方程式 10
2.3.3 鈮酸鋰(LiNbO3)中的電光效應 13
2.4 調變技術 16
第三章 偏振表示法及穆勒矩陣 20
3.1 史托克斯向量(Stokes Vector) 20
3.2 邦加球(Poincaré sphere) 23
3.3 穆勒矩陣(Mueller Matrix) 24
3.4 電光調變器的穆勒矩陣表示式 27
3.4.1 z方向偏壓調變器的穆勒矩陣 29
3.4.2 y、z方向偏壓調變器的穆勒矩陣 37
第四章 調變器系統的輸出光模擬 42
4.1 水平偏振調變 43
4.2 45度偏振調變 46
4.3 圓偏振調變 49
第五章 結論與未來展望 52
5.1 結論 52
5.2 未來展望 53
參考文獻 54

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