由於LiNbO3材料具有良好的耐酸耐鹼性能及顯著的電光效應，已廣泛應用於商用的光調制器產品中。本研究主要探討了波導材料為鈮酸鋰(LiNbO3)的L型偏振旋轉器，利用其折射率的各向異性來旋轉波導內入射光的偏振方向。我們使用有限時域差分法來模擬偏振光在波導中的傳輸的強度與偏振的變化。分析了不同尺寸的L型波導結構，經優化後，可達到近90o的偏振旋轉效果。並且為了減少優化L型波導結構尺寸所花費的時間，我們亦使用雙波導耦合的公式，推導出可用於計算L型偏振旋轉器波導的偏振旋轉率公式。只需將使用半向量光束傳播法(Semi-Vector Beam Propagation Method)所計算出之有效折射率視為未擾動的結果，並將全向量有限元素法(Full-Vector Beam Propagation Method)所計算出之有效折射率視為受擾動的結果，代入模態耦合公式中，即可精確計算偏振旋轉率。並且計算在波導中施加電場改變折射率後，偏振光的旋轉角度。計算了調整輸出光偏振方向所需之電壓強度。從而分析電控調制偏振在L型鈮酸鋰偏振旋轉器波導中的可行性。

LiNbO3 material is widely used in commercial optical modulators due to its exceptional acid and alkali resistance, as well as its strong electro-optic effect. This study examines an L-shaped polarization convertor made of LiNbO3 waveguide material, utilizing its refractive index anisotropy to rotate the polarization direction of incident light within the waveguide. We employed the Finite-Difference Time-Domain (FDTD) method to simulate changes in transmission intensity and polarization of the light within the waveguide. Various sizes of L-shaped waveguide structures were analyzed, and after optimization, nearly 90° polarization rotation was achieved.
To minimize the time spent optimizing the waveguide structure, we derived a formula for calculating the polarization rotation using the coupled waveguide equation. The effective refractive index, calculated with the Semi-Vector Beam Propagation Method, was treated as the unperturbed result, simplifying the calculation. Meanwhile, the effective refractive index from the Full-Vector Beam Propagation Method was treated as the perturbed result, enabling accurate calculation of the polarization rotation rate using the mode coupling formula. Additionally, we calculated the polarization rotation angle after applying an electric field to change the refractive index in the waveguide. We also determined the voltage required to adjust the output light’s polarization direction. This allowed us to evaluate the feasibility of electrically controlling polarization modulation in the L-shaped LiNbO3 waveguide polarization convertor.

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