Simulation of Molten-Zone Characteristics for Nd:YAG Crystal Using Laser-Heated Pedestal Growth

摻雜活性離子的釔鋁石榴石晶體近來被廣泛地應用在雷射增益介質中。由於增益介質中摻雜離子的種類與徑向濃度分佈影響雷射品質甚鉅，如何直接在長晶過程中適當地控制熔區特性以提升增益介質的品質，是近來重要的研究方向。我們在實驗上成功地利用雷射加熱基座法將摻銣釔鋁石榴石(Nd:YAG)晶體材料生長成峰值濃度高達2.4atm.%的晶體光纖。其中原始晶棒為端面邊長480 μm且平均濃度為1.15atm.%的方棒；成長後的晶體光纖為端面直徑220 μm 的圓棒。此時的長晶速度約為1.25 mm/min。 為了進一步瞭解晶纖的生長參數與徑向濃度分佈的關係來改善熔區特性，我們引用Lan 所發展出用來模擬大尺度下塊狀晶體的二維計算流體力學程式，並成功地將其改良為微尺度下晶體光纖二維流體力學的模型來與實驗作熔區特性的比較。模擬結果顯示熔區形狀與尺寸，以及熔區高度相對於輸入雷射功率的變化趨勢都與實驗觀察結果相符合。另外晶纖的徑向摻雜濃度分佈也與實驗結果相似，但在長晶速度與峰值濃度間的變化關係不盡相同，推測為實驗上過高的掺雜濃度造成應力集中使得晶體結構被破壞，造成更高的長晶速度反使得峰值濃度下降。模擬上最佳峰值濃度約為1.5 atm.%，與實驗也有所出入，相信未來在模擬中加入表面張力隨濃度變化，可縮小在定量上的差距。Yttrium aluminum garnet (YAG) crystal doped with active ions has been widely used as laser gain medium. It is important to control the molten-zone properties well during the drawing process to enhance the performance of the output laser beam, because the laser quality is affected significantly by the species of active ions and its radial dopant concentration distribution in the gain medium. We have experimentally demonstrated the neodymium-doped YAG crystal fiber with the maximum central dopant concentration up to 2.4 atm.% with a fiber diameter of 220 μm by laser-heated-pedestal-growth technique when the rawing velocity is 1.25 mm per minute. The source rod was square with an end facet area of 480 μm by 480 μm and an uniform dopant concentration of 1.15 atm.%. To further understand the relation between the drawing parameters and the radial dopant concentration of the crystal fiber and compare with the experiment, we modified a 2-dimensional computational-fluid-dynamic (CFD) program, which was written by Lan et. al. for bulk materials. Simulation results agree with the experimental ones in size and shape of the molten zone for various CO2 laser input powers. Moreover, the radial dopant distribution of the crystal fiber in the simulations is similar to that in the experiments, but there are differences in the ariation of the maximum central concentration by changing the drawing speed. It is speculated that the crystal lattices are damaged due to the residual strain caused by high maximum central dopant concentration. Besides, the highest maximum central dopant concentration was about 1.5 atm.% in the simulations which is different from that in the experiments. We believe that it could be improved quantitatively by considering the surface tension coefficient as a function of both concentration and temperature in the simulation.口試委員會審定書 ii 誌謝 ii 摘要 iv Abstract v 目錄 vi 圖目錄 viii 第一章 緒論 1 1.1 晶體生長 1 1.2 雷射加熱基座法 4 1.3 雷射加熱基座法之數值模擬 6 1.4 論文架構 7 第二章 數值方法與理論模型 8 2.1 主導方程式 8 2.1.1 連續方程式 10 2.1.2 能量方程式 11 2.1.3 動量方程式 14 2.1.4 質傳遞方程式 17 2.1.5 氣流函數 19 2.1.6 以氣流函數表示之主導方程式 22 2.1.7 無因次化參數 23 2.2 邊界條件 26 2.2.1 熱邊界條件 26 2.2.2 流場邊界條件 29 2.2.3 濃度邊界條件 32 2.3 數值計算方法架構 34 第三章 實驗架構與長晶方法 37 3.1 LHPG長晶系統 37 3.2 YAG材料之物理特性與參數 40 3.3 Nd:YAG生長參數與濃度分佈 41 3.4 偏析現象與偏析係數 46 第四章 熔區性質模擬結果與分析 48 4.1 雷射加熱場型與熔區形狀 48 4.1.1 雷射光束入射寬度與熔區高度的關係 50 4.1.2 雷射光束入射寬度與熔區固液界面形狀的關係 50 4.1.3 雷射光束入射寬度與熔區溫度梯度的關係 51 4.2雷射加熱功率與熔區高度 53 4.3熔區溫場與流場分佈 55 4.4晶纖摻雜濃度分佈 57 第五章 結論與未來工作 62 參考文獻 6