在本篇論文中，我們利用類型一臨界相位匹配三硼酸鋰，以高功率皮秒摻鐿光纖放大器做為基頻光產生二階諧波。根據Boyd–Kleinman理論對於聚焦高斯光束產生二倍頻的計算，我們得出最佳聚焦參數為2.8~2.9。然而不同的非線性晶體有不同的走離角，最佳聚焦參數會因此有所改變。類型一臨界相位匹配三硼酸鋰的走離角為0.4°，相對的最佳參數則變為1.8~1.9。我們根據此參數，選擇125 mm聚焦透鏡產生最有效率的二倍頻轉換。做為基頻光源的光纖放大器最高輸出功率為50瓦，光譜頻寬為4.8奈米。光纖放大器輸出為橢圓偏振，我們利用極化分光鏡，從40瓦的基頻光擷取出18.8瓦線性偏振光，並產生2.3瓦的綠光，轉換效率為12.2%。在高功率工作狀態，光纖放大器由於自我相位調制效應，光譜頻寬從1奈米擴大至4.8奈米。因此，二階諧波轉換效率於高功率範圍呈現飽和趨勢。根據Boyd–Kleinman理論計算高斯光束聚焦後的倍頻轉換效率，理論也與實驗結果相符。最後，我們利用四分之一波片調整基頻光的偏振態，在入射基頻光為50瓦的情形下得到5.5瓦的綠光。

In this thesis, by using type-I critical phase matching in Lithium Triborate (LBO), we demonstrate second harmonic generation of a high-power picosecond ytterbium-doped fiber laser system. Using the classical Boyd–Kleinman theory, we determined the optimal focal parameter to be 2.8 ~ 2.9 for second harmonic generation in focused beam case. However, the optimal focal parameter varies in different nonlinear crystals due to the walk-off effect. Type-I critical phase matching in Lithium Triborate has optimal focal parameter of 1.8 ~ 1.9. The corresponding walk-off angle is 0.4°. We get most efficient second harmonic generation by using lens of which the focal length was 125 mm. The maximum output power of our fiber laser system is 50 W, with a spectral bandwidth of 4.8 nm. Its polarization state is elliptical. With 18.8 W of linearly polarized incident light, we can generate 2.3 W of green light (λ=532 nm) with efficiency of 12.2 %. Due to self-phase modulation, the spectrum bandwidth broadens from 1 nm to 4.8 nm after fiber amplification. The conversion efficiency saturates in the high power region. The experimental data are in good agreement with simulation results using Boyd-Kleinman theory. By optimizing polarization state of the fundamental light at 50 W, we generate 5.5 W of the green output.

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