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研究生： 蘇丰彥
Feng-Yen Su
論文名稱： 基於鈮酸鋰晶體1550奈米兆瓦級光學參量放大器設計
Design of Lithium Niobate Crystal Based 1550-nm Terawatt Optical Parametric Amplifier
指導教授： 汪治平
Jyh-Pyng Wang
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 物理學系
Department of Physics
論文出版年： 2020
畢業學年度： 108
語文別： 中文
論文頁數： 168
中文關鍵詞： 光學參量放大 、啁啾脈衝放大 、鈮酸鋰晶體 、磷酸氧鈦鉀晶體 、角度色散 、非線性光學 、非同軸相位匹配 、紅外光 、高功率雷射
外文關鍵詞： Optical parametric amplification, Chirped-pulse amplification, Lithium niobate (LN) crystal, Potassium titanyl phosphate (KTP) crystal, Angular dispersion, Nonlinear optics, Non-collinear phase matching, Infrared, High-power laser
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    • 1550 nm 頻段光學參量放大器，與800 nm 摻鈦藍寶石雷射放大器相比，在雷射科技方面有以下特點: (1) 種子光來源為光纖振盪器，對環境的影響較不敏感，光纖振盪器穩
    定度比摻鈦藍寶石振盪器高。 (2) 光參量放大器有較高增益，可以大幅縮短整體光路。 (3) 幫浦光可以直接使用摻釹釔鋁石榴石雷射(Nd:YAG) ，不需要倍
    頻。 (4) 光柵脈衝延展器與脈衝壓縮器所產生的二階、三階色散與波長成正相關，因此將中心波長移至1550 nm 有助於縮小延展器與壓縮器的體積。

    然而，受限於晶體大小(磷酸氧鈦鉀, KTP) 、晶體吸收(硼酸鋇, BBO)，使得1550 nm 光學參量放大器能量受到限制。由於鈮酸鋰晶體
    尺寸可超過3 吋，利用此晶體來做為1550 nm 光學參量放大器的增益介質，放大器能量得以提升，但是種子光須有角度色散來滿足相位匹配條件。在2016, György Tóth [1] 設計使用2 片光柵產生角度色散滿足匹配條件，再利用另外2 片光柵補償角度色散與空間色散。

    在本論文中，我提出三等邊棱鏡架設來取代György Tóthn 所提出的雙光柵架設。首先，使用一組等邊棱鏡產生空間色散。再設計使用第三顆等邊棱鏡產生角度色散滿足放大匹配條件。並設計放大器幫浦光強度、種子光強度、相位匹配角與晶體厚度。放大後設計使用光學光柵壓縮器補償角度色散。此設計結構較為簡單，且稜鏡價格便宜。

    根據數值分析模擬， 使用此新設計可望在1550 nm 頻段產生 200 mJ，脈衝寬度50 fs 的脈衝雷射，尖峰功率為4 兆瓦。在強場
    雷射領域方面，由於有質動力與波長平方成正比，中心波長為1550 nm，雷射脈衝的有質動力增加為4 倍，有利於有質動力相關實驗，例如實驗室天文學、雷射加速器。

    In comparison with Ti:sapphire laser amplifiers in 800 nm band, the optical parametric amplifiers (OPA) in 1550 nm band shows four the merits: (1) Erbium-doped fiber oscillator generated seed pulse is insensitive to the environment. (2) The higher gain per pass for OPA shortens the optical path. (3) Nd:YAG laser without second-harmonic generation serves as the pumping
    laser. (4) The 1550-nm system shrinks the size of the grating-pair based stretcher and compressor because the second-order and third-order dispersion from the stretcher and compressor positively correlate with the wavelength.

    However, the output energy of 1550-nm OPA is limited by crystal size (Potassium titanyl phosphate, KTP) and crystal absorption (Barium borate, BBO). A lithium niobate (LN) crystal as the gain media for the 1550-nm OPA system enables to enhance the output energy since the fabrication of more than 3-inch crystal size is available, but the angular dispersion of seed is critical to the phase-matching condition. In 2016, György Tóth [1] utilized a double-grating setup to generate the required angular dispersion to match the phase-matching condition, and then utilized one
    more double-grating setup to compensate the spatial chirp and angular dispersion.

    In this thesis, I propose a triple-prism setup to replace the György Tóth's double-grating setup. Firstly, a prism-pair and other one prism generate a spatial chirp and the required angular dispersion for the phase-matching
    condition, respectively. Secondly, the pumping intensity, seed
    intensity, the phase-matching angle and the crystal length are designed for
    the amplification. Thirdly, a grating-pair based compressor to compensate
    the angular dispersion. Compared with György Tóth's double-grating setup, the triple-prism setup is concise and economical.

    According to the numerical simulation, this new design of 1550-nm OPA is expected to generate 50-fs pulse laser with output energy 200 mJ and peak power 4 TW. Furthermore, the ponderomotive energy is quadruple compared with the 800-nm Ti:sapphire lasers due to the double-larger wavelength. Hence, this new system of 1550-nm OPA benefits high energy
    density physics, e.g. laboratory astronomy and laser acceleration.

    摘要ix Abstract xi 目錄xiii 使用符號與定義xxv 一、緒論1 1.1 光學參量放大器...................................... 1 1.1.1 優點.............................................. 2 1.1.2 缺點與同步方式.....................................3 1.2 近期發展............................................ 3 1.3 我們的設計.......................................... 4 1.4 本論文章節描述...................................... 5 二、光學參量放大技術原理與相位匹配條件7 2.1 非線性光學的來源.................................... 7 2.1.1 二倍頻............................................ 8 2.1.2 合頻與差頻........................................ 9 2.1.3 極化響應函數...................................... 9 2.2 脈衝光晶體中的色散與二階非線性效應................. 11 2.2.1 波動方程式..................................................... 11 2.2.2 脈衝光在晶體中傳播的色散關係..................... 13 2.2.3 光在晶體中的合頻、差頻........................... 16 2.3 各向異性晶體與相位匹配............................. 17 2.3.1 各向異性晶體..................................... 17 2.3.2 雙軸、單軸晶體................................... 18 2.3.3 相位匹配......................................... 21 2.3.4 非同軸寬頻相位匹配原理........................... 22 2.3.5 單軸晶體、非同軸、類型一相位匹配................. 25 2.3.6 雙軸晶體、非同軸、類型二相位匹配................. 28 2.4 等效二階電極化率................................... 29 三、參量放大器設計35 3.1 前言............................................... 35 3.2 小訊號增益......................................... 36 3.2.1 晶體挑選......................................... 37 3.2.2 磷酸鈦氧鉀晶體(KTP) ............................. 38 3.2.3 鈮酸鋰晶體(LN) .................................. 42 3.3 飽和增益........................................... 50 3.3.1 數值模擬方法..................................... 50 3.3.2 前級放大器-KTP 晶體.............................. 57 3.3.3 能量放大器-鈮酸鋰晶體............................ 65 3.3.4 角度色散與空間色散補償........................... 74 3.3.5 雜訊估計......................................... 77 3.4 設計方案總成....................................... 78 四、總結85 附錄A 單軸晶體、非同軸、類型一相位匹配條件與小訊號增 益87 附錄B 雙軸晶體、非同軸、類型二相位匹配條件與小訊號增 益95 附錄C 等效二階電極化率103 附錄D 數值模擬107 附錄E 雜訊估算131 參考文獻135 索引139

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