在過去的二十年裡，超快雷射技術進展非常地迅速。強烈的雷射脈衝聚焦所產生的最大強度可以超過10^20方瓦/平方厘米。在這樣的強場機制下，雷射脈衝能量比一個電子的原子的鍵合能量高得多。因此，一個新的非線性光學領域已經啟動，並且有許多應用，如發展軟X射線雷射、雷射尾場電子加速器、雷射熔接，以及高階諧波產生。
本論文記錄了我在高階諧波產生的研究成果與貢獻。第一章介紹高階諧波產生的背景，並指出高效率諧波產生的障礙。第二章介紹我們做相位匹配的高階諧波實驗。實驗結果表明，第25階的高階諧波（32.4奈米）能量為約1.2 奈焦耳/脈衝，對應的階波能量轉換效率約為10^-7。第25階的高階諧波發射的峰值亮度達到1.3×10^23 photons/sec/mm^2/mrad^2/0.1%BW。第三章介紹我們發展單發式的高階諧波強度波形測量。實驗結果表明，使用40飛秒和80飛秒諧波驅動脈衝，輸出高階諧波的脈衝時寬分別為44.3 飛秒和78.6飛秒。 高階諧波的波形強度穩定度分別為6 % 和 10 %. 第四章介紹我們利用一道反向傳播的拍波脈衝串來做準相位匹配的高階諧波理論和模擬，並且實際建造一套雙色光雷射系統來產生非等間距的拍波脈衝串，為了演示這套系統產生的拍波脈衝串，73飛秒相等間距拍波脈衝串與間距由45飛秒到140飛秒拍波脈衝串皆成功被產生。第五章為總結。

Ultrafast laser technology has progressed rapidly in the past two decades. The maximum intensity produced at the focus of an intense laser pulse can exceed 10^20 W/cm^. In such high intensity regime, the laser pulse energy is much higher than the bonding energy of an electron to an atom. Therefore, a new field of nonlinear optics has been launched, and many applications such as soft x-ray lasers, laser-wakefield electron accelerators, laser fusion, and high-order harmonic generation (HHG) are developed.

This thesis records my efforts and accomplishments in the research of high-order harmonic generation. Chapter 1 reviews the background of high-order harmonic generation and indicates the obstacles of efficient harmonic generation. Chapter 2 reports the experiment of our phase-matched HHG. The results show that the energy of the 25-th harmonic (32.4~nm) is about 1.2 nJ per pulse, corresponding to a harmonic conversion efficiency of 10^-7 order. The peak brightness of the 25-th harmonic emission reaches 1.3×10^23 photons/sec/mm^2/mrad^2/0.1%BW. Chapter 3 presents our single-shot measurement of the HHG intensity waveform. The results show that by using 40-fs and 80-fs harmonic-driving pulses, the output HHG durations are 44.3 fs and 78.6 fs, respectively. The shot-to-shot fluctuation is about 6 % and 10 %, respectively. Chapter 4 reports our theory and simulation of quasi-phase matching (QPM) of HHG with a counter-propagating optical beat wave and describes the synthesis of a beat-wave pulse train with increasing pulse separation for QPM HHG. For demonstration, pulse trains with equal separation of 73~fs and increasing separation from 45~fs to 140~fs are constructed.

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