由於人們對於微觀世界的好奇心益增，我們需要更快的光源來作為量測工具。線性高次諧波已廣泛用於奈米材料結構和分子動態觀測，利用水窗波段的高次諧波，科學家實現活體細胞的觀測，如今高次諧波更是半導體產業用來進行曝光的關鍵光源。然而，近年來對於掌性異構物和磁性材料的量測，需要開發圓極化的高次諧波脈衝。目前人們可以利用很多方法產生圓極化脈衝，甚至是利用非同軸的方式產生單發孤立的圓極化脈衝，這種新的光源還有很多特性尚未了解。
在實驗中，我們利用兩道極化相同但旋性相反的雷射，以非同軸的方式得到另外兩道分別為左旋和右旋的極紫外光脈衝，再藉由調整入射光的極化，就可實現控制極紫外光脈衝的極化狀態。我們發現不同階數的極紫外光有不同的變化行為，卻可以保持很好的能量轉換效率，這不同的變化趨勢來自於高次諧波產生的過程中累積的電子偶極相位。類似於傳統紅外光和可見光的偏振測定法，這種全新的偏振測定法可以用來測定在長短軸上，非線性的原子偶極相位差和振幅比例。

Due to the endless curiosity of human beings, the requirement of a faster light source is necessary for the measurement. Linearly-polarized high-harmonic generation has been widely used for probing the dynamics of nanomaterials and molecules. With the high-harmonic generation in the water window region, biologists can observe live-cell. Moreover, it’s a key light source for lithography in semiconductor manufacturing nowadays. However, we need a circularly-polarized light source to characterize the chiral and magnetic material recently. There are several approaches to generate circularly-polarized light source so far, even producing the isolated circularly-polarized attosecond pulses using non-collinear geometry. There are still some unknown properties about this new light source.
In this thesis, we generate right- and left-hand circularly-polarized EUV in non-collinear geometry by two pulses with the same ellipticity but opposite helicity. By adjusting the ellipticity of input pulses, the polarization control of EUV is realized. We found each harmonic has a different scaling behavior while keeping a good up-conversion efficiency. The different scaling is mainly due to the dipole phase accumulated by the inherited high-harmonic process. Similar to the traditional infrared or visible light polarimetry, our new high-harmonic polarimetry scheme can be applied to identify the nonlinear dipole phase difference and amplitude ratio between long and short driving axes.

Chapter 1 Introduction 1
Chapter 2. Theory 4
2.1 High Harmonic Generation (HHG) 4
2.2 Microscopic View of HHG 6
2.2.1 Three-Step Model 6
2.2.2 Electron Trajectory 8
2.2.3 Intrinsic Dipole Phase 12
2.3 Macroscopic View of HHG 15
2.4 The Importance of Atomic Dipole Phase 22
2.5 Atomic Dipole Phase in NCP-HHG 28
Chapter 3 Experiment Result and Discussion 32
3.1 Polarization Control in Non-collinear Geometry 32
3.2 Polarization State Analytical Technique 36
3.3 High Harmonic Ellipsometry 38
3.4 Nonlinear Dipole Response in NCP-HHG 46
3.4.1 Polarization State of Overall Spectrum 46
3.4.2 Polarization State of Each Harmonics 49
3.4.3 Retrieval Ellipticity Scaling and Atomic Dipole Phase 52
3.5 Ellipticity Controlled by Input Driving Pulses 56
3.6 Retrieval Atomic Phase Difference and Amplitude Ratio for HH Ellipsometry 60
3.7 Ellipticity Controlled Mainly from the Single Atoms Response 62
3.8 Phase Control in Macroscopic 63
Chapter 4 Conclusion and Future Work 67
Reference 68

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