利用數值方法模擬雷射與離子交互作用產生水窗波段之高階諧波

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姓名

陳盈珊(Ying-Shan Chen) 查詢紙本館藏

畢業系所

物理學系

論文名稱

利用數值方法模擬雷射與離子交互作用產生水窗波段之高階諧波
(Numerical Simulation of Ion-Based Water-Window High-Harmonic Generation)

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★ 極紫外光與近紅外光在電漿中四波混頻的前期實驗	★ High-Harmonic Generation beyond the Traditional Phase-Matching Cutoff Energy

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至系統瀏覽論文 (2024-6-30以後開放)

摘要(中)

雷射與氣體交互作用激發高階諧波是X射線生成的重要方法，雷射打在氣體靶材上產生游離的自由電子，在經歷加速及與離子再結合過程會釋放短波長光子，目前高階諧波產生相關研究主要關注如何延伸截止光子能量與提高轉換效率。
為延伸高階諧波的截止光子能量，可以選用游離能較高的氣體離子作為靶材，以提高有質動力勢。例如以氦氣為靶材，並利用一價氦離子當作高階諧波波源，其光子截止能量可達keV硬X光波段，然而高度游離的電漿雖然代表高密度的高階諧波源，但同時卻也代表著電漿色散難以被平衡，因此要達成高效率的高階諧波生成便成為一個挑戰。我們規劃利用高階諧波內在偶極子相位變化來補償電漿色散與幾何相位變化，以達成相位匹配與高轉換效率。
本研究透過求解二維軸對稱柱坐標混合對流-擴散電磁（EM）包絡方程，結合Keldysh的電離模型，模擬氦氣靶材中雷射的傳播，並且利用模擬結果計算相位匹配條件和高階諧波產量。我們使用405-nm、半高全寬50-fs持續脈衝驅動和氦氣作用，模擬結果顯示95階諧波（4.26-nm）的輸出產量達到了完美相位匹配條件的66%，169階諧波（2.4-nm）的輸出也達到了完美相位匹配條件的78%。此模擬研究證明，數值模擬可以在進行實驗之前了解雷射和氣體參數對相位匹配條件的影響，進而提高了實驗的效率和成功率。

摘要(英)

The interaction between laser and gas to excite high-harmonics generation (HHG) is an important method of generating X-rays. The laser hits the gas target to generate free electrons, which will release short-wavelength photons during the process of acceleration and recombination with the parent ions. Currently, the researches related to the HHG mainly focuses on how to extend the cutoff photon energy and improve conversion efficiency.
In order to extend the cutoff photon energy of HHG, gaseous ions with higher ionization energy can be used as the interacting medium, which can increase the ponderomotive potential and thus the cutoff photon energy. For example, helium gas can be selected as the gas target, and HHG can be generated by singly ionized helium. The cutoff photon energy can reach keV hard x-ray range. However, the highly ionized plasma not only represents a high density HHG sources, but it also means that plasma dispersion is difficult to balance. Therefore, achieving high efficiency HHG remains a big challenge. Here we propose to utilize the HHG intrinsic dipole phase variation to balance the plasma dispersion and the geometrical phase shift. Then the phase-matching condition can be achieved and the conversion efficiency can be increased.
In this study, the propagation of laser in a helium target is simulated by solving the two-dimensional axisymmetric cylindrical coordinate with advective-diffusion electromagnetic (EM) envelope equation, combined with Keldysh′s optical field ionization model, and the simulation results are used to calculate the phase matching conditions, HHG yield. We used 405-nm, FWHM 50-fs driving laser to interact with helium gas. The simulation results show that the output yield of the 95th harmonic (4.26-nm) reaches 66% of the perfect phase matching condition, and the 169th harmonic (2.4-nm) output also reaches 78% of the perfect phase matching condition. This simulation study demonstrates that numerical experiments can know the effect of laser and gases’ parameters on phase matching conditions before conducting experiments, thereby improving the efficiency and success rate of experiments.

關鍵字(中)

★ 高階諧波
★ 雷射與電漿交互作用
★ 高游離電漿
★ 相位匹配條件
★ 數值模擬計算

關鍵字(英)

★ High-Harmonic Generation
★ Laser-Plasma Interaction
★ Highly-Ionized Plasma
★ Phase-Matching Condition
★ Numerical Simulation

論文目次

摘要 i
Abstract ii
致謝 iii
目錄 iv
圖目錄 vii
表目錄 ix
符號說明 x
一、緒論 1
1-1 引言 1
1-2 背景 2
1-2-1 典型高階諧波光譜 2
1-2-2 三步驟模型 2
1-2-3 相位匹配條件 5
1-3 模擬條件規劃 9
1-4 本論文的架構 9
二、數值模擬方法和參數選擇 11
2-1 數值實驗流程 11
2-2 控制方程式 11
2-2-1 電場在電漿內傳播的波包方程式 11
2-2-2 游離模型與游離率 12
2-2-3 更新離子密度以及電子密度 13
2-3 差分方程式（Difference equation） 13
2-3-1 波包方程式 14
2-3-2 游離率 14
2-3-3 氣體密度 14
2-4 系統架設 15
2-4-1 實驗條件 15
2-5 初始條件 16
2-5-1 滑窗內的雷射場 16
2-5-2 滑窗內的氣體分佈 17
2-6 資料後處理方法 17
2-6-1 模擬結果 17
2-6-2 氣體密度 18
2-6-3 雷射強度 18
2-7 計算相位匹配條件 19
2-7-1 中性氣體色散 19
2-7-2 電漿色散 19
2-7-3 幾何相位變化 19
2-7-4 內在偶極子相位變化 20
2-8 計算高階諧波的產生與傳播 20
2-8-1 重建雷射場 20
2-8-2 計算高階諧波場 21
2-8-3 計算高階諧波的強度 21
2-8-4 完美相位匹配條件 22
三、模擬結果 23
3-1 第95階高階諧波 23
3-1-1 系統參數和數值模擬結果 23
3-1-2 模擬結果診斷 25
3-1-3 相位匹配條件 27
3-1-4 生成與傳播過程 28
3-1-5 頻寬 29
3-2 第169階高階諧波 30
3-2-1 系統參數和數值模擬結果 30
3-2-2 模擬結果診斷 33
3-2-3 相位匹配條件 34
3-2-4 生成與傳播過程 35
3-2-5 頻寬 36
四、結論 38
4-1 總結 38
4-2 討論 38
4-2-1 穩態解 38
4-2-2 氣體被游離的瞬間雷射的強度 39
4-2-3 相速度差異 39
參考文獻 41
附錄一 44
附錄二 47
附錄三 50
附錄四 53
附錄五 56
附錄六 64

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指導教授

朱旭新(Hsu-hsin Chu)

審核日期

2024-1-15

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