利用超短強雷射脈衝與中性氣體所產生的高階諧波（High-Harmonic Generation, HHG）已被證實是一種穩定且相干的極紫外光源。提升其轉換效率與延伸截止能量範圍，始終是本領域的重要研究課題。本研究承襲前人提出的方法，結合短波長雷射脈衝、離子化氣體作為交互作用介質，以及毛細管波導結構，進一步透過數值模擬與CFD（Computational Fluid Dynamics）流場模擬手段，探討其物理機制與實驗可行性。
我們自建一套模擬程式，模擬波長405 nm、能量240 mJ、脈衝寬度30 fs的驅動雷射脈衝，在一段長度為4 mm、內徑為320 μm，且充滿氖氣（Ne）的毛細管波導中的傳播行為。設定氣體密度為4×10¹⁴ cm⁻³，並使Ne電離至2+態，透過控制雷射強度與氣體參數，有效平衡總色散效應，實現理想的相位匹配條件。在此條件下，我們成功產生延伸至水窗波段（對於生物成像與材料科學有重要應用價值）的第93階諧波（對應波長為4.35 nm），其轉換效率可達理想值的65%以上。
為評估毛細管波導在實驗應用中的可行性，我們設計了一組可固定並準確安裝毛細管的機構，並使用ANSYS Fluent軟體進行流場模擬。結果顯示，透過調整入口壓力可以有效控制毛細管內部的氣體密度分佈。為驗證模擬之準確性，我們將結果與中央大學古佳文同學所進行的實驗數據進行比較，結果顯示模擬值與實驗值之間的誤差皆不超過一個數量級，確認模擬結果在實驗上的實現性。
本研究證實，透過數值模擬結合CFD流場模擬的方法，能有效預測實際實驗條件下的高階諧波產生行為，並證明模擬所設定之雷射參數及氣體密度條件在現有的實驗技術條件下具有高可行性，進而提高實驗設計的效率與成功率。

High-harmonic generation (HHG), produced by ultrashort intense laser pulses interacting with neutral gases, has been demonstrated to be a stable and coherent extreme ultraviolet (EUV) light source. Improving its conversion efficiency and extending the cutoff energy range remain important research objectives in this field. Building upon previous studies, this work combines short-wavelength laser pulses, ionized gases as the interaction medium, and a capillary waveguide structure. Furthermore, numerical simulations and computational fluid dynamics (CFD) flow field simulations were conducted to investigate the physical mechanisms and experimental feasibility.
A custom simulation program was developed to model the propagation behavior of a driving laser pulse with a wavelength of 405 nm, energy of 240 mJ, and pulse duration of 30 fs in a 4 mm long, 320 μm inner diameter capillary waveguide filled with neon (Ne). The gas density was set to 4×10¹⁴ cm⁻³, and the interaction was modeled by assuming Ne was ionized to the 2+ state. By precisely controlling the laser intensity and gas parameters, we effectively balanced the overall dispersion effects to achieve optimal phase-matching conditions. Under these conditions, the 93rd harmonic (corresponding to a wavelength of 4.35 nm), extending into the water window region (which is valuable for biological imaging and materials science), was successfully generated, with a conversion efficiency exceeding 65% of the ideal value.
To evaluate the practical feasibility of using capillary waveguides in experiments, a mechanical fixture was designed to securely and accurately install the capillary. ANSYS Fluent software was then used to perform flow field simulations. The results showed that the gas density distribution inside the capillary could be effectively controlled by adjusting the inlet pressure. To verify the accuracy of the simulation, the results were compared with experimental data provided by Mr. Jia-Wen Gu from National Central University. The comparison revealed that the simulation and experimental values differed by less than one order of magnitude, confirming the experimental feasibility of the simulation results.
This study demonstrates that combining numerical simulations with CFD flow field modeling can effectively predict high-harmonic generation behavior under realistic experimental conditions. Furthermore, it confirms that the laser parameters and gas density settings used in the simulation are highly feasible within current experimental capabilities, thereby improving the efficiency and success rate of experimental design.

[1] T. Brabec and F. Krausz, "Intense few-cycle laser fields: Frontiers of nonlinear optics," Reviews of Modern Physics, vol. 72, no. 2, p. 545, 2000.
[2] P. B. Corkum and F. Krausz, "Attosecond science," Nature physics, vol. 3, no. 6, pp. 381-387, 2007.
[3] H. Kapteyn, O. Cohen, I. Christov, and M. Murnane, "Harnessing attosecond science in the quest for coherent X-rays," Science, vol. 317, no. 5839, pp. 775-778, 2007.
[4] P. B. Corkum, "Plasma perspective on strong field multiphoton ionization," Physical review letters, vol. 71, no. 13, p. 1994, 1993.
[5] M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’huillier, and P. B. Corkum, "Theory of high-harmonic generation by low-frequency laser fields," Physical Review A, vol. 49, no. 3, p. 2117, 1994.
[6] S.-c. Liu, "利用不同波長脈衝雷射產生高階諧波並最佳化相位匹配條件," National Central University, 2015.
[7] C.-H. Yang, "超短極紫外線脈衝之單發式波形強度量測," National Central University, 2015.
[8] A. L'Huillier, K. J. Schafer, and K. C. Kulander, "Theoretical aspects of intense field harmonic generation," Journal of Physics B: Atomic, Molecular and Optical Physics, vol. 24, no. 15, p. 3315, 1991.
[9] E. A. Gibson et al., "High-order harmonic generation up to 250 eV from highly ionized argon," Physical Review Letters, vol. 92, no. 3, p. 033001, 2004.
[10] M. Zepf, B. Dromey, M. Landreman, P. Foster, and S. Hooker, "Bright quasi-phase-matched soft-x-ray harmonic radiation from argon ions," Physical review letters, vol. 99, no. 14, p. 143901, 2007.
[11] P. Arpin et al., "Enhanced High Harmonic Generation from Multiply Ionized Argon above 500 eV<? format?> through Laser Pulse Self-Compression," Physical review letters, vol. 103, no. 14, p. 143901, 2009.
[12] K.-H. Hong et al., "High-order harmonic generation in Xe, Kr, and Ar driven by a 2.1-μ m source: High-order harmonic spectroscopy under macroscopic effects," Physical Review A—Atomic, Molecular, and Optical Physics, vol. 86, no. 4, p. 043412, 2012.
[13] H. Chen, "相位匹配之極紫外光高階諧波產生," National Central University, 2014.
[14] Kai-Xiang., "Diagnosing laser propagation in gas-filled capillary waveguide for high-order harmonic generation.,"http://ir.lib.ncu.edu.tw:444/thesis/view_etd.asp?URN=111222031, 2025.
[15] C. G. Durfee III, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, "Phase matching of high-order harmonics in hollow waveguides," Physical Review Letters, vol. 83, no. 11, p. 2187, 1999.
[16] Y.-L. Liu, J. Wang, and H.-h. Chu, "Ion-based high-order harmonic generation from water window to keV region with a transverse disruptive pulse for quasi-phase-matching," Optics Express, vol. 30, no. 2, pp. 1365-1380, 2022.
[17] E. A. Marcatili and R. A. Schmeltzer, "Hollow metallic and dielectric waveguides for long distance optical transmission and lasers," Bell System Technical Journal, vol. 43, no. 4, pp. 1783-1809, 1964.
[18] M. V. Ammosov, N. B. Delone, and V. P. Krainov, "Tunnel ionization of complex atoms and atomic ions in electromagnetic field," in High intensity laser processes, 1986, vol. 664: SPIE, pp. 138-141.
[19] K. Schafer, B. Yang, L. DiMauro, and K. Kulander, "Above threshold ionization beyond the high harmonic cutoff," Physical review letters, vol. 70, no. 11, p. 1599, 1993.
[20] A. Brantov, W. Rozmus, R. Sydora, C. Capjack, V. Y. Bychenkov, and V. Tikhonchuk, "Enhanced inverse bremsstrahlung heating rates in a strong laser field," Physics of Plasmas, vol. 10, no. 8, pp. 3385-3396, 2003.
[21] B. Shen, W. Yu, G. Zeng, and Z. Xu, "High order harmonic generation due to nonlinear Thomson scattering," Optics communications, vol. 136, no. 3-4, pp. 239-242, 1997.
[22] T. Auguste et al., "Theoretical and experimental analysis of quantum path interferences in high-order harmonic generation," Physical Review A—Atomic, Molecular, and Optical Physics, vol. 80, no. 3, p. 033817, 2009.
[23] J. Peatross, S. Voronov, and I. Prokopovich, "Selective zoning of high harmonic emission using counter-propagating light," Optics Express, vol. 1, no. 5, pp. 114-125, 1997.
[24] F. Menter, "Zonal two equation kw turbulence models for aerodynamic flows," in 23rd fluid dynamics, plasmadynamics, and lasers conference, 1993, p. 2906.
[25] F. R. Menter, "Two-equation eddy-viscosity turbulence models for engineering applications," AIAA journal, vol. 32, no. 8, pp. 1598-1605, 1994.
[26] F. Menter, J. Ferreira, T. Esch, and B. Konno, "The SST turbulence model with improved wall treatment for heat transfer predictions in gas turbines. Gas Turnine Congress (International) Proceedings. Tokyo. Paper No," Tokyo. Paper (IGTC2003), vol. 59, 2003.
[27] F. R. Menter, "Review of the shear-stress transport turbulence model experience from an industrial perspective," International journal of computational fluid dynamics, vol. 23, no. 4, pp. 305-316, 2009.
[28] F. R. Menter, R. Langtry, and S. Völker, "Transition modelling for general purpose CFD codes," Flow, turbulence and combustion, vol. 77, pp. 277-303, 2006.
[29] F. R. Menter, R. B. Langtry, S. Likki, Y. B. Suzen, P. Huang, and S. Völker, "A correlation-based transition model using local variables—part I: model formulation," Journal of turbomachinery, vol. 128, no. 3, pp. 413-422, 2006.
[30] R. B. Langtry and F. R. Menter, "Correlation-based transition modeling for unstructured parallelized computational fluid dynamics codes," AIAA journal, vol. 47, no. 12, pp. 2894-2906, 2009.
[31] J.-W. Gu, "Development of frequency-domain interferometry for high-order harmonic generation driven by laser.," http://ir.lib.ncu.edu.tw:444/thesis/view_etd.asp?URN=111222036, 2025.