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。 ;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.
