我們研究以同調多色脈衝在空氣中產生電漿誘發兆赫輻射，理論上，我們以瞬態電流模型(transient current model)為基礎，其中電流來自穿隧游離之電漿濃度變化部分以ADK 模型(Ammosov-Delone-Krainov tunneling ionization model)計算之；此外，模擬中將不同頻率光之焦點(光腰)大小不同納入考慮。就由理論模擬探討總泵浦能量、不同諧波之能量比例以及相對相位對所產生之兆赫輻射的影響，並將雙色與三色脈衝泵浦架構之結果做比較。
模擬結果指出，最佳能量比例方面，使用鈦藍寶石雷射基頻及二倍頻(二色)再加入三倍頻(三色)脈衝時，最佳的能量比例均會隨著總泵浦能量增加而趨向以基頻光為主。用有相位控與沒有相位控制下之二色及三色脈衝在空氣中產生電漿誘發兆赫輻射強度相差分別為三和四個數量級，由此可看出使用三色脈衝時，相位控制比起使用二色脈衝更為重要。使用二色脈衝時，基頻與二倍頻光之最佳相對相位為0.5π且不隨總泵浦能量改變；使用三色脈衝時，最佳基頻與二倍頻及基頻與三倍頻之相對相位則分別為0.5π、π且皆不隨總泵浦能量改變。值得注意的是，使用三色脈衝時，在2π之內最佳的相對相位會有兩個，分別為0.5π, π 以及 1.5π, π。且在最佳相對相位下之三色脈衝在空氣中產生電漿誘發兆赫輻射會比二色脈衝誘發之兆赫輻射強度增加一至三個數量級，但此增強效應會隨總泵浦能量增加而遞減。此外，經過與四波混頻模型(Four-wave rectification model)比較後得出，在實驗上，若要區分所產生的兆赫輻射是由電漿中之瞬態電流(transient current)或者是三階非線性(third order nonlinearity)所貢獻，可由不同總泵浦能量情況下之最佳的諧波間能量比例之關連區分之。

In this work, a theoretical method to investigate terahertz (THz) emission from gas plasma induced by multi-color femtosecond laser pulses has been developed on the basis of the well-known transient current model under the assumption of frequency dependent beam size. Instead of static tunneling ionization model, we adopted Ammosov-Delone-Krainov (ADK) tunneling ionization model to calculate the tunneling ionization rate. The relation between the terahertz yield from the air plasma and the total pump energy, power ratio, relative phase are investigated under both 2- and 3-color pumping schemes.
In both 2-color and 3-color pumping schemes, the optimal power ratio tends to require a larger amount of fundamental field with the increment of total pump energy. By applying optimal relative phases, the terahertz intensity can be enhanced by three and four orders in 2- and 3-color pumping schemes, respectively. This implies the relative-phase control is more critical in 3-color pumping scheme. On the other hand, the optimal relative phases are independent of the power in both schemes. In 2-color pumping scheme, the optimal relative phase of 2nd harmonic field is 0.5π. In 3-color pumping scheme, there will be two optimal relative phases for the 2nd harmonic field, 0.5π and 1.5π, while the 3rd harmonic stays at π. The optimal relative phases are 0.5π, π and 1.5π, respectively. However, the enhancement in 3-color scheme decreases as the total pump energy increases. Furthermore, after comparing the simulation results based on transient photocurrent model to that for four-wave rectification(FWR) model, it is possible to experimentally distinguish the contribution of the relationship between the total pump energy and its optimal power ratio to the emitted terahertz radiation.

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