本論文研究摻釹釔鋁石榴石(Nd:YAG)雷射與摻釹釩酸釔(Nd:YVO4)雷射在諧波泵源調制下的動態行為；我們用平均頻率差與Correlation between Probabilities of Recurrence(CPR)兩種方式去分析雷射調制訊號與輸出訊號的相位特性，並且搭配模擬與實驗做交互驗證。
當調制頻率與雷射鬆弛振盪頻率(F)相近時，雷射會產生混沌現象，我們稱之為主諧波調制(F)的混沌區域，在低於共振頻率區域的相位同步關係比高於共振頻率區域差，主因可能來自於一般共振調制系統在低於共振頻率與高於共振頻率之間存在有初始相位差。在副諧波(1/2 F)與二次諧波調制(2F)中，當調制頻率分別接近於二分之一倍或兩倍的鬆弛振盪頻率時，系統的狀態會由鬆弛振盪頻率作為主導，這會導致輸出頻率會以F的形式作為輸出。另外，CPR在主諧波調制下可以作為分界週期與混沌的方法。
另外模擬Lorenz混沌訊號調制Nd:YAG雷射。隨著調制頻率的改變，平均頻率差呈現出階段性的變化，原因是輸出頻率的變化量比調制頻率小。而CPR的分析方式表示出在低調制深度與共振頻率附近的調制會有良好的相位同步。

In this thesis, the dynamical behavior of the pump-modulation Nd:YAG and Nd:YVO4 lasers was studied under different harmonic modulations﹒Two methods associated with the average frequency difference and Correlation between Probabilities of Recurrence (CPR) were used to explore the phase synchronization between the laser output and modulation signal﹒The numerical simulations will compare with the experimental results﹒
When the modulation frequency approached to the relaxation oscillation frequency, F, the laser would be chaotic as the modulatin depth being greater than the threshold value﹒In this chaotic region, the capacibility of the phase synchronization for the region of the modulation frequency being less than the resonance frequency was worse than that for the region of the modulation frequency being greater than the resonance frequency﹒The behavior may be induced by that the lower and higher modulation frequency compared to the resonance have an initial phase difference in a general modulation harmonic system﹒Moreover, in the sub-harmonic(1/2 F) and the second harmonic(2F) modulations, the relaxtion oscillation frequency dominated the average frequency of the laser output, i.e., the average laser frequencies were near F﹒Since the analysis of the CPR, the sudden boundary agreed with the boundary of the threshold of the chaotic behavior﹒
In addition, the Nd:YAG laser was modulated by the simulation of the Lorenz chaotic signal﹒With the modulation frequency changed, gradations appeared on the method of the average frequency difference, because the change of the output frequency was smaller than that of the modulation frequency﹒The analysis of the CPR indicated that there was excellent phase synchronization near the resonance frequency in the low modulation depth.

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