此論文研究了調製泵源功率的 Nd:YVO4雷射系統以輸出各模態的光學渦流，我們取樣了ℓ=0、1、2 三個整數倍股數的單模態以及ℓ=0~1、ℓ=1~2兩單模態交界處的多模態，透過後續對調製訊號的處理整理出了各個模態的相關係數圖、bifurcation 圖等資訊，可以藉由這些數據觀察到多模態具有兩個單模態的特性。我們也將 808 泵源訊號與腔體輸出訊號做比較，利用擬合後的數據求出了相位差及振幅比等資訊，在 ROF 附近時振幅比皆有大幅度的改變，而相位差則是有大約移動了半個週期π的行為出現。

This thesis investigates the modulation of pump power in an Nd:YVO4 laser system to generate optical vortices in different modes. We sample the single-mode signals for ℓ =0, 1, and 2 (integer multiples) as well as the multimode signals at the boundary of ℓ=0~1 and ℓ=1~2. Through subsequent signal processing, we analyze and present various information such as correlation coefficient maps, bifurcation diagrams for each mode. These data allow us to observe the characteristics of multimode behavior, which exhibit the properties of two single modes. We also compare the 808nm pump source signal with the cavity output signal and extract information such as phase difference and amplitude ratio through data fitting. Near the relaxation oscillation frequency (ROF), we observe significant changes in the amplitude ratio, while the phase difference exhibits behavior similar to a half-period shift of π.

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