本實驗中，我們利用二極體泵源加Nd:YVO4晶體架設出幾何環形的四面鏡雷射共振腔，利用ABCD Law我們知道四面鏡的參數產生雷射腔的穩定區範圍。同時，操作在穩定區邊緣，改變共振腔長度，可以依序產生基本模態、光渦流、高階模態、環形模態及幾何模態。為了產生光渦流，我們在晶體前加入軸稜鏡(axicon)和透鏡產生瓶型光。完成瓶型光的架設與四面鏡的架設，我們利用1/2λ玻片改變泵源偏振並觀察輸出圖案的偏振方向改變，發現圖案的偏振方向主要由Nd:YVO4的光軸決定，改變偏振方向只會影響輸出圖案的光強度大小。而後，再利用針放在腔內改變腔內條件，我們可以觀察混合高階模態中，由於針改變腔內條件，使一些高階模態被損耗，留下單純的厄米-高斯模態(Hermite-Gaussian mode, HG mode)。最後為了確認光渦流，我們架設Mach-Zehnder干涉儀，再改變腔長，觀察干涉圖的變化，同時我們利用matlab模擬出一些特定的高階模態由HG mode產生。

In this thesis, we take advantage of a diode-pumped Nd:YVO4 laser that can obtain the vortex by a bottle beam. Utilizing the ABCD Law, we design the four-elements laser system. By adjusting the cavity length, we operated the edge of stable region to generate geometric mode for laser cavity. Therefore, we obtain the fundamental mode, vortex, high order node, ring mode and geometric mode by operating the cavity length. To generate the vortex, we add the axicon and lens to create the ring light. In this experiment, we set up the Mach-Zehnder interferometer to sure the pattern is vortex. However, we observed the pattern formation from vortex to geometric mode by adjusting the cavity length and recording the pattern interferogram form Mach-Zehnder interferometer. Furthermore, we add the needle in the laser cavity to change the laser condition. This is a way to observe the pattern formation. Nevertheless, by utilizing the needle to change pattern, we find the high order mode has the HG mode and fitting with the ideal HG mode. In this paper, we add the 1/2λ waveplate to change the pumping polarization, and we find the polarization of the output light influence by Nd:YVO4 optical axis. Finally, we generate the multi-singularity vortex beam by operating the cavity length.

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