大自然中充滿著具對稱性質的事物，像是花朵、雪花、車輪，我們的世界由這些美麗的圖案所構成。在光學雷射的領域，也有這樣的對稱性質的雷射模態。以往這些模態是由調整雷射共振腔中，各個光學元件來產生不同的變化。本篇論文將入射光束經過空間光調製器(spatial light modulator, SLM)，給予不同的光資訊圖，來產生具有輻射對稱性的模態，並分析其結構與特性。
使用柱面型共振腔產生的Laguerre-Gaussian 模態，在經過離軸、離焦、等實驗操作，可以得到具有輻射對稱性的Laguerre-Gaussian疊加模態，因為其圖案像花朵一樣漂亮，所以又稱之為花形模態(flower type mode)。在本實驗中，我們將SLM當作相位調製板，來改變入射光束在空間中的波前，以及將SLM當作光柵，讓入射光產生繞射。再用這兩種方法得到的花形模態，與數值模擬的結果做比照。最後，我們使用Mach-Zehnder干涉儀，經由干涉條紋，對照花形模態的相位圖來分析奇異點結構，以及軌道角動量的性質。

There are many symmetry objects in the nature, for instance, the flowers, the snowflake and the wheels, which beautiful patterns construct our wonderful world. Laser optics also exist the symmetry laser modes. In the past, those modes generated from the laser cavities by means of setting the optical elements. In this study, we generate the radial symmetry modes using the spatial light modulator (SLM), and analyze the structure and features of laser modes.
Laguerre-Gaussian modes can be generated from the hemi-cylindrical cavities. By means of adjusting the off-axis and pumping size, we can observe the radial symmetry Laguerre-Gaussian superposed modes, so called flower type modes due to its patterns is as beautiful as flowers. In the experiments, we take the SLM as a phase plate to modulate the wavefront of incident beams, and use the SLM as a grating, making the incident beams diffract to generate flower type modes. In the end, we compare the experimental results with numerical patterns in these two methods. Finally, we compare the interference pattern with numerical phase pattern to analyze the structure and the feature of singularity by means of the Mach-Zehnder interferometer.

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