雷射問世至今已超過五十年，不同於以往一般光的性質，雷射大大地吸引了人們的目光，旋即著手投入雷射領域的研究，隨著科技的快速演進，雷射不僅在各領域應用層面上大放異彩，且對於本身的研究更趨廣泛深入。

雷射有許多的特性，同調、能量集中、偏振與光場分布等，本篇對於雷射的模態、疊加模態及兩者的偏振態為主軸。利用數值模擬方法造出目標模態的光柵圖，將光柵圖資訊輸入空間光調製器(spatial light modulator, SLM)，再利用干涉儀與光學儀器予以輔助，產生圓柱座標型式下的高斯模態，即Laguerre-Gaussian模態與Laguerre-Gaussian疊加模態，因其疊加模態圖案複雜且具輻射對稱性，故又稱為花形模態(flower type mode)。此外，本實驗加入四分之一玻片(quarter wave plate, QWP)，並與干涉儀配合，調整雷射之偏振，產生空間非齊性之偏振(spatially inhomogeneous )，不同於以往的空間齊性偏振(spatially homogeneous)。最後，使用高階龐加萊球(high order Poincaré sphere, HOPS)輔助分析具空間非齊性偏振之雷射模態的偏振分布與模態的強度分布。

It has been more than fifty years that laser was invented, because of the properties of laser are not common with the general light. By the rapid development of technology not only the laser has a great applications in many other fields but also more thorough and wide we know about laser than before.

Laser has many different kinds of properties like coherent, polarization, distribution of intensity and concentrated energy. We focus on the laser modes, superposed modes and both the distribution of polarization in this topic. Using the method of numerical simulation to create the grating what we plan to study. Entering the grating into spatial light modulator and assisted by interferometer and other optical instruments to build the Gaussian laser mode which under the cylindrical coordinate we called Laguerre-Gaussian mode. Also we use the same method to build the superposed Laguerre-Gaussian mode, because of the complex composition and symmetry we called it flower type mode. In addition we employ quarter wave plate to adjust the distritubion of polarization to generate the spatilly inhomogeneous beam, not common with the general spatilly homogeneous beam. Finally we analyze the spatilly inhomogeneous beam and distribution of intensity by high order Poincaré sphere.

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