本文利用柱面鏡作為雷射共振腔的前鏡來產生具有像散特性的空間模態。
由於柱面鏡水平(x)方向和垂直(y)方向有不同的曲率半徑，造成雷射模態在x、y軸上有不同程度的聚焦，因而影響雷射模態在行進間的結構有所變化。我們針對這種特殊的共振腔進行實驗與理論分析。

另外在外部加上一柱狀透鏡後，可以將高階Hermite-Gaussian(HG)轉換成高階Laguerre-Gaussian (LG)模態，而這一個外部柱狀透鏡，會將原來柱面鏡雷射腔造成的聚焦差異修正回來，而隨著行進間的轉變，我們亦將其記錄。對照1993年L. Allen等人用HG基底重組後可得LG模態，此種方式只能處理遠場轉換完成的LG卻不能處理行進間的變化過程；本文運用海更士積分和ABCD法來呈現隨行進間的模態變化，並針對柱面鏡垂直兩軸的曲率半徑不同所改寫的HG模態，能以此描述行進中的模態變化，和以HG 基底重組後所呈現的LG模態，將模擬模態的行進過程和實驗記錄對照。

系統在裝置外加柱透鏡時，當拉大聚焦系統對雷射腔體的離焦或離軸時，會發現一些特殊的模態，非一般的LG模態，此類因為其特殊腔長下作離焦離軸所產生的模態稱為” flower-type mode”，其成因為相同能量的模態疊加而成，在本文中並對雷射腔體所呈現出的flower-type mode紀錄並對此嘗試做出數值模擬。

We experimentally researched the astigmatic fundamental mode and high order Hermite-Gaussian mode from hemi-cylindrical laser cavity which has cylindrical mirror as front mirror. Laser light profile is changing along propagation because beam divergence are different with cylindrical mirror different radius on x and y axis. This phenomenon called astigmatism. We recorded and analyzed these laser modes.

Another way, we set a plane-convex cylindrical lens as extra-cavity to transform high-order Hermite-Gaussian mode into high-order Laguerre-Gaussian mode because beam divergence can adjust by extra-cavity cylindrical lens. We also recorded the transform along propagation. Afterward, we followed L. Allen’s research’s concept at 1993 that they used Hermite-Gaussian mode as basis to reconstruct Laguerre-Gaussian mode. To present those mode’s numerical fitting, we combine Huygens integral and ABCD law to descript mode transform along propagation and revise the function for cylindrical mirror. Finally, we did numerical fitting to compare with experimental result.

Specially, when we increased the pump offset or the pump size, we observed some unique modes, called “flower-type mode” We displayed these kind mode related to the coherent superposition of Laguerre-Gaussian mode.

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