一個開放式的雷射共振腔和傳統固態雷射不同，它可以在各種元件上面操作各種不同的變化，例如：改變腔長、離軸、面鏡、晶體等，達成不同的共振腔條件來產生各式各樣的雷射橫向模態。本篇論文主要在探討特定的雷射橫向模態及其特性。

我們使用了 Nd:YVO 4 當作增益介質，並使用了球型雷射共振腔，藉由調整離軸，並且調整雷射共振腔腔長，使之處於特殊簡併共振腔，離軸激發光源使得HG模態疊加而產生其對應的利薩茹圖形(Lissajous)，最後再繼續增加單一方向的離軸程度，來產生其對應的橢圓類型雷射模態，我們稱之為 Herriott-type 模態。在本實驗中，將透過不同的簡併雷射共振腔，來產生不同的 Herriott-type 模態，並針對這類特殊的橫向雷射模態做近遠場觀察與計算光在腔內的等效長度，最後再利用數值分析法，透過由 HG 波函數為基底所建構出的廣義同調態(Generalized Coherent States)進行波函數的疊加來對照實驗結果。在實驗的第二個部分，我們將在簡併共振腔中，透過腔長的細微調整，來觀察其Herriott-type 模態的橢圓率和腔長之間的關係，並且和細微的離軸程度調整所產生的實驗結果作比對。

藉由本實驗的結果，我們透過特殊的 Herriott-type 模態，再次確立簡併共振腔的疊加特性，以及魔梯現象(Devil’s Staircase)的存在。廣義同調態的使用與對照，也大幅幫助了我們對此特殊橫向模態波函數結構上的了解，並由本篇論文的工作與結果，我們可以將廣義同調態加以延伸，應用至其他橫向模態。

A laser cavity system is very different from a traditional solid-state laser. By changing the optical components and optical coatings on the laser cavity, various laser patterns can be generated. In this thesis, an experiment on laser cavity and a theoretical explanation are presented.

In this experiment, we use a spherical laser cavity and an a-cut Nd:YVO 4 laser gain medium with off-axis pump to generate Herriott-type modes by laser diode in degenerate cavities. The optical geometry, near-far field, equivalent length in cavities and characteristics of different order of this system are studied.

As for the theoretical part, a set of Generalized Coherent States (GCS) was first constructed with Hermite-Gaussian function as the basic functions. Then the
experimental patterns were reconstructed successfully with the GCS.

In conclusion, we demonstrate that Herriot-type modes can be generated with off-axis pump, spherical laser cavity and an a-cut Nd:YVO4 gain medium within degenerated cavities. On the other hand, the Herriot type modes can be successfully reconstructed with GCS.

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