本論文透過c-cut Nd:YVO4晶體以及四面鏡的共振腔架構，產生出具有不同結構的的向量光束，隨著腔長的改變，我們從光形圖與功率觀察不同偏振模態的轉換動態，發現兩種具有不同偏振特性的模態會有競爭泵源能量的行為產生。藉由在泵源加入調製訊號，整理出分岔圖、相關係數及極端事件比例，了解在不同腔長下，不同偏振模態之間的競爭造成的非線性動態行為差異。透過比較兩個不同偏振模態的相關性，得出偏振特性不同確實會造成兩個相同的模態表現出不同的動力學行為。我們也針對幾何模態本身進行比較，探討幾何模態的生成與腔長之間的關聯性。

This paper utilizes a c-cut Nd:YVO4 crystal and a four-mirror resonator configuration to generate vector beams with different structures. By varying the cavity length, we observe the dynamic transition of different polarization modes through optical patterns and power measurements. We observe a competitive behavior in pump source energy between two polarization modes with distinct characteristics. By introducing modulation signals into the pump source, bifurcation diagrams, correlation coefficients, and extreme events are organized to comprehend the nonlinear dynamic differences arising from the competition between different polarization modes at varying cavity lengths. Comparing the correlation of two different polarization modes, we conclude that different polarization characteristics indeed lead to diverse dynamical behaviors in two identical modes. We also investigate the relationship between the generation of geometric modes and the cavity length by comparing the geometric modes themselves.

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