本實驗架設四面鏡系統之共振腔來產生幾何環形模態，由於在腔內會有順時針 (clockwise)與逆時針 (counterclockwise)兩種路徑，因此雷射光形呈現兩個分開的點，並藉由輸出耦合鏡的位置改變，來使兩個模態的發散角改變，來觀察其光形、功率及發散角的變化；並量測各位置之鬆弛震盪頻率，來觀察系統從高斯模態至幾何環形模態之鬆弛震盪頻率變化，及此系統下共振腔條件與鬆弛震盪頻率之關係。
　　泵源經訊號產生器調制，當調制頻率接近鬆弛震盪頻率時會與泵源產生共振，此時將調制深度逐漸加深至臨界值，可以觀察到訊號沿倍週期路徑進入混沌現象，此時有可能會產生極端事件；由功率量測以及訊號觀察，幾何環形模態的兩點會競爭泵源之能量，因此我們將會討論幾何環形模態的兩點模態競爭程度，與極端事件的產生機率之相關性。

We generated the geometric-ring-mode by a four-element Nd:YVO4 laser. There were two modes corresponding to the clockwise mode and the counterclockwise mode, respectively. First, we observed the characteristic of power, pattern, and divergence angles by gradually shortening cavity length. Second, we measured the relaxation oscillation frequency, observing the variance of value from Gaussian mode to the geometric-ring-mode.
Then we studied the nonlinear dynamics by pump modulation. When the modulation frequency was operated near the relaxation oscillation frequency, the period-doubling route to chaos was observed while increasing the modulation depth. Simultaneously, extreme events were observed right after chaos regime. Moreover, we observed obvious mode competition between two modes. Thus, we analyzed the noise caused by fluctuations, and then we calculated probabilities of the extreme events occurrence. Finally, we found a high correlation between extreme events and noise.

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