本實驗在雙平面的共振腔中加入兩個等焦距的透鏡，當將晶體與輸出耦合鏡操作在焦點位置附近時，由於增益導引的作用，在共振腔中會產生一個環形的模態（Ring mode），此模態中包含了一個正向與反向的模態，雷射輸出的圖形將會是夾著一個發散角的兩光點，隨著晶體與輸出耦合鏡和透鏡距離改變，兩光點的型態、發散角也會隨之改變；在共振腔加入一遮蔽物去做橫向的阻擋，可利用遮蔽物的寬度、光點消失區間與兩光點的發散角，推得環型幾何模態(Ring mode)在共振腔中的路徑．
　　當調製頻率與雷射鬆弛震盪頻率(F)相近時，調製泵源與Nd:YAG雷射的鬆弛震盪頻率會產生共振，當調製深度達到臨界值時，輸出的雷射訊號就會變成混沌訊號，接著我們分析環型幾何模態進入混沌的路徑，發現其是以近週期的路徑進入混沌，但其中又有類似倍週期的行為；同時我們也將示波器中正、反向的環形模態訊號加以分析，發現兩這的振幅的同步性，會因為調制深度的變化，而有所改變。

This study investigates laser characteristics and nonlinear dynamics in an four-element Nd:YVO4 laser with a ring-type geometric mode. The geometric modes formed when the cavity configuration operated near the product of the q-parameters having 1. The beam profile was a two-point pattern corresponding to a clockwise counterclockwise mode. These beams are characterized by oscillating off-axially in a ring-type path. Tuning the cavity configuration, the divergent angle, pattern, were discussed in detail.
Moreover, the nonlinear dynamics behavior of the mode were also explored by pump modulation. When the modulation frequency of the pump laser was comparable with the relaxation oscillation frequency of the laser mode, a mixing period-doubling and quasiperiod chaos occurred. Synchronization between the clockwise and the counterclockwise beams was observed as the periodic oscillation, and synchronization was gradually destroyed in chaotic oscillations as increasing the modulation depth.

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