In this Letter, we theoretically analyze cavity beam propagation in a gain medium and cavity using the rate equation and generalized Huygens integral, respectively. Spontaneous chaos and extreme events (EEs) occurred around the transverse-mode-degenerate cavity configuration because of transverse-mode competition. A closed occurrence region relating to varying pump power and cavity length was observed. The experimental results in a continuous-wave Nd:YVO4 laser agreed with the aforementioned numerical results. Because gain effect is essential to a laser, we assume that EEs can be intrinsic and universal in a well-aligned laser system if it satisfies the specific transverse-mode competition.
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