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通过对自由电子密度速率方程的简化,得到了计算光学击穿阈值的解析式。将计算结果与波长分别在可见光和近红外波段,脉宽分别为纳秒、皮秒和飞秒的激光脉冲在纯净水和含有杂质的水中实验测量的击穿阈值做了比较,吻合较好。对于纳秒激光脉冲,在纯净水中多光子电离提供初始电子,随后雪崩电离很快在电离的过程中占主导地位。对于短脉冲,多光子电离作用显得尤为重要,并且在击穿的过程中复合损失和碰撞损失对击穿阈值的影响逐渐消失。
Through the simplification of the free electron density rate equation, an analytical formula for calculating the optical breakdown threshold is obtained. Comparing the calculated results with the experimentally measured breakdown thresholds of pure water and impurity-containing water in the visible and near-infrared bands respectively with pulse widths of nanosecond, picosecond and femtosecond, respectively. For nanosecond laser pulses, multiphoton ionization provides the initial electrons in pure water, and then the avalanche ionization quickly dominates the ionization. For short pulses, multiphoton ionization is particularly important, and the impact of recombination loss and collision loss on the breakdown threshold disappears during breakdown.