We present a theoretical analysis of multi-photon absorption processes. We find an approximate closed-form expression of the normalized transmittance for a thin sample with two successive nonlinear absorption processes at a time ([Formula: see text]- and [Formula: see text]-photon absorption) in the presence of residual linear absorption. Our approach allows for simultaneous identification and evaluation of the nonlinear absorption coefficients and Rayleigh lengths of the incident elliptic Gaussian beam by fitting the open [Formula: see text]-scan traces.

中文翻译：

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用于同时吸收 n 和 (n+1) 光子的 Z 扫描理论模型

我们提出了多光子吸收过程的理论分析。我们找到了在存在残余线性的情况下一次具有两个连续非线性吸收过程（[公式：参见文本]-和[公式：参见文本]-光子吸收）的薄样品的归一化透射率的近似封闭形式表达式吸收。我们的方法允许通过拟合开放的[公式：见文本]扫描轨迹来同时识别和评估入射椭圆高斯光束的非线性吸收系数和瑞利长度。