一种改进的Beer吸收定律及其实验验证

传统Beer定律只有在入射功率密度小于几个kW时才能准确描述介质内部的光吸收,而对于较大入射功率密度情形,由于存在受激发射和自发发发过程,使得该定律不再适用。目前已有的能够分析含有吸收、受激发射和自发发射三种过程的模型都没有得出关于吸收定律的解析表达式。为此,本文在二能级系统模型中,利用LambertW函数解速率方程,推导出了吸收定律的广义解析表达式,并分析得出该广义定律的应用判据。在入射功率密度较低的情况下,该广义吸收定律可转化为传统Beer定律。通过实验测量与数值计算的对比分析,表明该广义定律能够快速准确地描述复杂介质内部的光吸收。

A Modified Beer Law for Absorption

The traditional Beer law for absorption in an optical medium is precise only at incident power densities lower than a few kW.At higher power densities this law fails because it neglects the processes of stimulated emission and spontaneous emission.In previous models that considering those processes,analytical expression for the absorption law could not be obtained.In order to solving this problem,the two-level energy rate equations is solved analytically and it leads to a generalized absorption law in this paper and then the applied criterion of the generalized Beer law is obtained and analyzed.The generalized absorption law reduces to Beer law at low power densities.By making comparison between the experimental result and the calculated result of the generalized Beer law,it shows that this generalized law is fast and exact because it accounts for absorption,stimulated and spontaneous emissions.