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根据麦克斯韦方程,结合超快激光脉冲的瞬态特性,在忽略色散的影响下,推导并得出了三阶非线性各向同性系统中以光强表示的非线性吸收偏微分方程。以高斯脉冲激光为例,给出了该方程的一个近似解。基于该近似解的非线性透射率,不仅与脉冲激光的峰值强度、样品厚度以及介质的双光子吸收系数有关,而且还与描述脉冲主要特性的物理量——激光脉冲半峰全宽以及激发光的频率有关。数值拟合Rhodamine等物质的非线性透射率的实验曲线的结果显示,基于超短脉冲瞬态特性的非线性透射率得出的介质双光子吸收系数大于传统非线性透射率参考公式给出的相应结果,与双光子诱导荧光法的结果基本吻合。
According to the Maxwell’s equation, combined with the transient characteristics of ultrafast laser pulses, the nonlinear absorption partial differential equations of light intensity in third-order nonlinear isotropic systems are derived and neglected under the influence of dispersion. Taking the Gaussian pulsed laser as an example, an approximate solution of this equation is given. The nonlinear transmittance based on the approximate solution is not only related to the peak intensity of the pulsed laser, the thickness of the sample and the two-photon absorption coefficient of the medium but also to the physical quantity describing the main characteristics of the pulse - the full width at half maximum of the laser pulse, Frequency related. The experimental results of the numerical fitting of the nonlinear transmittance of Rhodamine and other materials show that the two-photon absorption coefficient of the medium based on the nonlinear transmittance of the ultra-short pulse transients is larger than that given by the conventional nonlinear transmittance reference equation Results, consistent with the two-photon induced fluorescence method.