非线性有限束光声效应理论

当一束受正弦调制的激光入射于光声腔中的固体样品上时,由于非线性的光声效应,在光声腔中不仅能接收到基频成份的声信号,还能接收到其二次谐波成份。本文提出一个非线性热波束方程及其相应的非线性边界条件。借助于逐步近似法在光源为高斯径向分布的情形下,求解这一方程。利用Hankel变换获得这一方程的一级与二级近似解。解析结果表明,二次谐波的热波束仍然维持高斯径向分布,而其高斯半径比基频成份小。分析还表明,二次谐波的振幅不仅与线性热参数,而且也与非线性热参数有关。后者或许能提供样品的更多的有意义的信息。综合其各种特点, 关键词：

NONLINEAR THEORY OF PHOTOACOUSTIC EFFECT OF RESTRICTED BEAM

When a chopped light impinges on a solid sample in an photoacoustic cell, an acoustic signal is produced not only with the fundamental but also with the second harmonic component because of the nonlinear photoacoustic effect. An equation of nonlinear thermal wave beam is presented with nonlinear boundary conditions and solved by using the perturbation approach method under the case that the light source has a Gaussian profile. The Hankel transformation is utilized to attain the first and second order approximation solutions of the equation.The analytic results show that the thermal wave beam of second harmonic still maintains the Gaussian profile with a smaller Gaussian radius than that of the fundamental component and also the amplitude of the second harmonic relates with not only the linear but also the nonlinear thermal parameters which might be expected to provide more information from the sample than the linear one.Basing on these vesults, a new nonlinear paotoacoustic technique would be expected to develop.