利用级数展开的方法,对薄介质的Z扫描理论进行了分析,并对于通常所采用的级数展开和菲涅耳衍射分析方法进行了讨论,证明了在分析利用高斯光束对薄介质进行Z扫描测量时,即使对于大的非线性相移,高斯分解方法和菲涅耳衍射积分方法仍具有等效性,澄清了人们认识上的一些误解。同时分析了远场小孔的归一化透射率与积分限的关系,并对采用高斯分解方法时级数求和的振荡原因进行了分析和讨论,给出了消除振荡所需的最小求和数的判据。针对高斯分解方法和菲涅耳衍射积分方法的使用场合,也进行了讨论。根据所得结论,可以在具体的实验和理论分析中,正确地选择更高效的分析方法。

Using series expansion, the Z-scan characteristics of thin optically nonlinear medium are analyzed. Through discussing series expansion and Fresnel intergral method, It is verified that Gaussian decomposition method is equivalent to Fresnel integral method for(Z-scan) measurements of a thin medium using a Gaussian light beam even for a large nonlinear phase shift, and clarify some misunderstandings. Meanwhile, the relationship of normalized transmittance with upper limiter of Fresnel integral is analyzed, the reason for the oscillation of series summation is given and a criterion for minimum summation number of series needed to eliminate the oscillation is suggested while using a Gaussian decomposition method. The situations that are suitable to be applied for Gaussian decomposition method and Fresnel intergral method are discussed. The conclusion given can be used to choose the appropriate and high efficient analytic method in experimental and theoretical analysis.