相干反斯托克斯拉曼及相干反斯托克斯超拉曼光谱微观极化率张量元的简化方案-C∞v对称性

相干反斯托克斯拉曼光谱(CARS)和四阶相干反斯托克斯超拉曼光谱(CAHRS)广泛应用于分子界面和生物膜表面的研究。然而，高阶非线性光学过程中分子微观极化率张量元数量众多，关系复杂，使研究者对CARS和CAHRS很难进行定量分析。采取以下方案对属于C_∞v对称性的分子基团的CARS和CAHRS的微观极化率张量元进行简化。首先将CARS微观极化率张量元β_{i′j′k′l′}表示成拉曼微观极化率张量元微分α′_i′j′的乘积，CAHRS微观极化率张量元β_{i′j′k′l′m′}表示成超拉曼微观极化率张量元微分β′_i′j′k′和拉曼微观极化率张量元微分α′_i′j′的乘积，再利用α′_i′j′之间的比值及β′_i′j′k′之间的比值得到β_{i′j′k′l′}和β_{i′j′k′l′m′}之间的比值。使用这些CARS和CAHRS微观极化率张量元之间的关系，能够得到CARS和CAHRS光谱的广义取向泛函及其广义取向参数，进而对界面分子取向信息进行定量分析。

A Simplified Method of Microscopic Hyperpolarizability of Coherent Anti-Stokes Raman Spectroscopy and Coherent Anti-Stokes Hyper-Raman Spectroscopy-C∞v Symmetry

Coherent Anti-Stokes Raman Spectroscopy (CARS) and Coherent Anti-Stokes Hyper-Raman Spectroscopy (CAHRS) are widely used in the study of molecular interfaces and biological membrane surfaces. However, forsuchahigher order nonlinear optical process, the number of molecular microscopic polarization tensor elements areso larger and the relationships is so complexthatthe quantitative analysis of CARS and CAHRS is more difficult. In this paper, we present the simplified scheme for microscopic hyperpolarizability tensor elements of CARS and CAHRS. First, the CARS microscopic hyperpolarizability tensor elements β_{i′j′k′l′} are expressed as the product of the differentiation of Raman microscopic polarizability tensor α′_i′j′. Then the CAHRS microscopic hyperpolarizability tensor elements β_{i′j′k′l′m′} are expressed as the product of the differentiation of Raman microscopic polarizability tensor α′_i′j′ and the differentiation of hyper Raman microscopic polarizability tensor β′_i′j′k′. The ratios between the β_{i′j′k′l′} and the ratios between the β_{i′j′k′l′m′} are then obtained from the ratios of α′_i′j′ and the ratios of β′_i′j′k′. Using these relationships between the microscopic hyperpolarizability tensor elements of CARS and CAHRS obtained in this paper, the generalized orientational functional and generalized orientational parameters of CARS and CAHRS are obtained and ready to be used for quantitative analysis of interfacial molecular orientation information.