Third-harmonic scattering is a nonlinear optical process that involves the molecular second-hyperpolarizability, γ. This work presents a rigorous quantum electrodynamical analysis of the scattering process, involving a partially index-symmetric construction of the fourth-rank γ tensor—dispensing with the Kleinman symmetry condition. To account for stochastic molecular rotation in fluids, methods of isotropic averaging must be employed to relate the molecular properties to accessible experimental quantities such as depolarization ratio. A complete eighth-rank tensor rotational average yields results for observable third-harmonic scattering rates, cast as a function of the natural-invariant γ components, and the polarization geometry of the experiment. Decomposing the tensor γ into irreducible weights allows specific predictions to be made for each molecular point group, allowing greater discrimination between the results for different molecular symmetries.

中文翻译：

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液体中三次谐波散射的分子张量分析

三次谐波散射是一种非线性光学过程，涉及分子的第二超极化率γ。这项工作对散射过程进行了严格的量子电动力学分析，涉及到第四级γ张量的部分折射率对称构造-消除了Kleinman对称条件。为了解决流体中随机分子旋转的问题，必须采用各向同性平均的方法将分子特性与可访问的实验量（例如去极化率）相关联。完整的八阶张量旋转平均产生可观察到的三次谐波散射率的结果，该函数是自然不变γ分量和实验的极化几何函数的函数。