Division of Physics & Applied Physics, and Division of Chemistry & Biological Chemistry, School of Physical & Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore.
J Chem Phys. 2012 Feb 14;136(6):064504. doi: 10.1063/1.3682470.
The third-order polarization for coherent anti-Stokes Raman scattering (CARS) from a pure state is described by 48 terms in perturbation theory, but only 4 terms satisfy the rotating wave approximation. They are represented by Feynman dual time-line diagrams and four-wave mixing energy level diagrams. In time-resolved (tr) fs and fs/ps CARS from the ground vibrational state, one resonant diagram, which is the typical CARS term, with three field interactions-pump, Stokes, followed by probe-on the ket is dominant. Using the separable, displaced harmonic oscillators approximation, an analytic result is obtained for the four-time correlation function in the CARS third-order polarization. Dlott's phenomenological expression for off-resonance CARS from the ground vibrational state is derived using a three-state model. We calculated the tr fs and fs/ps CARS for toluene and Rhodamine 6G (R6G), initially in the ground vibrational state, to compare with experimental results. The observed vibrational features and major peaks for both tr fs and fs/ps CARS, from off-resonance (for toluene) to resonance (for R6G) pump wavelengths, can be well reproduced by the calculations. The connections between fs/ps CARS, fs stimulated Raman spectroscopy, and impulsive stimulated scattering for toluene and R6G are discussed.
相干反斯托克斯拉曼散射（CARS）的三阶极化可以通过微扰理论用 48 项来描述，但只有 4 项满足旋转波近似。它们由费曼双时线图和四波混频能级图表示。在时间分辨（tr）fs 和 fs/ps 从基态振动能级的 CARS 中，一个共振图是主导的，它是典型的 CARS 项，具有三个场相互作用——泵浦、斯托克斯，然后是探测——在 ket 上。使用可分离的、位移谐波振荡器近似，我们得到了 CARS 三阶极化中四时间相关函数的解析结果。使用三态模型推导出了用于基态振动能级非共振 CARS 的 Dlott 唯象表达式。我们计算了初始处于基态的甲苯和若丹明 6G（R6G）的 tr fs 和 fs/ps CARS，以便与实验结果进行比较。tr fs 和 fs/ps CARS 的观察到的振动特征和主要峰值，从非共振（对于甲苯）到共振（对于 R6G）的泵浦波长，都可以通过计算很好地再现。讨论了甲苯和 R6G 的 fs/ps CARS、fs 受激拉曼光谱和脉冲受激散射之间的关系。
