Williams Mathew D, Ford Jack S, Andrews David L
School of Chemistry, University of East Anglia, Norwich NR4 7TJ, United Kingdom.
J Chem Phys. 2015 Sep 28;143(12):124301. doi: 10.1063/1.4931584.
Hyper-Rayleigh scattering (HRS) is an incoherent mechanism for optical second harmonic generation. The frequency-doubled light that emerges from this mechanism is not emitted in a laser-like manner, in the forward direction; it is scattered in all directions. The underlying theory for this effect involves terms that are quadratic in the incident field and involves an even-order optical susceptibility (for a molecule, its associated hyperpolarizability). In consequence, HRS is often regarded as formally forbidden in centrosymmetric media. However, for the fundamental three-photon interaction, theory based on the standard electric dipole approximation, representable as E1(3), does not account for all experimental observations. The relevant results emerge upon extending the theory to include E1(2)M1 and E1(2)E2 contributions, incorporating one magnetic dipolar or electric quadrupolar interaction, respectively, to a consistent level of multipolar expansion. Both additional interactions require the deployment of higher orders in the multipole expansion, with the E1(2)E2 interaction analogous in rank and parity to a four-wave susceptibility. To elicit the correct form of response from fluid or disordered media invites a tensor representation which does not oversimplify the molecular components, yet which can produce results to facilitate the interpretation of experimental observations. The detailed derivation in this work leads to results which are summarized for the following: perpendicular detection of polarization components both parallel and perpendicular to the pump radiation, leading to distinct polarization ratio results, as well as a reversal ratio for forward scattered circular polarizations. The results provide a route to handling data with direct physical interpretation, to enable the more sophisticated design of molecules with sought nonlinear optical properties.
超瑞利散射（HRS）是一种用于光学二次谐波产生的非相干机制。通过这种机制产生的倍频光并非以类似激光的方式沿向前方向发射；而是向各个方向散射。这种效应的基础理论涉及与入射场呈二次方关系的项，并且涉及到一个偶数阶的光学极化率（对于分子而言，其相关的超极化率）。因此，在中心对称介质中，HRS通常被认为是形式上禁戒的。然而，对于基本的三光子相互作用，基于标准电偶极近似（可表示为E1(3)）的理论并不能解释所有的实验观测结果。当将理论扩展到包括E1(2)M1和E1(2)E2贡献时，相关结果就会出现，这分别将一个磁偶极或电四极相互作用纳入到一致的多极展开水平。这两种额外的相互作用都需要在多极展开中采用更高阶项，其中E1(2)E2相互作用在秩和宇称上类似于四波极化率。要从流体或无序介质中引出正确的响应形式，就需要一种张量表示，这种表示不会过度简化分子成分，但能产生有助于解释实验观测结果的结果。这项工作中的详细推导得出了以下总结的结果：垂直探测与泵浦辐射平行和垂直的偏振分量，会导致不同的偏振比结果，以及前向散射圆偏振的反转比。这些结果提供了一种对数据进行具有直接物理解释的处理方法，以便能够更精确地设计具有所需非线性光学性质的分子。
