The basic theory of sum-frequency generation (SFG) is revisited. A rigorous derivation showing that linear optical transmission and reflection at an interface result from the interference of the incident wave and induced radiation wave in a medium is presented. The derivation is extended to SFG in a medium with a finite interface layer to see how SFG evolves. Detailed description on interface vs bulk and electric dipole (ED) vs electric quadrupole (EQ) contribution to SFG are provided with essentially no model dependence, putting the theory of SFG on a solid ground and removing possible existing confusions. Electric-quadrupole contributions to SFG from the interface and bulk are discussed. It is seen that there is a relevant bulk EQ contribution intrinsically inseparable in measurement from the interface ED contribution but plays a major role among all EQ contributions; its importance relative to the ED part can only be judged by referring to the established reference cases.

中文翻译：

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回顾和频产生的基本理论

回顾了和频产生（SFG）的基本理论。给出了一个严格的推导，表明在界面上的线性光学传输和反射是由介质中的入射波和感应辐射波的干扰导致的。在具有有限接口层的介质中，将推导扩展到SFG，以了解SFG如何演化。界面对体积，电偶极子（ED）与电四极子（EQ）对SFG的贡献的详细说明基本上没有模型依赖性，这使SFG理论扎实了，并消除了可能存在的困惑。讨论了介电和四极杆对SFG的贡献。可以看出，与界面ED贡献在测量上存在本质上不可分割的相关的大量EQ贡献，但在所有EQ贡献中起着主要作用。它相对于ED部分的重要性只能通过参考已建立的参考案例来判断。