Sum-frequency generation through a unique Feynman diagram formalism: the case of bipartite organic/inorganic complexes

In quantum electrodynamics, optical processes are theoretically described by double-sided Feynman diagrams. This formalism is powerful in the case of molecules but proves inappropriate to account for light-matter interactions within complex hybrid systems constituted of organic and inorganic matter. The double-sided Feynman diagrams do not easily enable to implement the coupling between the electronic properties of the former and the vibrational response of the latter. Here we present a new general method bridging optics and condensed matter physics in order to properly account for the underlying fundamental process thanks to the classical Feynman diagrams dedicated to solid state physics, instead of the double-sided diagrams commonly used in nonlinear optics. In a manner both rigorous and pedagogical, we especially show how Feynman diagrams can be used to analytically derive the quantum expressions of second-order optical response functions which prove to be in complete agreement with previously established experimental results.