  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.
