A kinetic model for the equilibrium dynamics of absorption and scattering processes in four-wave mixing spectroscopy

We construct a kinetic model, analogous to a simple chemical reaction, to describe the spatial propagation of the electromagnetic fields in four-wave mixing spectroscopy in a two-level molecular model, explicitly taking into account the stochastic effects of the solvent. We show that in this case, the nonlinear optics processes (absorption and scattering) along the optical path can be described using an analogy with the kinetic processes that occur in a chemical reaction. A key result is that it is possible to define an apparent equilibrium constant that regulates the competition of the photonic processes that take place, an idea conceptually similar to Einstein's model for spontaneous emission and how it can be connected to induced emission in atoms and molecules but including an extension to nonlinear optical and relaxation processes. Our model can be generalized to describe a variety of phenomena in nano-photonics and plasmonic systems.