According to what I found, nonlinear optical process is related to nonequilibrium physics - nonequilibrium green's function (Keldysh green's function/formalism) appears in nonlinear optics. However, I don't know why nonequilibrium physics is required to explain nonlinear optics. Could you briefly explain why? It would be very helpful if you give any references.
Nonlinear optics involves the interaction of materials with strong electric fields that take the system far from equilibrium. There is a back and forth between the material's response to the electric field and the way in which the material changes the electric field, which in turn affects the response of the material again. The full many-body formalism with nonequilibrium Green's functions is the highest level of theory you would need to accurately describe the nonlinear response of a system because this recursive mechanism is described by a Dyson series.
In this sense, you would use this formalism simply because it gives you the most accurate wavefunction. There are many other ways to study nonlinear optics without getting into Green's functions, such as is detailed by Sharma and Ambrosch-Draxl, but if you want to study excitonic effects and other many-body phenomena you need to use nonequilibrium Green's functions.