A stochastic theory of second order optical processes

Perturbations acting on a radiative system in its excited states affect the coherence property of a second order optical response of the system. In order to understand general features of such effects, perturbations are considered as a stochastic Markoffian process. A general formalism is developed for calculations of spectral as well as temporal responses. In the static limit and also in the extremely fast limit of perturbation, only the coherent Raman or Rayleigh scattering is present, but in general intermediate cases the incoherent luminescence process coexists. The theory can cover the whole range from the static to the fast limit without appealing to the ordinary sort of perturbational calculation. It is illustrated for a three-level model, a four level model and for an optical center coupled with a quantum Brownian oscillator.