Non-Markovian theory of resonant nonlinear-optical phenomena in the frequency domain

The resonant nonlinear-optical phenomenon in condensed matter due to two-frequency excitation is investigated by a first-principles theory without using the phenomenological relaxation-time description. A new generalized nonlinear susceptibility is introduced in order to describe the non-Markovian process in the condensed phase associated with the resonant four-photon parametric effect. It is shown that the present non-Markovian version of the theory of the resonant Rayleigh-type optical mixing (RROM) naturally includes the resonant coherent anti-Stokes Raman scattering (RCARS) as the memory effect of the reservoir. That is, the two phenomena PROM and RCARS are unified from the microscopic viewpoint. The general expressions for nonlinear susceptibility for RROM and RCARS are obtained by taking into consideration the frequency dependence of the transverse relaxation time $T_2$. These provide us the general guide for the study of several relaxation phenomena in condensed materials by means of resonant coherent nonlinear-optical methods.