Abstract
Theory of the pump-and-probe-type nonlinear optical response is formulated for localized electrons strongly coupled with bulk phonon modes. The third-order nonlinear optical susceptibility is calculated exactly. It is predicted that peculiar structures in the gain spectrum for the probe light will be observed in the frequency region of the stimulated Rayleigh scattering, the stimulated Raman scattering, and the anti-Stokes inverse Raman scattering, which are superimposed on the broad gain band of the saturation of absorption. The origin of these structures is clarified in connection with the relaxation dynamics of the electron-phonon system.