Scattering of weak low-frequency light by three-level systems

We calculate analytically both coherent and incoherent parts of the total spectrum of light scattered by a three-level system in either lambda or ladder configurations. The spectrum is restricted to the cases of the incident light pulse weakly depopulating the initial level and of the carrier frequency much lower than the excitation frequency in the system. We give special attention to the spectra under the conditions of different multiphoton resonances in the system and emphasize the effects resulting from the presence of the third level. The analytic theory is shown to explain the numerically calculated spectra as far as the number of frequency components, their positions in the spectrum, relative intensities, and sensitivity to the pulse shape are concerned.