Asymptotic expansion for the polarization spectrum of two-level system driven by a polychromatic field in the limit of small amplitudes

A two-level media driven by a polychromatic field is considered in the limit of small amplitudes. In this limit the asymptotic expansions for the polarization spectra of an arbitrary order are obtained. The obtained polarization spectra were compared with the numerical solution of the density matrix equation. Compared to numerical methods, the asymptotic expansion allows analytically estimating the contribution of each individual component of the polychromatic field and describing the intermode interaction. However, as the intensity of the acting field grows, the computational efficiency of the method decreases and to achieve the required accuracy it is necessary to increase the order of the asymptotic expansion.