Extreme nonlinear optics of two-level systems

For Rabi frequencies comparable to, or even larger than, the transition frequency of a two-level system, the regime of extreme nonlinear optics is reached. Here, we give an overview of the radiated light intensity as a function of carrier frequency of light, transition frequency, Rabi frequency, spectrometer frequency, as well as of the shape and duration of the exciting optical pulses. The graphical representations reveal an amazing complexity and beauty of the nonlinear optical response. Analytical results within the ``square-wave approximation'' qualitatively reproduce many of the intricate features of the exact numerical calculations.