An iterative method for extreme optics of two-level systems
  We formulate the problem of a two-level system in a linearly polarized laser field in terms of a nonlinear Riccati-type differential equation and solve the equation analytically in time intervals much shorter than half the optical period. The analytical solutions for subsequent intervals are then stuck together in an iterative procedure to cover the scale time of the laser pulse. This approach is applicable to pulses of arbitrary (nonrelativistic) strengths, shapes and durations, thus covering the whole region of light-matter couplings from weak through moderate to strong ones. The method allows quick insight into different problems from the field of light--matter interaction. Very good quality of the method is shown by recovering with it a number of subtle effects met in earlier numerically calculated photon-emission spectra from model molecular ions, double quantum wells, atoms and semiconductors. The method presented is an efficient mathematical tool to describe novel effects in the region of, e.g., extreme nonlinear optics, i.e., when two--level systems are exposed to pulses of only a few cycles in duration and strength ensuring the Rabi frequency to approach and even exceed the laser light frequence. 
R. Parzynski, M. Sobczak and A. Plucinska