  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.
