We present a weak-coupling theory of semiclassical periodically driven two-level systems. The explicit analytical approximating solution is shown to reproduce highly accurately the exact results well beyond the regime of the rotating-wave approximation.
We present a simple but highly efficient iterating approach for strong-coupling periodically driven two-level systems. The obtained explicit approximating analytical solution reproduces accurately the exact numerical solution in the strong-coupling regime for a wide frequency range including resonance, far-off resonance, harmonic, and subharmonic cases. Our theory is suitable for single- and multi-period periodic driving and for the periodic driving with a few-cycle pulse as well, and it gives a general formula for calculating the strong-field ac Stark effect in such diverse situations.