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We consider the problem of two-level system dynamics induced by thetime-dependent field B={a(t)cos\omega t,a(t)sin\omega t,\omega_0}, with a(t)\sim cn(\nu t,k). The problem is exactly analytically solvable and we proposethe scheme for constructing the solutions. For all field configurations theresonance conditions are discussed. The explicit solutions for N=1,2 weobtained coincide at \omega=0 in the proper parameter domain with predictionsof the rotating wave approximation and agree nicely with numerical calculationsbeyond it.

Resonance in a driven two-level system: analytical results without the rotating wave approximation