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We present a two-timescale Floquet method that allows one to apply theKramers-Henneberger approach to short pulses and arbitrary laser frequencies.An efficient numerical procedure to propagate the Floquet Hamiltonian isprovided that relies on the Toeplitz matrix formalism and Fast FourierTransformations. It enables efficient time propagation with large Floquetexpansions, while still taking advantage of the cycle-averagedKramers-Henneberger basis. Three illustrative cases of ionization withdifferent photon energies are analyzed, where the envelope of a short andintense pulse is crucial to the underlying dynamics.

Floquet approach for dynamics in short and intense laser pulses