Floquet approach for dynamics in short and intense laser pulses

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