Floquet Hamiltonian approach for dynamics in short and intense laser pulses

We present a time-dependent Floquet method for short pulses and arbitrary laser frequencies that uses the cycle-averaged Kramers-Henneberger basis. By means of a particular plane-wave expansion we arrive at a time-dependent Schrodinger equation governed by a Floquet Hamiltonian, which consists of convolutions of momentum and Fourier components. A dedicated numerical treatment of these convolutions, based on Toeplitz matrices and fast Fourier transformations, allows for an efficient time-propagation of large Floquet expansions. 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