Harmonie generation in ionizing systems by the time-dependent complex coordinate floquet method

The time-dependent complex coordinate Floquet method was developed for the study of non-linear phenomena observed for atoms (or small molecules) in strong laser fields. On the basis of this method and by taking use of the special definition of the inner product for non-Hermitian operators a simple time-independent expression for the probability to obtain high harmonics was derived. This novel formula is used to investigate the phenomenon of harmonic generation for a model potential representing a single electron in the presence of an intense laser field. The parameters of the one-dimensional potential are chosen to fit two electronic states of the xenon atom. Numerical results indicate the existence of a correlation between harmonic generation and other non-linear effects occurring in this system such as avoided crossings of Floquet resonance states as the field strength amplitude is varied. The harmonic generation spectra obtained by the model presented here qualitatively agree with experimental results on rare gas atoms placed in strong laser fields. For strong laser fields (> 10¹⁴ W cm^-2), very- high-order harmonic generation is observed in numerical studies using both complex Floquet analysis and a simulation by a pseudo-spectral grid solution to the time-dependent Schrödinger equation with a non-periodic Hamiltonian. For extremely strong laser fields, numerical results predict that the most intense frequency emitted by an atom interacting with a monochromatic laser field might not be the irradiating laser frequency, but rather a high multiple of it.