Probing the spectral and temporal structures of high-order harmonic generation in intense laser pulses

We present an ab initio three-dimensional quantum study of high-order harmonic generation ~HHG! of atomic H in intense pulsed laser fields. Accurate time-dependent wave functions are obtained by means of the time-dependent generalized pseudospectral method recently developed and wavelet transform is used to per- form time-frequency analysis of the resulting HHG power spectra. The results reveal striking details of the spectral and temporal fine structures of HHG, providing insights regarding HHG mechanisms in different energy regimes and benchmark data for testing the validity of existing HHG models. PACS number~s!: 42.65.Ky, 32.80.Wr, 42.50.Hz Recently a great deal of attention has been devoted to the study of multiple high-order harmonic generation ~HHG! processes in intense short laser pulses @1-3#. Besides its fun- damental interest for strong-field atomic and molecular phys- ics, the HHG provides a potential tunable coherent light source in the extreme ultraviolet ~XUV! region, a so-called ''tabletop synchrotron'' @2#. Further, the HHG may lead to a promising way for generating subfemtosecond ~attosecond! pulses of radiation of high frequency @4,5#. For optimal con- trol of the HHG processes, it is essential to have a thorough understanding of the spectral and temporal structures of the high-order harmonics and the detailed underlying mecha- nisms for HHG. The first experimental observation of the temporal coherence of HHG has recently been reported @6#. In this Rapid Communication, we present an ab initio three- dimensional ~3D! precision quantum calculation of the time- dependent Schrodinger equation of atomic H in intense laser pulses and perform a detailed wavelet time-frequency analy- sis of the spectral and temporal structures of HHG. The re- sults reveal rich information on the fine structures of time- frequency spectra, providing insights regarding the underlying mechanisms for HHG. Further, the present study provides a benchmark calculation that can be used for the examination of the range of validity of the existing models for HHG @7-13#. In the presence of linearly polarized ~LP! laser fields, most HHG spectra show a similar generic behavior: a sharp decline of the harmonic intensity for the first few harmonics, then a plateau consisting of many harmonics, followed by a cutoff. A conceptual understanding of the origin of the har- monics with energies much in excess of the ionization po- tential I p is provided by the three-step quasiclassical model of Corkum @7# and Kulander et al. @8#. The mechanisms for the generation of lower and threshold harmonics are less well understood. The quasiclassical model involves tunnel ioniza- tion, acceleration of the free electron in the monochromatic laser field, and recollision of the electronic wave packet with the parent ionic core. Based on this model, the cutoff energy is predicted to be Ec5I p13.17 Up , where Up is the pon- deromotive energy @7,8#. This cutoff law was confirmed by