Study Of The Mechanism On Below-threshold Harmonic Generation In The Intense Laser Fields

With the development of laser technology,the interaction of high-intensity laser with atoms,molecules and clusters will release high-energy photons with frequency higher than that of laser,that is the emission of high-order harmonics.Because the high-order harmonic radiation can produce the extreme ultraviolet light source in the range of attosecond,and using this ultrashort attosecond laser pulse can realize the real-time observation and control of the electron dynamics in atoms or molecules at the micro scale,so more and more researches pay attention to it.The classical three-step model can explain the emission mechanism of high-order harmonics.First,electrons are tunneling ionized through the barrier,then electrons accelerated in laser field.When the direction of laser field changes,electrons reverse acceleration and return the parent nucleus,finally radiate out in the form of high-energy photons.In recent years,many researches have paid more attention to produce vacuum-ultraviolet frequency comb by harmonics lower than ionization threshold.Although the classical three-step model can give the physical image of high-order harmonic generation,it can not well explain the dynamic process of low-energy harmonic.In addition,the widely used strong field approximation method can not be used to describe the below-threshold harmonic generation(BTHG)because the contribution of bound states is ignored.The properties of BTHG are described by solving the time-dependent Schr?dinger equation.In this paper,the three-dimensional time-dependent Schr?dinger equation of hydrogen atom in a strong laser field is solved by the generalized pseudospectral method.We study the intensity dependence of the harmonic spectra below the ionization threshold of hydrogen atom in the intense laser field.Pseudo-spectral method has the following advantages in solving the time-dependent Schr?dinger equation,that is to say,according to the probability distribution of the electrons in the atom,the grid points near the nucleus are denser,and the grid points far away from the nucleus are less.This method can not only ensure the accuracy of the calculation results,but also reduce the calculation amount.once the time-dependent wave function at any time is obtained,the high-order harmonics can be obtained by the Fourier transform of the expected value of the time-dependent velocity or acceleration.It is find that the laser intensity plays an important role in the process of channel selection when the harmonic is generated below the ionization threshold.There are two kinds of quantum channels that contribute to BTHG,namely,the generalized short orbit and the long orbit,in which the long orbit is more sensitive to the laser field intensity.Combining with wavelet time-frequency transform,semiclassical trajectories simulation,and quantum channel analysis associated with the laser intensity,the dynamical origin of the BTHG is uncovered.