Numerical Simulation Of Ionization And High-order Harmonic Generation Of Atoms Irradiated By Intense Lasers

With the advancement of laser technology,it is possible to generate the ultra-short laser pulse whose intensity is closed to the electric field inside the atoms felt by the electrons.When atoms,molecules and crystals are irradiated by laser pulses,many nonlinear phenomena appear,such as non-sequential double ionization,high-energy upper-threshold ionization and high-order harmonic emission.Recently,in order to obtain shorter isolated attosecond pulses,the 800 nm driving laser is replacing by the mid-infrared wavelength laser,and the 3900 nm driving lasers is used to interact with atoms for generating harmonics with the cut-off order exceeding 5000.However,the numerical simulation has encountered great difficulties for this process.The reason is that the ionized electrons will be far away from the parent ions when irradiated by the mid-infrared driven laser,which requires large spatial boundaries and a large amount of computing resources to give accurate results,making the calculations very difficult.In order to solve this problem,we use the Finite Element Discrete Variable Representation（FEDVR）scheme and develop a time-dependent pseudospectral scheme based on the momentum space,and independently develop the corresponding calculation program to numerically study the ionization and the high-order harmonic emission process of the interaction between the laser and the atom,the main research contents include:（1）Based on the coordinate space FEDVR scheme,the ionization and the high-order harmonic emission processes of the atom are studied.Firstly,the influence of the accuracy of the initial state calculation of the system on the calculation results that the high-order harmonics of the atom irradiated by the mid-infrared laser is studied.It is found that for the commonly used imaginary time propagation scheme,it is necessary to propagate for a long enough time to obtain the accurate results of the initial state.By comparison,it shows that even the magnitude of error10^-7 in the wave function will affect the intensity and the cut-off energy of the harmonics generated in the case of 5000 nm driving laser.On this basis,the high-order harmonic emission generated by different wavelengths of the ultrashort laser pulses is studied under the condition of the constant ponderomotive energy.It indicates that as the driving laser wavelength increased,the intensity of the harmonic emission spectrum decreased and a new peak structure appeared.Through the analysis of the harmonic wavelet,the time-dependent evolution of the electron density and the eigenstate population,it is found that the new peaks of the harmonic spectrum are caused by the interference between the harmonic emission generated by the electrons returning to the parent ion after ionization from the excited state and the harmonic emission generated by the ionization from the ground state.As the driving laser wavelength increases,the electrons have the chance to ionize from the excited states,and in turn generate new higher harmonic emissions and affect the generation of the attosecond ultrashort pulse.For the two-dimensional calculation,due to the limitation of the computing resources,it is impossible to directly diagonalize the matrix to get all the eigen-states.So only part of the eigen-states can be accurately calculated by using the imaginary-time propagation,which makes the accurate calculation of the ionization difficult.Based on the polar coordinate FEDVR scheme,we transformed the two-dimensional problem into a one-dimensional eigenvalue problem,obtained all the eigenfunctions,and then calculated the ionization accurately.By using this scheme,the ionization of the atom in the initial states with different initial angular momenta in the high-frequency laser is investigated.It illustrates that in the high frequency laser field,when the initial angular momentum of the atom is opposite to the rotation direction of the circular polarization,the ionization probability is higher than that of the initial angular momentum of the atom is the same as the rotation direction of the circular polarization.Through the calculation of the transition dipole moment of the atom,this phenomenon is explained,and the difference of the atomic ionization stabilization phenomenon in different initial states is further analyzed.（2）Based on the momentum space time-dependent pseudospectral scheme,the ionization and the photoelectron emission of the atom are studied.In the coordinate representation,the electron will move to a larger space that far away from the nuclear region under the action of the laser field after ionization.Therefore,in order to obtain the accurate result,it is necessary to select a large space boundary and a large number of computational grids in the calculation,which makes the calculation very difficult.In the momentum representation,the maximum energy of the electron obtained from the laser field has an upper limit,and the corresponding momentum range is also limited.Therefore,we developed a scheme for solving the time-dependent Schr（?）dinger equation（TDSE）based on the momentum space.Firstly,using this scheme,we calculated the high-order harmonic emission spectrum,and found that the results are consistent with the calculation in the coordinate space.Under the same driving laser conditions,the need of the angle partial wave is less,and the calculation efficiency is improved.Based on this scheme,the variation of the harmonic emission near the ionization threshold with the driving laser intensity is analyzed.The efficiency of the ninth order harmonic emission near the ionization threshold is found to exhibit an oscillatory profile with the increase of the driving laser intensity.At the same time,it is found that the corresponding total excitation probability of the system also shows the oscillation.In a certain laser intensity,the enhancement of the excited state population corresponds to the reduction of the harmonic emission efficiency,so there is a clear competitive relationship between the two.Therefore,the regulation of the harmonic efficiency near the threshold can be achieved by optimizing the intensity of the driving laser.On this basis,the effect of the laser wavelength on the harmonic emission efficiency is further studied.It shows that the harmonic emission efficiency decreases rapidly with the wavelength increasing.But for the intensity of the driving laser with a Keldysh factor close to 1,the harmonic yield exhibits oscillatory behavior that can also be attributed to the excitation of the atom.Secondly,the photoelectron emission spectrum of the ionized electrons is studied based on the momentum space,and it was found that the accurate results can be obtained with fewer computational grid points,and the computational advantage in momentum space is more significant under the conditions of longer pulses and longer wavelengths.The photoelectron spectra with the same Keldysh factor are studied,and it shows that with the increase of the driving laser wavelength,the low-energy photoelectron spectra gradually changed from a plateau structure to a downward sloping structure.With the increase of the driving laser wavelength,the ionization probability decreases rapidly.The reason for this phenomenon is that with the same Keldysh factor,as the wavelength increases,the corresponding amplitude of the driving laser decreases accordingly,and the ionization probability varies exponentially with the peak amplitude of the driving laser.For the multi-cycle driving laser,the ionization probability oscillation decreases with the increase of the laser wavelength.The reason for this phenomenon can be attributed to the influence of the excited states of the atom.