Theoretical Study Of Continuum Spectra And Spectral Redshift Of High-order Harmonic Generation In Intense Laser Fields

With the development of science technology,the research on the interaction between laser and atom or molecule has attracted much attention.In 1993,Corkum proposed the semi-classical three-step model which gives a reasonable explanation to the quantum effect.Firstly,the initial electrons are in the ground state.When the Coulomb potential is suppressed,the electrons may undergo tunneling ionization or multiphoton ionization to enter the continuous state.Secondly,the ionized electrons can be regarded as free electrons,which are only controlled by the laser field.In this state,the trajectory of the electron changes with time and can be described by the classical Newtonian equation.Lastly,when the direction of the laser electric field is reversed,some electrons will return to the parent ion and release high-energy photons.HHG?High order harmonic generation?in atoms and molecules can be used to generate coherent attosecond pulses and to probe ultrafast dynamcs.The generation of harmonic makes coherent imaging of nanostructures with near-diffraction-limited spatial resolution and accesses to the fastest dynamics of atoms,molecules,solids and plasmas with unprecedented temporal resolution.The high harmonic generation is a nonlinear process which contains the quantum effect.In this paper,we present a study of continuum spectra and spectral redshift of high-order harmonic generation by solving the time-dependent Schr?dinger equation?TDSE?.The main contents are summarized as follows:The high-order harmonic generation and its spatial distribution of H₂⁺molecule under 3 fs and 800 nm laser pulse are investigated within non-Born Oppenheimer approximation.The spatial distribution can be used to determine the recombination processes of the electron with the two nuclei.The spatial distribution of the harmonic spectrum shows that the contribution in HHG from the origin and the equilibrium internuclear distance are very weak.Based on this,we further illustrated the spatial distribution by using the combination of a mid-infrared laserpulse and a terahertz?THz?pulse.We use a THz pulse to manipulate the electron motion and the results show that when the THz field is added,the cutoff of the harmonic from the recombination of the electron with the nucleus along the negative-z direction is enhanced and the case along the positive-z directionis suppressed.Next,we achieve the control of the spatial distribution in HHG by changing the time delay in the two-color field.When the time delay is 0 fs?1.34 fs?,the harmonic spectrum from the electrons recombined with the nuclei along the negative?positive?z-axis form a smooth continuous spectrum.When the time delay is 1.34 fs,an isolated attosecond pulse with a pulse duration of 99 as is synthesized.We investigate the molecular high-order harmonic generation?MHOHG?of the asymmetric molecule HeH²⁺by solving the time-dependent Schr?dinger equation within non-Born-Oppenheimer approximation.We illustrate the multichannel molecular high-order harmonic generation by using a chirped laser pulse with carrier envelope phase?CEP??=0 plus a unipolar pulse,and a chirped laser pulse with CEP?=?minus a unipolar pulse,respectively.At the same time,we investigate the spatial distribution in HHG of the asymmetric diatomic molecule HeH²⁺.The spatial distribution of the harmonic spectra indicates that the geometric center of two nuclei?z=1.17 a.u.?and the position of the equilibrium internuclear distance?z=3.11 a.u.?make almost no contribution to the harmonic emission.We verify the influence of carrier envelope phase?CEP?on the emission of high-order harmonics in few cycle laser pulses.The harmonics intensity when the electron recombines with the He nucleus is strongest at?=0.25?and weakest at?=0.75?.The high-order harmonic generation process is studied by the time-dependent electron density distribution.Time-frequency analysis of the two nuclei from the asymmetric molecules HeH²⁺further explains its underlying physical mechanism.We theoretically investigate the two-center interference in HHG from the H₂⁺in a mid-infrared laser and a combination of a mid-infrared laser and a THz field.According to the z-axis,we divide the dipole acceleration into two parts and study the contribution of HHG along the positive z-axis and the negative z-axis,respectively,and we verify the order of the interference minima.When the THz field is added,the interference minimum of high-order harmonic emissions is effectively suppressed.The contribution from the two separate nuclei to HHG demonstrates the locating order of the harmonic minima.In addition,we also study the harmonic emission time and the results show that the harmonic intensity of the short path near the 60^th order after adding a THz field is stronger than the intensity under the mid-infrared laser pulse,which further shows that the minimum value of the harmonic emission is effectively suppressed.The high-order harmonic generation of H₂⁺molecules and its isotopes with different initial vibrational states was studied.By numerically solving the TDSE,we investigate the frequency shift of HHG spectrum from the H₂⁺molecule and its isotope under trapezoidal laser pulses.For the H₂⁺molecules,the harmonic frequency shifts from red-shift to blue-shift when the initial vibrational state is gradually increased.For the initial vibration state v?28?0,we invesitigate the H₂⁺molecule harmonic spectrum with the changing internuclear distance R.The results show that the harmonic spectrum gradually shifts with the increase of the internuclear distance R,which means that the heavier isotopes are more difficult to happen frequency shift in HHG due to their slower nuclear motion.To verify this,we investigated the isotopes of H₂⁺molecules.For the isotopes of D₂⁺,T₂⁺molecules,the harmonic frequency changes tendency with vibration state is the same as that of H₂⁺.However,for the isotope X₂⁺molecules,only odd orders harmonics are observed as the vibrational state increases from v?28?0 to v?28?8.