Theoretical Research On The Application Of Odd And Even Harmonics In Higher Harmonic Spectroscopy

High harmonic spectroscopy(HHS)is a powerful tool in probing the structure and dynamics of atoms and molecules in ultrafast time scale.Present studies mainly focus on linear symmetric molecules which emit odd-order harmonics in strong laser fields.For linear asymmetric molecules,due to the symmetry breaking,both odd and even harmonics are emitted from asymmetric molecules.Present studies show that odd and even harmonics from asymmetric molecules possess different spectral properties and carry different information of the target.It has been shown that odd-even harmonics are closely associated with the structure of the asymmetric molecule and are subject to different intramolecular-interference effects.Odd-even harmonics thus show different time-frequency properties.Here,we will study the possible application of odd-even harmonics in HHS.First of all,this article studies the time-resolved dynamics of high-order harmonic generation(HHG)from oriented asymmetric molecules in intense laser fields theoretically.The HHG time-frequency distribution is obtained from solutions of the time-dependent Schrodinger equation(TDSE)with the help of the Gabor transform.Previous studies have shown that the odd-even HHG spectra of asymmetric molecules don't show the striking two-center-interference-induced minimum,as the symmetric molecules do,due to the symmetry breaking.Surprisingly,with considering only the short-trajectory contribution,an apparent groove with small amplitudes is observed in the HHG time-frequency distribution,which implies that the harmonic emission is strongly suppressed in a specific time-frequency region.The position of this groove is sensitive to the molecular parameters and the orientation.The analyses on this origin of the groove reveal different time-frequency properties of odd versus even signals,where the interplay of intramolecular interference and the permanent-dipole effect plays an important role.And the ratio of even versus odd HHG yields(the even-odd ratio)often used in high-harmonic spectroscopy can be influenced significantly by the interference effect.The finding of this part has important implications on the experimental study of HHS.Secondly,because many characteristics of harmonic radiation are related to the degree of orientation,which has important implications on the experimental study of HHS of asymmetric molecules.However,the degree of orientation achieved in experiments is difficult to evaluate,especially when three-dimensional orientation is involved.This article shows numerically and analytically that odd-even HHG from asymmetric molecules is sensitive to both the degree of orientation and the molecular structure,which implies that the even-odd ratio is not only related to the degree of orientation,but also related to the molecular structure.One can calibrate the degree of orientation using odd-even HHG without considering the influence of the molecular structure in the experiment.Based on the observations,considering the influence of the molecular structure,a simple procedure is proposed to probe the degree of orientation with odd-even HHG,without the need of solving the rotational equation.This procedure can be applied to 3D-oriented top molecules such as polar or nonpolar planar H32+ with high resolution.At last,this article extends the theoretical study of odd-even HHS to the vibrating asymmetric system in strong few-cycle laser pulses.Through solving the time-dependent Schrodinger equation(TDSE)for oriented HeH+ in a non-Born-Oppenheimer(non-BO)approach numerically,we study the electron-nuclear coupled dynamics for oriented HeH+ molecules in strong laser fields.At small orientation angles,the asymmetric molecule tends to stretch to distances larger than the equilibrium separation and stay near its equilibrium geometry at large angles.Strong even harmonics are observed from the system.Based on the analysis,the permanent dipole of the system plays an important role in the vibrational dynamics of the nuclear wave packet.The nuclear motion and the molecular structure can be read from the spectra and ellipticity of odd-even high harmonics.These results also have implications for strong-field ionization of the asymmetric system.The main results are obtained with a single-active-electron approximation and assuming perfect orientation of the asymmetric system.To check these results,this article also simulates the dynamics of the vibrating HeH+ system with the use of a simple two-electron model,and consider incomplete orientation of the asymmetric system in the paper.The HHG from the vibrating HeH+ system show some complex phenomena.To understand these phenomena,a comparison study is also performed with exploring the HHG from the vibrating H2.