Asymmetric Molecular Odd And Even Harmonic Radiation: Identification Mechanism

Due to the wide application of the higher-order harmonics generation(HHG),the higher-order harmonics of atoms and molecules in intense laser fields become a hot research in Atomic Physics.The mechanism of HHG can be described by a semi-classical three-step model:1,Electron tunneling ionization.2,Electrons accelerate in the laser field and gain energy.3,When the direction of the laser field changes,some of the electrons return to the vicinity of the nucleus and recombine with the nucleus,releasing high-energy photons.The main application of HHG has the following points:First,HHG can be used as an XUV and X-ray source.Second,HHG can generate attosecond pulses,which provides a new way to study the electron-dynamics and molecular structure.Such as,reconstruction of the outermost electron orbitals of linear molecules,tracing of molecular bond length in photochemical reactions,attosecond probing of the vibrational dynamics of asymmetric molecules,Reconstruct electron re-scattering orbit in attosecond scale.Third,the study of higher harmonics can promote the rapid development of strong field physics.The previous calculation of the transition dipole between the ground-continuum states produced by asymmetric molecules,we use a rough approximation for the ground state wave function of an asymmetric molecule.The results obtained are consistent with the theory in most cases,but in some cases,the result is not very good.There will be a detailed discussion of this issue later.In this article,we first introduce some basic theoretical knowledge.We introduced the mechanism of HHG,the Time-dependent Schrodinger equation(TDSE)and some basic methods for Numerical Solution of TDSE,using variational method to solve H2+,According to the molecular orbital theory,the variational method is used to improve the analytical description of the ground-state wave function and energy curve for the asymmetric system,with which the ground-state-continuum-state transition dipole is evaluated.We compare the R-dependent energy of HeH2+ obtained by the variational method with that obtained by the exact numerical simulations.The results of the two different methods show good agreement with each other.The wave function obtained with the variational method differs remarkably from the previous one.One can expect that this difference will play an important role in the calculation of the odd-even dipoles.In one-dimensional situations,the developed dipole is in better agreement with the exact dipole.Then we compare the calculated odd-even dipoles with the spectra and ellipticity of odd-even harmonics from the three-dimensional(3D)model HeH2+ obtained through numerical solution of the TDSE in different molecular parameters.In contrast,the positions of the minimum in improved dipoles are in better agreement with the harmonic order for the maximal ellipticity.As the minimum is usually absent in the HHG spectra of asymmetric molecules the ellipticity measurement of harmonics can be used as a tool to probe the position of the minimum.The one-to-one matching between the dipole minimum and the ellipticity maximum for odd or even harmonics also sheds light on the complex generation mechanism of odd-even harmonics from asymmetric molecules.