Generation Mechanism Of Below And Near-threshold Harmonics And Ellipticity From H₂⁺

In strong-field atomic,molecular and optical physics,high-order harmonics generation is an issue of wide interests.In the past decades,ones pay attention to plateau harmonics rather than below-and near-threshold harmonics for the study of high-order harmonics.And ones mainly focus on plateau harmonics spectra and its generation mechanism.The research project of this paper:H₂⁺is our main research-project in this paper,and choosing the ellipticity as entry point,it is convenient to discuss how can molecular axis-symmetry,symmetry of the excited states,multiphoton effect and orientation effect influence below-threshold parallel and perpendicular harmonics spectra.Besides,this paper shows that near-threshold harmonic spectra is closely associated to multiphoton effect by time-frequency analysis and electron density.The research method of this paper: on the basis of numerically solving the time-dependence Schr?dinger equation,this paper researches harmonics spectra radiation and ellipticity generation mechanism by combining numerical simulation and analytical model.This paper chooses moleculeH₂⁺as particle target,and researches ellipticity of specific harmonic orders for a wide laser-parameter region from 400 nm to 900 nm.We mainly focus on the laser wavelength of 400 nm and 760 nm,and research harmonic spectra intensity and ellipticity with changing the orientation angles.On the other hand,in order to verify the exist of resonance effect,this paper contrasts the population of excited states which can form resonance effect with the ground state between specific resonance wavelengths and its contiguous wavelengths.To research the contribution of resonance effect to below-threshold harmonics better,this paper chooses 760 nm laser wavelength as research object to build analytical model.And this model can explain the generation mechanisms of harmonics which are related to resonance effect at large and small orientation angles.Through absorbing the long orbit continuum wave packet,this paper researches the contribution of the interference between long and short orbits to near-and below-threshold harmonics spectra and ellipticity.In the end,this paper analysises the time-frequency analysis results bycontrasting the long and short coulomb potential,improved classical orbits and quantum orbits.Besides,the electron density which is gotten under long,short range coulomb potential and laser-parameters is researched,and those may provide some reliable proofs to research multiphoton effect.The research results of this paper: analyzing the results of numerical simulation,ones can find some rules for low-order harmonics ellipticity for the different laser-parameter region.The harmonic order which is radiated due to resonance effect between ground state and the second excited state has a higher ellipticity for smaller orientation angles,while there is a higher ellipticity for bigger orientation angles for the harmonics order due to the resonance between ground state and the first excited state.For the 400 nm and 760 nm,the fifth and ninth order harmonics have higher ellipticity with smaller orientation angles respectively.For the 400 nm wavelength,the field of the third order harmonic decreases with the increase of the orientation angles,while situation is opposite for the fifth order.For the 760 nm the situation of harmonics field of the seventh and ninth order is similar to that of the third and fifth order for the 400 nm.Through building simple analytical model,this paper can qualitatively explain the radiation mechanism of harmonic orders which are related to resonance effect at big and small angles for 760 nm.Besides we choose the wavelengths which can cause multiphoton resonance and neighboring wavelengths with them,and through comparing the probablies of the excited states between them,multiphoton resonance effect can be intuitively showed.On the other hand,through comparing the harmonics spectra between exact results and the results where we only consider the transition back to the ground state,ones can distinguish the low-order harmonics,near-threshold harmonics and high-order harmonics.Last,we compare the time-frequency analysis images,classical-orbits,improved classical-orbits and quantum-orbits when the long-range coulomb potential versuses short-range coulomb potential.Those results can show the contribution of multiphoton effect.The conclusions of this paper: the high ellipticity phenomenon is closely associated with two-center interference for the above-threshold harmonics of symmetry moleculeH₂⁺.While for the below-threshold harmonics,generation mechanism of harmonic spectra and harmonic ellipticity is related to symmetry of the bound states,multiphoton resonance effects and so on.Because of symmetry of ground state,the first and second excited states,electron transition is limited and harmonic spectra intensity shows obvious difference for different orientation angles.On the other hand,some harmonic orders show ellipticity peaks due to multiphoton resonance effects,and the peaks shift with changing the wavelength and orientation angles.For the near-threshold harmonics,through comparing the time-frequency analysis images,classical three-step model,improved three-step model and quantum orbits for the situation of high frequency laser and short trajectory,ones may get that the generation mechanism of near-threshold harmonic spectra is associated with multiphoton effects.On the other hand,in the situations of long and short range coulomb potentials,trajectory of electron are also described in this paper.Through researching the simple moleculeH₂⁺,the radiation-mechanisms of harmonic spectra and ellipticity are clear.For the more complex molecules,example forN₂andCO₂,there are more complex symmetry of the excited states,so multiphoton phenomenon is more obvious and generation mechanisms of below-threshold harmonic spectra and ellipticity are more complex.These results of this paper shed light on the complex generation mechanism of below-threshold of other molecules.