Amplitude And Rotation Of The Ellipticity Of Harmonics Of H₂⁺

The interaction of high-intensity laser pulses with atoms or molecules leads to high-order harmonic generation,greatly promoting the development of natural science.High-order harmonic is one of the effective means to obtain desktop short-wave coherent radiation source.Moreover,it has important applications for generating attosecond pulses and detecting the electronic structure of atoms and molecules.Attosecond pulse chains and single attosecond pulses generated from high-order harmonic provide a tool for real-time measurement of ultrafast electronic processes in atoms,molecules,and semiconductor nanostructures.In the gas harmonic experiment,the linearly polarized laser is used,so that harmonics are also linearly polarized,but the study of magnetic materials and chiral molecules requires circularly polarized high frequency light,so various methods have been used to generate high ellipticity polarization harmonics.However,the variation of harmonics ellipticity with parameters（such as laser intensity,alignment angle,molecular nuclear distance,etc.）has not been summarized in detail,the reason for the inversion of harmonics ellipticity only stays at the level of harmonic phase difference and amplitude analysis in two polarization directions,why the phase difference jumps is not well explained.If the above problems are studied and their mechanism is deeply analyzed,it will be helpful for the regulation of high harmonics to synthesize more optimized attosecond pulses and light sources of different energies,therefore,we systematically studied the ellipticity of harmonics generated by H₂⁺,the main research contents are as follows:Firstly,we simulate the dynamic response of H₂⁺in a linearly polarized laser field by numerically solving the time-dependent Schr（?）dinger equation.We systematically studied the harmonic intensity variation of H₂⁺at different alignment angle,it is found that the minimum value of the harmonics spectrum along the laser polarization direction is caused by the two-center interference,and due to the existence of minimum,the harmonic intensity of perpendicular the laser polarization direction is comparable to that along the laser polarization direction,ellipticity polarization harmonics are produced when the phase difference of two harmonics is close to±π/2.Secondly,we deeply analyzed the reason of rotation of the ellipticity of harmonics,that is the reason of harmonic phase difference jump.The phenomena result from the change in the direction of the total Coulomb forces from the two nuclear felt by the re-collided ionized electrons in the direction perpendicular to laser polarization direction.We discussed the change of electronic trajectory caused by the change of the direction of force felt by the ionized electron.According to the influence law,we select harmonics with specific frequency band under different alignment angles,then synthesize the single attosecond pulses with different rotation,which can be continuously converted from right-handed circular polarization,linear polarization and left-handed circular polarization with the change of the alignment angle.In addition,we study the ellipticity of harmonics by changing the nuclear distance of the molecule.Finally,under the linear polarization laser field,we add double frequency linear polarization laser in vertical polarization direction to form orthogonal two-color laser field.Studied the effects of the relative phase difference,relative intensity ratio and molecular nuclear distance on the ellipticity of harmonics at different alignment angles.The results show that when the phase difference is near 0.5π,odd harmonics are right-polarized and even harmonics are left-polarized from-90°to 0°,odd harmonics are left-polarized and even harmonics are right-polarized from 0°to 90°.Then we change the amplitude ratio of laser field intensity,find that the harmonic ellipticity will be affected when the double frequency laser field is enhanced or weakened,and even harmonic ellipticity increases,odd harmonic ellipticity decreases correspondingly.Therefore,if the ellipticity of certain order is increased,ellipticity of the next order will be decreased.The molecular nuclear distance has little effect on the harmonic ellipticity.It is difficult to measure the ellipticity of harmonics experimentally,so it is necessary to predict the amplitude and rotation of the ellipticity of high-order harmonics and attosecond pulses theoretically.In this paper,the amplitude and rotation of the ellipticity of harmonics of H₂⁺was studied deeply.The attosecond pulses of specific rotation can be synthesized according by this law,which provides useful reference for people to better understand the generation mechanism,law,and application of circular polarization harmonics.