The High-Order Harmonic Generation Of H₂⁺ Molecule In The Two-Color Counter-Rotating Circularly Laser Field

In the past few years,ultrashort and ultra-strong laser technology has been developed rapidly.With the improvement of laser intensity,not only the interaction between strong laser and materials such as atoms and molecules attract much attention,but also many emerging disciplines derived from it are very hot,such as the high-order harmonic generation and the ionization of atoms and molecules.The high-order harmonic generation are coherent radiation waves that emit an integer multiple of the laser frequency when strong laser pulses interact with atoms and molecules.In general,the high-order harmonic spectrum can be divided into three parts:first,in low-order region,the harmonic efficiency drops sharply;then,in a platform structure where the efficiency remains stable;finally,the harmonic efficiency drops sharply near a certain position.Due to the existence and stability of the platform structure,and the harmonic frequency interval distribution characteristics,high-order harmonic become one of the most effective means of synthesizing attosecond laser pulse.The internal electron motion of atoms and molecules is on the order of attosecond time,so the attosecond pulse can be used to effectively detect the internal structure of atoms and molecules.Because of the wide and potential application of high order harmonics,more and more researchers at home and abroad have devoted themselves to the study of high order nonlinear phenomena.The semi-classical three-step model theory proposed by Corkum et al.in 1993 can well simplify the understanding of the high-order harmonic emission process,and the research results can be corresponding to the results of the quantum model in many aspects,so it has been widely used.The content of the semi-classical three-step model is as follows:the first step is that under the action of the strong laser electric field,the coulomb barrier side of the atom is lowered to produce distortion,and the electron is released from the binding of the atomic coulomb potential by means of tunneling ionization or multi-photon ionization and enters the external laser electric field.The second step is that the electron entering the laser electric field can be regarded as a free electron,which moves under the action of the electric field and gains energy.The third step is that when the laser electric field is reversed,the electron may return to the vicinity of the parent nucleus and recombine with the parent nucleus,releasing high-energy photons.The three-step model of the molecule is a little more complicated,mainly reflected in the third step.Since the molecule has at least two nuclei,after the laser field is reversed,the electron driven by the laser electric field may compound with the nucleus of the parent nucleus,or with the nucleus of the attachment of the parent nucleus.At present,with the deepening of research,many new physical phenomena and potential physical mechanisms have been gradually discovered.In this paper,the initial wave function of H₂⁺is obtained through imaginary time evolution,and the time-dependent wave function is solved by splitting operator method.The enhancement and suppression of high harmonics of H₂⁺in a two-color counter-rotation circularly polarized laser field are studied,and the harmonic forbidden parity is realized through the regulation of combined laser field and the H₂⁺.The main content is as follows:?1?The enhancement and suppression mechanism of the high-order harmonic of H₂⁺is studied when the wavelength of the fundamental frequency laser is 800nm and the ratio of the multiplier laser frequency and the fundamental laser frequency is s?the value of s is 2,3,4,5?.Through digital simulation,we found that when the value of s for 2,4,only odd harmonics can be observed from the harmonic emission spectrum,when the value of s for 3,5,not only odd harmonic,but also even harmonic emission can be observed,then the underlying physical mechanism of enhancing and suppressing high-order harmonic generation is illustrated by the interference effect of the HHG spectra from two nuclei.In order to investigate the contributions of the HHG from two nuclei,the HHG is separated into two parts,which is originated from nucleus 1 and nucleus 2.We considering the two nuclei's contribution separately to the harmonic emission,and reached the conclusion that the destructive interference of harmonics and constructive interference caused:corresponding to different s,the regularity of interference effect are different.?2?Meanwhile,the interference term of the HHG spectra are shown to visually illustrate the constructive and destructive interference effect.The simulations with the fundamental laser wavelength 1600 nm and 2400 nm are also investigated for s=3,which shows an identical characteristic with the fundamental laser wavelength 800 nm.However,with the increase of laser wavelength,the cut-off energy of HHG becomes higher,and the intensity of harmonics decreases to a certain extent.?3?We have studied the high-order harmonic generation of H₂⁺in the two-color counter-rotation circularly polarized laser field and in the two-color co-rotating circularly polarized laser field.We have concluded that the harmonic in the two-color co-rotating circularly polarized laser field has low efficiency and narrow platform area,and its potential physical mechanism is similar to the high-order harmonic that cannot be generated by the circularly polarized laser.?4?We studied the high-order harmonic generation law of H₂⁺after adding an electrostatic field in the x direction of the two-color counter-rotation circularly polarized laser field.It is found that with the increase of the intensity of the electrostatic field,the efficiency of harmonics increases gradually,and the cutoff energy of harmonics increases gradually.We take the electrostatic parameter 0.1 as an example and compare it with the situation of the two-color anti-rotation circular polarization laser field.Through the analysis of the electron trajectory,we find that the electron motion distance will increase after the addition of the electrostatic field,so that the electron can obtain more energy in the external electric field.