The Research Of High-Order Harmonics Of Carbon Monoxide And Nitrogen Molecules

High-order harmonic generation（HHG）is an important physical phenomenon resulting from the interaction of strong laser fields with atoms and molecules.It is an ideal source of attosecond pulses and an effective tool for probing atomic and molecular dynamics.The multiple degrees of freedom of molecules give rise to rich physical processes in high-order harmonic phenomena.In this paper,we study two aspects of the high-order harmonic spectra of homonuclear and heteronuclear diatomic molecules.One of the two aspects is the dependence of the harmonics with different polarizations on the orientation angle between the laser electric field and the molecular axis.The other aspect is the effect of an external static electric field on the high-order harmonic spectra of two types of molecules when the orientation angle is zero degrees.This article uses Lewenstein analytic theory to calculate the high-order harmonic spectra of representative homonuclear and heteronuclear diatomic molecules N₂ and CO.We analyze the results by superposing four channels characterized by different ionization and recombination at different molecular ends,and provide clear explanations.The details are as follows:（1）This article first calculates the parallel and perpendicular high-order harmonic spectra of CO and N₂ molecules in a linearly polarized laser fields at different orientation angles.Parallel and perpendicular refer to the polarization direction of harmonics being parallel and perpendicular to the polarization direction of the field,respectively.The results indicate that:（a）for the high order harmonics of N₂,both parallel and perpendicular high order harmonics have only odd order harmonics.This can be explained by four channels,where the symmetry of the wave function determines that the contributions from the channels with ionization from both ends are equal.The disappearance of even-order harmonics comes from the coherent cancellation of the contributions from the channels with ionization from both ends.The parallel harmonics decrease with increasing orientation angle.The perpendicular harmonics are zero at both 0 and 90 degrees.The origin of these features lies in that the wave function is rotationally symmetric around the molecular axis and composed of p_z orbits of atoms.（b）For CO,similar to N₂,the intensity of parallel harmonics decreases with increasing angle.The perpendicular harmonics are zero at 0 degree.This is determined by the rotational symmetry of the wave function and the composition of the wave function by the P_z orbitals of two atoms.Unlike N₂,both perpendicular and parallel higher harmonics have not only odd-order harmonics but also even-order harmonics,which is caused by the asymmetry of wave function.From the channels,it can be seen that the contributions from the channels with ionization from both ends are different.As a result,it cannot coherently eliminate even order harmonics like N₂.When the orientation angle is 90 degrees,the parallel high order harmonics only have odd order harmonics,the parallel harmonics have only odd-order harmonics,and the perpendicular harmonics only have even order harmonics.The reason is that in both cases,the wave function of the harmonic polarization direction is symmetric or antisymmetric in the time over adjacent half-periods.（2）An external static electric field is added to the linearly polarized laser field,forming an asymmetric external electric field.A typical phenomenon of high order harmonics is the appearance of a double platform structure.The external electric field used in this paper is collinear with the polarization direction of the laser.We investigate the parallel HHG spectra at zero angle.The results indicate that for N₂,the harmonic spectrum contains not only even-order and odd-order harmonics,but also exhibits a double plateau feature.From the analysis of the channel,it can be seen that the external electric field modulates the cutoff order and the intensity of the harmonics from the channels with ionization from both ends.The corresponding electric field enhancement half-cycle reduces the cutoff frequency and increases the harmonic intensity of the channel that generates high-order harmonics.The corresponding electric field weakening half-cycle increases the cutoff frequency and decreases the harmonic intensity of the channel that generates high-order harmonics.The superposition of the two produces a double plateau in the harmonic spectrum.The superposition of the two generates a dual platform for harmonic spectrum.For CO,the harmonic spectrum is related to the orientation of CO.When the external electric field points from C to O,the platform width is extended and the harmonic cutoff order increases;when an external electric field pointing from O to C is applied,the harmonics show a double plateau structure,where the cutoff order of the first plateau is smaller than that without an external electric field,and the cutoff order of the second plateau is larger.It can also be explained by the superposition of four channels.When the external electric field points from O to C,the channel with ionization from C end is modulated by the external electric field,and its cutoff frequency becomes smaller;while the channel with ionization from O end has a larger cutoff frequency.However,the intensity of C-end ionization channel is larger than that of O-end ionization channel,resulting in a first plateau dominated by C-end channel and a second plateau dominated by O-end channel.When the direction of the external electric field is reversed,the cutoff frequency of C-end channel becomes larger and that of O-end channel becomes smaller.After superposition,O-end channel’s contribution is submerged in C-end channel’s contribution,and no obvious double plateau appears,only a larger cutoff frequency.The work provides a clear physical picture for the formation of high-order harmonic spectra of diatomic molecules in asymmetric fields.