Understanding Effects of Static Electric-field on High-order Harmonic Generation of O2 Molecules(Invited)
High-order Harmonic Generation(HHG)is an important phenomenon caused by the interaction between lasers and atoms or molecules.It is of great significance to attosecond physics.The mechanism of HHG is well understood in terms of the"three-step"model.Applying an external static electric field is an important method for modulating high-order harmonic generation.The external static electric field can cause atoms or symmetric molecules to generate even-order harmonics.Even-order harmonics have different characteristics from odd ones.For instance,the yield of even harmonics exhibits a linear relationship with the intensity of the external static electric field within a specific field intensity range.This property can be utilized to measure the waveform of terahertz electromagnetic fields.The external static electric field is also often used to extend the plateau of high-order harmonics and generate shorter attosecond pulses.The high-order harmonic spectrum of polar molecules in the presence of an external electric field is found to exhibit a double-plateau structure related to the orientation of the molecules,making it possible to measure the orientation degrees.All of these applications inspire a deep understanding of how external static electric fields affect high-order harmonic generation.In this paper,Lewenstein's strong field approximation method is used to obtain the high-order harmonic spectrum of the O2 molecule in a linearly polarized laser field combined with an external static electric field.The polarization direction of the linearly polarized laser field is at a 45 degree angle to the molecular nuclear axis.The amplitude of the external static electric field is one-tenth of the laser amplitude.Two types of external static electric fields are examined in this paper.One type is a parallel static electric field whose field direction aligns with the direction of the laser polarization;The other type is a vertical static electric field whose field direction is perpendicular to the direction of the laser polarization.The harmonics we calculate have the same polarization directions as the laser.The results show that:1)when the direction of the static electric field is parallel to the direction of laser polarization,the harmonic spectrum exhibits a double-plateau structure,the cutoff frequency increases,and the intensity of even and odd harmonics are on the same scale;2)when the direction of the static electric field is perpendicular to the direction of the laser polarization,the harmonic spectrum shows a single plateau structure,and the intensity of the even harmonics is approximately two orders of magnitude smaller than that of the odd harmonics;3)the external static electric field has minimal impact on the position of the two-center interference minimum on the harmonic spectra.Lewenstein's theory allows us to consider the molecular harmonic spectrum as a coherent superposition of four channels which characterized by the different ends of the molecule from which the electron ionizes and the various ends from which the ionized electron recombines.The different ends refer to the two oxygen atomic centers.We explain the double-plateau phenomenon and the generation of even harmonics by analyzing the coherent superposition between channels characterized by different ionization ends,and the two-center interference by analyzing the coherent superposition between channels characterized by different recombination ends.In order to understand the superposition between channels,we examine the amplitude of every harmonic for each channel,and estimate the phase difference of every harmonic of the relevant coherent channels in terms of its emission time obtained by the classical three-step model,so as to obtain a clear physical explanation of the calculated results.The analysis reveals the reason for the double-plateau structure of the harmonic spectrum.When the parallel electric field is applied,the adjacent positive and negative half-periods of the driven field along the laser polarization direction are no longer symmetric,hence the asymmetric adjacent positive and negative half-periods have different effects on the electrons so that the ionization channels of the two ends have different cutoff harmonic orders.Finally,the two-plateau structure is produced by the coherent superposition of the two end ionization channels.When a vertical static electric field is applied,the driving field in the laser polarization direction remains symmetric,thus eliminating the presence of a double-plateau on the harmonic spectrum.The intensity of even harmonics depends on whether the same-order harmonics generated from the ionization channels at two ends cancel out through destructive interference.When there is no external static electric field,the phase difference of even harmonics from the ionization channels at two ends is π.This implies there are no even harmonics in the spectrum.When a parallel static electric field is applied,the laser field along its polarization direction is no longer symmetric.Compared with the case of no external static electric field,the emission time of each harmonic changes.Therefore,the phase difference of even harmonics produced by the ionization channels at two ends is no longer π,it varies irregularly with the harmonic order,similar to that of the odd harmonics.As a result,the strengths of odd harmonics and even harmonics are on the same scale.It can be concluded that the generation of the harmonic is closely related to its classical emission time.When a vertical static electric field is applied,the electric field remains symmetric along its polarization direction.This external static electric field does not alter the driving field along the laser polarization direction and therefore does not change the classical emission time of the harmonics.However,it does impact the relative strength of harmonics at different classical emission times.As a result,the phase difference of even harmonics produced by ionization channels at two ends approaches π,resulting in weaker even harmonics being produced.Our work contributes to a comprehensive understanding of how an external static electric field influences high-order harmonics and provides valuable insights for effectively utilizing such fields to control high-order harmonic generation.
High-order harmonic generation spectra of O2External static electric fieldHarmonic phase analysisDouble plateauOdd-even harmonics
万方数据
维普
