Ellipticity Dependence Of High-order Harmonic Generation In Graphene

High-order harmonic generation（HHG）is a nonlinear and non-perturbative opti-cal phenomenon in the interaction between the laser and the matter,which has attracted widespread attentions over the several decades.Benefiting from HHG,many new tech-nologies have emerged and the natural science has been greatly promoted.For example,gas HHG can be applied not only in generating coherent soft XUV rays and isolated attosecond pulses,but also in probing molecular chirality and imaging the molecular or-bital.Recently,with the development of the laser technology,solid HHG has also been observed in the experiment.Compared with gases,solid HHG presents more abundant physical phenomena and more complex characteristics.One of them is the complex el-litpicity dependence of solid HHG.In gas,the ellipticity dependence of HHG not only confirms the recollision mechanism of harmonics generation,but also is the cornerstone of generating isolated attosecond pulses by the polarization gating and double optical gating technique.However,the ellipticity dependence of solid HHG are more complex and anomalous.For instance,in graphene,the harmonic yield increases firstly and then decreases with the increasing ellipticity,namely,the anomalous ellipticity dependence.However,the anomalous phenomenon in solids has not been well explained so far,and the physical mechanism is still under debate,which blocks the further application of polarization gating and double optical gating technique in solids.We theoretically investigate the ellipticity dependence of high-order harmonic gen-eration in graphene driven by the midinfrared laser field.The ellipticity dependence of the harmonic yield in the experiment by Yoshikawa et al is reproduced perfectly by solving the time-dependent Schr?dinger equation with the tight-binding approximation.Based on the semiclassical recollision model,it is found that the recollision distance of the electron-hole pair excited from the zone 0.5₀?Δ?2.5₀instead of the Dirac points can reach a minimum value at finite ellipticity,which enhances the harmonic yield.In addition,the ellipticity dependence of harmonics can be controlled by varying the chemical potential of graphene and opening a gap in graphene.Below are the main content of this thesis:Firstly,we investigate the main ionization mechanism of HHG in graphene and it is found that the zone of 0<Δ<2.5₀is the main excited zone in the generation of harmonics.By distinguishing the intraband and interband currents,we found that the anomalous ellipticity dependence of the harmonic yield mainly results from the in-terband harmonics.In this case,the electron-hole recollision model may play a very important role.Secondly,we identify the important role of recollision dynamics in the anomalous ellipticity dependence of HHG in graphene.Due to the zero-gap property of graphene,we expand the electron-hole recollision model and confirm the validity of the model by comparing the classical trajectories with the quantum trajectories in the time-frequency distributions.Based on this model,it is found that the enhancement of the harmonic yield at a finite ellpticity mainly results from the contributions of the zone of 0.5₀<Δ<2.5₀.In addition,the result shows that the smallest recollision distance is in-versely proportional to the harmonic yield,which proves that the recollision dynamics is still valid for the anomalous ellipticity dependence in graphene.Thirdly,we investigate the mechanism of anomalous ellipticity dependence of HHG in graphene and provide a clear physical picture.By analyzing the electron-hole trajec-tories in real space,we find that the electron-hole pair can form almost closed trajectories at a finite ellipticity.It increases the recollision probability of the electron-hole pair and then leads to the enhancement of the harmonic yield.Finally,we investigate the modulation of the ellipticity dependence of the harmonic yield in graphene.It is found that the ellipticity dependence can gradually transit to be the normal ellipticity dependence by adjusting the chemical potential and opening a band gap in graphene.Our work not only uncovers the underlying mechanism of the anomalous ellipticity dependence observed in graphene but also provides an intuitive physical picture for understanding the ellipticity-dependent behaviors in a variety of materials with the cone-shapeband structure,such as three-dimensional topological insulators,AA-and AB-stacked bilayer graphene.Our work provides the theoretical support for controlling the generation of harmonics in the future experiments in the elliptically polarized laser pules.