Interference Between Interband And Intraband Currents In High-order Harmonic Generation In Solids

The generation of ultrashort light sources and the observation and manipulation of electron motion are the frontier topics in the field of ultrafast optics.Researchers have studied the interaction between matters in different states and the intense ultrafast laser.After the development of plasma-phase and gas-phase high-order harmonics for many years,the nonlinear solid high-order harmonic generation was also realized in 2011 and has attracted wide attention of the peers.In the numerical simulation of solid high-order harmonic generation,the existing research methods have great limitations.For example,the computational complexity of time-dependent density functional theory(TDDFT)is in the order of kilo-cores,which is inefficient Solving the semiconductor Bloch equations(SBE)needs a small amount of calculation,but the problem of phase discontinuity of transition dipole moment may introduce non physical effects,so it is necessary to develop new methods.In addition,the high-order harmonic spectrum contains rich dynamic information,but the effective extraction of information is difficult.In view of the above scientific problems,this paper has made innovative research achievements in the following aspects:(1)A new simulation method based on the model potential of high-order harmonic generation from two-dimensional materials is developed.The high-order harmonic ellipticity,phase and other key information obtained by calculation is in good agreement with the experimental results.TDDFT needs a huge amount of computation,which makes TDDFT difficult to be extended to the simulation of larger systems.The SBE method needs the pre-calculated transition dipole moment,and the commonly used transition dipole moment comes from the calculation of density functional theory(DFT).The discontinuous phase of the dipole moment makes the simulation process difficult to be implemented.With the help of the Kohn-Sham equations,we simplify the multi-electron Schrodinger equation to a single electron Schrodinger equation with only one effective potential.Based on the energy band,the transition dipole moment and the charge density of graphene calculated by density functional theory,a model potential is constructed by iterative comparison.A simulation based on a potential rather than a transition dipole moment can avoid the problem of phase discontinuity of transition dipole moments.Using this model potential as the effective potential in the single electron Schrodinger equation,we have simulated the process of high-order harmonic generation from the laser-graphene interaction.The simulation of laser-graphene interaction with the same laser parameters as Yoshikawa et al.[Science 356,736(2017)]is performed with the time-dependent Schrodinger equation.The obtained driving laser ellipticity scaling,the harmonic ellipticity,and the harmonic major-axis angle can well reproduce the experimental results.Only the enhancement of the seventh harmonic in the y direction(perpendicular to the laser polarization direction)is not reproduced in our simulation.This is probably due to the lack of attenuation terms,such as the dephasing time,for the whole electron dynamic process.The effects of the carrier envelope phase and the laser chirp on the high-order harmonic generation in graphene is also studied.We find that although the carrier envelope phase can significantly shift the higher-order harmonics in the semiconductors with large band gap,it has little effect on the high-order harmonics from the zero band gap graphene.It only leads to the observable frequency shift of the ninth order harmonic,but has little effect on the lower order harmonics.When the pulses with the same chirp amplitude but opposite signs are applied to the monolayer graphene,there is a significant difference between the two cases.We give a qualitative analysis of the electron dynamics,which attributes the difference to the different excitation processes of electrons in the graphene.(2)The interference effect between inter-and intraband currents is found,and the influence of the synchronization of the group velocity and the phase velocity of the electron wave packet on high-order harmonic generation is revealed.The intra-and interband mechanisms of solid high-order harmonic generation have been widely accepted,but the internal relationship between them has been less studied.Through the interference effect between them,we find the internal factors of the total harmonic intensity changing with the laser parameters.Through a theoretical analysis,we give the mathematical formalism of the interference between intraband and interband currents.The interaction between the external laser field and the periodic model crystal is simulated by numerically solving the time-dependent Schrodinger equation,and the obvious interference region is found.The radiation time of harmonics in the constructive and destructive interference regions is determined by time-frequency analysis.Further analysis of the inraband and interband currents in the time range of the interference shows that the constructive interference and destructive interference of the intrband and interband currents correspond to the synchronization and asynchronization of the intraband and interband electron motion,respectively.The phase analysis of intra-and interband harmonics further confirms that this interference of harmonics comes from the interference between inra-and interband currents.This interference effect provides us with a new idea and a new tool to control harmonic radiation.Then we try to extract the dynamic process of electrons in the energy space when the intra-and interband currents interfere,because the transition process of electrons in energy space can be easily controlled by light It is found that the constructive interference is the strongest around the time when electrons make transitions from the valence band to the conduction band and the population on the conduction band reaches the peak value.While,the most intense destructive interference appears in the time period when electrons are transited from the conduction band to the valence band and the population of electrons on the valence band reaches the peak.The intraband current cannot be experimentally distinguished from the interband current directly,but the harmonic spectrum can be measured.So,we further study the influence of the interference effect of the intra-and interband current on the high-order harmonic spectrum.This intra-and interband current interference is electron dynamic interference,which strongly depends on laser parameters and material structures.We find the influence of this current-interference effect under different laser parameters.In the case of mid-infrared driving pulse,the intra-and interband interference split the single odd order harmonic into a multi-peak fine structure.In the case of a terahertz driving pulse,this interference effect leads to an obvious interference minimum at a specific frequency.These phenomena are expected to be observed directly in experiments.The consideration to both computational efficiency and accuracy is given to the new method developed in this paper,which is helpful for peers to carry out in-depth theoretical research.The intra-and interband interference effect is helpful to extract the instantaneous information of the phase and group velocities of electrons,which is of great significance to the generation and manipulation of high-order harmonics in solids.