Statistical Model For High-Order Harmonic Generation In Disordered Systems

One of the main focuses of strong-field ultrafast physics is the dynamics of electrons on their intrinsic time scales.With the wide application of intense femtosecond laser,people have made extensive progress in the ultrafast research field.Highorder harmonic generation(HHG),one of the most important processes in strong-field physics,can be treated as a secondary laser.By coherently superposing its wide spectrum,people can break through the detection and control time limit,thus opening the door to attosecond physics.Meanwhile,high harmonics are the direct product of laserinduced electron dynamics,and the ultrafast motion of electrons in the system would carry the intrinsic characteristics of the target.Thus,structure information and electronhole dynamic property can be extracted from HHG spectra.This all-optical detection technology has also attracted much attention.The means of generating high harmonics have been continuously developing.The targets exposed to laser fields evolve from plasma and gases to solids and other strongcorrelated systems,which are currently widely concerned.Recently,with the help of flat-microjet technology,people have observed the EUV HHG in liquid targets.This breakthrough experiment means that all four common substance forms in nature can radiate high harmonics under strong laser pulse irradiation,filling a major gap in the HHG research field.In a broad sense,it also indicates that the study of the HHG has entered a new field,that is,the HHG of disordered condensed matters.Currently,the investigations about condensed-state HHG mainly focus on the periodic crystals with translation invariance.The interest of the HHG from disordered materials is just beginning to sprout.In this paper,systematic theoretical investigations have been conducted in the field of HHG processes in disordered systems,and the innovative results obtained are as follows:(1)A statistical fluctuation model was proposed,revealing the mechanism of HHG processes in liquids.To understand the main mechanism of the liquid HHG,we simplify the liquid target to a one-dimensional linear chain.The harmonic spectra calculated by this model show a peculiar layered characteristic:in the low-energy region,the harmonics only contain odd orders;while in the high-energy region,even and odd orders appear simultaneously.We define the critical position of these two regions as the transition energy.We found that the transition energy depends on the fluctuation of structure and the field strength,but independent of the laser wavelength.Furthermore,a simple formula is proposed to identify the transition energy,from which we correctly reproduce the experimental cutoff energies of liquid HHG.(2)A classification method for HHG processes in disordered systems based on statistical correlations was proposed,establishing a connection between coherent radiation in disordered and crystalline systems.By modeling the random variables in the disordered lattice as random processes or random sequences,we introduce another feature of statistics-correlations.According to the decaying behavior of the correlation function,the correlations can be divided into two families:short-range correlation(SRC)and long-range correlation(LRC).The calculation results show that the harmonic spectra of the disordered lattice with different correlations also present two completely different behavior,and the electron dynamics also changes significantly with the change of the correlation function.In particular,the HHG spectrum from the disordered system with LRC exhibits remarkable consistency with the spectrum from the periodic lattice,revealing that the LRC links HHG processes in disordered and periodic systems.(3)An analytical model for the periodic decomposition of disordered systems was proposed,which can be applied to ultrafast dynamics studies of dipole disordered systems.It contains two key elements:an explicit solution for periodic crystal systems and the hypothesis of disorder uncorrelation.Firstly,we analytically solved the twoband equation for the periodic systems in lattice representation;Secondly,we propose a hypothesis of disordered uncorrelation between lattice sites;Finally,the analytical solution of periodic systems is directly extended to some specific disordered systems.We call this analytical approximation model a disorder-to-periodicity decomposition picture.The calculation results show that even under different laser and structural parameters,the electron time-dependent evolution and HHG spectrum obtained by the numerical solution and the analytical approximation method exhibit a high degree of quantitative consistency.This analytical method may be treated as a rudimentary theoretical framework for the HHG analysis in disordered materials.