Theoretical Investigation On The Mechanism Of The High-order Harmonic Generation In Quasicrystals

As an important product of the nonlinear interaction between ultrafast laser and matter,high-order harmonic generation has vital value in generating attosecond pulse and coherent extreme ultraviolet sources.In the past few decades,a series of important advances have been made in the synthesis of isolated attosecond pulses,extended cutoff energy,and molecular orbital imaging.To make up for the low atomic density of the gas,people focus on condensed matter systems such as crystal and liquid,and a series of important achievements have been made.In addition,high-order harmonic generation encodes the ultrafast dynamics of electrons and can be decoded to help us understand the microstructure of matter.For different matters(such as solid,liquid,and gas),the atomic arrangement and the dynamic process of electrons are different,and the harmonic radiations are disparate.With high-order harmonic generation as a bridge,condensed matter physics and strong-field physics intersect in many fields,such as Anderson localization,topological phase transition,strong correlation problem,etc.This greatly enriches the research object and physical connotation of strong-field physics.Quasicrystals,as an important part of solids,have changed the definition of crystal because of the special order without translational periodicity.Since the quasicrystals were discovered,many efforts have been made to study their atomic arrangement,electron’s physical properties.But the theoretical and experimental research on high-order harmonic generation in quasicrystals is still blank.In addition,the existing theoretical and experimental results show that there is a surprising relationship between the quasi-periodic system and the topological phase.So quasicrystal high-order harmonic generation is of great value in searching new attosecond sources and studying novel electronic structure of quasicrystals.Based on the time-dependent Schrodinger equation,we simulate the high-order harmonic radiation of Fibonacci or Harper quasicrystals and research the electronic structure or dynamic information encoded by the harmonics.The main contents are shown as following aspects:(1)This paper breaks down the barrier between two independent research fields about quasicrystals and ultrafast optics.It focuses on the electron ultrafast dynamics on fractal bands and reveals the mechanism of high-order harmonic generation in quasicrystals.Compared with crystal,the fractal band structure of Fibonacci quasicrystals leads to more electron excitation channels and more frequent backscattering.And the multichannel high-order harmonic generation in Fibonacci quasicrystals has the advantages of higher yield and wider spectral range.So quasicrystals are expected to become condensed matter harmonic generation media with higher efficiency than crystals.As the first step towards strong-field physics of quasicrystals,the concepts of electron acceleration theorem and quasi-Bloch state in Fibonacci quasicrystals are discussed in detail.(2)A scheme of detecting edge states in topologically nontrivial Harper quasicrystals by high-order harmonic generation is proposed,and extended to judge the topological equivalence of different systems.When the intraband harmonic generation is suppressed,the harmonic spectrum will appear a significant minimum below the minimum band gap.When topologically related local states exist,the harmonic minimum will be enhanced,which achieves the detection of edge states or topological phase transitions.Our results show that the detection is robust and does not depend on a periodic or quasi-periodic system.This paper provides an all-optical method for detecting topological states in complex quasicrystals.