High-order harmonic generation in imperfect crystals

Abstract

High-order harmonic generation (HHG) in imperfect crystals, where the disorder is modeled by random shifts of the ionic positions, is studied using time-dependent density-functional theory. When irradiated by midinfrared laser pulses, the disorder-free system produces HHG spectra with two plateaus. Compared with the disorder-free system, disordered systems are found to emit suppressed harmonics in the first plateau region and enhanced harmonics in the second plateau region. The suppression of harmonics in the first plateau becomes less pronounced when decreasing the displacement of the nuclei, while the enhancement in the second plateau region is insensitive to the range of the ionic displacement. We have confirmed these findings for many different disordered sample systems and for different laser field strengths. The increase of the HHG signals in the second plateau region is proposed to stem from a change of the dynamics in the system, evidenced by the transition matrix elements between the field-free Kohn-Sham orbitals. In addition, a time-frequency profile of HHG spectra shows that the emission of harmonics is less regular in the time domain for a disordered system than for the disorder-free system.

Effects of vacancies on high-order harmonic generation in a linear chain with band gap

“…As shown in Ref. [35], in the case of disorder in the ionic positions in the lattice, the emission of harmonics is also less regular in time. However, in this case, the irregularity is induced by breaking the lattice periodicity by random shifts of ionic locations.…”

“…In previous studies [30,[32][33][34][35], a model to study HHG in a linear chain of ions was introduced. As shown in Refs.…”

“…For example, interband HHG is produced in a process resembling the atomic three-step model [11,12] and involves the following steps: (i) an electron tunnels from the valence band to the conduction band, producing a hole in the valence band; (ii) the electron and its corresponding hole propagate in the solid, driven by the external field; and (iii) they recombine and emit HHG radiation with a frequency that corresponds to the band-gap energy at the crystal momentum at which the recollision occurs [13]. More generally, it has emerged that several aspects of the HHG process in solids can be captured by solving the time-dependent Schrödinger equation for Bloch electrons in single-active-electron models [14][15][16][17][18][19][20][21] by applying many-electron approaches such as the semiconductor Bloch equations [22][23][24][25], by time-dependent densityfunctional theory (TDDFT) [26][27][28][29][30][31][32][33][34][35][36][37], and by time-dependent Hartree-Fock theory [38].…”

“…Recently, the effects of both acceptor and donor-doping on the HHG spectra were investigated [34], and it was found that a donor-doped bandgap material, with an occupied donor state within the band gap, can enhance the overall HHG efficiency by several orders of magnitude, compared with undoped and acceptor-doped materials, where in the latter case the acceptor state within the band gap is unoccupied. Very recently, the effects of disorder were investigated by imparting random shifts of the ionic lattice positions [35], and disorder was found not to have a detrimental effect on the efficiency of the HHG process.…”

“…Finally, we explore a second realization of our linear chain model to further investigate the physical effects associated with the vacancy-type point defects. Similarly to previous studies [30,[32][33][34][35][36], we employ a TDDFT model to study the HHG spectra of a linear chain of ions exposed to linearly polarized laser pulses. In this approach, we go beyond the single-active electron models and take electron-electron interactions into account, at least on a mean-field level.…”