Effect of multiple conduction bands on high-harmonic emission from dielectrics

Abstract

We find that, for sufficiently strong mid-IR fields, transitions between different conduction bands play an important role in the generation of high-order harmonics in a dielectric. The transitions make a significant contribution to the harmonic signal, and they can create a single effective band for the motion of an electron wave packet. We show how high harmonic spectra produced during the interaction of ultrashort laser pulses with periodic solids provide a spectroscopic tool for understanding the effective band structure that controls electron dynamics in these media.PACS numbers: 42.50. Hz, 42.65.Ky, High-order harmonic generation (HHG) from gas targets is now used as a spectroscopic tool for imaging nuclear (see e.g. [1][2][3]) and electronic (see e.g. [4][5][6][7]) dynamics on the atomic time-and length scales. It is sensitive to various aspects of electronic dynamics, from attosecond processes in neutral systems [8,9] to hole dynamics in ions [4][5][6][7], correlation-driven channel interaction [10][11][12], and time-and space-resolved information on electronic transitions from different molecular orbitals [13][14][15].We show that HHG spectra from periodic solids give insight into the effective band structure established by a strong driving mid-infrared laser field. Pioneering experiments on high harmonic generation from dielectrics [16,17] stimulated a simple model offering semi-classical insight into the underlying physics. In this model ([16, 18]; see also [19]) electrons first tunnel from a valence band (VB) to a conduction band (CB) at the maxima of the electric field. There, they are driven along the single conduction band by the field. The harmonic intensity at frequency ω is then given by |ωJ(ω)| 2 , where J(ω) is the Fourier transform of the current, j(t), in the conduction band, ε(k). Since in this model j(t) ∝ v(t) ∝ dε/dk, where v(t) is the electron group velocity, analysis of the harmonic spectrum can yield information about the band structure (dε/dk). This picture predicts that, when the driving mid-IR laser is sufficiently strong to rapidly accelerate electrons to the edge of the Brillouin zone (BZ), Bragg reflections (Bloch oscillations) within the single band would generate most of the high harmonics.However, if electrons quickly move past the gap between adjacent CBs, they may undergo an interband transition. In this case, the harmonic signal also comes from coherences between all participating bands, including the VB [17,20]. Additionally it is also important to account for the temporal structure of all interband transitions, including the VB to CB transition, see e.g. [21]. Recent theoretical analysis of HHG in bulk solids by Vampa et al. [22] and Higuchi et al. [23] accounted for the temporal structure of interband excitations, but as two-band models were used in both cases, transitions between conduction bands were not considered.We show that the inclusion of multiple conduction bands leads to additional contributions to the highharmonic signal and that, in spite of the increasin...

Ab initio multiscale simulation of high-order harmonic generation in solids

“…S1) and a fine k-grid (∆k 0.01) have been found to be crucial prerequisites for convergence to the ab-initio TDDFT simulation. Another important convergence parameter is the number of VBs and CBs [27,28]. The present results (Fig.…”

“…Several simplifying models have been proposed accounting for Bloch oscillations within a single band ("intraband harmonics") [22,23] and non-linear interband polarization ("interband harmonics") [15,24,25] as sources of HHG. Most descriptions involve the semiconductor Bloch equations (SBE, [26]) using input parameters on various levels of sophistication and a varying number of energy bands [27,28]. Recently, first simulations employing time-dependent density functional theory (TDDFT, [29]) have become available [30,31].…”

Interband Bloch oscillation mechanism for high-harmonic generation in semiconductor crystals

“…First, the bandgap between first and second conduction band is usually smallest at the Brillouin zone edge, so that transitions to higher bands may become important [16]. Second, once a conduction electron has crossed the edge of the Brillouin zone, it will begin to move in the opposite * cmcdo059@uottawa.ca † gvamp015@uottawa.ca direction.…”

Anisotropic high-harmonic generation in bulk crystals

“…We find that harmonic e ciency is enhanced (diminished) for semi-classical electron trajectories that connect (avoid) neighbouring atomic sites in the crystal. These results indicate the possibility of using materials' own electrons for retrieving the interatomic potential and thus the valence electron density, and perhaps even wavefunctions, in an all-optical setting.High-harmonic generation (HHG) in bulk crystal is attributed to the sub-cycle electronic motion driven by an intense laser field [2][3][4][5][6][7][8][9][10][11] . There has been a growing interest in utilizing HHG to probe the electronic structure of solids 8,9,11 .…”

“…High-harmonic generation (HHG) in bulk crystal is attributed to the sub-cycle electronic motion driven by an intense laser field [2][3][4][5][6][7][8][9][10][11] . There has been a growing interest in utilizing HHG to probe the electronic structure of solids 8,9,11 .…”