Impact of the Electronic Band Structure in High-Harmonic Generation Spectra of Solids

Abstract

An accurate analytic model describing the microscopic mechanism of high-harmonic generation (HHG) in solids is derived. Extensive first-principles simulations within a time-dependent density-functional framework corroborate the conclusions of the model. Our results reveal that (i) the emitted HHG spectra are highly anisotropic and laser-polarization dependent even for cubic crystals; (ii) the harmonic emission is enhanced by the inhomogeneity of the electron-nuclei potential; the yield is increased for heavier atoms; and (iii) the cutoff photon energy is driver-wavelength independent. Moreover, we show that it is possible to predict the laser polarization for optimal HHG in bulk crystals solely from the knowledge of their electronic band structure. Our results pave the way to better control and optimize HHG in solids by engineering their band structure. DOI: 10.1103/PhysRevLett.118.087403 Atoms and molecules interacting with strong laser pulses emit high-order harmonics of the fundamental driving laser field. The high-harmonic generation (HHG) in gases is routinely used nowadays to produce isolated attosecond pulses [1][2][3][4] and coherent radiation ranging from the visible to soft x rays [5]. Because of a higher electronic density, solids are one promising route towards compact, brighter HHG sources. The recent observation of nonperturbative HHG in solids without damage [6][7][8][9][10], extending even beyond the atomic limit [10], has opened the door to the observation and control of attosecond electron dynamics in solids [8,9,11], all-optical band-structure reconstruction [12], and solid-state sources of isolated extreme-ultraviolet pulses [9,11]. However, in contrast to HHG from gases, the microscopic mechanism underlying HHG from solids is still controversially debated in the attoscience community, in some cases casting doubts on the validity of the proposed microscopic model and resulting in confusion about the correct interpretation of experimental data. Various competing simplified models have been proposed but they often are based on strong approximations and a priori assumptions, often stating that there is a strong similarity with the processes underlying atomic-gas HHG emission. However, it is clear that many-body effects due to the crystalline structure of solids and the fermionic nature of interaction electrons play a decisive role that fundamentally distinguishes the solid from the gas case. It is the scope of the present work to unravel within an ab initio approach what the impact is of the underlying electronic band structure of the solids in the observed HHG emission.The process of HHG from gases is by now well understood in terms of the three-step model [13][14][15] in which electrons are first promoted from the ground state of the atom (or molecule) to the continuum, then accelerated by the electric field, and finally recombine with the parent ion. With this simple, intuitive model most of the observed effects are well described, in particular, the dependence of the harmonic cutoff energ...

High-Order Harmonic Generation from Solids Dressed by an Intense Terahertz Field

“…2(b) shows the importance of controlling the polarization direction of the THz-dressing field with respect to the IR driving field. For parallel polarizations, the intensity of the transiently induced even-order harmonics is ~3 times higher than for orthogonal polarizations, in agreement with our simulations performed within a time-dependent density functional theory (TDDFT) framework [8,9] (not shown here). This level of control would not be possible with a custom-fabricated silicon platform, such as strained waveguides or MOS circuits.…”

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

“…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]. One major puzzle has remained so far unresolved: while many experiments display remarkably "clean" harmonic spectra with pronounced peaks near multiples of the driving frequency (odd multiples when inversion symmetry is preserved) all the way up to the cutoff frequency, corresponding simulations display a noisy spectrum lacking any clear harmonic structure over a wide range of frequencies in the "plateau" region above the band-gap energy.…”

Ultrafast Dynamics of High-Harmonic Generation in Terms of Complex Floquet Spectral Analysis

“…Most conventional theories, however, have employed phenomenological treatments that may terminate the quantum coherence in the HHG process: for example, the HHG emission spectrum is calculated classically based on Maxwell's equation [2,6,[33][34][35], or the Markov approximation is used in a master equation with a phenomenological parameter [18,27,30,36]. In fact, how to interpret the dissipative spontaneous photon emission within the framework of quantum mechanics has been a debate since the early days of the theory [37][38][39][40], as an irreversible decay process contradicts the time-reversible quantum dynamics.…”