# High-harmonic generation in solids

## TL;DR

This paper combines analytical and numerical methods to study high-harmonic generation in solids, revealing the importance of entire Brillouin zone contributions and providing predictions that align with experimental data.

## Contribution

It introduces a model using Houston states and a Kronig-Penney potential to analyze HHG, including multiband effects and BZ contributions, advancing understanding of solid-state HHG mechanisms.

## Key findings

- High-harmonic spectra depend on entire first Brillouin zone contributions.
- Derived cutoff harmonic orders match analytical predictions and experimental data.
- Multiband calculations provide detailed insights into intra- and interband HHG contributions.

## Abstract

We analytically and numerically investigate the emission of high-harmonic radiation from model solids by intense few-cycle mid-infrared laser pulses. In single-active-electron approximation, we expand the active electron's wavefunction in a basis of adiabatic Houston states and describe the solid's electronic band structure in terms of an adjustable Kronig-Penney model potential. For high-harmonic generation (HHG) from MgO crystals, we examine spectra from two-band and converged multiband numerical calculations. We discuss the characteristics of intra- and interband contributions to the HHG spectrum for computations including initial crystal momenta either from the $\Gamma-$point at the center of the first Brioullin zone (BZ) only or from the entire first BZ, demonstrating relevant contributions from the entire first BZ. From the numerically calculated spectra we derive cutoff harmonic orders as a function of the laser peak intensity that compare favorably with our analytical stationary-phase-approximation predictions and published data.