Introduction to theory of high-harmonic generation in solids: tutorial

High-harmonic generation (HHG) in solids has emerged recent years as a rapidly expanding and interdisciplinary field, attracting attention from both the condensed-matter atomic, molecular, optics communities. It exciting prospects for engineering of new light sources probing ultrafast carrier dynamics solids, theoretical understanding this process is fundamental importance. This tutorial provides hands-on introduction to description strong-field laser-matter interactions condensed-phase system that give rise HHG. We provide an overview ranging detailed different approaches calculating microscopic how these are intricately connected crystal structure, through conceptual HHG supported by semiclassical recollision model, finally brief calculate macroscopic response. also general Berry phase, we discuss important subtleties modelling HHG, such choice structure laser gauges, construction smooth periodic gauge nondegenerate degenerate bands. The advantages drawback laser-gauge choices discussed, terms their ability address specific questions numerical feasibility.