Reconstruction of crystal band structure by spectral caustics in high-order harmonic generation

Abstract

We propose a method to retrieve the band structure by measuring the caustic points of the harmonic spectrum generated by the interaction between laser and solid. The relation between the energy ${\ensuremath{\omega}}_{c}$ of the spectral caustic points and the external fields $F$ encodes the bandgap of the solid. Specifically, for a simple band structure, ${\ensuremath{\varepsilon}}_{g}(k)={\ensuremath{\varepsilon}}_{0}+{\ensuremath{\varepsilon}}_{1}[1\ensuremath{-}cos(k{a}_{0})]$, according to the semiclassical theory, we map the crystal momentum ${k}_{c}$ to the caustic point energy ${\ensuremath{\omega}}_{c}$ by $F$ since ${k}_{c}$ is independent of the parameters ${\ensuremath{\varepsilon}}_{0}$ and ${\ensuremath{\varepsilon}}_{1}$. Furthermore, for the general band structure, because its first-order form is a simple energy band, we can roughly retrieve the first-order form of the energy band and obtain the accurate band structure by iterative calculation. Using this method, we solve the deviation between the retrieved and the target bandgap near the Brillouin zone boundary. Also, we show that this method is suitable for wide-bandgap materials.