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We theoretically investigate the spectral caustics of high-order harmonics insolids. We analyze the 1-dimension model of solids HHG and find that, apartfrom the caustics originated from the van Hove singularities in the energy-bandstructure, another kind of catastrophe singularities also emerge when thedifferent branches of electron-hole trajectories generating high-orderharmonics coalesce into a single branch. We solve time-dependent Schr\"odingerequation in periodic potential and demonstrate the control of this kind ofsingularities in HHG with the aids of two-color laser fields. The diffractionpatterns of the harmonic spectrum near the caustics agree well with theinter-band electron-hole recombination trajectories predicted by thesemiconductor semi-classical equation. This work is expected to help tounderstand the HHG dynamics in solids and manipulate the harmonic spectrum byadjusting driving field parameters.

Spectral caustics of high-order harmonics in one-dimensional periodic crystals