Amplifying solid-state high harmonic generations with momentum k-gaps in band structure engineering

We propose a novel amplification mechanism for high harmonic generation (HHG) in solids by leveraging bandgap engineering with momentum k-gaps. By constructing a simple diatomic lattice featuring balanced, alternating gain and loss profiles, facilitated by an array of four-level systems, we explore the physics of k-gap-amplified Bloch oscillations in the intraband channel of solid-state HHG. Through numerical simulations, we elucidate the coexistence of amplification and harmonic radiation processes in a solid. Our finding reveals that advanced bandgap engineering can define k-space optical devices - such as Brillouin cavity, Bloch-Zener oscillator and k-gap amplifier - thereby enabling the coherent manipulation of semiconductor radiation and high harmonic generation in both semiconductor superlattices and artificial materials. Furthermore, we analyze the spectrogram and material realizations required for amplifying solid-state HHG. These results underscore the potential of k-gap band structure engineering to advance coherent light sources at extremely short wavelengths.