Amplifying Solid‐State High‐Harmonic Generation Through Momentum‐Bandgap Engineering

ABSTRACT We propose a mechanism for amplifying high‐harmonic generation (HHG) in solids through momentum‐bandgap (k‐gap) engineering. By constructing a diatomic lattice with balanced gain and loss, implemented through an effective four‐level recycling scheme, we study k‐gap‐amplified Bloch oscillations in the intraband channel of solid‐state HHG. Here, k‐gaps refer to momentum bandgaps where Bloch modes acquire complex quasienergy and can undergo temporal amplification. Numerical simulations show that amplification and harmonic radiation can coexist in the driven lattice. This framework suggests that engineered momentum‐space band structures can support k‐space optical functionalities, such as Brillouin cavities, Bloch‐Zener oscillators and k‐gap amplifiers, enabling coherent control of semiconductor radiation in both superlattices and artificial materials. We further analyze the time‐frequency emission spectrum and discuss possible material platforms. These results suggest that k‐gap band structure engineering provides a mechanism for controlling and amplifying intraband radiation in driven solid‐state systems, with potential relevance to coherent short‐wavelength emission.