Attosecond pulse trains from graphene via macroscopic phase-matching in high harmonic generation
Attosecond pulse generation in solids remains challenging due to the complex phase structure arising from multiple electronic pathways in high harmonic generation (HHG). Here, we identify the macroscopic conditions that enable the synthesis of attosecond pulse trains in graphene via HHG. Using numerical simulations that combine microscopic and macroscopic HHG in single-layer graphene, we show that harmonic contributions associated with different emission times acquire distinct far-field beam-divergence properties, analogous to the short- and long-trajectory contributions in gas-phase HHG. Our results identify how transverse phase-matching can be engineered in solid-state HHG to select short-time or long-time electronic contributions through proper tailoring of the driving-field waveform. In particular, the macroscopic suppression of long-time contributions associated with delayed electron-hole recombinations or imperfect recollisions (usually removed in semiconductor Bloch equation calculations by introducing artificial decoherence times) leads to clean, positively chirped, attosecond pulse trains with a temporal quality comparable to that achieved in gas-phase HHG. These results establish a general framework for controlling attosecond emission in solid-state HHG and provide a route toward compact solid-state attosecond sources.