Phase Matching of High Harmonic Generation in Twisted van der Waals Crystals.

High harmonic generation (HHG) in crystals could enable attosecond and ultraviolet light sources with high compactness, great controllability, and rich functions. However, the HHG process is accompanied by a quite large wave vector mismatch that is uncompensated by any traditional phase-matching method, directly limiting its energy conversion efficiency. Here, we propose an effective strategy for phase matching of HHG with arbitrary harmonic orders in crystals. Two flakes of twisted van der Waals crystals induce a nonlinear optical phase that depends on the crystal symmetry, twist angle, and harmonic order, which can be accurately designed to compensate for the phase mismatch in HHG. Guided by the twist-phase-matching theory, we achieved a record-high conversion efficiency of ∼4×10^{-5} for the fifth HHG in twisted hexagonal boron nitride crystals within thickness of ∼1  μm. Moreover, the designed crystal has the polarization controllability that can emit a pure circularly polarized HHG light. Our Letter establishes a foundation for developing ultrashort-wavelength and ultrafast-pulse laser sources in compact solid-state tabletop systems for fundamental and applied sciences.