Twist Phase Matching in Two-Dimensional Materials.

Optical phase matching involves establishing a proper phase relationship between the fundamental excitation and generated waves to enable efficient optical parametric processes. It is typically achieved through birefringence or periodic polarization. Here, we report that the interlayer twist angle in two-dimensional (2D) materials creates a nonlinear geometric phase that can compensate for the phase mismatch, and the vertical assembly of the 2D layers with a proper twist sequence generates a nontrivial "twist-phase-matching" (twist-PM) regime. The twist-PM model provides superior flexibility in the design of optical crystals, which can be applied for twisted layers with either periodic or random thickness distributions. The designed crystal from the twisted rhombohedral boron nitride films within a thickness of only 3.2 μm is capable of producing a second-harmonic generation with conversion efficiency of ∼8% and facile polarization controllability that is absent in conventional crystals. Our methodology establishes a platform for the rational design and atomic manufacturing of nonlinear optical crystals based on abundant 2D materials.