Spatiotemporal imaging of nonlinear optics in van der Waals waveguides.

Van der Waals (vdW) semiconductors have emerged as promising platforms for efficient nonlinear optical conversion, including harmonic and entangled photon generation. Although major efforts are devoted to integrating vdW materials in nanoscale waveguides for miniaturization, the realization of efficient, phase-matched conversion in these platforms remains challenging. Here, to address this challenge, we report a far-field ultrafast imaging method to track the propagation of both fundamental and harmonic waves within vdW waveguides with femtosecond and sub-50 nanometre spatiotemporal precision. We focus on light propagation in slab waveguides of rhombohedral-stacked MoS, a vdW semiconductor with large nonlinear susceptibility. Our method allows systematic optimization of nonlinear conversion by determining the phase-matching angles, mode profiles and losses in waveguides without prior knowledge of material optical constants. Using this approach, we show that both multimode and single-mode rhombohedral-stacked MoS waveguides support birefringent phase matching, demonstrating the material's potential for efficient on-chip nonlinear optics.