Efficient visible second harmonic generation in nanopatterned 3R-MoS₂ on Si₃N₄ ridge waveguides

We present a compact and efficient platform for visible second-harmonic generation (SHG) based on nanostructured 3R-phase MoS₂ integrated onto silicon nitride ridge waveguides. By patterning the MoS₂ layer into a one-dimensional photonic crystal and using a counter-propagating pump configuration, the design achieves in-plane phase matching and vertical outcoupling of the SH signal around 445 nm. Field localization near the photonic band edge enhances nonlinear interactions within a subwavelength active volume, with leaky-mode resonance enabling efficient SH extraction. Full-wave simulations predict SHG efficiencies up to 0.004% for pump intensities of ~300 MW/cm², in a footprint below 1 µm². The same architecture supports spontaneous parametric down-conversion (SPDC) with intrinsic modal and directional filtering. This work shows how combining material-phase engineering and photonic design can unlock efficient χ(2) processes at visible wavelengths in ultra-compact devices, paving the way for scalable nonlinear and quantum photonics on CMOS-compatible platforms.