Phase-Matched Design for Efficient Entangled Photon Pair Generation in 3R-MoS₂ Waveguides

Entangled photons are essential for photonic quantum technologies. Their generation typically relies on spontaneous parametric down-conversion, but conventional nonlinear crystals are bulky and hard to integrate on chips. Rhombohedral-stacked MoS${}_2$ combines a high refractive index, large second-order nonlinearity, and flexibility for heterogeneous integration, making it a promising platform for integrated quantum photonics. However, the typical thin-film form of 3R-MoS${}_2$ restricts the effective nonlinear interaction length, limiting entanglement generation efficiency in practical devices. To overcome this, phase-matching strategies in integrated waveguides are required but have so far remained undeveloped. Here, we introduce a waveguide-integrated 3R-MoS${}_2$ platform with periodic grooves to achieve quasi-phase matching, enhancing down-conversion efficiency. Leveraging ${\chi }^{\left(2\right)}$ tensor symmetries and orthogonal waveguide modes, the design efficiently generates entangled photons, providing a compact, scalable route toward 2D-material-based integrated quantum photonic circuits.